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Weighted Mean Variant with Exponential Decay Function of Grey Wolf Optimizer Under Swarm Based Algorithm

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Weighted Mean Variant with Exponential Decay Function of Grey Wolf Optimizer Under Swarm Based Algorithm Weighted mean variant with exponential decay function of Grey Wolf Optimizer under Swarm Based Algorithm Alok Kumar1, Avjeet Singh2, Lekhraj3, Anoj Kumar4 1,2,3,4 Motilal Nehru National Institute of Technology, Allahabad, Computer Science and Engineering Department, {alokkumar, 2016rcs01, lekhraj, anojk}@mnnit.ac.in1,2,3,4 Abstract. Nature-Inspired Meta-heuristic algorithms are optimization algorithms those are becoming famous day by day from last two decades for the researcher with many key features like diversity, simplicity, proper balance between exploration and exploitation, high convergence rate, avoidance of stagnation, flexibility, etc. There are many types of nature inspired meta- heuristics algorithms employed in many different research areas in order to solve complex type of problems that either single-objective or multi-objective in nature. Grey Wolf Optimizer (GWO) is one most powerful, latest and famous meta-heuristic algorithm which mimics the leadership hierarchy which is the unique property that differentiates it from other algorithms and follows the hunting behavior of grey wolves that found in Eurasia and North America. To implement the simulation, alpha, beta, delta, and omega are four levels in the hierarchy and alpha is most powerful and leader of the group, so forth respectively. No algorithm is perfect and hundred percent appropriate, i.e. replacement, addition and elimination are required to improve the performance of each and every algorithm. So, this work proposed a new variant of GWO namely, Weighted Mean GWO (WMGWO) with an exponential decay function to improve the performance of standard GWO and their many variants. The performance analysis of proposed variant is evaluated by standard benchmark functions. In addition, the proposed variant has been applied on Classification Datasets and Function Approximation Datasets. The obtained results are best in most of the cases. Keywords: GA, GP, ES, ACO, PSO, GWO, Exploitation, Exploration, Meta- heuristics, Swarm Intelligence. 1 Introduction Heuristic algorithms face some problems and limitations like it may stuck in local optima, produced limited number of solutions, problem dependent, and so forth. To overcome these types of issues, meta-heuristics algorithms come into the picture and play an important role to improve the performance and simplicity to the researchers. Nature-inspired meta-heuristic algorithms become inspired by nature and follow the teaching-learning process to the group elements. Nature-inspired meta-heuristic algorithms can be classified into four categories as shown in figure [1], Evolutionary algorithm, Swarm based algorithm, Physics Based Algorithms, and Biological inspired algorithms. Surprisingly, algorithms such as, Genetic Algorithm (GA), Genetic Programming (GP), Evolution strategy (ES), etc. comes under evolutionary algorithm, Ant Colony Optimization (ACO), Bat algorithm, Particle Swarm Optimization (PSO), Grey Wolf Optimizer (GWO), etc. comes under swarm based algorithm. In this paper, a focus on Grey Wolf Optimizer (GWO) of swarm based algorithm to improve the performance. A homogenous and large group of bird or animal is known to swarm. Surprisingly, an algorithm is employed on the intelligence of swarm that considered as swarm intelligence algorithms. GWO is a swarm intelligence algorithm and the scientific name of grey wolves is canis lupus that was inspiration of innovation of this proposed algorithm. Fig. 1. Classification of Nature-inspired meta-heuristic algorithms Genetic Algorithm (GA) [1-2] is an optimization algorithm and was introduced by John Holland in 1960 that follows the principle of Darwin's theory of evolution which state that “theory of natural selection and evaluation” regarding survival of fitness, i.e. eliminate those elements or species from the environment whose are not survive or fitted in the environment. Holland„s student David E. Goldberg further extended and proposed the GA in 1989. It is initiated with random solution called population and performs bio-inspired operators such as selection, crossover, and mutation relaying recursively until obtained the desired output. More chance to get the best solution in next generation than present one after implementation. Crossover and mutation operators of GA perform the exploration as well as exploitation property of optimization technique. GA comes under the evolutionary algorithms of nature inspired meta-heuristic optimization. This optimization algorithm employed in many research areas to solve complex type of problem. The problem of image segmentation and image classification are solved by GA which are the