Abstract: An improved Particle Swarm Optimization (PSO) algorithm based on Hamming distance was proposed to solve the discrete problems. The basic idea and process of traditional PSO was retained, and a new speed representation based on Hamming distance was defined. Meanwhile, in order to make the algorithm be more efficient and avoid the iterative process falling into the local optimum, new operators named 2-opt and 3-opt were designed, and the random greedy rule was also used to improve the quality of the solution and speed up the convergence. At the later period of the algorithm, in order to increase the global search ability of the particles in the whole solution space, a part of particles was regenerated to re-explore the solution space. Finally, a number of TSP standard examples were used to verify the effectiveness of the proposed algorithm. The experimental results show that the proposed algorithm can find the historical optimal solution for small scale TSP; for large-scale TSP, for example, the city number is more than 100, satisfactory solutions can also be found, and the deviations between the known and the optimal solutions are small, usually within 5%.

Key words: Particle Swarm Optimization (PSO) algorithm, Hamming distance, random greedy rule, 2-opt operator, 3-opt operator, Traveling Salesman Problem (TSP)

摘要： 针对传统粒子群算法不适合求解离散型问题，提出一种基于汉明距离的改进粒子群算法。该算法保留了粒子群算法的基本思想和流程，并基于汉明距离为粒子定义了一种新型的速度表示。同时，为了使算法寻优能力更高、避免迭代过程陷入局部最优无法跳出，设计了2-opt和3-opt算子，结合随机贪婪规则，使求解质量更高、收敛更快。在算法后期，为了提高粒子在整体解空间中的全局搜索能力，采用一部分粒子重新生成的方式去重新探索解空间。为了验证算法的有效性，采用了众多旅行商问题（TSP）标准算例进行测试。实验结果表明，对于小规模TSP，该算法可以找到历史最优解；对于大规模TSP，如城市数在100以上的问题，也可以找到满意解，与已知最优解之间偏差度较小，通常在5%以内。

关键词: 粒子群优化算法, 汉明距离, 随机贪婪规则, 2-opt算子, 3-opt算子, 旅行商问题