A New Lagrangian Problem Crossover—A Systematic Review and Meta-Analysis of Crossover Standards

Abstract

The performance of most evolutionary metaheuristic algorithms relies on various operators. The crossover operator is a standard based on population-based algorithms, which is divided into two types: application-dependent and application-independent crossover operators. In the process of optimization, these standards always help to select the best-fit point. The high efficiency of crossover operators allows engineers to minimize errors in engineering application optimization while saving time and avoiding overpricing. There are two crucial objectives behind this paper; first, we provide an overview of the crossover standards classification that has been used by researchers for solving engineering operations and problem representation. This paper proposes a novel standard crossover based on the Lagrangian Dual Function (LDF) to enhance the formulation of the Lagrangian Problem Crossover (LPX). The LPX for 100 generations of different pairs parent chromosomes is compared to Simulated Binary Crossover (SBX) standards and Blended Crossover (BX) for real-coded crossovers. Three unimodal test functions with various random values show that LPX has better performance in most cases and comparative results in other cases. Moreover, the LPB algorithm is used to compare LPX with SBX, BX, and Qubit Crossover (Qubit-X) operators to demonstrate accuracy and performance during exploitation evaluations. Finally, the proposed crossover stand operator results are demonstrated, proved, and analyzed statistically by the Wilcoxon signed-rank sum test.