A Novel Selection Approach for Genetic Algorithms for Global Optimization of Multimodal Continuous Functions.

Ehtasham-Ul Haq,Abid Hussain,Ishfaq Ahmad,Ibrahim M Almanjahie

doi:10.1155/2019/8640218

Abstract

Genetic algorithms (GAs) are stochastic-based heuristic search techniques that incorporate three primary operators: selection, crossover, and mutation. These operators are supportive in obtaining the optimal solution for constrained optimization problems. Each operator has its own benefits, but selection of chromosomes is one of the most essential operators for optimal performance of the algorithms. In this paper, an improved genetic algorithm-based novel selection scheme, i.e., stairwise selection (SWS) is presented to handle the problems of exploration (population diversity) and exploitation (selection pressure). For its global performance, we compared with several other selection schemes by using ten well-known benchmark functions under various dimensions. For a close comparison, we also examined the significance of SWS based on the statistical results. Chi-square goodness of fit test is also used to evaluate the overall performance of the selection process, i.e., mean difference between observed and expected number of offspring. Hence, the overall empirical results along with graphical representation endorse that the SWS outperformed in terms of robustness, stability, and effectiveness other competitors through authentication of performance index (PI).

Highlights

Genetic algorithms (GAs) are stochastic-based heuristic search techniques that incorporate three primary operators: selection, crossover, and mutation. ese operators are supportive in obtaining the optimal solution for constrained optimization problems
E basic objective of this study is to make a comparison between different conventional selection schemes with the proposed one in the context of optimal solution by using benchmark functions. e overall statistical results of Table 4 clearly show that stairwise selection (SWS) obtained a minimum mean value and low S.D compared to other selection techniques from 10 to 100 dimensions
Another unimodal function is Rosenbrock; its statistical results about SWS are close to the theoretical optimum value which means that the proposed selection technique is efficiently handle complex problems at higher dimensions. e average rate of change in the Schaffer function is considerably low which shows that SWS efficiently performs at higher dimensions. e optimum value of SWS is ranging from 4.14 to 45.61 in the Schaffer function for 10–100 dimensions

Summary

Introduction

Genetic algorithms (GAs) are stochastic-based heuristic search techniques that incorporate three primary operators: selection, crossover, and mutation. ese operators are supportive in obtaining the optimal solution for constrained optimization problems. Ese algorithms are able to effectively handle both unconstrained and constrained optimization problems depending on a process of natural selection through biological evolution. Each part of the search space represents one sufficient solution, and its fitness values will be marked by these sufficient solutions, and a set of these solutions is called a population. Ere are two significant points in the GA process: one is starting point initialization in search space and other is assigning of fitness function [3]. If the problem statement is to have a minimum cost of some product, the optimization function here is to find the lowest of the fitness values [7]. Specification in the fitness function is one of the crucial problems in GA because it will determine which chromosomes can survive to the generation and which will be eliminated from the population

Methods

Results

Conclusion