NOVEL NATURE INSPIRED POPULATION-BASED METAHEURISTIC

ALGORITHMS FOR OPTIMISATION

Rethishkumar S 1, Dr.R.Vijayakumar

2

1 Research Scholar, School of Computer Sciences, Mahatma Gandhi University, Kottayam, Kerala

rethishsnair3@gmail.com 2

Professor, School of Computer Sciences, Mahatma Gandhi University, Kottayam, Kerala.

vijayakumar@mgu.ac.in

Abstract-Nature-Inspired Optimization Algorithms provides a systematic introduction to all major nature-

inspired algorithms for optimization. The book's unified approach, balancing algorithm introduction, theoretical

background and practical implementation, complements extensive literature with well-chosen case studies to

illustrate how these algorithms work. Topics include particle swarm optimization, ant and bee algorithms,

simulated annealing, cuckoo search, firefly algorithm, bat algorithm, flower algorithm, harmony search,

algorithm analysis, constraint handling, hybrid methods, parameter tuning and control, as well as multi-objective

optimization. This book can serve as an introductory book for graduates, doctoral students and lecturers in

computer science, engineering and natural sciences. It can also serve a source of inspiration for new applications.

Researchers and engineers as well as experienced experts will also find it a handy reference.

Keywords- Ant Colony, Honey Bee lane, Mosquito flying behaviour, Moth flying, Bat follow, Firefly trail,

Frog leaping, Cuckoo search, Fish flow, Bacterial Foraging, Flower pollination and Genetic Algorithms etc

naturally inspired algorithms and particle swarm optimization algorithms.

I. INTRODUCTION

Nature is a great source of inspiration for solving complex problems in networks. It helps to find the optimal

solution. Metaheuristic algorithm is one of the nature-inspired algorithm which helps in solving routing problem

in networks. The dynamic features, changing of topology frequently and limited bandwidth make the routing,

challenging in MANET. Implementation of appropriate routing algorithms leads to the efficient transmission of

data in mobile ad hoc networks. The algorithms that are inspired by the principles of naturally-

distributed/collective behavior of social colonies have shown excellence in dealing with complex optimization

problems. Thus some of the bio-inspired metaheuristic algorithms help to increase the efficiency of routing in ad

hoc networks. This survey work presents the overview of bio-inspired metaheuristic which support the efficiency

of routing in mobile ad hoc networks.

II. TYPES OF NATURE-INSPIRED ALGORITHMS

Latest developed and widely used bio inspired metaheuristic pollination algorithm for optimisation problem

is describes below. This revels a new era in Computer science for finding an optimum solution classification and

clustering functions. According to the context, best suited algorithms can be used for optimisation problem.

(i). Ant Colony optimization

ACO is a population-based metaheuristic that can be used to find approximate solutions to difficult

optimization problems. In ACO, a set of software agents called artificial ants search for good solutions to a

given optimization problem [1]. To apply ACO, the optimization problem is transformed into the problem of

finding the best path on a weighted graph. The artificial ants (hereafter ants) incrementally build solutions by

moving on the graph. The solution construction process is stochastic and is biased by a pheromone model, that

is, a set of parameters associated with graph components (either nodes or edges) whose values are modified at

runtime by the ants.

The first step for the application of ACO to a combinatorial optimization problem (COP) consists in defining a

model of the COP as a triplet (S,Ω,f) , where:

S is a search space defined over a finite set of discrete decision variables;

Ω is a set of constraints among the variables; and

f:S→R+0 is an objective function to be minimized (as maximizing over f is the same as minimizing

over −f , every COP can be described as a minimization problem).

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The search space S is defined as follows. A set of discrete variables Xi , i=1,…,n , with

values vji∈Di={v1i,…,v|Di|i} , is given. Elements of S are full assignments, that is, assignments in which each

variable Xi has a value vji assigned from its domain Di . The set of feasible solutions SΩ is given by the elements

of Sthat satisfy all the constraints in the set Ω .

A solution s∗∈SΩ is called a global optimum if and only if

f(s∗)≤f(s) ∀s∈SΩ .

The set of all globally optimal solutions is denoted by S∗Ω⊆SΩ . Solving a COP requires finding at least

one s∗∈S∗Ω .

In ant colony optimization metaheuristic, artificial ants build a solution to a combinatorial optimization problem

by traversing a fully connected construction graph, defined as follows. First, each instantiated decision

variable Xi=vji is called a solution component and denoted by cij . The set of all possible solution components is

denoted by C . Then the construction graph GC(V,E) is defined by associating the components C either with the

set of vertices V or with the set of edges E. A pheromone trail value τij is associated with each

component cij . (Note that pheromone values are in general a function of the algorithm's iteration t:τij=τij(t) .)

Pheromone values allow the probability distribution of different components of the solution to be modelled.

Pheromone values are used and updated by the ACO algorithm during the search [2].

The ants move from vertex to vertex along the edges of the construction graph exploiting information provided

by the pheromone values and in this way incrementally building a solution. Additionally, the ants deposit a

certain amount of pheromone on the components, that is, either on the vertices or on the edges that they traverse.

The amount Δτ of pheromone deposited may depend on the quality of the solution found. Subsequent ants utilize

the pheromone information as a guide towards more promising regions of the search space.

The ACO metaheuristic is:

Set parameters, initialize pheromone trails

SCHEDULE_ACTIVITIES

ConstructAntSolutions

DaemonActions {optional}

UpdatePheromones

END_SCHEDULE_ACTIVITIES

The metaheuristic consists of an initialization step and of three algorithmic components whose activation is

regulated by the SCHEDULE_ACTIVITIES construct. This construct is repeated until a termination criterion is

met. Typical criteria are a maximum number of iterations or a maximum CPU time.

