doshisha univ., kyoto japan ncga : neighborhood cultivation genetic algorithm for multi-objective...
DESCRIPTION
Doshisha Univ., Kyoto Japan MOPs solved by Evolutionary algorithms EMO VEGA :Schaffer (1985) MOGA :Fonseca (1993) DRMOGA :Hiroyasu, Miki, Watanabe (2000) SPEA2 :Zitzler (2001) NPGA2 :Erickson, Mayer, Horn (2001) NSGA-II :Deb, Goel (2001) Typical method on EMO EMO Evolutionary Multi-criterion OptimizationTRANSCRIPT
Doshisha Univ., Kyoto Japan
NCGA : Neighborhood Cultivation Genetic Algorithm
for Multi-Objective Optimization Problems
Intelligent Systems Design Laboratory,Doshisha University, Kyoto Japan
○ Shinya Watanabe Tomoyuki Hiroyasu
Mitsunori Miki
Doshisha Univ., Kyoto Japan
Multi-objective Optimization Problems●Multi-objective Optimization Problems (MOPs)
In the optimization problems, when there are several objective functions, the problems are called multi-objective or multi-criterion problems.
f 1(x)
f 2(x)
Design variables
Objective function
ConstraintsGi(x)<0 ( i = 1, 2, … , k)
F={f1(x), f2(x), … , fm(x)}
X={x1, x2, …. , xn} Feasible regionFeasible region
Pareto optimal solutions
Doshisha Univ., Kyoto Japan
• MOPs solved by Evolutionary algorithms
EMO
•VEGA :Schaffer (1985)
•MOGA :Fonseca (1993)
•DRMOGA :Hiroyasu, Miki, Watanabe (2000)
• SPEA2 :Zitzler (2001)
•NPGA2 :Erickson, Mayer, Horn (2001)
•NSGA-II :Deb, Goel (2001)
Typical method on EMO
• EMOEvolutionary Multi-criterion Optimization
Doshisha Univ., Kyoto Japan
• The following topics are the mechanisms that the recent GA approaches have.
EMO
• Archive of the excellent solutions• Cut down (sharing) method of the reserved excellent solu
tions• An appropriate assign of fitness• Reflection to search solutions mechanism of the reserve
d excellent solutions• Unification mechanism of values of each objective
Doshisha Univ., Kyoto Japan
• NCGA : Neighborhood Cultivation GA
• The neighborhood crossover• Archive of the excellent solutions• Cut down (sharing) method of the reserved
excellent solutions• An appropriate assign of fitness• Reflection to search solutions mechanism of the
reserved excellent solutions• Unification mechanism of values of each objective
The features of NCGA
Neighborhood Cultivation GA (NCGA)
Doshisha Univ., Kyoto Japan
• A neighborhood crossover– In MOPs GA, the searching area is wide and the searc
hing area of each individuals are different.
f2(x)
f1(x)
If the distance between two selected parents is so large, cross over may have no effect for local search.
Neighborhood Cultivation GA (NCGA)
Doshisha Univ., Kyoto Japan
• One of the objectives is changed at every generation.
• The pair for the mating is changed based on a probabillity.
f2(x)
f1(x)
Neighborhood Cultivation GA (NCGA)• A neighborhood crossover
• Two parents of crossover are chosen from the top of the sorted individuals.
In order not to make the same couple.
Doshisha Univ., Kyoto Japan
• Continuous Function– ZDT4
]5,5[]1,0[
)4cos(1091)(
)(1)()(min
)(min
1
10
2
2
12
11
i
iii
xx
xxxg
xgxxgxf
xxf
Test Problems
Doshisha Univ., Kyoto Japan
• Continuous Function– KUR
100,,1,]5,5[
)sin(5||)(min
))2.0exp(10()(min38.0
2
100
1
21
21
nnixxxxf
xxxf
i
ii
i ii
Test Problems
Doshisha Univ., Kyoto Japan
Objectives
Constraints
• Combination problem– KP 750-2
2,1)(750
1,
ixpxfj
jjii
750
1,
jijji cxw
1,0),,,( 75021 jxxxxx pi,j = profit of item j according to knapsack i
Test Problems
wi,j = weight of item j according to knapsack ici,= capacity of knapsack i
Doshisha Univ., Kyoto Japan
Applied models and ParametersGA Operator•Applied models
• Crossover– One point crossover
• Mutation– bit flip
• SPEA2• NSGA-II• NCGA• non-NCGA
(NCGA except neighborhood croosover )
population size 100crossover rate 1.0mutation rate 0.01
Parameters
terminal condition 250
250
2000number of trial 30
Doshisha Univ., Kyoto Japan
Results (Pareto solutions of ZDT4)
Doshisha Univ., Kyoto Japan
Results (Pareto solutions of KUR)
Doshisha Univ., Kyoto Japan
Results (Pareto solutions of KP750-2)
Doshisha Univ., Kyoto Japan
• We proposed a new model for Multi-objective GA.– NCGA: Neighborhood Cultivation GA
Effective method for multi objective GA • Neighborhood crossover• Reservation mechanism of the excellent solutions• Reflection to search solutions mechanism of the reserved
excellent solutions• Cut down (sharing) method of the reserved excellent soluti
ons• Assignment method of fitness function• Unification mechanism of values of each objective
Conclusion
Doshisha Univ., Kyoto Japan
• NCGA was applied to test functions and results were compared to the other methods; those are SPEA2, NSGA-II and non-NCGA.
