research article an improved artificial colony...

Research ArticleAn Improved Artificial Colony Algorithm Model forForecasting Chinese Electricity Consumption and AnalyzingEffect Mechanism

Jingmin Wang Jian Zhang and Jing Nie

Department of Business Administration North China Electric Power University Baoding 071000 China

Correspondence should be addressed to Jian Zhang zj ncepu sub163com

Received 22 March 2016 Revised 27 June 2016 Accepted 20 July 2016

Academic Editor Marek Lefik

Copyright copy 2016 Jingmin Wang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Electricity consumption forecast is perceived to be a growing hot topic in such a situation that Chinarsquos economy has entered aperiod of new normal and the demand of electric power has slowed down Therefore exploring Chinese electricity consumptioninfluence mechanism and forecasting electricity consumption are crucial to formulate electrical energy plan scientifically andguarantee the sustainable economic and social development Research has identifiedmediumand long term electricity consumptionforecast as a difficult study influenced by various factors This paper proposed an improved Artificial Bee Colony (ABC) algorithmwhich combined with multivariate linear regression (MLR) for exploring the influencing mechanism of various factors on Chineseelectricity consumption and forecasting electricity consumption in the future The results indicated that the improved ABCalgorithm in view of the various factors is superior to traditional models just considering unilateralism in accuracy and persuasionThe overall findings cast light on this model which provides a new scientific and effective way to forecast the medium and longterm electricity consumption

1 Introduction

With the development of economy and technology par-ticularly in thirty years or so of reform and opening-upChinese electricity consumption achieves a sustained andrapid development However as illustrated in Figure 1 alongwith the economic development entering the ldquonew normalrdquothe national economy is in a period of transition from rapidgrowth to steady growth and the electricity consumption hasbeen fluctuating

Starting in 2012 on account of the decline in electricityconsumption proportion of high energy-intensive industriesthe growth of electricity demand in power industry hasslowed down significantly Pumping capital into installedcapacity in early time brought about relative surplus buyerrsquosmarket and the buying-market has gradually formed in recentyears [1 2] Nevertheless electric power replacement asone of the major initiatives to realize energy consumptiontransition and solve environmental pollution problems in the

current situation is conducive to increase the proportion ofelectricity in the energy consumption As a result facing thenew normal and power supply and demand contradictionit is important to explore Chinese electricity consumptioninfluence mechanism and forecast electricity consumptionwhich is significant for scientifically formulating electricalenergy plan and guaranteeing the sustainable economic andsocial development [3ndash5]

At present studies on forecasting medium and long termelectricity consumption have proposed multiple methodswhich contain traditional linear regression time series andemerging grey prediction [6ndash10] and so forth While thesemethods only rely on electricity consumption data to predictthe future and ignore the various factors closely relatedactually electricity consumption is relevant to numerousmultidimensional and dynamically changing factors andsome correlation may exist between themThe parameter setof higher complexity is necessary to express the changingtendency under the impact of these factors

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 8496971 14 pageshttpdxdoiorg10115520168496971

2 Mathematical Problems in Engineering

GDP growth rateElectricity consumption growth rate

004

006

008

01

012

014

016

Gro

wth

rate

()

2006 2007 2008 2009 2010 2011 2012 2013 20142005Year

Figure 1 GDP growth rate and electricity consumption growth rate

What is more it is improper to use Artificial NeuralNetwork (ANN) and Kalman Filtering for medium and longterm electricity consumption forecast in years because thesemethods usually need large amounts of data [11 12] And theycould not show the relationship between each influencingfactor and electricity consumption excellently or provide agood guidance for electrical energy plan

Combined with the feedback at home or abroad thehistorical situation of Chinese electricity use and the changein demand of ldquonew normalrdquo electricity this paper putsforward the main influence mechanism between electricityconsumption and the variables from economy society indus-try and environment Thereby an improved ABC method issuggested to forecast electricity consumption

This study will make a significant contribution that willbe embodied in the following two aspects firstly this studyprovides a full and objective analysis of influence mechanismbetween the electricity consumption and the variables fromeconomy society industry and environment and elucidatesthe relationship between them by mathematical statisticsmethod based on a large amount of literature data andthe actual situation of Chinese development secondly animproved ABC method was used to forecast electricityconsumption by creating intendedmodel Given the examplecalculation the model presented herein can assess the effectof various factors on the electricity consumption clearly andconfer further advantages on medium and long term fore-casting In the field of prediction many scholars regard ABCmethod as an auxiliary algorithm for numerical optimizationand little attention has been focused on a direct use of theadvantages of the ABC method to build a model to predictmedium and long term electricity consumption in the lastyears Taken together our studies have certain innovation andapplication value

This paper is divided into six sections After a briefintroduction Section 2 presents the influence factors andforecasting methods of electricity consumption Section 3describes the data in detail and Section 4 presents the ABCalgorithm and the improvement in this paper Numericalresults which are then discussed are described in Section 5The conclusions of the paper are summarized in Section 6

2 Literature Review

Electricity as a special commodity which has difficulty instoring has to be fully prepared for the forecast cohesionand balance of total supply and demand And as a resulta healthy grid situation will be manifest that the reasonabledemand will be met by scientific supply and the problem ofregional excess and overall energy shortage will be graduallysolved The objective of accurate modeling of the electricityconsumption calls for attention to a few extremely importantpoints The first point is to discern all of the necessaryvariables that are bound up with electricity consumption ina given area [13] the second point is to choose a suitablemodelingmethodology according to the characteristics of theelectricity consumption that can handle the difficulties of theconsumption modeling task and obtain the accurate result

21 The Literature of the Influence Factors of ElectricityConsumption On account of the effect of socioeconomicdevelopment and the changes in policy environment thefactors which could act on electricity consumption tend tobe nonlinear and nonstationary and it is conceivable thatthe relationship between the input variables and the outputvariable is undiscovered [14ndash16]

Previous studies have established that many differentvariables have been used to model the electricity consump-tion Table 1 presents a brief summary of some of theimportant recent studies on the field

The first aspect is to ascertain a causal relationshipbetween the economic factors and electricity consumptionAlong with economic growth the productivity and livingreveal a growing reliance on electricity demand and morethan that the interaction between electricity consumptionand economy growth is becoming more and more obviousIn the light of most theories and empirical researches theeconomic development which regards real GDP fixed assetsinvestment and foreign direct investment as the test variablesis central to electricity consumption

In a study undertaken by Karanfil and Li [17] it wasshown that the relationship between electricity consumptionand economic growth was affected at the national incomelevel geographic location development level and otherfactors considering the power dependence and urbanizationwith the panel data of 160 countries from 1980 to 2010Ciarreta and Zarraga have demonstrated that the strongcausality from electricity consumption to real GDP has char-acteristics of unidirectional and negative in the perspectiveof dynamic during a certain time period [18] Bianco et al[19] developed linear regression models using historical elec-tricity consumption gross domestic product (GDP) GDPper capita and population and the models showed annualelectricity consumption was strongly related to the selectedvariables Moreover their time sequence would maintain astate of relative balance in the long term Tang et al [20]have highlighted that electricity consumption and economicgrowth in Portugal have a bidirectional causality from a longterm point of view adopting boundary detection methodGranger causality test based on vector error correctionmodel and other statistical methods Polemis andDagoumas

Mathematical Problems in Engineering 3

Table1Summaryof

literaturer

eviewon

relationshipbetweenfactorsa

ndelectricity

consum

ption

Num

ber

Authors

Cou

ntry

Timep

eriod

Metho

dology

Varia

bles

Relatio

nships

1Ka

ranfi

land

Li[17]

160coun

tries

1980ndash2010

Cointegratio

ntechniqu

esElectricity

consum

ption

econ

omic

grow

th

Theree

xists

acausalrelationshipbetween

electricity

consum

ptionandecon

omic

grow

th

2CiarretaandZa

rraga

[18]

European

coun

tries

1970ndash2007

Apaneld

ataa

pproach

Electricity

consum

ption

econ

omic

grow

thTh

eree

xists

anegativea

ndstrong

causality

from

electric

ityconsum

ptionto

GDP

3Bianco

etal[19]

Italy

1970ndash2007

Linear

regressio

nmod

elsElectricity

consum

ption

GDPGDP

perc

apita

and

popu

latio

nAnn

ualelectric

ityconsum

ptionwas

stron

glyrelatedto

thes

elected

varia

bles

4Tang

etal[20]

Portug

al1974ndash200

9Multiv

ariatemod

els

Electricity

consum

ption

econ

omic

grow

th

Theree

xists

alon

grunPo

rtugalGranger

causality

betweenelectricity

consum

ption

andecon

omicgrow

th

5Po

lemisand

Dagou

mas

[21]

Greece

1970ndash2011

Cointegratio

ntechniqu

esElectricity

consum

ption

econ

omic

grow

th

Theree

xists

abidire

ctionalcausality

betweenelectricity

consum

ptionand

econ

omicgrow

th

6Za

man

etal[22]

Pakista

n1975ndash2010

Theb

ound

s-testing

procedure

Electricity

consum

ption

popu

latio

nTh

eree

xists

apositive

relationshipbetween

popu

latio

ngrow

thandele

ctric

ityconsum

ption

7Ka

vaklioglu[23]

Turkey

1975ndash200

6Th

e120576-SVRmod

elsElectricity

consum

ption

popu

latio

nTh

eree

xists

astro

ngcausality

between

popu

lationandele

ctric

ityconsum

ption

8Lidd

leandLu

ng[24]

105coun

tries

1971ndash200

9Heterogeneous

panel

metho

dsElectricity

consum

ption

urbanizatio

nTh

eree

xists


electricity

consum

ptionandurbanizatio

n

9Solarin

andShahbaz

[25]

Ang

ola

1971ndash200

9Th

eVEC

MGrang

ercausality

test

Electricity

consum

ption

urbanizatio

nandecon

omicgrow

th

Theree

xists

abidire

ctionalcausality

betweenelectricity

consum

ption

econ

omic

grow

thand

urbanizatio

n

10Za

chariadisa

ndPashou

rtidou

[26]

Cyprus

1960ndash200

4Times

eriesa

nalysis

techniqu

esElectricity

consum

ption

the

resid

entia

land

thes

ervicessectors

Theree

xistlong

-term

elasticities

ofele

ctric

ityconsum

ptionabovethe

resid

entia

land

thes

ervicessectors

11Pao[11]

Taiwan

1990ndash2002

Statisticalmod

els

Electricity

consum

ption

natio

nal

incomepo

pulatio

nGDPandCP

IPO

PandNIinfl

uencee

lectric

ityconsum

ptionthem

ostbu

tGDPtheleast

12Zh

angetal[27]

China

1985ndash2010

Principalcom

ponent

analysis

Electricity

consum

ption

indu

strial

factors

Theree

xists

apositive

correlationbetween

electric

ityconsum

ptionandindu

strial

factors

13MengandNiu

[28]

China

1990ndash2007

Partialleastsquare

mod

eling

Electricity

consum

ption

gross

domestic

prod

ucto

find

ustry

Thep

rimaryandthes

econ

dary

indu

stry

take

moree

lectric

ityconsum

ption

increasin

gthan

thetertia

ryon

e

14Shahbaze

tal[29]

UnitedArabEm

irates

1975ndash2011

TheV

ECM

Granger

causality

Electricity

consum

ption

CO2

emissions

Theree

xists

anegativec

orrelationbetween

electric

ityconsum

ptionandCO2em

issions

15Cow

anetal[30]

TheB

RICS

coun

tries

1990ndash2010

Panelcausalityanalysis

Electricity

consum

ption

CO2

emissions

Thed

ifferingresults

have

been

achieved

for

theB

RICS

coun

tries


[21] using the same statistical methods have indicated thecausal correlation between electricity consumption and eco-nomic growth in the case ofGreece is bidirectional Especiallyin the past ten years a relatively strong impact is performedfrom the electricity consumption to GDP

The second aspect takes the social factors that affectthe electricity consumption into consideration With regardto the development of any country the social factors arethought to be prerequisite and impact on the development ofeconomy and industry directly Social factors mainly containthree aspects they are population urbanization level andpeople living standard For electricity consumption it is acore problem whether the growth of electricity consumptioncan match the trend of population economic and socialdevelopment [22] And one can even say the social changesin all aspects will make a far-reaching difference in electricitysales market in the future

Before Kavaklioglu [23] conducted a study of electricityconsumption forecast in Turkey utilizing the 120576-SVR modelshe obtained that the electricity consumption would riseaccordingly as the growth of the population allowing forthe influence factors including GNP population importsand exports Collecting urbanization level and other relatedfactors index data of 105 countries from 1971 to 2009 Liddleand Lung [24] clearly pointed out that the improvementof urbanization level would bring the increase in electricityconsumption largely based on heterogeneous panel methodsnevertheless the connection found that the relationshipbetween urbanization level and electricity consumption wasnot a simple linear relationship In both Solarin and Zachari-adis investigations on the correlativity between economicgrowth urbanization and electricity consumption the find-ings raised the same conclusion that electricity consumptionnot only with economic growth but also with urbanizationlevel is in a significant causal relationship in the long term[25 26] Another study aimed at the interrelation of electricityconsumption and consumer price index (CPI) certified CPIhas an effect on electricity consumption in Taiwan [11] Theelectricity price was involved in some discussions while as forChina it is not an effective index by reason that the price ofChinese electricity consumption is fixed and rarely changed