(ii). Honey Bee Optimisation Algorithm

In nature, honey bees have several complicated behaviors such as mating, breeding and foraging. These

behaviors have been mimicked for several honey bee based optimization algorithms. One of the famous mating

and breeding behavior of honey bees inspired algorithm is Marriage in Honey Bees Optimization (MBO). The

algorithm starts from a single queen without family and passes on to the development of a colony with family

having one or more queens. In the literature, several versions of MBO have been proposed such as Honey-Bees

Mating Optimization (HBMO), Fast Marriage in Honey Bees Optimization (FMHBO) and The Honey-Bees

Optimization (HBO).

The other type of bee-inspired algorithms mimics the foraging behavior of the honey bees [3]. These algorithms

use standard evolutionary or random explorative search to locate promising locations. Then the algorithms utilize

the exploitative search on the most promising locations to find the global optimum. The following algorithms

were inspired from foraging behavior of honey bees; Bee System (BS), Bee Colony Optimization (BCO),

Artificial Bee Colony (ABC) and The Bees Algorithm (BA). Bee System is an improved version of the Genetic

Algorithm (GA). The main purpose of the algorithm is to improve local search while keeping the global search

ability of GA.

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Bee Colony Optimization (BCO) was proposed to solve combinatorial optimization problems by BCO has two

phases called forward pass and backward pass. A partial solution is generated in the forward pass stage with

individual exploration and collective experience, which will then be employed at the backward pass stage. In the

backward pass stage the probability information is utilized to make the decision whether to continue to explore

the current solution in the next forward pass or to start the neighborhood of the new selected ones. The new one

is determined using probabilistic techniques such as the roulette wheel selection.

The algorithm consists of the following bee groups: employed bees, onlooker bees and scout bees as in nature.

Employed bees randomly explore and return to the hive with information about the landscape. This explorative

search information is shared with onlooker bees. The onlooker bees evaluate this information with a probabilistic

approach such as the roulette wheel method to start a neighborhood search. Meanwhile, the scout bees perform a

random search to carry out the exploitation.

The Bees Algorithm, which is very similar to the ABC in the sense of having local search and global search

processes [4]. However there is a difference between both algorithms during the neighborhood search process.

As mentioned above, ABC has a probabilistic approach during the neighborhood stage; however the Bees

Algorithm does not use any probability approach, but instead uses fitness evaluation to drive the search. In the

following section the Bees Algorithm will be explained in detail.

The bees algorithm consists of an initialisation procedure and a main search cycle which is iterated for a given

number T of times, or until a solution of acceptable fitness is found [5]. Each search cycle is composed of five

procedures: recruitment, local search, neighbourhood shrinking, site abandonment, and global search.

Pseudocode for the standard bees algorithm

1 for i=1,…,ns

i scout[i]=Initialise_scout()

ii flower_patch[i]=Initialise_flower_patch(scout[i])

2 do until stopping_condition=TRUE

i Recruitment()

ii for i =1,...,nb

1 flower_patch[i]=Local_search(flower_patch[i])

2 flower_patch[i]=Site_abandonment(flower_patch[i])

3 flower_patch[i]=Neighbourhood_shrinking(flower_patch[i])

iii for i = nb,...,ns

1 flower_patch[i]=Global_search(flower_patch[i])}

In the initialisation routine ns scout bees are randomly placed in the search space, and evaluate the fitness of the

solutions where they land. For each solution, a neighbourhood (called flower patch) is delimited.

(iii). Mosquito flying optimisation

Mosquito Swarm Algorithm (MSA) is defined as a meta-heuristics algorithm based on the social

behavior of mosquito swarm. Mosquitoes (gnats) have sensors designed to track their prey [6].

A) By utilizing the Chemical sensing capacity, the mosquitoes can sense carbon dioxide and lactic acid up

to 36 meters away. Mammals and birds give off these gases as part of their normal breathing. Certain

chemicals in sweat also seem to attract mosquitoes.

B) By utilizing the Heat sensing capacity, the Mosquitoes can detect heat, so they can find warm-blooded

mammals and birds very easily once they get close enough. A mosquito swarm exists close to areas

with standing water.

C) C) They go to their pray through flying motion and slide around it to find the most favourable point.

This combined effort of flying and sliding motion of the mosquitoes has been imitated in the present

algorithm.

This algorithm has been used to find cluster centre among the high and low accuracy prediction values. The main

aid of this algorithm is to cluster the high and low accuracy values and choose the high accuracy value for kernel

function [7]. The step by step process of this algorithm is given below

Input: n-number of mosquitoes (i.e kernel parameters)

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1. A Mosquito Population Initialized with Chemical Sensors (CS) and Heat Sensors (HS). // here the CS

defined the fuzzification parameter and HS defined the number of iterations

2. The initial locations (x) of the mosquitoes (n) generated.

3. The temperature (t) and Maximum Temperature (T) are initialized. // the temperature has been

considered as maximum accuracy

4. Find the fitness function based on the maximum temperature

5. Applying the sliding motion to find fitness value

6. Repeated the mosquitoes by parallel or distributed processing

7. Maximum temperature repeat

8. New solutions Generated by adjusting the HS and updating the locations (x).

9. Verified and assigned the feasibility of the solution by the CS.

10. Applying the flying motion

11. Evaluated the new particles

12. Modified the fitness function if new fitness is better

13. The best solution (S) is Selected.

14. While t < T // Maximum Temperature

15. While (n total of mosquitoes)

The best solutions are displayed. Based on the above description of mosquito swarm process, the proposed

kernel parameters are optimized. It improved the classification accuracy [8].