• In some the test functions, NCGA derives the good results.
• Comparing to NCGA and NCGA without neighborhood crossover, the former is obviously superior to the latter in all problems.
NCGA is good model of Multi-objective GA
Conclusion
Doshisha Univ., Kyoto Japan
Results (RNI of KP750-2)
Doshisha Univ., Kyoto Japan
• EMO 全般に関して– http://www.lania.mx/~ccoello/EMOO/EMOObib.html
• 多目的 0 /1 ナップザック問題に関して– http://www.tik.ee.ethz.ch/~zitzler/
• 発表に用いたソースプログラム– http://mikilab.doshisha.ac.jp/dia/research/mop_ga/archive/
• 発表者の電子メールアドレス– [email protected]
参照 URL
Doshisha Univ., Kyoto Japan
• The Ratio of Non-dominated Individuals (RNI) is derived from two types of Pareto solutions.
Performance Measure
(x)f 1
f 2(x
) Method B
(x)f 1
f 2(x
) Method A
(x)f 1
f 2(x
)
Method AMethod B
0.3330.666
Doshisha Univ., Kyoto Japan
Results (RNI of KUR)
Doshisha Univ., Kyoto Japan
Performance Assessment• The Ratio of Non-dominated Individuals :RNI
– The Performance measure perform to compare two type of Pareto solutions.
– Two types of pareto solutions derived by difference methods are compared.
• Cover Rate Index– Diversity of the Pareto optimum.
• Error – The distance between the real pareto front and
derived solutions.• Various rate
– Diversity of the pareto optimum individuals.
Measures
Doshisha Univ., Kyoto Japan
数値結果 ( KP750-2 )
Doshisha Univ., Kyoto Japan
• Continuous Function– ZDT4
]5,5[]1,0[
)4cos(1091)(
)(1)()(min
)(min
1
10
2
2
12
11
i
iii
xx
xxxg
xgxxgxf
xxf
Test Problems
Doshisha Univ., Kyoto Japan
Results (Pareto solutions of ZDT4)
Doshisha Univ., Kyoto Japan
Results (RNI of ZDT4)
Doshisha Univ., Kyoto Japan
数値結果 (ZDT4)
Doshisha Univ., Kyoto Japan
数値結果 (KUR)
Doshisha Univ., Kyoto Japan
数値結果 (ZDT4)
Doshisha Univ., Kyoto Japan
数値結果 (KUR)
Doshisha Univ., Kyoto Japan
数値結果 ( KP750-2 )
Doshisha Univ., Kyoto Japan
• パレート保存個体群の利用– 多目的では,最終的に求める解候補 (パレート
解)が複数存在するため,探索途中での優良な個体の欠落を防ぐ必要がある.
f2(x
)
f1(x)
探索個体群 優良個体保存群 探索個体群に優良個体群を反映させることにより探索の高速化,効率化を期待することができる.
近傍培養型マスタースレーブモデル
Doshisha Univ., Kyoto Japan
多目的多目的 GAGA では,求める解が複数存在するためでは,求める解が複数存在するため単一目的と比較して,単一目的と比較して,十分な個体数と探索世代数十分な個体数と探索世代数が必要となる.が必要となる.
多目的 GA の問題点
・探索効率の良いアルゴリズム・探索効率の良いアルゴリズム
・膨大な評価計算回数
・非常に高い計算負荷
Doshisha Univ., Kyoto Japan
GA による多目的最適化への応用・多目的・多目的 GAGA
交叉・突然変異を用いてパレート最適解集合の探索を行う
ff11(x)(x)
ff 22(x)
(x)
1st generation5th generation
10th generation50th generation30th generation
Doshisha Univ., Kyoto Japan
Multi-Criterion Optimization Problems(2)
・・ Pareto dominant and Ranking methodPareto dominant and Ranking method
Pareto-optimal Set
Ranking
Rank = 1+ number of dominant individuals
The set of non-inferior individuals in each
generation.
f2
f1
1
3
1Pareto optimal solutions
Doshisha Univ., Kyoto Japan
クラスタシステム
Spec. of Cluster (16 nodes)Processor Pentium
(Coppermine)ⅢClock 600MHz# Processors 1 × 16Main memory 256Mbytes × 16Network Fast Ethernet (100Mbps)Communication TCP/IP, MPICH 1.2.1OS Linux 2.4Compiler gcc 2.95.4