The third aspect focuses on industrial factors Industrialstructure refers to the structure of a country or a regionrsquoseconomic industry and their mutual relations Researchescould measure a country or a regionrsquos industrial structurefrommultiple angles such as the output value structure laborstructure and relative labor productivity

Regarding industrial factors including industrial outputvalue commodity exports and added services industry valueZhang et al [27] utilized principal component analysis andcarried on the analysis to show the existence of the positivecorrelativity between electricity consumption and industrialfactors Meng and Niu [28] have stated that the relationshipbetween electricity consumption and its factors was not ascomplexity as imagined so that it was not complicated toachieve the relationship between them using multivariateregression modelThrough partial least square modeling theresults of variables importance analysis were elucidated thatthe secondary industry took more electricity consumption

increasing than the primary and the tertiary one [31]Therefore most of the studies chose the secondary industrycontribution to the GDP as the main indicator measuring theindustrial structure during the period

The fourth aspect is with respect to the environmentalfactors In the process of construction of low-carbon societyelectricity development plays an important role Practice hasproven that greenhouse gas emissions have been the top inall industries during the link of electricity production whichis predominantly coal-firedMeanwhile the emissions duringthe link of using electricity are less than the emissions of otherprimary energy (mainly including coal oil and natural gas)for the environmentHence themutual influencemechanismhas existed distinctly between electricity consumption andenvironmental factors

The result of Shahbaz et alrsquos study pointed out a negativecorrelation relationship and a back donation between elec-tricity consumption and carbon emissions in United ArabEmirates [29] In allusion to the different situations of theBRICS countries Cowan et al [30] verified that electricityconsumption was the Granger causality of CO

2emissions

in India while there was no Granger causality betweenelectricity consumption and CO

2emissions in Brazil Russia

China and South AfricaThe summary of literature reviewon relationship between

factors and electricity consumption is shown in Table 1

22The Literature of Forecasting Methods regarding ElectricityConsumption The common methods among the researchstudies on electricity consumption forecast derive from tra-ditional consumption method elasticity coefficient methodregression analysis gray prediction method Support VectorMachine (SVM) and then modern intelligent algorithmssuch as Neural Network and Wavelet Analysis method andother meta-heuristics such as Genetic Algorithms and Par-ticle Swarm Optimization In addition prediction accuracieshave discrepancies owing to different methods

At present the scientific research strength ofmedium andlong term electricity consumption forecast has less adequacythan short term load forecast technology because of itsmore impact factors the small amount of historical dataand having more difficulties in making accurate quantitativeresearch

Via the statistical analysis to determine the relationshipbetween variables the traditional forecast method suchas grey prediction and regression analysis shows a goodfitting capacity whereas the forecast results cause big errorin the future changing trend Fitting degree and predictionprecision perform unsatisfactorily although many scholarsuse some combination methods to ameliorate the accuracyespecially when the model has many variables [32ndash38] SVMmethod can better deal with the nonlinearity and uncertaintyamong factors influencing the long termpower consumptionbut it still has some risks appearing localminimumvalue [39]

So far some intelligence algorithms such as ANNGenetic Algorithm (GA) and Ant Colony Optimizationhave received particular attention in estimating electric-ity consumption and especially in short term electricity


consumption forecasting since they can handle current datato an arbitrary degree of accuracy [40 41]

Through the comparison with conventional regressionmodel Azadeh et al showed the estimation of Iran electricityconsumption done by GA is more fitted than regressionmethod [42] They also used an integrated GA and ANNto estimate and predict electricity consumption while therelative error of the method was small [43] Kiran et alverified the results of forecasting electricity consumptionin Turkey by ABC and PSO techniques outperformed theresults forecasted by Ant Colony Optimization [44] Azadehet al compared three meta-heuristics namely GAs ArtificialImmune System (AIS) and Particle Swarm Optimization(PSO) with each other in estimation of electricity consump-tion in the selected countries With fitted random variablesAIS method with the Clonal Selection Algorithm showssatisfactory results and has been selected as the preferredmethod [45]

Some of these algorithms require large amounts of histor-ical load data processing to let the computer learning map-ping relationships predict the future of the load Some havestrong randomness and fall into local optimum Modelingthe consumption carried out with these algorithms has strongrobustness and nonlinear mapping ability to solve currentdata but they are not good for prediction since they do notuse any mathematical models and present a slow learningconvergence speed and a weak generalization ability

In consequence with the purpose of exhibiting goodglobal optimization and robustness characteristics as well asaccuracy in prediction it is necessary to build a forecastmodel under the support of mathematical theory coalescingboth mathematical analysis methods and intelligent algo-rithms

3 Data Source

This study is based on annual data of electricity consumptionreal gross domestic product (GDP) fixed asset investment(FAI) foreign direct investment (FDI) population urban-ization level household consumption level real GDP ofsecondary industry and carbon emission covering a timeperiod from 1990 to 2014 in China The time series dataare collected from International Monetary Fund Data andStatistics (IMF 2015) and World Bank world developmentindicators (WDI 2015) The real GDP series are transformedfrom the nominal GDP in constant 1990 prices These factorsselection is based on the above literature analysis andChineseactual conditions

In the process of modeling and predicting of electricityconsumption the real GDP and fixed assets investmentneed to be deemed as important factors into considerationAlthough there is no strict sense of the causality betweenelectricity consumption and economic growth in Chinaelectricity consumption as a reflection of the power industrydevelopment in the economic system can ahow a country ora regionrsquos economic operation Meanwhile FDI is thought toact as a vital economic factor in view of the advancement ofenergy internet globalization

Population and urbanization level as important factorsshould be taken into account in the study as well There isexplanation of urbanization level that it is generally repre-sented with the proportion of urban population accountingfor total population And it is exceedingly significant indexto measure economic development of a country or area Inaccelerating the process of urbanization it brings a series ofelectrification development of the society which will lead toincreasing power consumption and increasing populationwill also pull the economic development and growth inelectricity consumption sequentially

It can give no cause for much criticism of the interactionbetween electricity consumption and industrial structureThe adjustment of the industry is an important cause of pro-moting economic development and fluctuating of electricityconsumption due to the different electricity consumption perunit GDP of industrial sectors

Apart from that carbon emission is supposed to be anessential factor in the study of electricity consumption invirtue of a strategy of low carbon energy development viaimproving the power conversion efficiency and realizing theenergy alternative which build electricity as the core

Table 2 shows the primary data of electricity consumptionand the factors mentioned before

On account of different numerical size and dimension ofvarious factors this paper applies the method of 119885-Score tonormalizing them according to the annual orderThe processis as follows

1198831015840

119894=

(119883119894minus 119883)

119878119894

(1)

119883119894and 119883

1015840

119894represent primary data and normalized data

respectively 119883 is the average value and 119878119894is the standard

deviationThe values of these standardized variables fluctuatearound zero Greater than zero is above the average and lessthan zero is under the averageThe normalized data is shownin Table 3

In order to find some relationship between electricityconsumption and various factors the contrast of changetrend of these variables is illustrated by Figure 2

In Figure 2 we can see the change trend of electricityconsumption is same to these factors And we can trust theremust be some relationship between electricity consumptionand these factors Moreover correlation analysis of thefactors and electricity consumption also show the intimateconnection between them Because the counting process issubordinate the results of correlation analysis are exhibited inSupplementaryMaterial available online at httpdxdoiorg10115520168496971

4 Methodological Framework

41 Introduction of ABC Algorithm Artificial Bee Colony(ABC) algorithm as a swarm intelligence optimization algo-rithm has a superior convergence speed on the basis of theintelligent behavior of honey bees The main characteristicof ABC algorithm is that it only needs to contrast theadvantages or disadvantages with other solutions rather than


Table 2 Primary data of various factors and electricity consumption

YearRealGDP(billionRMB)

FAI(billionRMB)

FDI(milliondollars)

Population(millionpeople)

Urbanizationlevel ()

Householdconsumption

level(RMB)

Real GDP ofsecondaryindustry(billionRMB)

Carbonemission

(million tons)

Electricityconsumption

(billionkWsdoth)

1990 18825 4517 10289 1143 02641 1510 743 2458 6231991 19548 5595 11550 1158 02694 1701 1252 2591 6801992 21342 8080 19202 1172 02746 2027 1481 2723 7591993 24381 13072 38955 1185 02799 2577 1719 2877 8431994 27785 17042 43206 1199 02851 3496 2001 3029 9261995 31419 20019 48133 1211 02904 4283 2104 3228 10021996 34850 22914 54804 1224 03048 4839 2290 3323 10761997 38339 24941 64408 1236 03191 5160 2372 3314 11281998 41904 28406 58557 1248 03335 5425 2588 3312 11601999 45185 29855 52659 1258 03478 5854 2650 3423 12312000 48628 32918 59360 1267 03622 6280 3010 3514 13472001 52728 37213 49670 1276 03766 6860 2531 3674 14632002 57104 43500 55010 1285 03909 7703 2940 4025 16472003 62289 55567 56140 1292 04053 8472 3807 4723 19032004 68537 70477 64072 1300 04176 9422 3742 5521 21972005 75452 88774 63805 1308 04299 10493 4052 6326 24942006 83986 109998 67080 1314 04434 11760 4493 6926 28592007 94635 137324 78340 1321 04589 13786 5171 7518 32712008 108035 172828 95253 1328 04699 15781 5499 7663 34382009 118439 224599 91804 1335 04834 17175 6439 8037 36432010 129348 251684 108820 1341 04995 19109 7849 8472 41922011 142864 311485 117698 1347 05127 21810 7738 9206 46932012 156151 374695 113294 1354 05257 24565 7982 9415 49762013 168096 446294 118721 1361 05373 26955 8368 9674 53222014 180989 512761 119705 1368 05477 28844 8811 9761 5523

comprehending the special information of the problemGradually the global optimal value will emerge through thelocal optimization of each individual worker bee

However many intelligent algorithms have been broughtforward in recent decades such as Particle Swarm Optimiza-tion (PSO) and Artificial Neural Network (ANN) algorithmand Genetic Algorithm (GA) In many areas it cannot bedenied that these algorithms have solved a great deal ofproblems and made difference [46ndash51] But in this paperthese algorithms could be not so appropriate Obviouslythe most important reason is that the data quantity is toolacking to use these intelligent algorithms and it could leadto a huge error which does not want to be seen Fortunatelythe initial purpose of putting forward ABC algorithm isto solve the optimization problem of multivariate function[52] And Akay and Karaboga analyzed the size of thepopulation for ABC algorithm and drew a conclusion thatABC algorithm did not have to use a big value of colony sizeto solve optimization problems [53] Just because of these the

improved ABC algorithm is believed to solve the problem inthe field of electricity consumption although this is the firstattempt

42 Traditional Algorithm Procedure of ABC In ABC algo-rithm the swarm is composed of employed bees onlookersand scouts and the location of a food source is abstractedinto a point of 119863-dimensional space The process of findingthe optimal food source is the procedure of searching forthe optimal solution The position of the swarm representsthe solution of optimization problem and the benefit of thesource symbolizes the adaptive value of the optimizationproblem

The bees search all of the food sources recurrently andlocation of food source is denoted with a 119863-dimensionalvector quantity

119883119895= (1199091 1199092 119909

119863) 119895 isin [1 119863] (2)


Table 3 Normalized data of various factors and electricity consumption

Year RealGDP FAI FDI Population Urbanization

level


level

Real GDP ofsecondaryindustry

Carbonemission


1990 minus111 minus078 minus175 minus193 minus141 minus112 minus134 minus112 minus1071991 minus108 minus078 minus171 minus171 minus134 minus110 minus113 minus107 minus1041992 minus103 minus076 minus147 minus151 minus127 minus105 minus104 minus102 minus0991993 minus097 minus074 minus085 minus131 minus120 minus096 minus095 minus096 minus0931994 minus090 minus071 minus072 minus111 minus113 minus090 minus083 minus090 minus0881995 minus084 minus068 minus057 minus092 minus106 minus086 minus079 minus083 minus0831996 minus077 minus066 minus036 minus073 minus092 minus079 minus072 minus079 minus0791997 minus071 minus065 minus006 minus055 minus077 minus070 minus068 minus080 minus0761998 minus065 minus062 minus024 minus038 minus062 minus066 minus060 minus080 minus0741999 minus059 minus061 minus043 minus023 minus047 minus060 minus057 minus075 minus0692000 minus051 minus059 minus022 minus009 minus033 minus051 minus043 minus072 minus0622001 minus044 minus056 minus052 005 minus018 minus038 minus062 minus066 minus0552002 minus034 minus052 minus035 017 minus003 minus030 minus045 minus052 minus0432003 minus023 minus044 minus032 028 012 minus018 minus010 minus026 minus0272004 minus010 minus036 minus007 040 025 minus009 minus013 005 minus0092005 005 minus022 minus008 051 038 002 minus001 036 0102006 024 minus007 002 061 053 019 017 059 0332007 049 009 037 071 069 035 045 082 0582008 067 027 090 081 081 061 058 087 0692009 087 076 079 091 095 081 096 101 0822010 112 084 132 101 112 105 153 118 1162011 137 118 159 110 127 132 148 146 1472012 158 172 146 120 141 165 158 154 1652013 182 222 163 130 154 196 173 164 1872014 206 267 166 141 167 222 191 168 199