(iv). Moth flame optimization

Moth-Flame Optimization (MFO) algorithm was proposed in 2016 as one of the seminal attempt to

simulate the navigation of moths in computer and propose an optimization algorithm [9]. This algorithm has

been widely used in science and industry. In the MFO algorithm, it is assumed that the candidate solutions are

moths and the problem’s variables are the position of moths in the space. Therefore, the moths can fly in 1-D, 2-

D, 3-D, or hyper dimensional space with changing their position vectors. Since the MFO algorithm is a

population-based algorithm.

It should be noted here that moths and flames are both solutions. The difference between them is the way we

treat and update them in each iteration. The moths are actual search agents that move around the search space,

whereas flames are the best position of moths that obtains so far. In other words, flames can be considered as

flags or pins that are dropped by moths when searching the search space. Therefore, each moth searches around a

flag (flame) and updates it in case of finding a better solution. With this mechanism, a moth never lose its best

solution. A logarithmic spiral has been chosen as the main update mechanism of moths in this paper. However,

any types of spiral can be utilized here subject to the following conditions: Spiral’s initial point should start from

the moth Spiral’s final point should be the position of the flame Fluctuation of the range of spiral should not

exceed from the search space Considering these points, we define a logarithmic spiral for the MFO algorithm

[10].

where indicates the distance of the moth for the flame, is a constant for defining the

shape of the logarithmic spiral, and t is a random number in [-1,1].

The spiral flying path of moths is simulated. As may be seen in this equation, the next position of a moth is

defined with respect to a flame. The t parameter in the spiral equation defines how much the next position of the

moth should be close to the flame (t = -1 is the closest position to the flame, while t = 1 shows the farthest).

Therefore, a hyper ellipse can be assumed around the flame in all directions and the next position of the moth

would be within this space. Spiral movement is the main component of the proposed method because it dictates

how the moths update their positions around flames. The spiral equation allows a moth to fly “around” a flame

and not necessarily in the space between them. Therefore, the exploration and exploitation of the search space

can be guaranteed.

The pseudo code of the WOA algorithm is presented below:

Update the number of flames (FlameNumber)

Initialise the population of moths

Calculate the objective values

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for all moths

for all paramters

update r and t

Calculate D with respect to the corresponding moth

Update the matrix M with respect to the corresponding moth

end calculate the objective values

Update flames

end

(v). Bat algorithm

BA is a recent optimization algorithm based on swarm intelligence and inspiration from the

echolocation behavior of bats. One of the issues in the standard bat algorithm is the premature convergence that

can occur due to the low exploration ability of the algorithm under some conditions [11]. To overcome this

deficiency, directional echolocation is introduced to the standard bat algorithm to enhance its exploration and

exploitation capabilities. In addition to such directional echolocation, three other improvements have been

embedded into the standard bat algorithm to enhance its performance. The new proposed approach, namely the

directional Bat Algorithm (dBA), has been then tested using several standard and non-standard benchmarks from

the CEC2005 benchmark suite. The performance of dBA has been compared with ten other algorithms and BA

variants using non-parametric statistical tests. The statistical test results show the superiority of the directional

bat algorithm

The Bat algorithm is a metaheuristic algorithm for global optimization. It was inspired by the echolocation

behaviour of microbats, with varying pulse rates of emission and loudness. Search is intensified by a

local random walk. Selection of the best continues until certain stop criteria are met. This essentially uses a

frequency-tuning technique to control the dynamic behaviour of a swarm of bats, and the balance between

exploration and exploitation can be controlled by tuning algorithm-dependent parameters in bat algorithm.

Bat algorithm is a swarm-intelligence-based algorithm, inspired by the echolocation behavior of microbats. BA

automatically balances exploration (long-range jumps around the global search space to avoid getting stuck

around one local maximum) with exploitation (searching in more detail around known good solutions to find

local maxima) by controlling loudness and pulse emission rates of simulated bats in the multi-dimensional

search space.

A detailed introduction of metaheuristic algorithms including the bat algorithm is given by Yang where a demo

program in MATLAB/GNU Octave is available, while a comprehensive review is carried out by Parpinelli and

Lopes. A further improvement is the development of an evolving bat algorithm (EBA) with better efficiency.

Recently, bat-inspired algorithm has been proposed as a population-based algorithm to mimic the echolocation

system involved in micro-bat. The main drawback of bat-inspired algorithm is its inability to preserve the

diversity during the search and thus the prematurity can take place. The sensitivity analysis for the main

parameters of island bat-inspired algorithm is well-studied to show their effect on the convergence properties.

For comparative evaluation, island bat-inspired algorithm is compared with 17 competitive methods and shows

very successful outcomes. Furthermore, the proposed algorithm is applied for three real-world cases of economic

load dispatch problem where the results obtained prove considerable efficiency in comparison with other state-

of-the-art methods.

(vi). Firefly algorithm

The firefly algorithm (FA) is one of the latest swarm intelligence algorithms created by Yang. In the

work presented by Gao et al. (2015), an improved particle filter based on FA is proposed to solve a main

handicap of the particle filter. The particles in the particle filter are optimized using FA before resampling [12].

As is known, particle filter algorithm has been proven to be a powerful tool in solving visual tracking problems.

However, the problem of sample impoverishment that is brought by the procedure of resampling is a main

obstacle of the particle filter. Thus, the proposed method in this work is to increase the number of meaningful

particles, and the particles can approximate the true state of the target more accurately.

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FA is classified as swarm intelligent, metaheuristic and nature-inspired, and it is developed by Yang in 2008 by

animating the characteristic behaviors of fireflies. In fact, the population of fireflies show characteristic luminary

flashing activities to function as attracting the partners, communication, and risk warning for predators. As

inspiring from those activities, Yang formulated this method under the assumptions of all fireflies are unisexual

such that all fireflies has attracting potential for each other and the attractiveness is directly proportionate to the

brightness level of individuals [13]. Hence, the brighter fireflies attract to the less brighter ones to move toward

to them, besides that in the case of no fireflies brighter than a certain firefly then it moves randomly.

