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

TL;DR

This paper reviews crossover standards in evolutionary algorithms, introduces a novel Lagrangian-based crossover standard, and demonstrates its superior performance over existing standards through statistical analysis on test functions.

Contribution

It proposes a new Lagrangian Problem Crossover (LPX) standard based on Lagrangian Dual Function, advancing systematic operator design in evolutionary algorithms.

Findings

LPX outperforms BX and SBX in accuracy and performance.

Statistical tests confirm LPX's superior ability to generate optimized solutions.

LPX enhances the efficiency of evolutionary algorithms in engineering problems.

Abstract

The performance of most evolutionary metaheuristic algorithms relays on various operatives. One of them is the crossover operator, which is divided into two types: application dependent and application independent crossover operators. These standards always help to choose the best-fitted point in the evolutionary algorithm process. High efficiency of crossover operators allows engineers to minimize errors in engineering application optimization while saving time and avoiding costly. There are two crucial objectives behind this paper; at first, it is an overview of crossover standards classification that has been used by researchers for solving engineering operations and problem representation. The second objective of this paper; The significance of novel standard crossover is proposed depending on Lagrangian Dual Function (LDF) to progress the formulation of the Lagrangian Problem Crossover (LPX) as a new standard of systematic operator. The proposed crossover standards result for 100 generations of parent chromosomes are compared to the BX and SBX standards, which are the communal real-coded crossover standards. The accuracy and performance of the proposed standard have evaluated by three unimodal test functions. Besides, the proposed standard results are statistically demonstrated and proved that it has an excessive ability to generate and enhance the novel optimization algorithm compared to BX and SBX