Cuckoo Search Optimization- A Review

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the search space as its step length is much longer in the long run. ... Representation of a nest solution in the Cuckoo search algorithm. ELR = α × ... When all cuckoos immigrated toward goal point and new habitats were specified, each ... Due to the fact that there is always equilibrium in birds population, so a number of ...

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ScienceDirect Materials Today: Proceedings 4 (2017) 7262–7269

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ICAAMM-2016

Cuckoo Search Optimization- A Review Ms.Anuja.S.Joshi1, Mr. Omkar Kulkarni2, Dr. Kakandikar G. M.3, Dr. Nandedkar V.M.4 1,2

P.G. research Scholar in Mechanical Engineering, Zeal College of Engineering & Research, Narhe, Pune-41,India 3

4

Asso. Prof at MAEER’S MIT Kothrud, Pune-38,India

Professor in Production Engineering, Shri Guru Govind Singhji Institute of Engineering and Technology, Nanded , India

Abstract The Cuckoo Search algorithm is a recently developed meta-heuristic optimization algorithm, which is used for solving optimization problems. This is a nature-inspired metaheuristic algorithm, which is based on the brood parasitism of some cuckoo species, along with Levy flights random walks. Normally, the parameters of the cuckoo search are kept constant for certain duration , this results into decrease the efficiency of the algorithm. To make a deal with this issue, a proper strategy for tuning the cuckoo search parameters is to be defined. Cuckoos are fascinating birds, not only because of the beautiful sounds they can make but also because of their aggressive reproduction strategy. Some species such as the Ani and Guira cuckoos lay their eggs in host bird nest, and they may remove others eggs to increase the hatching probability of their own. In this paper, cuckoos behaviour & their egg laying strategy in the nests of other host birds is explained.

© 2017 Published by Elsevier Ltd. Selection and Peer-review under responsibility ofthe Committee Members of International Conference on Advancements in Aeromechanical Materials for Manufacturing (ICAAMM-2016). Keywords:Cuckoo Search Optimization,Applications

1. Introduction Cuckoo Optimization Algorithm is based on the life of a bird called ‘cuckoo’[1]. The basic of this novel optimization algorithm is specific breeding and egg laying of this bird. Adult cuckoos and eggs used in this modeling. The cuckoos which are adult lay eggs in other birds habitat. Those eggs grow and become a mature cuckoo if are not finds and not removed by host birds. The immigration of groups of cuckoos and environmental specifications hopefully lead them to converge and reach the best place for reproduction and breeding. The objective 2214-7853© 2017 Published by Elsevier Ltd. Selection and Peer-review under responsibility ofthe Committee Members of International Conference on Advancements in Aeromechanical Materials for Manufacturing (ICAAMM-2016).