In the formulation of firefly algorithm, the objective function is associated with flashing light characteristics of

the firefly population. Considering the physical principle of the light intensity, it is inversely quadratic

proportional to the square of the area, so that this principle enables to define fitting function for the distance

between any two fireflies. For the optimization of fitting function, the individuals are forced to systematic or

random moves in the population. In this way, it is ensured that all the fireflies move toward to more attractive

ones which have brighter flashing until the population converge to brightest one. Within this procedure, firefly

algorithm is executed by three parameters which are attractiveness, randomization, and absorption.

Attractiveness parameter is based on light intensity between two fireflies and defined with exponential functions.

When this parameter is set to zero, then it happens to the random walk corresponding to the randomization

parameter which is determined by Gaussian distribution principle as generating the number from the interval. On

the other hand, absorption parameters affect to the value of attractiveness parameters as changing from zero to

infinity. And, for the case of converging to the infinity, the move of fireflies appears as random walk.

In mathematical optimization, the firefly algorithm is a metaheuristic proposed by Xin-She Yang and inspired by

the flashing behavior of fireflies.

In pseudocode the algorithm can be stated as:

While (t < MaxGeneration)

for i = 1 : n (all n fireflies)

for j = 1 : i (n fireflies)

if ({\displaystyle I_{j}>I_{i}} ),

Vary attractiveness with distance r via {\displaystyle \exp(-\gamma \;r)} ;

move firefly i towards j;

Evaluate new solutions and update light intensity;

end if

end for j

end for i

Rank fireflies and find the current best;

end while

Post-processing the results and visualization;

End

In essence, FA uses the following three idealized rules:

1. Fireflies are unisexual so that one firefly will be attracted to other fireflies regardless of their sex.

2. The attractiveness is proportional to the brightness and they both decrease as their distance increases. Thus,

for any two flashing fireflies, the less brighter one will move toward the more brighter one. If there is no brighter

one than a particular firefly, it will move randomly.

3. The brightness of a firefly is determined by the landscape of the objective function.

The movement of a firefly i is attracted to another, more attractive (brighter) firefly j is determined by

xit+1=xit+β0e−γrij2(xjt−xit)+αεit

where β0 is the attractiveness at the distance r=0, and the second term is due to the attraction. The third term

is randomization with αbeing the randomization parameter, and εit is a vector of random numbers drawn from

a Gaussian distribution or uniform distribution at time t [14]. If β0=0, it becomes a simple random walk.

Furthermore, the randomization εit can easily be extended to other distributions such as Lévy flights.

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(vii). Frog leaping algorithm

The shuffled frog-leaping algorithm (SFLA) has been developed for solving combinatorial optimization

problems. The SFLA is a population-based cooperative search metaphor inspired by natural memetics. The

algorithm contains elements of local search and global information exchange. The SFLA consists of a set of

interacting virtual population of frogs partitioned into different memeplexes. The virtual frogs act as hosts or

carriers of memes where a meme is a unit of cultural evolution. The algorithm performs simultaneously an

independent local search in each memeplex [15]. The local search is completed using a particle swarm

optimization-like method adapted for discrete problems but emphasizing a local search. To ensure global

exploration, the virtual frogs are periodically shuffled and reorganized into new memplexes in a technique

similar to that used in the shuffled complex evolution algorithm. In addition, to provide the opportunity for

random generation of improved information, random virtual frogs are generated and substituted in the

population.The algorithm has been tested on several test functions that present difficulties common to many

global optimization problems. The effectiveness and suitability of this algorithm have also been demonstrated by

applying it to a groundwater model calibration problem and a water distribution system design problem.

Compared with a genetic algorithm, the experimental results in terms of the likelihood of convergence to a

global optimal solution and the solution speed suggest that the SFLA can be an effective tool for solving

combinatorial optimization problems.

SFLA is a recently popular meta-heuristic based on the memetic evolution of a group of frogs when seeking for

the location that has the maximum amount of available food. Proposed in 2003, SFLA is the combination of the

merits of memetic algorithm (MA) and PSO. In SFLA, the population consists of a group of frogs (solutions)

that is partitioned into subsets (memeplexes). Different memeplexes, each performs a local search, are

considered as different cultures (memes) of frogs. The SFLA is described as follows: assume that the initial

population is formed by P randomly generated frogs. For L-dimensional problems (L variables), a frog i is

represented as Xi=(xi1, xi2,., xiL). Afterwards, the frogs are sorted in a descending order according to their

fitness. Then, the entire population is divided into m memeplexes, each containing n frogs (i.e.P = mun). In this

process, the first frog goes to the first memeplex, the second frog goes to the second memeplex, frog m goes to

the mth memeplex, and frog m+1 goes back to the first memeplex, etc. Within each memeplex, the frogs with

the best and the worst fitness are denoted by Xb and Xw. The frog with the global best fitness is identified as Xg.

Here, a process similar to PSO is applied to improve Xw (not all frogs) in each small group.

where i = 1, 2, ..., Ngen; D is the movement of a frog whereas Dmax represents the maximum

permissible movement of a frog in feasible domain; Ngen is maximum generation of evolution in each

subset. The old frog is replaced if the evolution produces the better solution else Xb is replaced by

Xg(optimal solution). If no improvement is observed then a random frog is generated and replaces the old

frog. This process of evolution continues till the termination criterion met. Shuffling Process The frogs

are again shuffled and sorted to complete the round of evolution. Again follow the same four steps until the

termination condition met.