The formula of determining the initial solution is

119909119894119895= 119909min119895 + rand (0 1) (119909max119895 minus 119909min119895)

119895 isin [1 119863] 119894 isin [1 119878119873]

(3)

119862 and 119878119873 are the cycle index and the number of honey beesrespectively The bees select the food source in accordancewith the roulette wheel Fitness

119894is the adaptation degree

fitness119894=

1

1 + 119891 (119883119894)

119891 (119883119894) ge 0

1 +1003816100381610038161003816119891 (119883119894)1003816100381610038161003816

119891 (119883119894) lt 0

(4)

119875119894 the selected probability is

119875119894=

fitness119894

sum119865119873

119895=1fitness

119895

(5)

The bigger value of 119875119894means the better nectar source

and then the better nectar source will gather more scouts Sothe onlookers could find the best nectar source The search

formula of onlookers updating the location of nectar sourceby employed bees is

V119894119895= 119909119894119895+ 119903119894119895(119909119894119895minus 119909119896119895)

119895 = 119896 119895 isin [1 119863] 119894 isin [1 119878119873]

(6)

Hereinto 119896 isin (1 2 3 119878119873) 119895 isin 1 2 119863 119903119894119895isin [1

1] However this method also has disadvantages such asdealing with multiobjective or multiextreme problems Con-sequently it is always used to optimize the parameters andthresholds in other algorithms as an auxiliary method whichcan reduce the training time [54]

43 ABC Model in This Paper This paper suggests thatinfluence factors and electricity consumption are regarded asindependent variables (119860 = 119886

1 1198862 1198863 119886

119863) and dependent

variable separately In the previous studies Bianco et al [19]andMeng andNiu [28] both have developed linear regressionmodels to forecast electricity consumption and the modelsshowed an outstanding outcome So there is linear functionbetween the variables

Tec = 119891 (1198861 1198862 1198863 119886

119863) (7)


20142010

20062002

Time (year)19989 8 7 6 19945 4 3 2Each index11990

(1) Electricity consumption(2) Urbanization level(3) Real GDP of secondary industry(4) FAI(5) FDI(6) Carbon emission(7) Household consumption level(8) Real GDP(9) Population

minus2

minus1

0

1

2

3

Nor

mal

ized

val

ue

Figure 2 The contrast of change trend between electricity con-sumption and various factors

This can also be written as follows

11988611199091+ 11988621199092+ 11988631199093+ sdot sdot sdot + 119886

119863119909119863+ 119909119863+1

= 0 (8)

Apparently 119883 = [1199091 1199092 1199093 119909

119863 119909119863+1

] is the solutionof the linear equations By choosing 119873 years data we canobtain an equation set containing 119873 equations with (119863 + 1)

unknowns 1199091minus 119909119863+1

Specific equations are as follows

119886111199091+ 119886211199092+ 119886311199093+ sdot sdot sdot + 119886

1198631119909119863+ 119909119863+1

= 0

119886121199091+ 119886221199092+ 119886321199093+ sdot sdot sdot + 119886

1198632119909119863+ 119909119863+1

= 0

119886131199091+ 119886231199092+ 119886331199093+ sdot sdot sdot + 119886

1198633119909119863+ 119909119863+1

= 0

11988611198731199091+ 11988621198731199092+ 11988631198731199093+ sdot sdot sdot + 119886

119863119873119909119863+ 119909119863+1

= 0

(9)

Similarly this is equivalent to obtain the minimum of theequation below

min119865 (119860)

=

119873

sum

119873=1

[119891 (1198861119873 1198862119873 1198863119873 119886

119863119873) minus Tec

119873]2

lb le 119886119863119873

le ub

(10)

The subsequent procedure is using Artificial Bee Colony(ABC) algorithm to solve the multivariate linear equationsand get coefficient 119883 = [119909

1 1199092 1199093 119909

119863 119909119863+1

] Thenthe relationship between the various factors and electricityconsumption is explicit

As a general rule if an equation set has solutions thenumber of independent variables (119863 + 1) should be greaterthan or equal to the number of equations (119873) Neverthelessin this paper (119863 + 1) will be less than 119873 and consequentlyit will result in no solution in this equation set Underthis circumstance ABC algorithm cannot be used directlyTherefore there are two improvements used in traditionalABC algorithm To begin with we apply multivariate linearregression (MLR) to ABC algorithm so that the no solutionequation set can be solved In other words although thesolution equation set is no solution an optimal solution canbe found when the error becomes the minimum Secondlywe set a cycle index CYCLE2 which should be at least as bigin order to avoid running into local optimum as much aspossible The concrete implementation steps are as follows

Step 1 (initialization parameter) Set the population size 119878119873the maximum of iterative times CYCLE1 each iteration stepsize 119881 cycle index CYCLE2 the upper bound ub and lowerbound lb data volume 119873 and the number of independentvariables119863 + 1 120576 is 119865(119860) and Lim is limit

Step 2 (generate the initial solution) In the light of (3) it willgenerate 119878119873 initial solutions randomlyThen according to (4)and (5) calculate the fitness and selected probability of eachsolution At last choose the best fitness nectar source as theinitial solution

Step 3 (iterative optimization) Scouts search the neighbor-hood of the nectar source and calculate the fitness andthe probability according to (4) and (5) If near honey isbetter than original nectar source record new nectar sourcelocation and send to employed bees Onlookers choose thenectar source according to 119875

119894and record new nectar source

location according to (6) Then search the neighborhood ofthe new nectar source until there is no better one At thismoment the number of iterations needs to be plus 1

Step 4 (limit judge) Save the current location of nectarsource if the number of iteration is beyond the maximumiterations CYCLE1 Step 2 is in return Do like this CYCLE2times

Step 5 (find the optimal solution) Select the best solutionfrom CYCLE2 nectar sources and it is perceived to be theoptimal solution

The program flow chart is shown in Figure 3This study forecasts the electricity consumption using an

improved Artificial Bee Colony (ABC) algorithm to solve themultivariate linear equations The data from 1990 to 2009 20years in the aggregate is the basis and the data from 2010to 2014 5 years is used to test So in this paper specificparameter is as follows 119878119873 = 40 CYCLE1 = 200 119881 = 00001


Start

Initialization parameter

Generate the initial solution

Scouts search the neighborhoodof the nectar source

Record new nectarsource location andsend to employed bees

Yes

The iterations add 1

If the iteration biggerthan the limit

No

Yes

No

Onlookers

Save the current location of nectar source


No

Select the best solution

End

The iterationsneed to add 1

If the fitness of the newnectar source better thanprevious one

Yes

Figure 3 The program flow chart of the improved ABC model

CYCLE2 = 1000 ub = 1 and lb = minus1 Lim = 001119863 = 8 and119873= 20There are some explanations about the determination ofparameters

(1) Usually the population size 119878119873 is always 40 and thereis no necessity to change in this paper

(2) Because of 119863 + 1 = 9 as a computational algorithmstochastic algorithm is a pseudorandom algorithm soCYCLE1 = 200 is enough to insure that every variablecan be turned to when119863 = 8

(3) 119881 and CYCLE2 can improve the accuracy of theprediction Under ideal conditions 119881 should be assmall as possible and CYCLE2 should be as big aspossible However in consideration of the actualconditions we valued119881=00001 andCYCLE2= 1000

(4) Because the data has been standardized the coeffi-cient can not be beyond [minus1 1] So ub = 1 and lb =

minus1

(5) Lim is a parameter which is used to control the endtime If Lim lt 001 120576 is small enough for us to doprediction So we valued Lim = 001

To test whether the algorithm is correct or not thefollowing models are chosen to compare (I) quadraticregression (II) Artificial Neural Network (ANN) (III)Genetic Algorithm (GA) (IV) Particle Swarm Optimization(PSO)

As one of the most primitive prediction models thequadratic regression mode should be selected to clarifywhether this kind of models is still adaptive or not in such acomplex circumstance ANN algorithm is a representation ofearly artificial intelligence algorithm It can tell uswhether theemerging intelligence algorithm is better than the old oneGAand PSO are used to represent two classes of meta-heuristicsseparately and they will prove whether the improved ABCalgorithm is superior to others


Actual valuesImproved ABC model

Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year

Figure 4 Numerical results of the improved ABC model

Actual valuesQuadratic regression model

Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year

Figure 5 Numerical results of the quadratic regression model

5 Result and Discussion

In this test five algorithms run on matlab2015b and experi-mental results are shown in Figures 4ndash8

Numerical results of the improved ABCmodel comparedwith actual values are shown in Figure 4

Numerical results of the quadratic regression modelcompared with actual values are shown in Figure 5

Numerical results of the ANN model compared withactual values are shown in Figure 6

Numerical results of the GAmodel compared with actualvalues are shown in Figure 7

Numerical results of the PSO model compared withactual values are shown in Figure 8

Although there are figures of five models predictionresults we can not clearly see whether the results of electricityconsumption based on the improved ABC algorithm aresuperior to the results based on othermodels only by our eyesFor the purpose of better reflection of differences Table 4was made and it provided precise predictions and the errorbetween predictions and actual values The performance ofthe proposed method is evaluated by two indices namelythe mean absolute error (MAE) and the mean absolute

Actual valuesANN model

Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

2006

2004

2000

2002

2014

1990

2008

2010

2012

1996

1998

Year

Figure 6 Numerical results of the ANN model

Actual valuesGA model

Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year

Figure 7 Numerical results of the GA model

Actual valuesPSO model

Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1996

2012

2008

1992

2000

2002

2004

2006

1994

2014

1990

1998

2010

Year

Figure 8 Numerical results of the PSO model

percentage error (MAPE) The forecasting error of thesemodels is shown in Table 4

The forecasting error curves of these models are shown inFigure 9

From error comparisons the predicted effect of variousmethods can be clearly seen


Table 4 The forecasting error of these models

Predictionmethods Year

TEC(billionkWsdoth)

Predictions(billion kWsdoth) AE APE MAE MAPE

The improved ABCmodel

2010 4192300 4177958 14342 0342

38895 09282011 4692800 4623169 69631 14842012 4976264 4945553 30711 06172013 5322300 5269857 52443 09852014 5523300 5550647 27347 0495

The quadraticregression mode

2010 4192300 4056341 135959 3243

157654 37612011 4692800 4427643 265157 56502012 4976264 4818710 157554 31662013 5322300 5229545 92755 17432014 5523300 5660146 136846 2478

The ANNmodel

2010 4192300 4321285 128985 3077

133566 31862011 4692800 4581430 111370 23732012 4976264 5069392 93128 18712013 5322300 5407438 85138 16002014 5523300 5772506 249206 4512

The GA model

2010 4183890 4187005 3115 0074

65923 15762011 4650354 4605959 44396 09552012 4988191 4923622 64569 12942013 5349377 5247652 101725 19022014 5633092 5517284 115808 2056

The PSO model

2010 4192300 4187005 5295 0126

45089 10762011 4692800 4605959 86841 18512012 4976264 4923622 52642 10582013 5322300 5247652 74648 14032014 5523300 5517284 6016 0109

minus3000

minus2000

minus1000

0

1000

2000

3000

Erro

rs (B

illio

n kW

middoth)

2004

1998

1996

2006

1990

2002

1994

1992

2008

2010

2012

2014

2000

Year

DatumQuadratic regression modelANN model

GA modelPSO modelImproved ABC model

Figure 9 The forecasting errors curves of these models

To begin with the accuracy of quadratic regression modeis the worst It is expected that the errors will be even biggerif the forecast period becomes longer ANN model is betterthan quadratic regression mode at accuracy However there

is still a greater error from actual value Maybe it due to thetraining data is too little So quadratic regression mode andANN model are not so appropriate to forecasting Chineseelectricity consumption under this situation

What is more the GA model and PSO model makea progress in accuracy and the MAE and MAPE are alsosmall enough to the actual application However this paperproved that the improved ABC algorithm combined withmultivariate linear regression model is better than others inaccuracy and it is more appropriate to forecast the electricityconsumption in such a circumstance

Thirdly along with the running of these meta-heuristicsalgorithm the error namely 120576

119894(119894 = 1 2 3 1000) will be

created Rank 120576119894in descending order is shown in Figure 10

From Figure 10 it is obvious that the change of 120576 becomessmaller and smaller and the solution corresponding to themin-120576 is perceived to be the optimal solution Although allthese three models can find an optimal solution and theiroptimal solutions do not have much difference we also canfind the convergence speed of the improved ABC algorithmis faster than GA and PSO So in this paper the improvedABC algorithm is proved to be the best model to forecastingChinese electricity consumption



200 400 600 800 10000Cycle times

0

05

1

15

2

25

3

Erro

r val

ues

Figure 10 120576119894in descending order ofGA PSP and the improvedABC

algorithm

Finally the optimal solution of the improved ABCalgorithm corresponding to the min-120576 is 119883 = (0385 0434

0584 0486 0375 0722 0265 0052 0883) Thereinto0883 is the constant term 0052 is the coefficient ofpopulation 0722 is the coefficient of carbon emissionFrom the coefficients we can see that the population isunimportant influencing electricity consumption and thereis close relation between carbon emission and electricityconsumption As for other factors although they are not themost important factors they should be taken into account

Therefore while forecasting the electricity consumptionit should not only focus on itself The preferable way is toreference various factors associatedwith electricity consump-tion and find the relationship between them It is reliableto get the electricity consumption through predicting thevarious factorsrsquo change in the future