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function is in this best place .Cuckoo Optimization was developed by Yang and Deb in 2009 that inspired from the nature. Cuckoo Optimization Algorithm was developed by Rajabioun in 2011. Cuckoo Optimization Algorithm (COA) is really a new continuous over all aware search based on the life of a cuckoo bird. Similar other meta heuristic, COA begins with an primary population, a group of cuckoos. These cuckoos lay some eggs in the habitat of other host birds. A random group of potential solutions is generated that represent the habitat in COA. 1. Cuckoo Breeding Behavior StrategyThe CS algorithm was inspired by the obligate brood parasitism of some cuckoo species by laying their eggs in the nests of host birds. Some cuckoos have involved in such a way that female parasitic cuckoos can imitate various colours and patterns of the eggs of a few chosen host species. This reduces the probability of the eggs being abandoned so re-productivity increases. It is important to mention that several host birds engage direct conflict with intruding cuckoos. If host birds discover the eggs are not their own, they will either throw them away or simply abandon their nests and build new ones. Parasitic cuckoos often choose a nest where the host bird just laid its own eggs. In general, the cuckoo eggs hatch slightly earlier than their host eggs. Once the first cuckoo chick is hatched, his first instinct action is to evict the host eggs by blindly propelling the eggs out of the nest. This action results in increasing the cuckoo chick’s share of food provided by its host bird (Payne 2005). Moreover, studies show that a cuckoo chick can imitate the call of host chicks to gain access to more feeding opportunity. The breeding behaviour of cuckoo can be applied to various optimization problems. Lévy Flights mechanism is used instead of simple random walk to improve the performance of CS by Yang and Deb[1]. 2.1. Lévy Flights mechanismAnimals search for food in a random or quasirandom manner in the nature. The foraging path of an animal is effectively a random walk because the next move is based on both the current location/state and the transition probability to the next location. The chosen directions probability modelled mathematically. Various studies had shown that the flightbehaviour of many animals and insects demonstrates the typical characteristics of Lévy flights. A Lévy flight is a random walk in which the step-lengths are calculated according to a heavy-tailed probabilitydistribution. The distance from the origin of the random walk tends to a stable distribution after a large number of steps. 2.2 Cuckoo Search Implementation stepsEach egg in a nest represents a solution, and a cuckoo egg represents a new occurred solution. The aim is to employ the new and potentially better solutions (cuckoos) to replace not-so-good solutions 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 (Yang 2009; Yang 2010). The CS algorithm is based on three idealized rules: • Each cuckoo lays one egg at a time, and dumps it in a randomly chosen nest. • The best nests with high quality of eggs (solutions) will carry over to the next generations. • The number of available host nests is fixed, and a host can discover an alien egg with probability pa ε[0,1] . In this case, the host bird can either throw the egg away or abandon the nest to build a completely new nest in a new location (Yang 2009). For simplicity, the last assumption can be approximated by a fraction pa of the n nests being replaced by new nests, having new random solutions. For a maximization problem, the quality or fitness of a solution can simply be proportional to the objective function. In a similar way other forms of fitness can be defined by fitness function in

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genetic algorithms. Bacanin provided an object-oriented software implementation of cuckoo search..On the other hand, unconstrained optimization problems defined by a modified cuckoo search algorithm. Other forms of fitness can be defined in a similar way to the fitness function in genetic algorithms (Yang 2009). When generating new solutions x(t+1) for, say, a cuckoo is a Lévy flight is performed. Xi(t+1) = Xi(t)| + α ⊕ Lévy( )(1) Where, α > 0 is the step size which should be related to the scales of the problem of interests & in most cases, we can use α = 1. The above equation is essentially the stochastic equation for random walk. In general, a random walk is a Markov chain whose next status/location only depends on the current location (the first term in the above equation) and the transition probability (the second term) & the product mean sentry wise multiplications. This entry wise product is similar to those used in PSO, but here the random walk via Lévy flight is more efficient in exploring the search space as its step length is much longer in the long run. The Lévy flight essentially provides a random walk while the random step length is drawn from a Lévy distribution. Lévy~ u = t−λ, (1 < λ ≤ 3) (2) Which has an infinite variance with an infinite mean. Here the steps essentially form a random walk process with a power law step-length distribution with a heavy tail. Some of the new solutions should be generated by L´evy walk method around the best solution obtained so far, this will speed up the local search. However, a substantial fraction of the new solutions should be generated by far field randomization and whose locations should be far enough from the current best solution, this will make sure that the system will not be trapped in a local optimum. CS is a population based algorithm, in a way similar to GA and PSO. The Second one is the randomization is more efficient as the step length is heavy tailed, and any large step is possible. And Third one is, the number of parameters to be tuned is less than GA and PSO, and thus it is potentially more generic to adapt to a wider class of optimization problems. In addition, each nest can represent a set of solutions so CS can be extended to the type of metapopulation algorithm. 2.2.1 Generating initial cuckoo habitat In order to solve an optimization problem, it’s necessary that the values of problem variables be formed as an array. In GA and PSO terminologies this array is called “Chromosome” and “Particle Position”, respectively. But here in Cuckoo Optimization Algorithm(COA) it is called “habitat”. In a Nvar-dimensional optimization problem, a habitat is an array of 1×Nvar, representing current living position of cuckoo. This array is defined as follows: habitat=[x1, x2, . . . , xNvar ] Each of the variable values (x1, x2, . . . ,xNvar) is floating point number. The profit of a habitat is obtained by evaluation of profit function fpat a habitat of (x1, x2, . . . ,xNvar). So Profit =fp (habitat) =fp (x1, x2, . . . ,xNvar) As it is seen COA is an algorithm that maximizes a profit function. To use COA in cost minimization problems, one can easily maximize the following profit function: Profit=Cost(habitat)=fc(x1, x2, . . . ,xNvar) To start the optimization algorithm, a candidate habitat matrix of size Npop×Nvar is generated. Then some randomly produced number of eggs is supposed for each of these initial cuckoo habitats. In nature, each cuckoo lays from 5 to 20 eggs. These values are used as the upper and lower limits of egg dedication to each cuckoo at different iterations. Another habit of real cuckoos is that they lay eggs within a maximum distance from their habitat. From now on, this maximum range will be called “Egg Laying Radius (ELR)”. In an optimization problem with upper limit of varhi and lower limit of varlow for variables, each cuckoo has an egg laying radius (ELR)which is proportional to the total number of eggs in nest, number of current cuckoo’s eggs and also variable limits of varhi and varlow. So ELR is defined as