Like all heuristics, parameter selection is critical to SFLA performance. SFLA has five parameters: the number

m of memeplexes, the number n of frogs in a memeplex, the number q of frogs in a submemeplex, the number N

of evolution or infection steps in a memeplex between two successive shufflings and the maximum step size

Smax allowed during an evolutionary step. At this point in the development of this meta-heuristic, no clear

theoretical basis is available to dictate parameter value selection. Based on experience, the sample size F (the

number m of memeplexes multiplied by the number n of frogs in each memeplex), in general, is the most

important parameter. An appropriate value for F is related to the complexity of the problem. The probability of

locating the global (or near-global) optima increases with increasing sample size. However, as the sample size

increases, the number of function evaluations to reach the goal increases, hence making it more computationally

burdensome. In addition, when selecting m, it is important to make sure that n is not too small. If there are too

few frogs in each memeplex, the advantage of the local memetic evolution strategy is lost [16]. The response of

the algorithm performance to q is that, when too few frogs are selected in a submemeplex, the information

exchange is slow, resulting in longer solution times. On the other hand, when too many frogs are selected, the

frogs are infected by unwanted ideas that trigger the censorship phenomenon that tends to lengthen the search

period. The fourth parameter, N, can take any value greater than 1. If N is small, the memeplexes will be

shuffled frequently, reducing idea exchange on the local scale. On the other hand, if N is large, each memeplex

will be shrunk into a local optimum. The fifth parameter, Smax, is the maximum step size allowed to be adopted

by a frog after being infected. Smax actually serves as a constraint to control the SFLA’s global exploration

ability. Setting Smax to a small value reduces the global exploration ability making the algorithm tend to be a

local search. On the other hand, a large Smax may result in missing the actual optima, as it is not fine-tuned.

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Although, at present, there is no guidance to select proper values for the parameters, experimental results

presented in the next section provide a better understanding of the parameters’ impacts.

(viii). Cuckoo search algorithm

Cuckoo search is an optimization algorithm developed by Xin-she Yang and Suash Deb in 2009. It was

inspired by the obligate brood parasitism of some cuckoo species by laying their eggs in the nests of other host

birds (of other species). Some host birds can engage direct conflict with the intruding cuckoos [17]. For example,

if a host bird discovers the eggs are not their own, it will either throw these alien eggs away or simply abandon

its nest and build a new nest elsewhere. Some cuckoo species such as the New World brood-

parasitic Tapera have evolved in such a way that female parasitic cuckoos are often very specialized in the

mimicry in colors and pattern of the eggs of a few chosen host species Cuckoo search idealized such breeding

behavior, and thus can be applied for various optimization problems.

Each egg in a nest represents a solution, and a cuckoo egg represents a new solution. The aim is to use the new

and potentially better solutions (cuckoos) to replace a not-so-good solution in the nests. In the simplest form,

each nest has one egg. The algorithm can be extended to more complicated cases in which each nest has multiple

eggs representing a set of solutions.

CS is based on three idealized rules:

Each cuckoo lays one egg at a time, and dumps its egg in a randomly chosen nest; The best nests with high

quality of eggs will carry over to the next generation; The number of available hosts nests is fixed, and the egg

laid by a cuckoo is discovered by the host bird with a probability {\displaystyle p_{a}\in (0,1)}. Discovering

operate on some set of worst nests, and discovered solutions dumped from farther calculations [18]. In addition,

Yang and Deb discovered that the random-walk style search is better performed by Lévy flights rather than

simple random walk.

Algorithm, The pseudo-code can be summarized as:

Objective function:

{\displaystyle f(\mathbf {x} ),\quad \mathbf {x} =(x_{1},x_{2},\dots ,x_{d});\,}

Generate an initial population of

{\displaystyle n}

host nests;

While (t<MaxGeneration) or (stop criterion)

Get a cuckoo randomly (say, i) and replace its solution by performing Lévy flights;

Evaluate its quality/fitness

{\displaystyle F_{i}}

[For maximization,

{\displaystyle F_{i}\propto f(\mathbf {x} _{i})}

];

Choose a nest among n (say, j) randomly;

if (

{\displaystyle F_{i}>F_{j}}

),

Replace j by the new solution;

end if

A fraction (

{\displaystyle p_{a}}

) of the worse nests are abandoned and new ones are built;

Keep the best solutions/nests;

Rank the solutions/nests and find the current best;

Pass the current best solutions to the next generation;

end while

An important advantage of this algorithm is its simplicity. In fact, comparing with other population- or agent-

based metaheuristic algorithms such as particle swarm optimization and harmony search, there is essentially only

a single parameter {\displaystyle p_{a}} in CS (apart from the population size {\displaystyle n}). Therefore, it is

very easy to implement.

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(ix). Fish flow optimisation algorithm

In the development of the FSOA, the following characteristics are considered (Li et al. 2002; Madeiro,

2010): (i) each fish represents a candidate solution of the optimization problem; (ii) food density is related to an

objective function to be optimized (in an optimization problem, the amount of food in a region is inversely

proportional to value of objective function); and (iii) the aquarium is the design space where the fish can be

found [19].

As noted earlier, the fish weight at the swarm represents the accumulation of food (e.g., the objective function)

received during the evolutionary process. In this case, the weight is an indicator of success (Li et al. 2002;

Madeiro, 2010). Basically, the FSOA presents four operators that can be classified as "search" and "movement".

Details on each of these operators are shown next.

Individual Movement Operator

This operator contributes to the individual and collective movements of fishes in the swarm. Each fish updates

its new position by using the Equation (1):

where xi is the final position of fish i at current generation, rand is a random generator and sind is a weighted

parameter.

Food Operator

The weight of each fish is a metaphor used to measure the success of food search. The higher the weight of a

fish, the more likely this fish be in a potentially interesting region in design space. According to Madeiro (2010),

the amount of food that a fish eats depends on the improvement in its objective function in the current

generation. The weight is updated according to Equation (2):

where Wit is the fish weight i at generation t and ∆fi is the difference of the objective function between the

current position and the new position of fish i. It is important to emphasize that ∆fi=0 for the fishes in same

position.