6 Conclusions

This paper suggests an improved ABC algorithm to explorethe influencing mechanism of various factors on Chineseelectricity consumption and forecast electricity consumptionThough arranging the research achievement the historicalsituation ofChinese electricity use and the change in demandof ldquonew normalrdquo electricity eight factors are brought forwardBy employing improvedABC and the eight factors this paperinvestigates the influence mechanism of Chinese electricityconsumption and builds a corresponding prediction modelExperiments proved that the model can well predict theChinese electricity consumption in the future and have anadvantage over simple ANN model and quadratic regressionmodel in accuracy It provides a new scientific and effectiveway to forecast the medium and long term electricity con-sumption

Abbreviations

ABC Artificial Bee ColonyMLR Multivariate linear regressionANN Artificial Neural NetworkGDP Gross domestic productGNP Gross national productCPI Consumer price indexSVM Support Vector MachineFAI Fixed asset investmentFDI Foreign direct investment

Competing Interests

The authors declare no conflict of interests

Authorsrsquo Contributions

Professor Jingmin Wang planned the work Under herguidance and encouragement Jing Nie summarized thedevelopment of the research status and designed the modelpresented in this work Jian Zhang implemented the mainpart of the different prediction methods and error analysis

Acknowledgments

This work is part of Beijing Social and Scientific Fund whichprovides scientific supervision and guidance The authorswould like to express their acknowledgements to the BeijingSocial and Scientific Fund for the financial support under15JGB050

References

[1] M-X Cui and J-S Wang Annual Report on Chinarsquos EnergyDevelopment (2013) vol 1 Social Sciences Academic PressBeijing China 2014

[2] China National Renewable Energy Center The RenewableEnergy Industrial Development Report 2014 China Environ-mental Science Press Beijing China 2014

[3] E Almeshaiei andH Soltan ldquoAmethodology for Electric PowerLoad Forecastingrdquo Alexandria Engineering Journal vol 50 no2 pp 137ndash144 2011

[4] M J OrtizBevia A RuizdeElvira and F J Alvarez-GarcıaldquoThe influence of meteorological variability on the mid-termevolution of the electricity loadrdquo Energy vol 76 pp 850ndash8562014

[5] W-J Lee and J Hong ldquoA hybrid dynamic and fuzzy time seriesmodel for mid-term power load forecastingrdquo InternationalJournal of Electrical Power amp Energy Systems vol 64 pp 1057ndash1062 2015

[6] V Bianco O Manca and S Nardini ldquoElectricity consumptionforecasting in Italy using linear regression modelsrdquo Energy vol34 no 9 pp 1413ndash1421 2009

[7] E Erdogdu ldquoElectricity demand analysis using cointegrationand ARIMA modelling a case study of Turkeyrdquo Energy Policyvol 35 no 2 pp 1129ndash1146 2007

[8] Z Dilaver Zafer and L C Hunt ldquoIndustrial electricity demandfor Turkey a structural time series analysisrdquo Energy Economicsvol 33 no 3 pp 426ndash436 2011


[9] Z Dilaver and L C Hunt ldquoModelling and forecasting Turkishresidential electricity demandrdquo Energy Policy vol 39 no 6 pp3117ndash3127 2011

[10] D Akay andM Atak ldquoGrey prediction with rolling mechanismfor electricity demand forecasting of Turkeyrdquo Energy vol 32 no9 pp 1670ndash1675 2007

[11] H-T Pao ldquoComparing linear and nonlinear forecasts forTaiwanrsquos electricity consumptionrdquo Energy vol 31 no 12 pp1793ndash1805 2006

[12] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Journal of Basic Engineering vol 82 no 1 pp 35ndash451960

[13] R Inglesi ldquoAggregate electricity demand in South Africaconditional forecasts to 2030rdquo Applied Energy vol 87 no 1 pp197ndash204 2010

[14] H Hahn S Meyer-Nieberg and S Pickl ldquoElectric load fore-casting methods tools for decision makingrdquo European Journalof Operational Research vol 199 no 3 pp 902ndash907 2009

[15] H R S Keyno F Ghaderi A Azade and J Razmi ldquoForecastingelectricity consumption by clustering data in order to declinethe periodic variablersquos affects and simplification the patternrdquoEnergy Conversion andManagement vol 50 no 3 pp 829ndash8362009

[16] Y Chen G-F Zhang T-D Jin S-M Wu and B Peng ldquoQuan-titative modelling of electricity consumption using computa-tional intelligence aided designrdquo Journal of Cleaner Productionvol 69 pp 143ndash152 2014

[17] F Karanfil and Y-J Li ldquoElectricity consumption and economicgrowth exploring panel-specific differencesrdquo Energy Policy vol82 no 1 pp 264ndash277 2015

[18] A Ciarreta and A Zarraga ldquoEconomic growth-electricityconsumption causality in 12 European countries a dynamicpanel data approachrdquo Energy Policy vol 38 no 7 pp 3790ndash3796 2010

[19] V Bianco O Manca and S Nardini ldquoLinear regression modelsto forecast electricity consumption in ItalyrdquoEnergy Sources PartB Economics Planning and Policy vol 8 no 1 pp 86ndash93 2013

[20] C F Tang M Shahbaz and M Arouri ldquoRe-investigatingthe electricity consumption and economic growth nexus inportugalrdquo Energy Policy vol 62 pp 1515ndash1524 2013

[21] M L Polemis and A S Dagoumas ldquoThe electricity con-sumption and economic growth nexus evidence from GreecerdquoEnergy Policy vol 62 pp 798ndash808 2013

[22] K Zaman M M Khan M Ahmad and R Rustam ldquoDetermi-nants of electricity consumption function in Pakistan old winein a new bottlerdquo Energy Policy vol 50 pp 623ndash634 2012

[23] K Kavaklioglu ldquoModeling and prediction of Turkeyrsquos electricityconsumption using support vector regressionrdquo Applied Energyvol 88 no 1 pp 368ndash375 2011

[24] B Liddle and S Lung ldquoMight electricity consumption causeurbanization instead Evidence fromheterogeneous panel long-run causality testsrdquoGlobal Environmental Change vol 24 no 1pp 42ndash51 2014

[25] S A Solarin and M Shahbaz ldquoTrivariate causality betweeneconomic growth urbanisation and electricity consumption inAngola cointegration and causality analysisrdquo Energy Policy vol60 pp 876ndash884 2013

[26] T Zachariadis and N Pashourtidou ldquoAn empirical analysis ofelectricity consumption in Cyprusrdquo Energy Economics vol 29no 2 pp 183ndash198 2007

[27] J Zhang X-Y Yang F Shen et al ldquoPrincipal componentanalysis of electricity consumption factors in Chinardquo EnergyProcedia vol 16 pp 1913ndash1918 2012

[28] M Meng and D Niu ldquoAnnual electricity consumption analysisand forecasting of China based on few observations methodsrdquoEnergy Conversion and Management vol 52 no 2 pp 953ndash9572011

[29] M Shahbaz R Sbia H Hamdi and I Ozturk ldquoEconomicgrowth electricity consumption urbanization and environ-mental degradation relationship in United Arab EmiratesrdquoEcological Indicators vol 45 pp 622ndash631 2014

[30] W N Cowan T Chang R Inglesi-Lotz and R Gupta ldquoThenexus of electricity consumption economic growth and CO

2

emissions in the BRICS countriesrdquo Energy Policy vol 66 pp359ndash368 2014

[31] L Liu X-QMa and J-L Sun ldquoAn investigation of the relation-ship between economic growth and electricity consumptionwith different industrial structures in different regions inChinardquo in Proceedings of the 48th International UniversitiesrsquoPower Engineering Conference (UPEC rsquo13) pp 1ndash6 DublinIreland September 2013

[32] W Sun C-J Lu and M Meng ldquoThe application of optimalcombined forecasting technique based on GRA in Midlongterm load forecastingrdquo in Proceedings of the China InternationalConference on Electricity Distribution (CICED rsquo06) BeijingChina September 2006

[33] M Xing S-J Yang D-X Niu and W Sun ldquoResearch ongray optimization combination power load forecasting based onmultivariate exponential weightingrdquo Power System Technologyvol 29 pp 8ndash11 2005

[34] P Zhou B W Ang and K L Poh ldquoA trigonometric greyprediction approach to forecasting electricity demandrdquo Energyvol 31 no 14 pp 2503ndash2511 2006

[35] Y Ohtsuka T Oga and K Kakamu ldquoForecasting electricitydemand in Japan a bayesian spatial autoregressive ARMAapproachrdquo Computational Statistics and Data Analysis vol 54no 11 pp 2721ndash2735 2010

[36] RWeronModeling and Forecasting Electricity Loads and PricesA Statistical Approach John Wiley amp Sons Ltd Oxford UK2006

[37] P Li M Li and D-C Liu ldquoPower load forecasting based onimproved regressionrdquo Power System Technology vol 30 pp 99ndash104 2006

[38] S S Pappas L Ekonomou P Karampelas et al ldquoElectricitydemand load forecasting of the Hellenic power system using anARMA modelrdquo Electric Power Systems Research vol 80 no 3pp 256ndash264 2010

[39] X-R Song L Li and L-Q Zhang ldquoStudy on long-term powerload forecastingrdquo Computer Simulation vol 31 pp 132ndash1352014

[40] R P Lippmann ldquoAn introduction to computing with neuralnetsrdquo IEEE ASSP Magazine vol 4 no 2 pp 4ndash22 1987

[41] K Metaxiotis A Kagiannas D Askounis and J PsarrasldquoArtificial intelligence in short term electric load forecastinga state-of-the-art survey for the researcherrdquo Energy Conversionand Management vol 44 no 9 pp 1525ndash1534 2003

[42] A Azadeh S F Ghaderi and S Tarverdian ldquoElectrical energyconsumption estimation by genetic algorithmrdquo inProceedings ofthe International Symposium on Industrial Electronics (ISIE rsquo06)vol 7 pp 395ndash398 Montreal Canada July 2006


[43] A Azadeh S F Ghaderi S Tarverdian and M Saberi ldquoInte-gration of artificial neural networks and genetic algorithm topredict electrical energy consumptionrdquo Applied Mathematicsand Computation vol 186 no 2 pp 1731ndash1741 2007

[44] M S Kiran E Ozceylan M Gunduz and T Paksoy ldquoSwarmintelligence approaches to estimate electricity energy demandin Turkeyrdquo Knowledge-Based Systems vol 36 pp 93ndash103 2012

[45] A Azadeh M Taghipour S M Asadzadeh and M AbdollahildquoArtificial immune simulation for improved forecasting ofelectricity consumption with random variationsrdquo InternationalJournal of Electrical Power amp Energy Systems vol 55 pp 205ndash224 2014

[46] D Karaboga ldquoAn idea based on honey bee swarm for numer-ical optimizationrdquo Technical Report TR06 Erciyes UniversityKayseri Turkey 2005

[47] D Karaboga and B Basturk ldquoOn the performance of artificialbee colony (ABC) algorithmrdquo Applied Soft Computing vol 8no 1 pp 687ndash697 2008

[48] N Karaboga ldquoA new design method based on artificial beecolony algorithm for digital IIR filtersrdquo Journal of the FranklinInstitute vol 346 no 4 pp 328ndash348 2009

[49] W Szeto and Y Jiang ldquoHybrid artificial bee colony algorithmfor transit network designrdquoTransportation Research Record vol2284 pp 47ndash56 2012

[50] PM Pradhan ldquoDesign of cognitive radio engine using artificialbee colony algorithmrdquo in Proceedings of the InternationalConference on Energy Automation and Signal (ICEAS rsquo11) pp399ndash402 Odisha India December 2011

[51] L Chen L Zhang and Y Guo ldquoBlind image separationmethodbased on artificial bee colony algorithmrdquo Advanced MaterialsResearch vol 468ndash471 pp 583ndash586 2012

[52] D Karaboga and B Akay ldquoA comparative study of Artificial BeeColony algorithmrdquo Applied Mathematics and Computation vol214 no 1 pp 108ndash132 2009

[53] B Akay and D Karaboga ldquoParameter tuning for the artificialbee colony algorithmrdquo in Proceedings of the 1st InternationalConference on Computation Collective Intelligence pp 608ndash619Springer Berlin Germany 2009

[54] B Li ldquoResearch on WNN modeling for gold price forecastingbased on improved Artificial Bee Colony algorithmrdquo Com-putational Intelligence and Neuroscience vol 2014 Article ID270658 10 pages 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


GDP growth rateElectricity consumption growth rate

004

006

008

01

012

014

016

Gro

wth

rate

()

2006 2007 2008 2009 2010 2011 2012 2013 20142005Year

Figure 1 GDP growth rate and electricity consumption growth rate

What is more it is improper to use Artificial NeuralNetwork (ANN) and Kalman Filtering for medium and longterm electricity consumption forecast in years because thesemethods usually need large amounts of data [11 12] And theycould not show the relationship between each influencingfactor and electricity consumption excellently or provide agood guidance for electrical energy plan

Combined with the feedback at home or abroad thehistorical situation of Chinese electricity use and the changein demand of ldquonew normalrdquo electricity this paper putsforward the main influence mechanism between electricityconsumption and the variables from economy society indus-try and environment Thereby an improved ABC method issuggested to forecast electricity consumption

