Enhancing probabilistic based real-coded crossover genetic algorithms with authentication of VIKOR multi-criteria optimization method

Jalal-ud-Din; Ehtasham-ul-Haq; Ibrahim M. Almanjahie; Ishfaq Ahmad; Jalal-ud-Din; Ehtasham-ul-Haq; Ibrahim M. Almanjahie; Ishfaq Ahmad

doi:10.3934/math.20241418

AIMS Mathematics

2024, Volume 9, Issue 10: 29250-29268. doi: 10.3934/math.20241418

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Enhancing probabilistic based real-coded crossover genetic algorithms with authentication of VIKOR multi-criteria optimization method

1.
Department of Mathematics and Statistics, International Islamic University, 44000 Islamabad, Pakistan, Email: jalaluddin.phdst18@iiu.edu.pk
2.
Department of Mathematics and Statistics, Faculty of Basic and Applied Sciences, International Islamic University, 44000 Islamabad, Pakistan, Email: ehtasham.malik@iiu.edu.pk
3.
Department of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi Arabia, Email: imalmanjahi@kku.edu.sa
4.
Department of Mathematics and Statistics, Faculty of Basic and Applied Sciences, International Islamic University, 44000 Islamabad, Pakistan, Email: Ishfaq.ahmad@iiu.edu.pk

Received: 02 August 2024 Revised: 16 September 2024 Accepted: 26 September 2024 Published: 15 October 2024
MSC : 60-xx, 68W50

To improve the performance of genetic algorithms (GAs) in complex optimization settings, this work offered two novel real-coded crossover operators: one based on the Gumbel distribution (GX) and the other on the Rayleigh distribution (RX). These innovative operators, when combined with three different mutation techniques, created a significant improvement in GA methodology. Our meticulous simulations showed that the GX operator significantly outperformed RX and other traditional operators, demonstrating its superior capacity to address complex optimization problems. The GX operator's unusual robustness was further validated through detailed performance analysis utilizing the VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) multi-criteria decision-making technique, setting a new standard in crossover operator design and significantly improving the state of the art in GAs.
- genetic algorithms,
- Gumbel crossover,
- Rayleigh crossover,
- global optimization,
- real-coded crossover operator,
- VIKOR method
Citation: Jalal-ud-Din, Ehtasham-ul-Haq, Ibrahim M. Almanjahie, Ishfaq Ahmad. Enhancing probabilistic based real-coded crossover genetic algorithms with authentication of VIKOR multi-criteria optimization method[J]. AIMS Mathematics, 2024, 9(10): 29250-29268. doi: 10.3934/math.20241418

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Abstract

To improve the performance of genetic algorithms (GAs) in complex optimization settings, this work offered two novel real-coded crossover operators: one based on the Gumbel distribution (GX) and the other on the Rayleigh distribution (RX). These innovative operators, when combined with three different mutation techniques, created a significant improvement in GA methodology. Our meticulous simulations showed that the GX operator significantly outperformed RX and other traditional operators, demonstrating its superior capacity to address complex optimization problems. The GX operator's unusual robustness was further validated through detailed performance analysis utilizing the VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) multi-criteria decision-making technique, setting a new standard in crossover operator design and significantly improving the state of the art in GAs.

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