Multi-stage parameter adjustment to enhance metaheuristics for optimal design

Optimization has been a field of interest in science and engineering and many metaheuristic algorithms have been developed and applied to various problems. These, however, often require parameter adjustments to achieve a suitable performance. This paper proposes a new framework to improve the performance of metaheuristics, termed Multi-Stage Parameter Adjustment (MSPA), which integrates Metaheuristics, an efficient sampling approach, and Machine Learning. The sampling method utilized here known as Extreme Latin Hypercube Sampling (XLHS) is used to divide parameter spaces into equally probable subspaces, ensuring better coverage due to the continuous nature of variables. These parameters are then improved through a primary optimizer for different numbers of variables using a selected benchmark problem. The resultant data are utilized to train an artificial neural network (ANN). The adjusted metaheuristic algorithm is subsequently employed for structural optimization. In this respect, the input data for the ANN comprise the average of the lower and upper bounds of each subspace and the number of variables, while output data are the optimized values obtained using the Primary Optimizer, which does not require extensive parameter adjustments. To evaluate the efficiency of the proposed framework in comparison with the original version and some other algorithms in the literature, the parameters of Particle Swarm Optimization, chosen for its widespread applicability, are adjusted and tested against some mathematical benchmarks, two engineering, and two truss structural optimization problems. Results demonstrate the efficacy of the presented framework in enhancing the performance of metaheuristic algorithms, particularly in the optimal design of truss structures.