This study will make a significant contribution that willbe embodied in the following two aspects firstly this studyprovides a full and objective analysis of influence mechanismbetween the electricity consumption and the variables fromeconomy society industry and environment and elucidatesthe relationship between them by mathematical statisticsmethod based on a large amount of literature data andthe actual situation of Chinese development secondly animproved ABC method was used to forecast electricityconsumption by creating intendedmodel Given the examplecalculation the model presented herein can assess the effectof various factors on the electricity consumption clearly andconfer further advantages on medium and long term fore-casting In the field of prediction many scholars regard ABCmethod as an auxiliary algorithm for numerical optimizationand little attention has been focused on a direct use of theadvantages of the ABC method to build a model to predictmedium and long term electricity consumption in the lastyears Taken together our studies have certain innovation andapplication value

This paper is divided into six sections After a briefintroduction Section 2 presents the influence factors andforecasting methods of electricity consumption Section 3describes the data in detail and Section 4 presents the ABCalgorithm and the improvement in this paper Numericalresults which are then discussed are described in Section 5The conclusions of the paper are summarized in Section 6

2 Literature Review

Electricity as a special commodity which has difficulty instoring has to be fully prepared for the forecast cohesionand balance of total supply and demand And as a resulta healthy grid situation will be manifest that the reasonabledemand will be met by scientific supply and the problem ofregional excess and overall energy shortage will be graduallysolved The objective of accurate modeling of the electricityconsumption calls for attention to a few extremely importantpoints The first point is to discern all of the necessaryvariables that are bound up with electricity consumption ina given area [13] the second point is to choose a suitablemodelingmethodology according to the characteristics of theelectricity consumption that can handle the difficulties of theconsumption modeling task and obtain the accurate result

21 The Literature of the Influence Factors of ElectricityConsumption On account of the effect of socioeconomicdevelopment and the changes in policy environment thefactors which could act on electricity consumption tend tobe nonlinear and nonstationary and it is conceivable thatthe relationship between the input variables and the outputvariable is undiscovered [14ndash16]

Previous studies have established that many differentvariables have been used to model the electricity consump-tion Table 1 presents a brief summary of some of theimportant recent studies on the field

The first aspect is to ascertain a causal relationshipbetween the economic factors and electricity consumptionAlong with economic growth the productivity and livingreveal a growing reliance on electricity demand and morethan that the interaction between electricity consumptionand economy growth is becoming more and more obviousIn the light of most theories and empirical researches theeconomic development which regards real GDP fixed assetsinvestment and foreign direct investment as the test variablesis central to electricity consumption

In a study undertaken by Karanfil and Li [17] it wasshown that the relationship between electricity consumptionand economic growth was affected at the national incomelevel geographic location development level and otherfactors considering the power dependence and urbanizationwith the panel data of 160 countries from 1980 to 2010Ciarreta and Zarraga have demonstrated that the strongcausality from electricity consumption to real GDP has char-acteristics of unidirectional and negative in the perspectiveof dynamic during a certain time period [18] Bianco et al[19] developed linear regression models using historical elec-tricity consumption gross domestic product (GDP) GDPper capita and population and the models showed annualelectricity consumption was strongly related to the selectedvariables Moreover their time sequence would maintain astate of relative balance in the long term Tang et al [20]have highlighted that electricity consumption and economicgrowth in Portugal have a bidirectional causality from a longterm point of view adopting boundary detection methodGranger causality test based on vector error correctionmodel and other statistical methods Polemis andDagoumas


Table1Summaryof

literaturer

eviewon


ndelectricity

consum

ption

Num

ber

Authors

Cou

ntry

Timep

eriod

Metho

dology

Varia

bles

Relatio

nships

1Ka

ranfi

land

Li[17]

160coun

tries

1980ndash2010

Cointegratio

ntechniqu

esElectricity

consum

ption

econ

omic

grow

th

Theree

xists


electricity

consum

ptionandecon

omic

grow

th

2CiarretaandZa

rraga

[18]

European

coun

tries

1970ndash2007

Apaneld

ataa

pproach

Electricity

consum

ption

econ

omic

grow

thTh

eree

xists

anegativea

ndstrong

causality

from

electric

ityconsum

ptionto

GDP

3Bianco

etal[19]

Italy

1970ndash2007

Linear

regressio

nmod

elsElectricity

consum

ption

GDPGDP

perc

apita

and

popu

latio

nAnn

ualelectric

ityconsum

ptionwas

stron

glyrelatedto

thes

elected

varia

bles

4Tang

etal[20]

Portug

al1974ndash200

9Multiv

ariatemod

els

Electricity

consum

ption

econ

omic

grow

th

Theree

xists

alon

grunPo

rtugalGranger

causality

betweenelectricity

consum

ption

andecon

omicgrow

th

5Po

lemisand

Dagou

mas

[21]

Greece

1970ndash2011

Cointegratio

ntechniqu

esElectricity

consum

ption

econ

omic

grow

th

Theree

xists

abidire

ctionalcausality

betweenelectricity

consum

ptionand

econ

omicgrow

th

6Za

man

etal[22]

Pakista

n1975ndash2010

Theb

ound

s-testing

procedure

Electricity

consum

ption

popu

latio

nTh

eree

xists

apositive

relationshipbetween

popu

latio

ngrow

thandele

ctric

ityconsum

ption

7Ka

vaklioglu[23]

Turkey

1975ndash200

6Th

e120576-SVRmod

elsElectricity

consum

ption

popu

latio

nTh

eree

xists

astro

ngcausality

between

popu

lationandele

ctric

ityconsum

ption

8Lidd

leandLu

ng[24]

105coun

tries

1971ndash200

9Heterogeneous

panel

metho

dsElectricity

consum

ption

urbanizatio

nTh

eree

xists


electricity

consum

ptionandurbanizatio

n

9Solarin

andShahbaz

[25]

Ang

ola

1971ndash200

9Th

eVEC

MGrang

ercausality

test

Electricity

consum

ption

urbanizatio

nandecon

omicgrow

th

Theree

xists

abidire

ctionalcausality

betweenelectricity

consum

ption

econ

omic

grow

thand

urbanizatio

n

10Za

chariadisa

ndPashou

rtidou

[26]

Cyprus

1960ndash200

4Times

eriesa

nalysis

techniqu

esElectricity

consum

ption

the

resid

entia

land

thes

ervicessectors

Theree

xistlong

-term

elasticities

ofele

ctric

ityconsum

ptionabovethe

resid

entia

land

thes

ervicessectors

11Pao[11]

Taiwan

1990ndash2002

Statisticalmod

els

Electricity

consum

ption

natio

nal

incomepo

pulatio

nGDPandCP

IPO

PandNIinfl

uencee

lectric

ityconsum

ptionthem

ostbu

tGDPtheleast

12Zh

angetal[27]

China

1985ndash2010

Principalcom

ponent

analysis

Electricity

consum

ption

indu

strial

factors

Theree

xists

apositive

correlationbetween

electric

ityconsum

ptionandindu

strial

factors

13MengandNiu

[28]

China

1990ndash2007

Partialleastsquare

mod

eling

Electricity

consum

ption

gross

domestic

prod

ucto

find

ustry

Thep

rimaryandthes

econ

dary

indu

stry

take

moree

lectric

ityconsum

ption

increasin

gthan

thetertia

ryon

e

14Shahbaze

tal[29]

UnitedArabEm

irates

1975ndash2011

TheV

ECM

Granger

causality

Electricity

consum

ption

CO2

emissions

Theree

xists

anegativec

orrelationbetween

electric

ityconsum

ptionandCO2em

issions

15Cow

anetal[30]

TheB

RICS

coun

tries

1990ndash2010


Electricity

consum

ption

CO2

emissions

Thed

ifferingresults

have

been

achieved

for

theB

RICS

coun

tries










2emissions














3 Data Source








1198831015840

119894=

(119883119894minus 119883)

119878119894

(1)

119883119894and 119883

1015840











FAI(billionRMB)

FDI(milliondollars)




level(RMB)


Carbonemission

(million tons)


(billionkWsdoth)

1990 18825 4517 10289 1143 02641 1510 743 2458 6231991 19548 5595 11550 1158 02694 1701 1252 2591 6801992 21342 8080 19202 1172 02746 2027 1481 2723 7591993 24381 13072 38955 1185 02799 2577 1719 2877 8431994 27785 17042 43206 1199 02851 3496 2001 3029 9261995 31419 20019 48133 1211 02904 4283 2104 3228 10021996 34850 22914 54804 1224 03048 4839 2290 3323 10761997 38339 24941 64408 1236 03191 5160 2372 3314 11281998 41904 28406 58557 1248 03335 5425 2588 3312 11601999 45185 29855 52659 1258 03478 5854 2650 3423 12312000 48628 32918 59360 1267 03622 6280 3010 3514 13472001 52728 37213 49670 1276 03766 6860 2531 3674 14632002 57104 43500 55010 1285 03909 7703 2940 4025 16472003 62289 55567 56140 1292 04053 8472 3807 4723 19032004 68537 70477 64072 1300 04176 9422 3742 5521 21972005 75452 88774 63805 1308 04299 10493 4052 6326 24942006 83986 109998 67080 1314 04434 11760 4493 6926 28592007 94635 137324 78340 1321 04589 13786 5171 7518 32712008 108035 172828 95253 1328 04699 15781 5499 7663 34382009 118439 224599 91804 1335 04834 17175 6439 8037 36432010 129348 251684 108820 1341 04995 19109 7849 8472 41922011 142864 311485 117698 1347 05127 21810 7738 9206 46932012 156151 374695 113294 1354 05257 24565 7982 9415 49762013 168096 446294 118721 1361 05373 26955 8368 9674 53222014 180989 512761 119705 1368 05477 28844 8811 9761 5523






119883119895= (1199091 1199092 119909

119863) 119895 isin [1 119863] (2)




level


level


Carbonemission





119895 isin [1 119863] 119894 isin [1 119878119873]

(3)



fitness119894=

1

1 + 119891 (119883119894)

119891 (119883119894) ge 0

1 +1003816100381610038161003816119891 (119883119894)1003816100381610038161003816

119891 (119883119894) lt 0

(4)


119875119894=

fitness119894

sum119865119873

119895=1fitness

119895

(5)




V119894119895= 119909119894119895+ 119903119894119895(119909119894119895minus 119909119896119895)

119895 = 119896 119895 isin [1 119863] 119894 isin [1 119878119873]

(6)




1 1198862 1198863 119886



Tec = 119891 (1198861 1198862 1198863 119886

119863) (7)


20142010

20062002



minus2

minus1

0

1

2

3

Nor

mal

ized

val

ue



11988611199091+ 11988621199092+ 11988631199093+ sdot sdot sdot + 119886

119863119909119863+ 119909119863+1

= 0 (8)

Apparently 119883 = [1199091 1199092 1199093 119909

119863 119909119863+1


unknowns 1199091minus 119909119863+1


119886111199091+ 119886211199092+ 119886311199093+ sdot sdot sdot + 119886

1198631119909119863+ 119909119863+1

= 0

119886121199091+ 119886221199092+ 119886321199093+ sdot sdot sdot + 119886

1198632119909119863+ 119909119863+1

= 0

119886131199091+ 119886231199092+ 119886331199093+ sdot sdot sdot + 119886

1198633119909119863+ 119909119863+1

= 0

11988611198731199091+ 11988621198731199092+ 11988631198731199093+ sdot sdot sdot + 119886

119863119873119909119863+ 119909119863+1

= 0

(9)


min119865 (119860)

=

119873

sum

119873=1

[119891 (1198861119873 1198862119873 1198863119873 119886

119863119873) minus Tec

119873]2

lb le 119886119863119873

le ub

(10)


1 1199092 1199093 119909

119863 119909119863+1













Start





Yes



No

Yes

No

Onlookers



No


End



Yes







minus1






Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year











Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

2006

2004

2000

2002

2014

1990

2008

2010

2012

1996

1998

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1996

2012

2008

1992

2000

2002

2004

2006

1994

2014

1990

1998

2010

Year








TEC(billionkWsdoth)



2010 4192300 4177958 14342 0342

38895 09282011 4692800 4623169 69631 14842012 4976264 4945553 30711 06172013 5322300 5269857 52443 09852014 5523300 5550647 27347 0495


2010 4192300 4056341 135959 3243

157654 37612011 4692800 4427643 265157 56502012 4976264 4818710 157554 31662013 5322300 5229545 92755 17432014 5523300 5660146 136846 2478

The ANNmodel

2010 4192300 4321285 128985 3077

133566 31862011 4692800 4581430 111370 23732012 4976264 5069392 93128 18712013 5322300 5407438 85138 16002014 5523300 5772506 249206 4512

The GA model

2010 4183890 4187005 3115 0074

65923 15762011 4650354 4605959 44396 09552012 4988191 4923622 64569 12942013 5349377 5247652 101725 19022014 5633092 5517284 115808 2056

The PSO model

2010 4192300 4187005 5295 0126

45089 10762011 4692800 4605959 86841 18512012 4976264 4923622 52642 10582013 5322300 5247652 74648 14032014 5523300 5517284 6016 0109

minus3000

minus2000

minus1000

0

1000

2000

3000

Erro

rs (B

illio

n kW

middoth)

