Notwithstanding the superior performance of the Whale optimization algorithm (WOA) on a wide range of optimization issues, the exploitation in WOA gets more preference during the search process, thereby compromising the solution accuracy and diversity and also increases the chance of premature convergence. In this study, a novel modified WOA (m-SDWOA) is presented where the conventional WOA is combined with the modified mutualism phase of symbiotic organisms search (SOS), \(DE/rand/1/bin\) mutation strategy of differential evolution (DE), and commensalism phase of SOS. A new selection parameter γ is introduced to select between exploration and exploitation phases of the algorithm. This overall arrangement balances the ability of the algorithm to explore or exploit. The algorithm’s efficiency is verified through 42 benchmark functions and IEEE CEC 19 test suite and comparing the results with various state−of-the−art algorithms comprising basic methods, WOA variants, and DE variants. Statistical analyses like Friedman’s test, box plot comparison, and Nemenyi multiple comparison tests are employed to check the proposed algorithm's consistency and statistical superiority. Finally, four real-life engineering design problems have been solved to confirm the problem-solving capability of the proposed m-SDWOA. All these analyses demonstrate the superiority of the proposed algorithm over the compared algorithms.

尽管 Whale 优化算法 (WOA) 在广泛的优化问题上具有卓越的性能，但 WOA 中的开发在搜索过程中获得了更多的偏好，从而影响了解决方案的准确性和多样性，也增加了早熟收敛的机会。在这项研究中，提出了一种新的改良 WOA (m-SDWOA)，其中传统 WOA 与共生生物搜索 (SOS) 的改良共生阶段相结合，\(DE/rand/1/bin\)差异进化 (DE) 的突变策略，以及 SOS 的共生阶段。引入了一个新的选择参数 γ 来在算法的探索和开发阶段之间进行选择。这种整体安排平衡了算法探索或利用的能力。该算法的效率通过 42 个基准函数和 IEEE CEC 19 测试套件进行验证，并将结果与​​各种最先进的算法（包括基本方法、WOA 变体和 DE 变体）进行比较。使用弗里德曼检验、箱线图比较和 Nemenyi 多重比较检验等统计分析来检查所提出算法的一致性和统计优越性。最后，解决了四个实际工程设计问题，以证实所提出的 m-SDWOA 的解决问题的能力。