Anuja S.Joshi / Materials Today: Proceedings 4 (2017) 7262–7269

ELR = α ×

× (varhi - varlow)

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(3)

Where α is an integer which is supposed to handle the maximum value of ELR. 2.2.2 Cuckoos’ style for egg laying Each cuckoo starts laying eggs randomly in some other host bird’s nests within herELR. After all cuckoos eggs are laid in host bird’s nests, some of them that are less similar to host bird’s own eggs, are detected by host birds and thrown out of the nest. So after egg laying process, p% of all eggs (usually 10%), with less profit values, will be killed. These eggs have no chance to grow further. Rest of the eggs growing by host nests, hatch and are fed by host birds. Another interesting point about laid cuckoo eggs is that only one egg in a nest has the chance to grow. This is because when cuckoo egg hatches and the chicks come out, she throws the host bird’s own eggs out of the nest. In case that host bird’s eggs hatch earlier and cuckoo egg hatches later, cuckoo’s chick eats most of the food host bird brings to the nest (because of her 3 times bigger body, she pushes other chicks and eats more). After couple of days the host bird’s own chicks die from hunger and only cuckoo chick remains in the nest. Fig.1shows a Representation of a nest solution in the Cuckoo search algorithm.

Fig.1.Representation of a nest solution in the Cuckoo search algorithm

2.2.3 Immigration of cuckoos When young cuckoos grow and become mature, they live in their own area and society for some time. But when the time for egg laying approaches they immigrate to new and better habitats with more similarity of eggs to host birds and also with more food for new youngsters. After the cuckoo groups are formed in different areas, the society with best profit value is selected as the goal point for other cuckoos to immigrate. When mature cuckoos live in all over the environment it’s difficult to recognize which cuckoo belongs to which group. To solve this problem, the grouping of cuckoos is done with K means clustering method. Now that the cuckoo groups are constituted their mean profit value is calculated. Then the maximum value of these mean profits determines the goal group and consequently that group’s best habitat is the new destination habitat for immigrant cuckoos. When moving toward goal point, the cuckoos do not fly all the way to the destination habitat. They only fly a part of the way and also have a deviation. This movement is clearly shown in. each cuckoo only flies λ% of all distance toward goal habitat and also has a deviation of ϕ radians. These two parameters, λand ϕ, help cuckoos search much more positions in all environment. For each cuckoo and ϕ are defined as follows: ~ U(0,1) Φ ~ U(-ω, ω)

