An Analysis of the Operation Factors of Three PSO-GA-ED Meta-Heuristic Search Methods for Solving a Single-Objective...

Area of Science:

• Computational mathematics
• Optimization algorithms
• Evolutionary computation

Background:

• Nongradient search strategies are crucial for minimizing complex mathematical functions.
• Evolutionary algorithms offer robust approaches to optimization problems.
• Evaluating algorithm efficiency requires analysis of iterations, accuracy, and runtime.

Purpose of the Study:

• To evaluate and compare the efficacy of genetic algorithms (GA), particle swarm optimization (PSO), and differential evolution (DE) for optimizing mathematical functions.
• To assess the impact of parameters like crossover rate, mutation rate, and scaling factor on algorithm performance.
• To determine the most efficient and reliable optimization strategy among the tested methods.

Main Methods:

• Implementation and testing of GA, PSO, and DE algorithms.
• Optimization of 12 diverse mathematical functions (e.g., Easom, Ackley, Rastrigin, Himmelblau's).
• Comparative analysis based on time complexity, number of iterations, accuracy, and runtime.

Main Results:

• Differential evolution (DE) exhibited the lowest time complexity.
• Genetic algorithms (GA) demonstrated the highest temporal complexity.
• Particle swarm optimization (PSO) yielded inconsistent results, indicating low reliability in locating optimal solutions.

Conclusions:

• DE is the most time-efficient algorithm for the tested mathematical optimization tasks.
• GA is computationally intensive, making it less suitable for time-sensitive applications.
• PSO's unreliability necessitates caution when applied to similar optimization problems.