A global optima search field division method for evolutionary algorithms

Abstract

This study aims to investigate the deployment of a proposed search field division method (SFDM) within evolutionary algorithms (EAs) to enhance the capability of searching for the global optima in nonlinear problems. The proposed technique is benchmarked against the following eight widely-used single-modal, multi-modal, and unimodal benchmark functions: Sphere, Rosenbrock, Rastringin, Griewank, Ackley, Fletcher, Quartic, and Schwefel functions, and the outcome is compared to their standard EAs counterparts to validate the effectiveness of the deployed approach in EAs. In the proposed method, we apply three low, medium, high field divisions (1, 2, and 5) dimensions on nine different EAs simultaneously with two different scenarios, 10 and 100 variables, to reach the optimal solution. Then for the validity of our proposed SFDM technique, we examined the exploration-exploitation search space rates and diversity behavior. The results of the implementation of SFDM on eight benchmark test functions show that the consideration of dimensions using SFDM for EAs improves the outcomes of all nine tested EAs. In our proposed method, we find better compatibility with the integration of SFDM in the Particle Swarm Optimization Algorithm concerning searching for the optimum solution relative to the other EAs.

Highlights

• A novel Search Field Division Method (SFDM) for evolutionary algorithms.

• Applying three field divisions (1, 2, and 5) dimensions on nine different Evolutionary Algorithms (EAs) simultaneously to reach the optimal global solution.

• The implementation of SFDM on eight benchmark functions shows significant improvement in all nine tested EAs.

• In our proposed method, we find the Particle Swarm Optimization Algorithm has better compatibility with respect to the other EAs.

Keywords:

• Evolutionary algorithms
• search field division method
• search dimensions
• nonlinear problems

Acknowledgements

The authors are thankful to the respectful editors and anonymous reviewers for their very constructive comments to improve the quality of our paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

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