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

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.