research domains of image processing. Genetic Programming (GP) [3-4] is a sub class of Evolutionary Algorithms and based on evolution theory. It was introduced by Jone Koza in 1992 and performed reproduction, crossover, and mutation operators initially and architecture-altering operations at the end to implement this algorithm. This algorithm is an elongation of GA and a domain-independent method. This optimization algorithm employed in many research areas to solve complex type of problem. The problem of image segmentation and image classification are solved by GP which are the research domains of image processing. GP can exploit complex and variable length representation that uses various kinds of operator to combine the input in linear or non- linear form which is suitable to construct new features. Evolution strategy (ES) [5-8] also comes under the evolutionary algorithms of nature inspired meta-heuristic optimization and was introduced in early 1960s by Ingo Rechenberg, Hans-Paul Schwefel and Bienert. It was further developed in 1970 and based on evolution theory. Mutation and recombination operators are employed to perform the process of evaluation of algorithm to obtain the batter results in each generation. (1+1) in [6], (1+λ) and (1, λ) in [7] are categories of ES which are used to select the parent. This optimization algorithm employed in many research areas with different domains. The problem of image segmentation and medical image are solved by ES which are the research domains of image processing. Ant Colony Optimization (ACO) [9-11] is a sub class of Swarm Based Algorithms, based on the concept of swarm intelligence, and during searching the food by ants is the inspiration of this algorithm. It was initially proposed by Marco Dorigo in 1992 in his Ph.D. thesis. Ant has the capability or ability to find the food source from their nest with best possible shortest path. To find the optimal path, ants disperse the pheromone (a special type of perfume or chemical) to indirect communication between them. This meta-heuristic optimization algorithm employed in many research areas commonly to solve graphical type of problems. The problem of image classification is solved by ACO which comes under the research domains of image processing. The Bat algorithm [12] is also a meta-heuristic algorithm, sub class of Swarm Based Algorithms, and inspired by echolocation behavior of micro bats. In 2010, Xin- She Yang developed this algorithm for global optimization. A highly innovative aesthesia of hearing have developed by few bats in their path and generates echoes back to bats. Simplicity and flexibility are the main advantages of this algorithm and it is very easy to design. This meta-heuristic optimization algorithm employed in many research areas to solve complex type of problem. The problem of image compression is solved by bat algorithm which is the research domains of image processing. Particle Swarm Optimization (PSO) [13] proposed and design by Kennedy and Eberhart in 1995. The simulation of swarm (group of particles) optimization algorithm based on social behavior or social intelligence of species such as fish schooling (In biological vocabulary, any group of fishes that halt together for untidily reason known as shoaling, further, if the group of fishes swims in same direction for hunting in unified manner, that known as schooling) and bird flocking (an assembly of group of similar types of animals in order to travel, pasturage or jaunt with one another, that known as Flocking). PSO is implemented with only two paradigms, PBEST (particle best or personal best) and GBEST (Global best). Individual best solution of any particle during any course of generation called personal best solution, subsequently best out of all personal best solution is known as Global best. The velocity and Position vector simulate the mathematical model to generate optimal results. This swarm based optimization algorithm employed in many research areas to solve complex type of problem. The problems of image segmentation and medical image which are the research domains of image processing are solved by PSO. 3 2 Literature Review In this section, a description and brief literature review of variants of Grey Wolf Optimizer and their applications in different research domain. The literature of GWO is as follows: Al-Aboody et al. [14] devised a three-level clustered routing protocol using GWO for wireless sensors to increase the performance and stability. The procedure done completely in three phases, in the first level centralized selection helps in finding the cluster heads from the base level, in the second level routing for data transfer is done where the nodes select the best route to the base station to consume less energy, and in the third & last level, distributed clustering is introduced. The evaluation of the algorithm was done through the network's lifetime,
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