<p>The multiple traveling salesman problem (mTSP) is an extension of the traveling salesman problem, which involves multiple salespeople visiting a set of cities, with each city being visited only once. It is widely used in logistics distribution, traffic scheduling, and multi robot collaboration, but faces challenges such as high computational complexity, difficult task allocation, and susceptibility to local optimal solutions. Most existing methods focus on finding solutions from scratch, primarily aiming to minimize the total travel distance, with insufficient attention paid to balancing travel costs among salespeople. This article proposes a matrix based multi strategy integrated particle swarm optimization algorithm, which improves efficiency through matrix representation and parallel computing, and introduces a dynamic diversity mechanism to balance local and global search capabilities. In addition, a new fitness evaluation function has been designed to effectively address significant route differences among salespeople. Among the five typical TSP problems, the performance of this algorithm is superior to MPSO, HJSPSO and standard PSO algorithms. It significantly improves solving efficiency and enhances result balance. This study provides an efficient and robust solution for the mTSP problem, which has important theoretical significance and practical application value.</p>