Instinctive collective movement operator

This operator is important for the individual movement of fishes when ∆fi≠0. Thus, only the fishes whose

individual execution of the movement resulted in improvement of their fitness will influence the direction of

motion of the school, resulting in instinctive collective movement. In this case, the resulting direction ( ),

calculated using the contribution of the directions taken by the fish, and the new position of the ith fish are given

by:

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It is important to emphasize that in the application of this operator, the direction chosen by a fish that located the

largest portion of food to exert the greatest influence on the swarm [20]. Therefore, the instinctive collective

movement operator tends to guide the swarm in the direction of motion chosen by fish who found the largest

portion of food in it individual movement.

(x). Bacterial Foraging Optimization Algorithm

Bacterial Foraging Optimization Algorithm (BFOA) is proposed by Kevin Passino (2002), is a new

comer to the family of nature inspired optimization algorithms. Application of group foraging strategy of a

swarm of E.coli bacteria in multi-optimal function optimization is the key idea of this new algorithm. Bacteria

search for nutrients is a manner to maximize energy obtained per unit time [21]. Individual bacterium also

communicates with others by sending signals. A bacterium takes foraging decisions after considering two

previous factors. The process, in which a bacterium moves by taking small steps while searching for nutrients, is

called chemotaxis. The key idea of BFOA is mimicking chemotactic movement of virtual bacteria in the problem

search space.

p : Dimension of the search space,

S : Total number of bacteria in the population,

Nc : The number of chemotactic steps,

Ns : The swimming length.

Nre : The number of reproduction steps,

Ned : The number of elimination-dispersal events,

Ped : Elimination-dispersal probability,

C(i): The size of the step taken in the random direction specified by the tumble.

Foraging theory is based on the assumption that animals search for and obtain nutrients in a way that

maximizes their energy intake E per unit 65 time T spent foraging. Hence, they try to maximize a function like

E/T (or they maximize their long-term average rate of energy intake). Maximization of such a function provides

nutrient sources to survive and additional time for other important activities (e.g., fighting, fleeing, mating,

reproducing, sleeping, or shelter building). Shelter building and mate finding activities sometimes bear

similarities to foraging. Clearly, foraging is very different for different species. Herbivores generally find food

easily but must eat a lot of it. Carnivores generally find it difficult to locate food but do not have to eat as much

since their food is of high energy value. The “environment” establishes the pattern of nutrients that are available

(e.g., via what other organisms are nutrients available, geological constraints such as rivers and mountains and

weather patterns) and it places constraints on obtaining that food (e.g., small portions of food may be separated

by large distances). During foraging there can be risks due to predators, the prey may be mobile so it must be

chased and the physiological characteristics of the forager constrain its capabilities and ultimate success.

Bacterial Foraging optimization theory is explained by following steps.

x Chemotaxis

x Swarming

x Reproduction and

x Eliminational-Dispersal 5.2.1 Chemotaxis

This process simulates the movement of an E.coli cell through swimming and tumbling via flagella.

Biologically an E.coli bacterium can move in two different ways. It can swim for a period of time in the same

direction or it may tumble and alternate between these two modes of operation for the entire lifetime [22].

Suppose T i ( j, k, l) represents i th bacterium at 66 j th chemotactic, k th reproductive and l th elimination-

dispersal step. C(i) is the size of the step taken in the random direction specified by the tumble (run length unit).

Taxonomy: The Bacterial Foraging Optimization Algorithm belongs to the field of Bacteria Optimization

Algorithms and Swarm Optimization, and more broadly to the fields of Computational Intelligence and

Metaheuristics. It is related to other Bacteria Optimization Algorithms such as the Bacteria Chemotaxis

Algorithm [Muller2002], and other Swarm Intelligence algorithms such as Ant Colony Optimization and Particle

Swarm Optimization.

Inspiration: The Bacterial Foraging Optimization Algorithm is inspired by the group foraging behavior of

bacteria such as E.coli and M.xanthus. Specifically, the BFOA is inspired by the chemotaxis behavior of bacteria

that will perceive chemical gradients in the environment (such as nutrients) and move toward or away from

specific signals.

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Metaphor: Bacteria perceive the direction to food based on the gradients of chemicals in their environment.

Similarly, bacteria secrete attracting and repelling chemicals into the environment and can perceive each other in

a similar way. Bacterial cells are treated like agents in an environment, using their perception of food and other

cells as motivation to move, and stochastic tumbling and swimming like movement to re-locate. Depending on

the cell-cell interactions, cells may swarm a food source, and/or may aggressively repel or ignore each other.

Strategy: The information processing strategy of the algorithm is to allow cells to stochastically and collectively

swarm toward optima. This is achieved through a series of three processes on a population of simulated cells: 1)

'Chemotaxis' where the cost of cells is derated by the proximity to other cells and cells move along the

manipulated cost surface one at a time (the majority of the work of the algorithm), 2) 'Reproduction' where only

those cells that performed well over their lifetime may contribute to the next generation, and 3) 'Elimination-

dispersal' where cells are discarded and new random samples are inserted with a low probability. The algorithm

was designed for application to continuous function optimization problem domains. Given the loops in the

algorithm, it can be configured numerous ways to elicit different search behavior. It is common to have a large

number of chemotaxis iterations, and small numbers of the other iterations.

