An enhanced seasons optimization algorithm for numerical optimization and engineering design

This paper introduces an Enhanced Seasons Optimization (ESO) algorithm that significantly enhances the search performance and solution quality of the standard Seasons Optimization (SO) algorithm. The SO shows promising results for numerical and engineering optimization tasks, but has weaknesses in balancing exploitation and exploration, resulting in suboptimal solutions and premature convergence. To address these limitations, the ESO incorporates four key innovations: (i) a root spreading operator which enhances local exploitation, (ii) a wildfire operator that enhances the diversity of population, (iii) refined competition and resistance operators that strengthen solution quality and convergence performance, and (iv) opposition-based learning to avoid local optimums. The effectiveness of the ESO algorithm is examined through a comparative analysis against a diverse set of counterpart optimizers, including foundational and highly cited algorithms (PSO, DE), top-performing algorithms (CMAES, LSHES, RRTO, ALA, THRO), and novel nature-inspired algorithms (SO, HO, CBKA). The set of benchmarks comprises 25 numerical optimization functions and 4 engineering design problems. Statistical results demonstrate that the ESO significantly outperforms the original SO algorithm and exhibits competitive or superior performance compared to the counterpart optimizers regarding convergence performance and solution quality. Our key findings include: (i) ESO is the top-performing algorithm in 16 out of 25 of the numerical functions and 3 out of 4 engineering design problems; (ii) it achieved an average ranking of 3.68 in the Friedman test on all numerical benchmarks, outperforming all counterpart algorithms in solving numerical benchmarks; Meanwhile, the second-ranked THRO algorithm attains the average ranking of 4.5 on all functions; (iii) ESO generated the best results in shifted and composite numerical functions, and (iv) it obtained the best performance in the scalability analysis test on 1000-dimensional numerical problems.