鸽群优化(Pigeon-Inspired Optimization，PIO)算法是一种通过研究鸽群归巢行为总结出的新型仿生智能优化算法，具有原理简单、调参少、易于实现等优点，故而受到国内外学者的广泛关注。虽然鸽群优化算法有其自身的优势，但是也存在易于早熟收敛，陷入局部最优和求解精度低的不足。本文针对鸽群优化算法存在的问题，提出了基于模糊交叉变异算子和基于正态分布衰减惯性权重的两种改进鸽群优化算法，并将改进算法应用到旅行商问题中，具体研究工作如下： (1) 在对传统鸽群优化算法进行深入研究的基础上，针对鸽群信息之间交互不足且易于早熟收敛、过早陷入局部最优等不足，考虑到模糊交叉变异算子有利于种群之间的信息交换，提高鸽子的种群多样性，扩展种群的全局搜索范围等优势，提出了一种基于模糊交叉变异算子的改进鸽群优化算法。仿真实验表明：改进算法在求解精度和收敛速度方面均有了很大改进，算法的有效性和全局寻优能力也得到相应的提高，同时，有效地避免了传统鸽群过早陷入局部最优的状况。 (2) 考虑到传统鸽群优化算法更易在大范围内搜索解的优势，为平衡局部搜索能力和全局搜索能力，引入正态分布衰减惯性权重，同时通过加入非线性衰减学习因子来调节鸽群向全局优秀鸽子学习的能力，减少算法因局部极值对优化解的干扰。进而提出了一种基于正态分布衰减惯性权重的改进鸽群优化算法。仿真实验表明：改进算法在求解精度、跳出局部最优等方面都优于其他3种算法。 (3) 利用测试函数对两种改进算法进行验证，结果表明两种算法都具有很好的寻优能力，基于模糊交叉变异算子的改进鸽群优化算法和基于正态分布衰减惯性权重的改进鸽群优化算法对于不同的问题有不同的适用性。其次，将两种改进算法应用于求解旅行商问题中，仿真实验表明两种改进算法比其他3种算法在克服早熟现象和寻优结果的精度以及时间效率方面显示出相对较好的优越性，充分论证了改进算法的有效性和可行性。

Pigeon-inspired Optimization (PIO) algorithm is a new bionic intelligent optimization algorithm summarized by studying the homing behavior of pigeons, which has the advantages of simple principle, few parameters and easy to implement, so it has been widely concerned by scholars at home and abroad. Although the pigeon-inspired optimization algorithm has its own advantages, there are still problems such as tending to converge early, falling into local optimization, and low solution accuracy. In this paper, aiming at the existing problem that pigeon-inspired optimization algorithm, two improved pigeon-inspired algorithms based on crossover mutation operators and normal distribution decay inertial weight, and the improved algorithms were applied to TSP problems. The specific research work is as follows:

(1) On the basis of the in-depth exploration of the traditional pigeon herd optimization algorithm, aiming at the insufficient interaction of information between pigeons, and the inability to converge prematurely and fall into local optimization too early, etc., considering that the crossover mutation operators is conducive to information exchange between populations, improving the population diversity of pigeons, and expanding the global search range of the population, Fuzzy crossover mutation operators pigeon-inspired optimization (FCMPIO) algorithm based on crossover mutation operators was proposed. Simulation experiments show that the improved algorithm has greatly improved in terms of solution precision and convergence speed, the effectiveness of the algorithm and global search ability of the algorithm have also been correspondingly improved, at the same time, the traditional pigeons has been effectively avoided from falling into the local optimal condition prematurely.

(2) Considering the advantages of the traditional pigeon herd optimization algorithm to search for solutions in a small range, in order to balance the local search ability and the global search ability, the normal distribution decay inertial weight is introduced, and the learning ability of the pigeons to the global optimal pigeon is adjusted by adding a nonlinear decay learning factor, which reduces the interference of the algorithm on the optimized solution due to local extremums, an improved pigeon herd optimization (NDWPIO) algorithm based on normal distribution decay inertial weight was proposed. Simulation experiments show that the improved algorithm is better than the other three algorithms in terms of solving accuracy and jumping out of local optimization.

(3) The test functions were used to test the two improved algorithms, and the results show that both algorithms have well optimization ability, FCMPIO and NDWPIO have different applicability to different problems. Secondly, the two improved algorithms were applied to solve TSP problems, and simulation experiments show that the two improved algorithms are better than the other three algorithms in overcoming precocious puberty and the accuracy of the optimization results and time efficiency. The effectiveness and feasibility of the improved algorithms are fully demonstrated.

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