Enhancing the Arithmetic Optimization Algorithm Using Fuzzy Parameter Adaptation and Novel Evolutionary Operators

Abstract

This paper presents an enhanced version of the Arithmetic Optimization Algorithm (AOA), a mathematically inspired metaheuristic optimization method that has received significant attention in recent literature. The proposed Improved AOA (IAOA) integrates three novel mechanisms to address the limitations of the original AOA. First, a new metric-Dispersion of Solutions (DOS)-is introduced to dynamically estimate the algorithm's convergence behavior, enabling adaptive control over key parameters. Second, a fuzzy parameter adaptation scheme is developed to regulate the Math Optimizer Accelerated (MOA) parameter, providing a flexible and intelligent mechanism for balancing exploration and exploitation. Third, chaotic and triangular search operators are incorporated into the population update process to enhance diversity and prevent premature convergence. Theoretical analysis and extensive empirical evaluations on eighteen benchmark test functions and two real-world engineering optimization problems demonstrate that the proposed IAOA outperforms the original AOA in terms of convergence speed. These results confirm the effectiveness and generalizability of the proposed enhancements.