Affiliations: [a] Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan
| [b] Department of Statistics, Faculty of Natural Sciences, Quaid-i-Azam University, Islamabad, Pakistan
| [c] Department of Mathematics, College of Science, King Khalid University, Abha, Kingdom of Saudi Arabia | [d] Statistical Research and Study Support Unit, King Khalid University, Abha, Kingdom of Saudi Arabia
Abstract: In the present simulation-based study, a novel parent-centric real-coded crossover operator is introduced with a unique probabilistic aspect of the mixture distribution. Moreover, the mixture distribution is a co-integration of double Pareto and Laplace probability distributions with various parameters. The key objective of the newly proposed methodology is to obtained optimal solutions for complex multimodal optimization problems. Hence, for its global comparison, the newly proposed mixture distribution crossover operator (MDX) is compared with double Pareto (DPX), Laplace (LX), and simulated binary (SBX) crossover operators within the conjunction of three mutation operators (MTPM, PM, and NUM). After a descriptive comparison, a Quade multiple comparison test is also administered to examine its statistical significance. Furthermore, the performance of the genetic algorithm (GA) is also examined on a set of twenty-one unconstraint benchmark functions with diverse features. The empirical results of the simulation-based study reveal that the mixture-based crossover operator obtained a substantial dominance over all considered crossover operators in terms of computational complexity, robustness, scalability, and capability of exploration and exploitation. Moreover, the Quade multiple comparison test also showed a significant superiority with graphical authentication of the performance index (PI).
Keywords: Genetic algorithms, two-component mixture model, real coded crossover, Quade test, Performance Index