2004

1998

1996

2006

1990

2002

1994

1992

2008

2010

2012

2014

2000

Year








119894(119894 = 1 2 3 1000) will be





200 400 600 800 10000Cycle times

0

05

1

15

2

25

3

Erro

r val

ues


algorithm




6 Conclusions


Abbreviations


Competing Interests




Acknowledgments


References
































2


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table1Summaryof

literaturer

eviewon


ndelectricity

consum

ption

Num

ber

Authors

Cou

ntry

Timep

eriod

Metho

dology

Varia

bles

Relatio

nships

1Ka

ranfi

land

Li[17]

160coun

tries

1980ndash2010

Cointegratio

ntechniqu

esElectricity

consum

ption

econ

omic

grow

th

Theree

xists


electricity

consum

ptionandecon

omic

grow

th

2CiarretaandZa

rraga

[18]

European

coun

tries

1970ndash2007

Apaneld

ataa

pproach

Electricity

consum

ption

econ

omic

grow

thTh

eree

xists

anegativea

ndstrong

causality

from

electric

ityconsum

ptionto

GDP

3Bianco

etal[19]

Italy

1970ndash2007

Linear

regressio

nmod

elsElectricity

consum

ption

GDPGDP

perc

apita

and

popu

latio

nAnn

ualelectric

ityconsum

ptionwas

stron

glyrelatedto

thes

elected

varia

bles

4Tang

etal[20]

Portug

al1974ndash200

9Multiv

ariatemod

els

Electricity

consum

ption

econ

omic

grow

th

Theree

xists

alon

grunPo

rtugalGranger

causality

betweenelectricity

consum

ption

andecon

omicgrow

th

5Po

lemisand

Dagou

mas

[21]

Greece

1970ndash2011

Cointegratio

ntechniqu

esElectricity

consum

ption

econ

omic

grow

th

Theree

xists

abidire

ctionalcausality

betweenelectricity

consum

ptionand

econ

omicgrow

th

6Za

man

etal[22]

Pakista

n1975ndash2010

Theb

ound

s-testing

procedure

Electricity

consum

ption

popu

latio

nTh

eree

xists

apositive

relationshipbetween

popu

latio

ngrow

thandele

ctric

ityconsum

ption

7Ka

vaklioglu[23]

Turkey

1975ndash200

6Th

e120576-SVRmod

elsElectricity

consum

ption

popu

latio

nTh

eree

xists

astro

ngcausality

between

popu

lationandele

ctric

ityconsum

ption

8Lidd

leandLu

ng[24]

105coun

tries

1971ndash200

9Heterogeneous

panel

metho

dsElectricity

consum

ption

urbanizatio

nTh

eree

xists


electricity

consum

ptionandurbanizatio

n

9Solarin

andShahbaz

[25]

Ang

ola

1971ndash200

9Th

eVEC

MGrang

ercausality

test

Electricity

consum

ption

urbanizatio

nandecon

omicgrow

th

Theree

xists

abidire

ctionalcausality

betweenelectricity

consum

ption

econ

omic

grow

thand

urbanizatio

n

10Za

chariadisa

ndPashou

rtidou

[26]

Cyprus

1960ndash200

4Times

eriesa

nalysis

techniqu

esElectricity

consum

ption

the

resid

entia

land

thes

ervicessectors

Theree

xistlong

-term

elasticities

ofele

ctric

ityconsum

ptionabovethe

resid

entia

land

thes

ervicessectors

11Pao[11]

Taiwan

1990ndash2002

Statisticalmod

els

Electricity

consum

ption

natio

nal

incomepo

pulatio

nGDPandCP

IPO

PandNIinfl

uencee

lectric

ityconsum

ptionthem

ostbu

tGDPtheleast

12Zh

angetal[27]

China

1985ndash2010

Principalcom

ponent

analysis

Electricity

consum

ption

indu

strial

factors

Theree

xists

apositive

correlationbetween

electric

ityconsum

ptionandindu

strial

factors

13MengandNiu

[28]

China

1990ndash2007

Partialleastsquare

mod

eling

Electricity

consum

ption

gross

domestic

prod

ucto

find

ustry

Thep

rimaryandthes

econ

dary

indu

stry

take

moree

lectric

ityconsum

ption

increasin

gthan

thetertia

ryon

e

14Shahbaze

tal[29]

UnitedArabEm

irates

1975ndash2011

TheV

ECM

Granger

causality

Electricity

consum

ption

CO2

emissions

Theree

xists

anegativec

orrelationbetween

electric

ityconsum

ptionandCO2em

issions

15Cow

anetal[30]

TheB

RICS

coun

tries

1990ndash2010


Electricity

consum

ption

CO2

emissions

Thed

ifferingresults

have

been

achieved

for

theB

RICS

coun

tries










2emissions














3 Data Source








1198831015840

119894=

(119883119894minus 119883)

119878119894

(1)

119883119894and 119883

1015840











FAI(billionRMB)

FDI(milliondollars)




level(RMB)


Carbonemission

(million tons)


(billionkWsdoth)

1990 18825 4517 10289 1143 02641 1510 743 2458 6231991 19548 5595 11550 1158 02694 1701 1252 2591 6801992 21342 8080 19202 1172 02746 2027 1481 2723 7591993 24381 13072 38955 1185 02799 2577 1719 2877 8431994 27785 17042 43206 1199 02851 3496 2001 3029 9261995 31419 20019 48133 1211 02904 4283 2104 3228 10021996 34850 22914 54804 1224 03048 4839 2290 3323 10761997 38339 24941 64408 1236 03191 5160 2372 3314 11281998 41904 28406 58557 1248 03335 5425 2588 3312 11601999 45185 29855 52659 1258 03478 5854 2650 3423 12312000 48628 32918 59360 1267 03622 6280 3010 3514 13472001 52728 37213 49670 1276 03766 6860 2531 3674 14632002 57104 43500 55010 1285 03909 7703 2940 4025 16472003 62289 55567 56140 1292 04053 8472 3807 4723 19032004 68537 70477 64072 1300 04176 9422 3742 5521 21972005 75452 88774 63805 1308 04299 10493 4052 6326 24942006 83986 109998 67080 1314 04434 11760 4493 6926 28592007 94635 137324 78340 1321 04589 13786 5171 7518 32712008 108035 172828 95253 1328 04699 15781 5499 7663 34382009 118439 224599 91804 1335 04834 17175 6439 8037 36432010 129348 251684 108820 1341 04995 19109 7849 8472 41922011 142864 311485 117698 1347 05127 21810 7738 9206 46932012 156151 374695 113294 1354 05257 24565 7982 9415 49762013 168096 446294 118721 1361 05373 26955 8368 9674 53222014 180989 512761 119705 1368 05477 28844 8811 9761 5523






119883119895= (1199091 1199092 119909

119863) 119895 isin [1 119863] (2)




level


level


Carbonemission





119895 isin [1 119863] 119894 isin [1 119878119873]

(3)



fitness119894=

1

1 + 119891 (119883119894)

119891 (119883119894) ge 0

1 +1003816100381610038161003816119891 (119883119894)1003816100381610038161003816

119891 (119883119894) lt 0

(4)


119875119894=

fitness119894

sum119865119873

119895=1fitness

119895

(5)




V119894119895= 119909119894119895+ 119903119894119895(119909119894119895minus 119909119896119895)

119895 = 119896 119895 isin [1 119863] 119894 isin [1 119878119873]

(6)




1 1198862 1198863 119886



Tec = 119891 (1198861 1198862 1198863 119886

119863) (7)


20142010

20062002



minus2

minus1

0

1

2

3

Nor

mal

ized

val

ue



11988611199091+ 11988621199092+ 11988631199093+ sdot sdot sdot + 119886

119863119909119863+ 119909119863+1

= 0 (8)

Apparently 119883 = [1199091 1199092 1199093 119909

119863 119909119863+1


unknowns 1199091minus 119909119863+1


119886111199091+ 119886211199092+ 119886311199093+ sdot sdot sdot + 119886

1198631119909119863+ 119909119863+1

= 0

119886121199091+ 119886221199092+ 119886321199093+ sdot sdot sdot + 119886

1198632119909119863+ 119909119863+1

= 0

119886131199091+ 119886231199092+ 119886331199093+ sdot sdot sdot + 119886

1198633119909119863+ 119909119863+1

= 0

11988611198731199091+ 11988621198731199092+ 11988631198731199093+ sdot sdot sdot + 119886

119863119873119909119863+ 119909119863+1

= 0

(9)


min119865 (119860)

=

119873

sum

119873=1

[119891 (1198861119873 1198862119873 1198863119873 119886

119863119873) minus Tec

119873]2

lb le 119886119863119873

le ub

(10)


1 1199092 1199093 119909

119863 119909119863+1













Start





Yes



No

Yes

No

Onlookers



No


End



Yes







minus1






Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year











Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

2006

2004

2000

2002

2014

1990

2008

2010

2012

1996

1998

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1996

2012

2008

1992

2000

2002

2004

2006

1994

2014

1990

1998

2010

Year








TEC(billionkWsdoth)



2010 4192300 4177958 14342 0342

38895 09282011 4692800 4623169 69631 14842012 4976264 4945553 30711 06172013 5322300 5269857 52443 09852014 5523300 5550647 27347 0495


2010 4192300 4056341 135959 3243

157654 37612011 4692800 4427643 265157 56502012 4976264 4818710 157554 31662013 5322300 5229545 92755 17432014 5523300 5660146 136846 2478

The ANNmodel

2010 4192300 4321285 128985 3077

133566 31862011 4692800 4581430 111370 23732012 4976264 5069392 93128 18712013 5322300 5407438 85138 16002014 5523300 5772506 249206 4512

The GA model

2010 4183890 4187005 3115 0074

65923 15762011 4650354 4605959 44396 09552012 4988191 4923622 64569 12942013 5349377 5247652 101725 19022014 5633092 5517284 115808 2056

The PSO model

2010 4192300 4187005 5295 0126

45089 10762011 4692800 4605959 86841 18512012 4976264 4923622 52642 10582013 5322300 5247652 74648 14032014 5523300 5517284 6016 0109

minus3000

minus2000

minus1000

0

1000

2000

3000

Erro

rs (B

illio

n kW

middoth)

2004

1998

1996

2006

1990

2002

1994

1992

2008

2010

2012

2014

2000

Year








119894(119894 = 1 2 3 1000) will be





200 400 600 800 10000Cycle times

0

05

1

15

2

25

3

Erro

r val

ues


algorithm




6 Conclusions


Abbreviations


Competing Interests




Acknowledgments


References
































2


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


















2emissions














3 Data Source








1198831015840

119894=

(119883119894minus 119883)

119878119894

(1)

119883119894and 119883

1015840











FAI(billionRMB)

FDI(milliondollars)




level(RMB)


Carbonemission

(million tons)


(billionkWsdoth)

1990 18825 4517 10289 1143 02641 1510 743 2458 6231991 19548 5595 11550 1158 02694 1701 1252 2591 6801992 21342 8080 19202 1172 02746 2027 1481 2723 7591993 24381 13072 38955 1185 02799 2577 1719 2877 8431994 27785 17042 43206 1199 02851 3496 2001 3029 9261995 31419 20019 48133 1211 02904 4283 2104 3228 10021996 34850 22914 54804 1224 03048 4839 2290 3323 10761997 38339 24941 64408 1236 03191 5160 2372 3314 11281998 41904 28406 58557 1248 03335 5425 2588 3312 11601999 45185 29855 52659 1258 03478 5854 2650 3423 12312000 48628 32918 59360 1267 03622 6280 3010 3514 13472001 52728 37213 49670 1276 03766 6860 2531 3674 14632002 57104 43500 55010 1285 03909 7703 2940 4025 16472003 62289 55567 56140 1292 04053 8472 3807 4723 19032004 68537 70477 64072 1300 04176 9422 3742 5521 21972005 75452 88774 63805 1308 04299 10493 4052 6326 24942006 83986 109998 67080 1314 04434 11760 4493 6926 28592007 94635 137324 78340 1321 04589 13786 5171 7518 32712008 108035 172828 95253 1328 04699 15781 5499 7663 34382009 118439 224599 91804 1335 04834 17175 6439 8037 36432010 129348 251684 108820 1341 04995 19109 7849 8472 41922011 142864 311485 117698 1347 05127 21810 7738 9206 46932012 156151 374695 113294 1354 05257 24565 7982 9415 49762013 168096 446294 118721 1361 05373 26955 8368 9674 53222014 180989 512761 119705 1368 05477 28844 8811 9761 5523






119883119895= (1199091 1199092 119909

119863) 119895 isin [1 119863] (2)




level


level


Carbonemission





119895 isin [1 119863] 119894 isin [1 119878119873]

(3)



fitness119894=

1

1 + 119891 (119883119894)

119891 (119883119894) ge 0

1 +1003816100381610038161003816119891 (119883119894)1003816100381610038161003816

119891 (119883119894) lt 0

(4)


119875119894=

fitness119894

sum119865119873

119895=1fitness

119895

(5)




V119894119895= 119909119894119895+ 119903119894119895(119909119894119895minus 119909119896119895)

119895 = 119896 119895 isin [1 119863] 119894 isin [1 119878119873]

(6)




1 1198862 1198863 119886



Tec = 119891 (1198861 1198862 1198863 119886

119863) (7)


20142010

20062002



minus2

minus1

0

1

2

3

Nor

mal

ized

val

ue



11988611199091+ 11988621199092+ 11988631199093+ sdot sdot sdot + 119886

119863119909119863+ 119909119863+1

= 0 (8)

