Exploratory power of the harmony search algorithm: analysis and improvements for global numerical optimization.

Area of Science:

• Computational Intelligence
• Optimization Algorithms
• Mathematical Analysis

Background:

• Theoretical analysis of evolutionary algorithms is crucial for understanding and improving their search mechanisms.
• Harmony Search (HS) is a derivative-free metaheuristic optimization algorithm inspired by musical improvisation.

Purpose of the Study:

• To provide a simple mathematical analysis of the explorative search behavior of the Harmony Search (HS) algorithm.
• To propose a modification to the classical HS algorithm based on theoretical insights.
• To evaluate the efficiency of the modified HS algorithm.

Main Methods:

• Mathematical analysis of population-variance evolution over generations in HS.
• Development of a modified HS algorithm.
• Comparative performance evaluation on 15 unconstrained and 5 constrained benchmark functions.

Main Results:

• The analysis provides insights into the explorative power of HS.
• The proposed modification enhances HS performance.
• The modified HS demonstrates superior final accuracy, convergence speed, and robustness compared to other state-of-the-art algorithms.

Conclusions:

• The theoretical analysis of HS is valuable for understanding its search dynamics.
• The modified HS algorithm offers an efficient and robust solution for optimization problems.
• Further research into theoretical analysis can lead to more effective optimization algorithms.