# Comparative analysis of real-coded genetic algorithms for mixture distribution models: Insights from TOPSIS

## TL;DR

This study introduces two new crossover operators for genetic algorithms that improve their performance in solving complex optimization problems.

## Contribution

The paper proposes two novel parent-centric real-coded crossover operators, MGGX and MRRX, for genetic algorithms.

## Key findings

- MGGX outperformed other operators in 20 out of 36 mean values cases.
- MRRX achieved the lowest standard deviation in 21 out of 36 cases.
- Quade test, PI, and TOPSIS confirmed the operators' efficiency and robustness.

## Abstract

This particular study presents two novel parent-centric real-coded crossover operators, named mixture-based Gumbel crossover (MGGX) and mixture-based Rayleigh crossover (MRRX), to increase the efficiency of genetic algorithms (GAs) in tackling complex optimization problems. Conventional crossover operators often struggle in multimodal and extremely restricted situations and fail to find the ideal balance between exploration and exploitation. Proposed parent-centric real-coded crossover operators increase the precision and robustness of GAs, which is confirmed by empirical results on testing constrained and un-constrained benchmark functions having different complexity levels. MGGX parent-centric real-coded crossover operator performs best in 20 out of 36 mean values cases and achieves the lowest standard deviation values in 21 out of 36 cases. Likewise, to confirm the efficiency, robustness, and reliability of the proposed crossover operator the Quade test, Performance index (PI), and multi-criteria TOPSIS method are utilized.