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Where, λ∼U (0, 1) means that λis a random number between 0 and 1. Ω is a parameter that constrains the deviation from goal habitat. A ω of λ/6 (rad) seems to be enough for good convergence of the cuckoo population to global maximum profit. When all cuckoos immigrated toward goal point and new habitats were specified, each mature cuckoo is given some eggs. Then considering the number of eggs dedicated to each bird, an ELR is calculated for each cuckoo. Afterward new egg laying process starts over. 2.2.4 Eliminating cuckoos in worst habitats Due to the fact that there is always equilibrium in birds population, so a number of Nmax controls and limits the maximum number of live cuckoos in the environment. This balances food limitations, being killed by predators and also inability to find proper nest for eggs. In the modelling only those Nmax number of cuckoos survive that have better profit values, others demises. 2. Application Area The applications of Cuckoo Search into engineering optimization problems have shown its promising efficiency. CS obtained better solutions than existing solutions in literature. Some of applications areLim Huai Tein [17]used Cuckoo Search method to solve problems on Nurse scheduling. Nurse scheduling process is playing an important role in healthcare institutions around the world. So that there are few decades of studies that applying various techniques or algorithms to develop effective nurse schedule which from exploring optimization methods to search methods. M. Dhivya et.al [18] developed Cuckoo based particle approach to achieve energy efficient Wireless Sensor Network and multimodal objective functions. Optimization of network is formulated by Cuckoo Based Particle Approach (CBPA) in this paper. In this case nodes are deployed randomly and organized as static clusters by Cuckoo Search (CS) algorithm & After the cluster heads are selected, the information is collected, aggregated and forwarded to the base station by using generalized particle approach algorithm. Cuckoo search is applied for cluster head selection and formation of clusters among the Sensor nodes in this paper. After making comparison of proposed CBPA with standard LEACH protocol simulation results shows that CBPA produces comparable results mainly due to optimal search process in cluster formation and allocation of appropriate paths in transmission of sensed data. This developed algorithm reduces complexity in chain formation and prolongs the longevity of the Sensor Network. The final result obtained by doing number of simulation iterations. A. Layeb [19] has found a new inspired algorithm called Quantum Inspired Cuckoo Search Algorithm (QICSA),this is depends on Quantum Computing principles and Cuckoo Search algorithm.This consists of defining an appropriate representation scheme in the cuckoo search algorithm that allows applying successfully on combinatorial optimization problems some quantum computing principles like qubit superposition of states, measurement, representation, and interference .With a certain probability, the quantum representation of the solutions allows the coding of all the potential solutions. Application of cuckoo search dynamics in optimization process enhanced by quantum operations such as the interference, the quantum mutation and measurement. The population size and the number of iterations to have the optimal solution efficiently reduced by this proposed algorithm. There are some issues to improve the algorithm, one of it is integrate a local search method like Tabu Search in the core of the algorithm in order to increase the effectiveness of algorithm & the second one is the better use of parallels machines because it was verified effectively that quantum inspired algorithms can work better on parallels machines.

