A Novel Parent Centric Crossover with the Log-Logistic Probabilistic Approach Using Multimodal Test Problems for Real-Coded Genetic Algorithms

Ehtasham Ul Haq,Ibrahim M Almanjahie,Ishfaq Ahmad,Predrag S Stanimirović

doi:10.1155/2020/2874528

Abstract

In this paper, a comprehensive empirical study is conducted to evaluate the performance of a new real-coded crossover operator called Fisk crossover (FX) operator. The basic aim of the proposed study is to preserve population diversity as well as to avoid local optima. In this context, a new crossover operator is designed and developed which is linked with Log-logistic probability distribution. For its global performance, a realistic comparison is made between FX versus double Pareto crossover (DPX), Laplace crossover (LX), and simulated binary crossover (SBX) operators. Moreover, these crossover operators are also used in conjunction with three mutation operators called power mutation (PM), Makinen, Periaux, and Toivanen mutation (MPTM), and nonuniform mutation (NUM) for inclusive evaluation. The performance of probabilistic-based algorithms is tested on a set of twenty-one well-known nonlinear optimization benchmark functions with diverse features. The empirical results show a substantial dominance of FX over other crossover operators with authentication of performance index (PI). Moreover, we also examined the significance of the proposed crossover scheme by administrating ANOVA and Gabriel pairwise multiple comparison test. Finally, the statistically significant results of the proposed crossover scheme have a definite edge over the other schemes, and it is also expected that FX has a great potential to solve complex optimization problems.

Highlights

In many real-life decision-making problems, it is often the best possible solutions are required. ese problems may be anything from engineering, science, economics, and finance [1,2,3]
In the current empirical study, our main contribution is introducing a new real-coded crossover operator (FX), and the focus of our study is to evaluate the performance of proposed crossover operators in the context of simulation results
In most of the multimodal test problems, the empirical results are considered close to the theoretical optimum value which reflects the improved performance of the newly proposed crossover scheme. e performance of FX in terms of mean values, standard deviation, and average execution time is exceptionally ideal and helpful to overcome the shortcomings of the genetic algorithms (GAs) process including exploitation and exploration

Summary

Introduction

In many real-life decision-making problems, it is often the best possible solutions are required. ese problems may be anything from engineering, science, economics, and finance [1,2,3]. In many real-life decision-making problems, it is often the best possible solutions are required. When the quality of potential solutions can be modeled mathematically, it may be possible to algorithmically find a better and sometimes optimal solution. In this case, decisions are made by developing optimization models that describe the nature of the problem, and mathematical procedures are applied to solve these models. Unconstrained nonlinear optimization problem may be mathematically defined as. Ese are commonly known as bounds which are based on the decision variables. A point y+ ∈ S is known as local minima of f if f(y+) ≤ f(y) y ∈ Nε(y+) ∩ S, where Nε(y+) 􏼈y ‖y − y+‖ < ε, ε > 0􏼉 is the small neighborhood of the point (y+). If f(y+) ≤ f(y) y ∈ S, y+ is said to be the global minima of f

Methods

Results

Conclusion