改进鲸鱼优化算法及其在混流U型装配线平衡问题的应用

为提高鲸鱼优化算法的寻优效果和求解稳定性，通过改进算法的种群初始化、局部搜索、越界处理方法和收敛因子，提出一种改进的鲸鱼优化算法 。 采用基于切割法的均匀设计种群初始化方法，改善算法初始种群的均匀性；通过引入基于NEWUOA算法的局部搜索算子，提高算法的局部搜索能力；在算法的越界处理方面，提出一种基于环形区间和随机波动的方式，降低算法陷入局部最优的可能；引入了非线性收敛因子和自适用权重，均衡算法的局部和全局搜索，并进一步增强搜索的精细度。通过7个单模态、多模态以及固定维度的基准测试函数进行了数值仿真实验，验证了改进的鲸鱼优化算法相较于遗传算法、鲸鱼优化算法以及其他改进的鲸鱼优化算法，在寻优效果和求解稳定性方面具有优越性。 针对混流U型装配线平衡问题，考虑最小化装配线的节拍时间，将改进的鲸鱼优化算法用于问题求解；在解码阶段，设计一种基于阈值的解码方法，优化工序的分配过程；最后计算了21个混流装配线算例，结果表明，改进的鲸鱼优化算法在20个算例中求得了更优解，相较于其它算法，节拍时间平均降低3.02%。

Improved Whale Optimization Algorithm and Its Application to Mixed-model U-shaped Assembly Line Balancing Problem

In order to improve the optimization effect and solution stability of the whale optimization algorithm, an improved whale optimization algorithm is proposed by improving the population initialization, local search, out-of-bounds processing method and convergence factor of the algorithm. The uniform design population initialization method based on cutting method is adopted to improve the homogeneity of the initial population of the algorithm; The local search operator based on NEWUOA algorithm is introduced to improve the local search ability of the algorithm; In the aspect of boundary crossing, a method based on annular interval and random fluctuation is proposed to reduce the possibility of the algorithm falling into local optimum; The nonlinear convergence factor and adaptive weight are introduced to balance the local and global search of the algorithm and further enhance the precision of the search. Numerical simulation experiments were carried out on seven single mode, multimodal and fixed dimension benchmark test functions, which verified that the improved whale optimization algorithm has advantages in terms of optimization effect and solution stability compared with genetic algorithm, whale optimization algorithm and other improved whale optimization algorithms. Aiming at the mixed-model U-shaped assembly line balancing problem, the improved whale optimization algorithm is used to solve the problem, considering the minimum cycle time of the assembly line; In the decoding stage, a threshold-based decoding method is designed to optimize the allocation process of tasks; Finally, 21 examples of mixed-model assembly lines are calculated. The results show that the improved whale optimization algorithm obtains better solutions in 20 examples. Compared with other algorithms, the cycle time is reduced by 3.02% on average.