(xi). Flower Pollination Algorithm

The flower pollination algorithm (FPA) is a novel optimization technique derived from the pollination

behavior of flowers. However, the shortcomings of the FPA, such as a tendency towards premature convergence

and poor exploitation ability, confine its application in engineering problems. To further strengthen FPA

optimization performance, an orthogonal learning (OL) strategy based on orthogonal experiment design (OED)

is embedded into the local pollination operator [23]. OED can predict the optimal factor level combination by

constructing a smaller but representative test set based on an orthogonal array. Using this characteristic of OED,

the OL strategy can extract a promising solution from various sources of experience information, which leads the

population to a potentially reasonable search direction. Moreover, the catfish effect mechanism is introduced to

focus on the worst individuals during the iteration process. This mechanism explores new valuable information

and maintains superior population diversity [24]. The experimental results on benchmark functions show that our

proposed algorithm significantly enhances the performance of the basic FPA and offers stronger competitiveness

than several state-of-the-art algorithms.

Flower Pollination Algorithm Flower pollination algorithm (FPA) is swarm intelligence optimization algorithm

proposed by to simulate flower pollination. The dynamic control on the process of global search and local search

is realized by adjusting parameter P. Flower pollination process is achieved through cross-pollination or self-

pollination in the nature. The position of the pollinator is random or similar to random in the process of

pollination. In order to simulate the way of flower pollination, the following four rules are set. Rule 1: The biotic

and cross-pollination can be recognized as a global pollination, where the pollinators follow the Levy

distribution. Rule 2: The abiotic and self-pollination can be interpreted as a local pollination. Rule 3: The flower

constancy property can be considered as a reproduction ratio that is proportional to the degree of similarity

between two flowers. Rule 4: Due to the physical proximity and wind, local pollination has a slight advantage

over global pollination. Both are controlled by the value of the variable P [0,1] . In the global pollination, the

fittest reproduction is ensured through insects that can travel for long distances [25]. If the fittest is represented

as g * , the flower constancy and the first rule can be mathematically formulated as follows: 1 ( ) t t t i i i x x L g

x (1) where, t i x is a solution vector at iteration t , g * is the best found solution at iteration t ,

represents the step size scaling factor, and L is the pollination strength or the step size. The insect’s long moves

can be mimicked using Levy flight. For this reason, the step size L is derived from the Levy distribution. 1 ( )sin(

) 1 2 L s (2) where, 1.5 and represents the typical Gamma function. The local pollination

based on Rule 2 can be formulated as follows: 1 ( ) t t t t i i j k x x x x (3) where, t j x and tk x are

pollens (solution vectors) that are transferred from different flowers, but these flowers belong to a single plant

species. It simulates the flower constancy in a small neighborhood. The variable is derived from a uniform

distribution in the range [0,1] . The pollination process can be either local or global, so a switch probability P is

presented to switch between the two types of pollination (Rule 4).

(xii). Genetic Algorithm

Genetic Algorithms (GAs) are adaptive heuristic search algorithms that belong to the larger part of

evolutionary algorithms. Genetic algorithms are based on the ideas of natural selection and genetics [26]. These

are intelligent exploitation of random search provided with historical data to direct the search into the region of

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better performance in solution space. They are commonly used to generate high-quality solutions for

optimization problems and search problems.

Genetic algorithms simulate the process of natural selection which means those species who can adapt to

changes in their environment are able to survive and reproduce and go to next generation. In simple words, they

simulate “survival of the fittest” among individual of consecutive generation for solving a problem. Each

generation consist of a population of individuals and each individual represents a point in search space and

possible solution. Each individual is represented as a string of character/integer/float/bits. This string is

analogous to the Chromosome

In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process

of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are

commonly used to generate high-quality solutions to optimization and search problems by relying on bio-

inspired operators such as mutation, crossover and selection [27]. Problems which appear to be particularly

appropriate for solution by genetic algorithms include timetabling and scheduling problems, and many

scheduling software packages are based on GAs. It has also been applied to engineering. Genetic algorithms are

often applied as an approach to solve global optimization problems.

As a general rule of thumb genetic algorithms might be useful in problem domains that have a complex fitness

landscape as mixing, i.e., mutation in combination with crossover, is designed to move the population away

from local optima that a traditional hill climbing algorithm might get stuck in. Observe that commonly used

crossover operators cannot change any uniform population. Mutation alone can provide ergodicity of the overall

genetic algorithm process.

(xiii). Particle swarm optimization

Particle swarm optimization (PSO) is a computational method that optimizes a problem

by iteratively trying to improve a candidate solution with regard to a given measure of quality. It solves a

problem by having a population of candidate solutions, here dubbed particles, and moving these particles around

in the search-space according to simple mathematical formulae over the particle's position and velocity [28].

Each particle's movement is influenced by its local best known position, but is also guided toward the best

known positions in the search-space, which are updated as better positions are found by other particles. This is

expected to move the swarm toward the best solutions

PSO is a metaheuristic as it makes few or no assumptions about the problem being optimized and can search

very large spaces of candidate solutions. However, metaheuristics such as PSO do not guarantee an optimal

solution is ever found. Also, PSO does not use the gradient of the problem being optimized, which means PSO

does not require that the optimization problem be differentiable as is required by classic optimization methods

such as gradient descent and quasi-newton methods.

Formally, let f: ℝn → ℝ be the cost function which must be minimized. The function takes a candidate solution

as an argument in the form of a vector of real numbers and produces a real number as output which indicates the

objective function value of the given candidate solution [29]. The gradient of f is not known. The goal is to find a

solution a for which f(a) ≤ f(b) for all b in the search-space, which would mean a is the global minimum.

