Emami Hojjat, Fardi Mojtaba, Azarnavid Babak
Department of Computer Engineering, University of Bonab, Bonab, Iran.
Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord, Iran.
Sci Rep. 2025 Jul 16;15(1):25675. doi: 10.1038/s41598-025-11626-2.
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.
本文介绍了一种增强季节优化（ESO）算法，该算法显著提高了标准季节优化（SO）算法的搜索性能和求解质量。SO算法在数值和工程优化任务中显示出有前景的结果，但在平衡利用和探索方面存在弱点，导致次优解和早熟收敛。为了解决这些局限性，ESO算法包含四项关键创新：（i）增强局部利用的根扩展算子；（ii）增强种群多样性的野火算子；（iii）强化求解质量和收敛性能的精细竞争与抗性算子；（iv）基于反向学习以避免局部最优。通过与一系列不同的对应优化器进行对比分析，检验了ESO算法的有效性，这些对应优化器包括基础且被高度引用的算法（粒子群优化算法、差分进化算法）、性能最优的算法（协方差矩阵自适应进化策略、局部搜索混合进化策略、随机半径搜索算法、人工蜂群算法、基于阈值的随机优化算法）以及新颖的自然启发式算法（季节优化算法、和谐搜索算法、基于乌鸦行为的优化算法）。基准测试集包括25个数值优化函数和4个工程设计问题。统计结果表明，ESO算法显著优于原始SO算法，并且在收敛性能和求解质量方面与对应优化器相比表现出具有竞争力或更优的性能。我们的主要发现包括：（i）在25个数值函数中的16个以及4个工程设计问题中的3个中，ESO算法是性能最优的算法；（ii）在所有数值基准测试的Friedman检验中，它的平均排名为3.68，在求解数值基准测试方面优于所有对应算法；同时，排名第二的基于阈值的随机优化算法在所有函数上的平均排名为4.5；（iii）ESO算法在移位和复合数值函数中产生了最佳结果；（iv）在1000维数值问题的可扩展性分析测试中，它获得了最佳性能。