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Aziz Ouaarab et.al [20] told about an improved and discrete version of the Cuckoo Search algorithm to solve the famous Traveling Salesman Problem. The original cuckoo search algorithm is improved by introducing a new category of cuckoos so that it can solve combinatorial problems as well as continuous problems. Symmetric traveling salesman problem solved by using improved cuckoo search algorithm. By making study of interpretation of the terminology used in CS and in its inspiration source this adaptation is done. The goal of this Discrete CS is to give good ideas for designing new generations of more efficient meta-heuristic algorithms. Cuckoos have mimic nature so that very complex problems can efficiently solve by algorithms with apparent simplicity. They also want to develop new algorithms which will be more intelligent, more controllable & less complex compared with other algorithms. G. Zheng et al [21] proposed a three-step polynomial metamodel-assisted OP-AMP optimization flow ,address the issues of optimized OP-AMPs do not guarantee an optimal system performance.This paper presents such a design flow for state-of-the art OP-AMP optimization. To estimate OP-AMP performance ultra-fast and highly accurate polynomialmeta models are generated &to facilitate fast time-domain simulations an OP-AMP metamacromodel is constructed and is integrated into a Verilog-AMS module. Promised optimized results are produced by customizing cuckoo search algorithm. OP-AMP performance accurately predicted by OP-AMP characteristics with ultra-high speed. In the future result will be done on system-level optimization using the developed OP-AMP meta-macro model. A. R. Yildiz [23] used a newly developed Cuckoo search algorithm to solve manufacturing optimization problem. For that manufacturing optimization problem was solved to demonstrate effectiveness of Cuckoo Search &results were compared with other algorithms such as immune algorithm, hybrid immune algorithm, hybrid particle swarm algorithm, genetic algorithm, ant colony algorithm. CS is performed effectively on the optimization of machining parameters of the milling operation problem finding better solutions compared to other approaches. T he CS is a generalized solution method so that it can be easily employed to consider the optimization models of milling regarding various objectives and constraints. The Cuckoo Search is very effective and robust approach for machining optimization problem. S. Burnwal et.,al [24] developed cuckoo search based approach for scheduling optimization of flexible manufacturing system by minimizing penalty cost due to delay in manufacturing and maximizing machine utilization time. To find optimum job, the proposed scheme has been applied with slight modification in its Levy Flight operator because of discrete nature of solution on standard FMS scheduling problem containing 43 jobs & 16 machines which is taken from literature to demonstrate cuckoo search algorithm. Matlab is used to implement CS and results were compared with other soft computing based approaches such as Particle swarm optimization, Genetic algorithm. In flexible manufacturing system (FMS), scheduling is important decision making to decide effectiveness and capability of the system to increase operational efficiency. Cuckoo search based approach simplifies it. Ahmed T. Sadiq Al-Obaidi [25] presents enhanced scatter search algorithm using CS algorithm. Testing is done on travelling salesman problem by original and improved Scatter Search. The Scatter Search (SS) is a deterministic strategy that has been applied successfully to some combinatorial and continuous optimization problems ,one of it is travelling salesman problem. The improvement in scatter Search with random exploration for search space of problem and more of diversity and intensification for promising solutions. The results are reported & demonstrate

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that the improved Scatter Search algorithms produce better performance than original Scatter Search algorithm &improvement in the value of average fitness is 23.2% comparing with original SS. It is found that The elapsed time for the improved SS is larger than the elapsed time for original SS in a reasonable value. The optimal solution of the improved SS is better than some algorithms but is far away from some others. Aminreza Noghrehabadi et.al [27] applied hybrid Power series and Cuckoo Search via L´evy Flight Optimization algorithm (PS-CS) method to solve a system of nonlinear differential equations arising from the Distributed parameter model of a micro fixed-fixed switch subject to electrostatic force and fringing filed effect. A trial solution of the differential equation is defined as sum of two polynomial parts. The first part of it satisfies the boundary conditions and does not contain any adjustable parameter and the second part of it which is constructed so as not to affect the boundary conditions and involves adjustable parameters. PS-CS method is used here. This method provides more details about deflection shape of micro beams than lumped models. Micro fixed- fixed beams were computed using a combination of power series and heuristic Cuckoo Search optimization algorithm. This method is capable to obtain magnitude of bending moment and shear forces of micro fixed beam.PS-CS results are compared with the numerical results which show the PS-CS method using eight terms is in very good agreement with numerical results.

3. Conclusion In this paper, Cuckoo search Optimization, its working principle and its various application areas are described. This report also focuses on the Cuckoo feeding behaviour, Levy Flight mechanism. An important advantage of this algorithm is its simplicity. In fact, comparing with other population- or agent-based metaheuristic algorithms such as optimization and harmony search, there is essentially only a single parameter in CS (apart from the population size ). Therefore, it is very easy to implement.

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