Let S be the number of particles in the swarm, each having a position xi ∈ ℝn in the search-space and a

velocity vi ∈ ℝn. Let pi be the best known position of particle i and let g be the best known position of the entire

swarm. A basic PSO algorithm is then:

for each particle i = 1, ..., S do

Initialize the particle's position with a uniformly distributed random vector: xi ~ U(blo, bup)

Initialize the particle's best known position to its initial position: pi ← xi

if f(pi) < f(g) then

update the swarm's best known position: g ← pi

Initialize the particle's velocity: vi ~ U(-|bup-blo|, |bup-blo|)

while a termination criterion is not met do:

for each particle i = 1, ..., S do

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for each dimension d = 1, ..., n do

Pick random numbers: rp, rg ~ U(0,1)

Update the particle's velocity: vi,d ← ω vi,d + φp rp (pi,d-xi,d) + φg rg (gd-xi,d)

Update the particle's position: xi ← xi + vi

if f(xi) < f(pi) then

Update the particle's best known position: pi ← xi

if f(pi) < f(g) then

Update the swarm's best known position: g ← pi

The values blo and bup represents the lower and upper boundaries of the search-space. The termination criterion

can be the number of iterations performed, or a solution where the adequate objective function value is

found. The parameters ω, φp, and φg are selected by the practitioner and control the behaviour and efficacy of the

PSO method.

Table 1. List of Nature Inspired Algorithms with input parameters, evolutionary strategies and

applications [31]

S.No. Algorithm Input parameters Evolutionary

Mechanism

Applied Application Area

1.

Genetic Algorithm

(GA)

Crossover rate and

Mutation rate.

Selection,

Recombination and

Mutation

Machine Learning , Code

Breaking, Computer automated

design , Computer architecture,

Bayesian inference, forensic

science, Data Center/Server Farm,

File allocation for a distributed

system, game theory, robot

behavior etc.

2.

Ant Colony

Optimization (ACO)

τ(e) is pheromone update

of a path e (edge), is

evaporation rate

τ(e)= τ τ The generalized assignment

problem (GAP), and the set

covering problem (SCP) ,

Classification, AntNet for network

routing applications, Multiple

Knapsack Problem.

3.

Particle Swarm

Optimization (PSO)

Learning factors C1 and

C2, inertia weight w,

maximum change of a

particle velocity Vmax,

Pg is position of best

particle (g), Xi is the

current position of

particle (i), Pi is best

position of particle in

previous cycle.

New Velocity Vi = w *

current Vi + C1*rand()

* (Pi – Xi) + C2 *

Rand() * (Pg-Xi)

New position Xi =

current position Xi +

New Vi;

Vmax >=Vi >=Vmax

conjunction with a back

propagation algorithm, to train a

neural network system design,

multi-objective optimization,

classification, pattern recognition

and image processing , image

clustering, robotic applications,

decision making, simulation and

identification, time-frequency

analysis, image segmentation etc.

4.

Bacterial Foraging

Algorithm (BFOA)

Step size Z(i), position

vector of ith of bacterium

O(i) at jth chemotactic step

and kth reproductive step,

Δ indicates a vector in the

random direction whose

elements lie in [-1, 1].

O(i,j+1,k) = O(i,j,k) +

Z(i)

Job Scheduling, machine learning,

to train a Wavelet-based Neural

Network (WNN), face recognition,

Image Edge detection, Image

Segmentation, Color Image

Quantization

5.

Shuffled frog

Leaping Algorithm

(SFLA)

Number of memeplexes,

number of memeplex

iterations and maximum

change in position Dmax

Change in frog position

(Di) = rand () *(Xb-

Xw)

New Position Xw = Xw

+ Di (Dmax >= Di >=-

Dmax)

multi-user detection in DS-CDMA

Communication System,

multivariable PID controllers and

web document classification,

image watermarking, clustering

6.

Artificial Bee

Colony Algorithm

(ABC)

Φij, a uniformly

distributed real random

number in the range [-1,

1]. i,j is food source

New position

POSij = Xij + Φij(Xij -

Xkj)

train neural networks, medical

pattern classification and clustering

problems, solving TSP, leaf-

constrained minimum spanning

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having different values

and j is dimension

tree, network reconfiguration

problem in a radial distribution

system

7.

Firefly Algorithm

(FFA)

β is variation of

attractiveness, r is

distance between two files

xi and xj. αt is step size, γ

is the light absorption

coefficient, ∈ is a random

variable

= + βexp[- γ ] ( - ) + αt∈ Digital Image Compression and

Image Processing, Feature

selection and fault detection, trail

neural network, Semantic Web

Composition, Classification and

Clustering, Rigid Image

Registration Problems, Parameter

Optimization of SVM

8.

Cuckoo Search

Algorithm (CSA)

Xi(t+1) is new solution

(nest) of ith cuckoo, ⊕ entry wise multiplication

of α step size and levy

flight

Xi(t+1)=Xi(t)+α⊕Lēvy(

λ)

Spring design optimization,

Welded Beam Design, software

testing and data generation,

wireless sensor network, Knapsack

problems, train neural network

19.

Bat Algorithm (BA) Fi is frequency of ith bat,

Vi is velocity and Xi is

position vector of bat, β ia

random vector between

(0,1)

Fi = Fmin + (Fmax – Fmin)β

= + X* ) Fi i

Continuous optimization,

classification, clustering and data

mining, inverse problem and

parameter estimation,

combinatorial optimization and

scheduling, image processing,

fuzzy logic and other applications

10.

Flower Pollination

Algorithm (FPA)

is the pollen i at tth

iteration, and are pollens

of different flowers, ∈ is

random number over [-

1,1]

= + ∈ ( ) Pattern recognition, Design of disc

brake

III. CONCLUSION

Nature inspired metaheuristic pollination algorithms are commenced a new era in Computer Science and

motivated from natural ecosystem and simulate the behavior of bio insects and creatures. The main aim of this

paper was to familiar with these types of bio inspired algorithms for optimisation of objects. Hence, this paper

also helps researcher or practitioner to gain insight of the various toolboxes available for simulating nature

inspired algorithms over benchmark problems. Overview of around 12 numbers of nature inspired pollination

algorithms are described in this paper for research community.

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