Abstract: Aiming at the shortcomings of gray wolf optimizer in solving optimization problems, such as slow convergence speed and weak global search ability, Chebyshev and wolf swarm cooperative attack strategy of grey wolf optimizer (CCA-GWO) is proposed and it is successfully applied to PID (proportion integration differen-tiation) parameter optimization. Firstly, by comparing the advantages and disadvantages of three chaotic maps, Chebyshev map is used to initialize the algorithm to enhance the diversity of initial solutions. Secondly, in order to balance the global exploration and local mining ability of the algorithm, a new nonlinear strategy is proposed to modify the control parameters [A] and [C] and the position update equation by simulating the alternate behavior of the first wolf and the second wolf when the gray wolf group is hunting. Finally, the improved algorithm is applied to PID parameter optimization. 8 benchmark functions are tested in 10, 30 and 100 dimensions, and the improved algorithm is compared with BOA, MFO, ASO, MVO, WOA and GWO. Numerical results show that CCA-GWO not only has better optimization and stability in solving benchmark functions of different dimensions, but also has better optimization performance than 6 meta-heuristic algorithms in PID parameter optimization.

Key words: meta-heuristic algorithms, gray wolf optimizer, wolf swarm cooperative attack strategy, Chebyshev map, multi-dimensional function optimization, PID parameter optimization

摘要： 针对灰狼优化算法（GWO）在求解优化问题时收敛速度慢和全局搜索能力弱的缺点，提出一种基于Chebyshev融合狼群协同围攻策略的改进GWO算法（CCA-GWO）并成功应用于PID参数优化。首先，通过对比三种混沌映射优缺点并最终将Chebyshev映射用于算法初始化中以增强初始解的多样性；其次，为平衡算法的全局勘探和局部开采能力，通过模拟灰狼群狩猎时头狼和次头狼的交替行为，提出一种新的非线性策略对控制参数[A]和[C]及位置更新方程进行修正；最后，将改进算法应用于PID参数优化。通过8组基准测试函数在10维、30维和100维下进行实验，并与BOA、MFO、ASO、MVO、WOA、GWO进行对比，数值实验结果表明，CCA-GWO不仅在求解不同维度的基准测试函数上具有更好的寻优性和稳定性，而且在PID参数优化中相较于6种元启发式算法表现出更好的优化性能。

关键词: 元启发式算法；灰狼算法, 狼群协同围攻策略；Chebyshev映射；多维函数优化；PID参数优化