一种基于思维创新策略改进的鲸鱼迁徙算法及应用

An Improved Whale Migration Algorithm Based on Innovative Thinking Strategies and Its Application

摘要: 针对鲸鱼迁徙算法(WMA)在求解复杂优化问题时难以有效协调全局探索与局部开发，导致易陷入局部最优且收敛精度不足的问题，本文提出了一种基于思维创新策略改进的鲸鱼迁徙算法(TWMA)。该算法在WMA的基础上引入思维创新策略(TIS)，通过模拟人类认知的“信息事件”、“知识深度”及“想象力”机制，构建历史最优解记忆库，并利用正切函数的非线性突变特性及自适应参数，增强了种群多样性并赋予算法在收敛停滞时跳出局部极值的能力。为验证改进算法的有效性，本文采用CEC2022基准函数集进行仿真测试，并将TWMA与原始WMA及其他算法进行对比。仿真结果表明，TWMA在多数测试函数上的寻优精度、收敛速度及鲁棒性均优于对比算法。最后，将TWMA应用于行星轮系设计工程优化问题，结果进一步证实了该算法在解决非线性约束工程问题上的可行性与优越性。

Abstract: To address the problem that the Whale Migration Algorithm (WMA) struggles to effectively coordinate global exploration and local exploitation when solving complex optimization problems, leading to susceptibility to local optima and insufficient convergence accuracy, this paper proposes an improved Whale Migration Algorithm (TWMA) based on a Thinking Innovation Strategy (TIS). This algorithm introduces a Thinking Innovation Strategy (TIS) to WMA, simulating the mechanisms of “information events,” “knowledge depth,” and “imagination” in human cognition to construct a historical optimal solution memory bank. Furthermore, it utilizes the nonlinear mutation characteristics of the tangent function and adaptive parameters to enhance population diversity and endow the algorithm with the ability to escape local optima when convergence stalls. To verify the effectiveness of the improved algorithm, simulation tests are conducted using the CEC2022 benchmark function set, and TWMA is compared with the original WMA and other algorithms. Simulation results show that TWMA outperforms the compared algorithms in terms of optimization accuracy, convergence speed, and robustness on most test functions. Finally, TWMA is applied to the engineering optimization problem of planetary gear train design, and the results further confirm the feasibility and superiority of this algorithm in solving nonlinearly constrained engineering problems.