Apparently 119883 = [1199091 1199092 1199093 119909

119863 119909119863+1


unknowns 1199091minus 119909119863+1


119886111199091+ 119886211199092+ 119886311199093+ sdot sdot sdot + 119886

1198631119909119863+ 119909119863+1

= 0

119886121199091+ 119886221199092+ 119886321199093+ sdot sdot sdot + 119886

1198632119909119863+ 119909119863+1

= 0

119886131199091+ 119886231199092+ 119886331199093+ sdot sdot sdot + 119886

1198633119909119863+ 119909119863+1

= 0

11988611198731199091+ 11988621198731199092+ 11988631198731199093+ sdot sdot sdot + 119886

119863119873119909119863+ 119909119863+1

= 0

(9)


min119865 (119860)

=

119873

sum

119873=1

[119891 (1198861119873 1198862119873 1198863119873 119886

119863119873) minus Tec

119873]2

lb le 119886119863119873

le ub

(10)


1 1199092 1199093 119909

119863 119909119863+1













Start





Yes



No

Yes

No

Onlookers



No


End



Yes







minus1






Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year











Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

2006

2004

2000

2002

2014

1990

2008

2010

2012

1996

1998

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1996

2012

2008

1992

2000

2002

2004

2006

1994

2014

1990

1998

2010

Year








TEC(billionkWsdoth)



2010 4192300 4177958 14342 0342

38895 09282011 4692800 4623169 69631 14842012 4976264 4945553 30711 06172013 5322300 5269857 52443 09852014 5523300 5550647 27347 0495


2010 4192300 4056341 135959 3243

157654 37612011 4692800 4427643 265157 56502012 4976264 4818710 157554 31662013 5322300 5229545 92755 17432014 5523300 5660146 136846 2478

The ANNmodel

2010 4192300 4321285 128985 3077

133566 31862011 4692800 4581430 111370 23732012 4976264 5069392 93128 18712013 5322300 5407438 85138 16002014 5523300 5772506 249206 4512

The GA model

2010 4183890 4187005 3115 0074

65923 15762011 4650354 4605959 44396 09552012 4988191 4923622 64569 12942013 5349377 5247652 101725 19022014 5633092 5517284 115808 2056

The PSO model

2010 4192300 4187005 5295 0126

45089 10762011 4692800 4605959 86841 18512012 4976264 4923622 52642 10582013 5322300 5247652 74648 14032014 5523300 5517284 6016 0109

minus3000

minus2000

minus1000

0

1000

2000

3000

Erro

rs (B

illio

n kW

middoth)

2004

1998

1996

2006

1990

2002

1994

1992

2008

2010

2012

2014

2000

Year








119894(119894 = 1 2 3 1000) will be





200 400 600 800 10000Cycle times

0

05

1

15

2

25

3

Erro

r val

ues


algorithm




6 Conclusions


Abbreviations


Competing Interests




Acknowledgments


References
































2


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra














3 Data Source








1198831015840

119894=

(119883119894minus 119883)

119878119894

(1)

119883119894and 119883

1015840











FAI(billionRMB)

FDI(milliondollars)




level(RMB)


Carbonemission

(million tons)


(billionkWsdoth)

1990 18825 4517 10289 1143 02641 1510 743 2458 6231991 19548 5595 11550 1158 02694 1701 1252 2591 6801992 21342 8080 19202 1172 02746 2027 1481 2723 7591993 24381 13072 38955 1185 02799 2577 1719 2877 8431994 27785 17042 43206 1199 02851 3496 2001 3029 9261995 31419 20019 48133 1211 02904 4283 2104 3228 10021996 34850 22914 54804 1224 03048 4839 2290 3323 10761997 38339 24941 64408 1236 03191 5160 2372 3314 11281998 41904 28406 58557 1248 03335 5425 2588 3312 11601999 45185 29855 52659 1258 03478 5854 2650 3423 12312000 48628 32918 59360 1267 03622 6280 3010 3514 13472001 52728 37213 49670 1276 03766 6860 2531 3674 14632002 57104 43500 55010 1285 03909 7703 2940 4025 16472003 62289 55567 56140 1292 04053 8472 3807 4723 19032004 68537 70477 64072 1300 04176 9422 3742 5521 21972005 75452 88774 63805 1308 04299 10493 4052 6326 24942006 83986 109998 67080 1314 04434 11760 4493 6926 28592007 94635 137324 78340 1321 04589 13786 5171 7518 32712008 108035 172828 95253 1328 04699 15781 5499 7663 34382009 118439 224599 91804 1335 04834 17175 6439 8037 36432010 129348 251684 108820 1341 04995 19109 7849 8472 41922011 142864 311485 117698 1347 05127 21810 7738 9206 46932012 156151 374695 113294 1354 05257 24565 7982 9415 49762013 168096 446294 118721 1361 05373 26955 8368 9674 53222014 180989 512761 119705 1368 05477 28844 8811 9761 5523






119883119895= (1199091 1199092 119909

119863) 119895 isin [1 119863] (2)




level


level


Carbonemission





119895 isin [1 119863] 119894 isin [1 119878119873]

(3)



fitness119894=

1

1 + 119891 (119883119894)

119891 (119883119894) ge 0

1 +1003816100381610038161003816119891 (119883119894)1003816100381610038161003816

119891 (119883119894) lt 0

(4)


119875119894=

fitness119894

sum119865119873

119895=1fitness

119895

(5)




V119894119895= 119909119894119895+ 119903119894119895(119909119894119895minus 119909119896119895)

119895 = 119896 119895 isin [1 119863] 119894 isin [1 119878119873]

(6)




1 1198862 1198863 119886



Tec = 119891 (1198861 1198862 1198863 119886

119863) (7)


20142010

20062002



minus2

minus1

0

1

2

3

Nor

mal

ized

val

ue



11988611199091+ 11988621199092+ 11988631199093+ sdot sdot sdot + 119886

119863119909119863+ 119909119863+1

= 0 (8)

Apparently 119883 = [1199091 1199092 1199093 119909

119863 119909119863+1


unknowns 1199091minus 119909119863+1


119886111199091+ 119886211199092+ 119886311199093+ sdot sdot sdot + 119886

1198631119909119863+ 119909119863+1

= 0

119886121199091+ 119886221199092+ 119886321199093+ sdot sdot sdot + 119886

1198632119909119863+ 119909119863+1

= 0

119886131199091+ 119886231199092+ 119886331199093+ sdot sdot sdot + 119886

1198633119909119863+ 119909119863+1

= 0

11988611198731199091+ 11988621198731199092+ 11988631198731199093+ sdot sdot sdot + 119886

119863119873119909119863+ 119909119863+1

= 0

(9)


min119865 (119860)

=

119873

sum

119873=1

[119891 (1198861119873 1198862119873 1198863119873 119886

119863119873) minus Tec

119873]2

lb le 119886119863119873

le ub

(10)


1 1199092 1199093 119909

119863 119909119863+1













Start





Yes



No

Yes

No

Onlookers



No


End



Yes







minus1






Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year











Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

2006

2004

2000

2002

2014

1990

2008

2010

2012

1996

1998

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1996

2012

2008

1992

2000

2002

2004

2006

1994

2014

1990

1998

2010

Year








TEC(billionkWsdoth)



2010 4192300 4177958 14342 0342

38895 09282011 4692800 4623169 69631 14842012 4976264 4945553 30711 06172013 5322300 5269857 52443 09852014 5523300 5550647 27347 0495


2010 4192300 4056341 135959 3243

157654 37612011 4692800 4427643 265157 56502012 4976264 4818710 157554 31662013 5322300 5229545 92755 17432014 5523300 5660146 136846 2478

The ANNmodel

2010 4192300 4321285 128985 3077

133566 31862011 4692800 4581430 111370 23732012 4976264 5069392 93128 18712013 5322300 5407438 85138 16002014 5523300 5772506 249206 4512

The GA model

2010 4183890 4187005 3115 0074

65923 15762011 4650354 4605959 44396 09552012 4988191 4923622 64569 12942013 5349377 5247652 101725 19022014 5633092 5517284 115808 2056

The PSO model

2010 4192300 4187005 5295 0126

45089 10762011 4692800 4605959 86841 18512012 4976264 4923622 52642 10582013 5322300 5247652 74648 14032014 5523300 5517284 6016 0109

minus3000

minus2000

minus1000

0

1000

2000

3000

Erro

rs (B

illio

n kW

middoth)

2004

1998

1996

2006

1990

2002

1994

1992

2008

2010

2012

2014

2000

Year








119894(119894 = 1 2 3 1000) will be





200 400 600 800 10000Cycle times

0

05

1

15

2

25

3

Erro

r val

ues


algorithm




6 Conclusions


Abbreviations


Competing Interests




Acknowledgments


References
































2


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












FAI(billionRMB)

FDI(milliondollars)




level(RMB)


Carbonemission

(million tons)


(billionkWsdoth)

1990 18825 4517 10289 1143 02641 1510 743 2458 6231991 19548 5595 11550 1158 02694 1701 1252 2591 6801992 21342 8080 19202 1172 02746 2027 1481 2723 7591993 24381 13072 38955 1185 02799 2577 1719 2877 8431994 27785 17042 43206 1199 02851 3496 2001 3029 9261995 31419 20019 48133 1211 02904 4283 2104 3228 10021996 34850 22914 54804 1224 03048 4839 2290 3323 10761997 38339 24941 64408 1236 03191 5160 2372 3314 11281998 41904 28406 58557 1248 03335 5425 2588 3312 11601999 45185 29855 52659 1258 03478 5854 2650 3423 12312000 48628 32918 59360 1267 03622 6280 3010 3514 13472001 52728 37213 49670 1276 03766 6860 2531 3674 14632002 57104 43500 55010 1285 03909 7703 2940 4025 16472003 62289 55567 56140 1292 04053 8472 3807 4723 19032004 68537 70477 64072 1300 04176 9422 3742 5521 21972005 75452 88774 63805 1308 04299 10493 4052 6326 24942006 83986 109998 67080 1314 04434 11760 4493 6926 28592007 94635 137324 78340 1321 04589 13786 5171 7518 32712008 108035 172828 95253 1328 04699 15781 5499 7663 34382009 118439 224599 91804 1335 04834 17175 6439 8037 36432010 129348 251684 108820 1341 04995 19109 7849 8472 41922011 142864 311485 117698 1347 05127 21810 7738 9206 46932012 156151 374695 113294 1354 05257 24565 7982 9415 49762013 168096 446294 118721 1361 05373 26955 8368 9674 53222014 180989 512761 119705 1368 05477 28844 8811 9761 5523






119883119895= (1199091 1199092 119909

119863) 119895 isin [1 119863] (2)




level


level


Carbonemission





119895 isin [1 119863] 119894 isin [1 119878119873]

(3)



fitness119894=

1

1 + 119891 (119883119894)

119891 (119883119894) ge 0

1 +1003816100381610038161003816119891 (119883119894)1003816100381610038161003816

119891 (119883119894) lt 0

(4)


119875119894=

fitness119894

sum119865119873

119895=1fitness

119895

(5)




V119894119895= 119909119894119895+ 119903119894119895(119909119894119895minus 119909119896119895)

119895 = 119896 119895 isin [1 119863] 119894 isin [1 119878119873]

(6)




1 1198862 1198863 119886



Tec = 119891 (1198861 1198862 1198863 119886

119863) (7)


20142010

20062002



minus2

minus1

0

1

2

3

Nor

mal

ized

val

ue



11988611199091+ 11988621199092+ 11988631199093+ sdot sdot sdot + 119886

119863119909119863+ 119909119863+1

= 0 (8)

Apparently 119883 = [1199091 1199092 1199093 119909

119863 119909119863+1


unknowns 1199091minus 119909119863+1


119886111199091+ 119886211199092+ 119886311199093+ sdot sdot sdot + 119886

1198631119909119863+ 119909119863+1

= 0

119886121199091+ 119886221199092+ 119886321199093+ sdot sdot sdot + 119886

1198632119909119863+ 119909119863+1

= 0

119886131199091+ 119886231199092+ 119886331199093+ sdot sdot sdot + 119886

1198633119909119863+ 119909119863+1

= 0

11988611198731199091+ 11988621198731199092+ 11988631198731199093+ sdot sdot sdot + 119886

119863119873119909119863+ 119909119863+1

= 0

(9)


min119865 (119860)

=

119873

sum

119873=1

[119891 (1198861119873 1198862119873 1198863119873 119886

119863119873) minus Tec

119873]2

lb le 119886119863119873

le ub

(10)


1 1199092 1199093 119909

119863 119909119863+1













Start





Yes



No

Yes

No

Onlookers



No


End



Yes







minus1






Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year











Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

2006

2004

2000

2002

2014

1990

2008

2010

2012

1996

1998

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1996

2012

2008

1992

2000

2002

2004

2006

1994

2014

1990

1998

2010

Year








TEC(billionkWsdoth)



2010 4192300 4177958 14342 0342

38895 09282011 4692800 4623169 69631 14842012 4976264 4945553 30711 06172013 5322300 5269857 52443 09852014 5523300 5550647 27347 0495


2010 4192300 4056341 135959 3243

157654 37612011 4692800 4427643 265157 56502012 4976264 4818710 157554 31662013 5322300 5229545 92755 17432014 5523300 5660146 136846 2478

The ANNmodel

2010 4192300 4321285 128985 3077

133566 31862011 4692800 4581430 111370 23732012 4976264 5069392 93128 18712013 5322300 5407438 85138 16002014 5523300 5772506 249206 4512

