Comparative analysis of direct search methods for material design optimization

This paper contributes to the field of optimization for periodic composite material design by systematically evaluating the performance of four direct search algorithms: greedy, simulated annealing (SA), genetic algorithms (GA), and particle swarm optimization (PSO). The central goal is to determine the optimal arrangement of two material domains inside a representative volume element (RVE) while respecting the constraint that half volume of the domains is composed of a specific material, with the effective shear modulus as the objective function. The main contribution of this work is the detailed comparison of these algorithms in terms of success rates and computational efficiency, providing critical insights into their suitability for different problem scales. For a small-scale problem (16 cells), PSO achieves a 100% success rate, while SA demonstrates over 90% success but at a higher computational cost. The greedy algorithm, despite its simplicity, achieves a 72% success rate with the lowest computational effort, requiring an average of 256 objective function evaluations. GA, however, exhibits the lowest success rate at 52% and requires the highest average number of evaluations (5003.2). Furthermore, the paper extends the analysis to a more complex problem (36 cells), where the adaptability and efficiency of the algorithms are tested. This investigation highlights the trade-offs between algorithmic complexity, success rate, and computational cost, offering practical guidelines for selecting suitable optimization methods based on problem size and characteristics.