The GA model

2010 4183890 4187005 3115 0074

65923 15762011 4650354 4605959 44396 09552012 4988191 4923622 64569 12942013 5349377 5247652 101725 19022014 5633092 5517284 115808 2056

The PSO model

2010 4192300 4187005 5295 0126

45089 10762011 4692800 4605959 86841 18512012 4976264 4923622 52642 10582013 5322300 5247652 74648 14032014 5523300 5517284 6016 0109

minus3000

minus2000

minus1000

0

1000

2000

3000

Erro

rs (B

illio

n kW

middoth)

2004

1998

1996

2006

1990

2002

1994

1992

2008

2010

2012

2014

2000

Year








119894(119894 = 1 2 3 1000) will be





200 400 600 800 10000Cycle times

0

05

1

15

2

25

3

Erro

r val

ues


algorithm




6 Conclusions


Abbreviations


Competing Interests




Acknowledgments


References
































2


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












level


level


Carbonemission





119895 isin [1 119863] 119894 isin [1 119878119873]

(3)



fitness119894=

1

1 + 119891 (119883119894)

119891 (119883119894) ge 0

1 +1003816100381610038161003816119891 (119883119894)1003816100381610038161003816

119891 (119883119894) lt 0

(4)


119875119894=

fitness119894

sum119865119873

119895=1fitness

119895

(5)




V119894119895= 119909119894119895+ 119903119894119895(119909119894119895minus 119909119896119895)

119895 = 119896 119895 isin [1 119863] 119894 isin [1 119878119873]

(6)




1 1198862 1198863 119886



Tec = 119891 (1198861 1198862 1198863 119886

119863) (7)


20142010

20062002



minus2

minus1

0

1

2

3

Nor

mal

ized

val

ue



11988611199091+ 11988621199092+ 11988631199093+ sdot sdot sdot + 119886

119863119909119863+ 119909119863+1

= 0 (8)

Apparently 119883 = [1199091 1199092 1199093 119909

119863 119909119863+1


unknowns 1199091minus 119909119863+1


119886111199091+ 119886211199092+ 119886311199093+ sdot sdot sdot + 119886

1198631119909119863+ 119909119863+1

= 0

119886121199091+ 119886221199092+ 119886321199093+ sdot sdot sdot + 119886

1198632119909119863+ 119909119863+1

= 0

119886131199091+ 119886231199092+ 119886331199093+ sdot sdot sdot + 119886

1198633119909119863+ 119909119863+1

= 0

11988611198731199091+ 11988621198731199092+ 11988631198731199093+ sdot sdot sdot + 119886

119863119873119909119863+ 119909119863+1

= 0

(9)


min119865 (119860)

=

119873

sum

119873=1

[119891 (1198861119873 1198862119873 1198863119873 119886

119863119873) minus Tec

119873]2

lb le 119886119863119873

le ub

(10)


1 1199092 1199093 119909

119863 119909119863+1













Start





Yes



No

Yes

No

Onlookers



No


End



Yes







minus1






Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year











Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

2006

2004

2000

2002

2014

1990

2008

2010

2012

1996

1998

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1996

2012

2008

1992

2000

2002

2004

2006

1994

2014

1990

1998

2010

Year








TEC(billionkWsdoth)



2010 4192300 4177958 14342 0342

38895 09282011 4692800 4623169 69631 14842012 4976264 4945553 30711 06172013 5322300 5269857 52443 09852014 5523300 5550647 27347 0495


2010 4192300 4056341 135959 3243

157654 37612011 4692800 4427643 265157 56502012 4976264 4818710 157554 31662013 5322300 5229545 92755 17432014 5523300 5660146 136846 2478

The ANNmodel

2010 4192300 4321285 128985 3077

133566 31862011 4692800 4581430 111370 23732012 4976264 5069392 93128 18712013 5322300 5407438 85138 16002014 5523300 5772506 249206 4512

The GA model

2010 4183890 4187005 3115 0074

65923 15762011 4650354 4605959 44396 09552012 4988191 4923622 64569 12942013 5349377 5247652 101725 19022014 5633092 5517284 115808 2056

The PSO model

2010 4192300 4187005 5295 0126

45089 10762011 4692800 4605959 86841 18512012 4976264 4923622 52642 10582013 5322300 5247652 74648 14032014 5523300 5517284 6016 0109

minus3000

minus2000

minus1000

0

1000

2000

3000

Erro

rs (B

illio

n kW

middoth)

2004

1998

1996

2006

1990

2002

1994

1992

2008

2010

2012

2014

2000

Year








119894(119894 = 1 2 3 1000) will be





200 400 600 800 10000Cycle times

0

05

1

15

2

25

3

Erro

r val

ues


algorithm




6 Conclusions


Abbreviations


Competing Interests




Acknowledgments


References
































2


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










20142010

20062002



minus2

minus1

0

1

2

3

Nor

mal

ized

val

ue



11988611199091+ 11988621199092+ 11988631199093+ sdot sdot sdot + 119886

119863119909119863+ 119909119863+1

= 0 (8)

Apparently 119883 = [1199091 1199092 1199093 119909

119863 119909119863+1


unknowns 1199091minus 119909119863+1


119886111199091+ 119886211199092+ 119886311199093+ sdot sdot sdot + 119886

1198631119909119863+ 119909119863+1

= 0

119886121199091+ 119886221199092+ 119886321199093+ sdot sdot sdot + 119886

1198632119909119863+ 119909119863+1

= 0

119886131199091+ 119886231199092+ 119886331199093+ sdot sdot sdot + 119886

1198633119909119863+ 119909119863+1

= 0

11988611198731199091+ 11988621198731199092+ 11988631198731199093+ sdot sdot sdot + 119886

119863119873119909119863+ 119909119863+1

= 0

(9)


min119865 (119860)

=

119873

sum

119873=1

[119891 (1198861119873 1198862119873 1198863119873 119886

119863119873) minus Tec

119873]2

lb le 119886119863119873

le ub

(10)


1 1199092 1199093 119909

119863 119909119863+1













Start





Yes



No

Yes

No

Onlookers



No


End



Yes







minus1






Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year











Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

2006

2004

2000

2002

2014

1990

2008

2010

2012

1996

1998

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1996

2012

2008

1992

2000

2002

2004

2006

1994

2014

1990

1998

2010

Year








TEC(billionkWsdoth)



2010 4192300 4177958 14342 0342

38895 09282011 4692800 4623169 69631 14842012 4976264 4945553 30711 06172013 5322300 5269857 52443 09852014 5523300 5550647 27347 0495


2010 4192300 4056341 135959 3243

157654 37612011 4692800 4427643 265157 56502012 4976264 4818710 157554 31662013 5322300 5229545 92755 17432014 5523300 5660146 136846 2478

The ANNmodel

2010 4192300 4321285 128985 3077

133566 31862011 4692800 4581430 111370 23732012 4976264 5069392 93128 18712013 5322300 5407438 85138 16002014 5523300 5772506 249206 4512

The GA model

2010 4183890 4187005 3115 0074

65923 15762011 4650354 4605959 44396 09552012 4988191 4923622 64569 12942013 5349377 5247652 101725 19022014 5633092 5517284 115808 2056

The PSO model

2010 4192300 4187005 5295 0126

45089 10762011 4692800 4605959 86841 18512012 4976264 4923622 52642 10582013 5322300 5247652 74648 14032014 5523300 5517284 6016 0109

minus3000

minus2000

minus1000

0

1000

2000

3000

Erro

rs (B

illio

n kW

middoth)

2004

1998

1996

2006

1990

2002

1994

1992

2008

2010

2012

2014

2000

Year








119894(119894 = 1 2 3 1000) will be





200 400 600 800 10000Cycle times

0

05

1

15

2

25

3

Erro

r val

ues


algorithm




6 Conclusions


Abbreviations


Competing Interests




Acknowledgments


References
































2


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Start





Yes



No

Yes

No

Onlookers



No


End



Yes







minus1






Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year











Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

2006

2004

2000

2002

2014

1990

2008

2010

2012

1996

1998

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1996

2012

2008

1992

2000

2002

2004

2006

1994

2014

1990

1998

2010

Year








TEC(billionkWsdoth)



2010 4192300 4177958 14342 0342

38895 09282011 4692800 4623169 69631 14842012 4976264 4945553 30711 06172013 5322300 5269857 52443 09852014 5523300 5550647 27347 0495


2010 4192300 4056341 135959 3243

157654 37612011 4692800 4427643 265157 56502012 4976264 4818710 157554 31662013 5322300 5229545 92755 17432014 5523300 5660146 136846 2478

The ANNmodel

2010 4192300 4321285 128985 3077

133566 31862011 4692800 4581430 111370 23732012 4976264 5069392 93128 18712013 5322300 5407438 85138 16002014 5523300 5772506 249206 4512

The GA model

2010 4183890 4187005 3115 0074

65923 15762011 4650354 4605959 44396 09552012 4988191 4923622 64569 12942013 5349377 5247652 101725 19022014 5633092 5517284 115808 2056

The PSO model

2010 4192300 4187005 5295 0126

45089 10762011 4692800 4605959 86841 18512012 4976264 4923622 52642 10582013 5322300 5247652 74648 14032014 5523300 5517284 6016 0109

minus3000

minus2000

minus1000

0

1000

2000

3000

Erro

rs (B

illio

n kW

middoth)

2004

1998

1996

2006

1990

2002

1994

1992

2008

2010

2012

2014

2000

Year








119894(119894 = 1 2 3 1000) will be





200 400 600 800 10000Cycle times

0

05

1

15

2

25

3

Erro

r val

ues


algorithm




6 Conclusions


Abbreviations


Competing Interests




Acknowledgments


References
































2


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year











Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

2006

2004

2000

2002

2014

1990

2008

2010

2012

1996

1998

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

1990

Year



Actu

al v

alue

s and

pre

dict

ions

times104

0

1

2

3

4

5

6

(Bill

ion

kWmiddoth

)

1996

2012

2008

1992

2000

2002

2004

2006

1994

2014

1990

1998

2010

Year








TEC(billionkWsdoth)



2010 4192300 4177958 14342 0342

38895 09282011 4692800 4623169 69631 14842012 4976264 4945553 30711 06172013 5322300 5269857 52443 09852014 5523300 5550647 27347 0495


2010 4192300 4056341 135959 3243

157654 37612011 4692800 4427643 265157 56502012 4976264 4818710 157554 31662013 5322300 5229545 92755 17432014 5523300 5660146 136846 2478

The ANNmodel

2010 4192300 4321285 128985 3077

133566 31862011 4692800 4581430 111370 23732012 4976264 5069392 93128 18712013 5322300 5407438 85138 16002014 5523300 5772506 249206 4512

The GA model

2010 4183890 4187005 3115 0074

65923 15762011 4650354 4605959 44396 09552012 4988191 4923622 64569 12942013 5349377 5247652 101725 19022014 5633092 5517284 115808 2056

The PSO model

2010 4192300 4187005 5295 0126

45089 10762011 4692800 4605959 86841 18512012 4976264 4923622 52642 10582013 5322300 5247652 74648 14032014 5523300 5517284 6016 0109

minus3000

minus2000

minus1000

0

1000

2000

3000

Erro

rs (B

illio

n kW

middoth)

2004

1998

1996

2006

1990

2002

1994

1992

2008

2010

2012

2014

2000

Year








119894(119894 = 1 2 3 1000) will be





200 400 600 800 10000Cycle times

0

05

1

15

2

25

3

Erro

r val

ues


algorithm




6 Conclusions


Abbreviations


Competing Interests




Acknowledgments


References
































2


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












TEC(billionkWsdoth)



2010 4192300 4177958 14342 0342

38895 09282011 4692800 4623169 69631 14842012 4976264 4945553 30711 06172013 5322300 5269857 52443 09852014 5523300 5550647 27347 0495


2010 4192300 4056341 135959 3243

157654 37612011 4692800 4427643 265157 56502012 4976264 4818710 157554 31662013 5322300 5229545 92755 17432014 5523300 5660146 136846 2478

The ANNmodel

2010 4192300 4321285 128985 3077

133566 31862011 4692800 4581430 111370 23732012 4976264 5069392 93128 18712013 5322300 5407438 85138 16002014 5523300 5772506 249206 4512

The GA model

2010 4183890 4187005 3115 0074

65923 15762011 4650354 4605959 44396 09552012 4988191 4923622 64569 12942013 5349377 5247652 101725 19022014 5633092 5517284 115808 2056

The PSO model

2010 4192300 4187005 5295 0126

45089 10762011 4692800 4605959 86841 18512012 4976264 4923622 52642 10582013 5322300 5247652 74648 14032014 5523300 5517284 6016 0109

minus3000

minus2000

minus1000

0

1000

2000

3000

Erro

rs (B

illio

n kW

middoth)

2004

1998

1996

2006

1990

2002

1994

1992

2008

2010

2012

2014

2000

Year








119894(119894 = 1 2 3 1000) will be





200 400 600 800 10000Cycle times

0

05

1

15

2

25

3

Erro

r val

ues


algorithm




6 Conclusions


Abbreviations


Competing Interests




Acknowledgments


References
































2


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











200 400 600 800 10000Cycle times

0

05

1

15

2

25

3

Erro

r val

ues


algorithm




6 Conclusions


Abbreviations


Competing Interests




Acknowledgments


References
































2


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
































2


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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