Particle Swarm Optimization Algorithm for Multi- salesman Problem with Time and Capacity Constraints

Classic multiple traveling salesman problem (MTSP) requires to find the k closed circular paths which minimize the sum of the path lengths, and each vertex is visited only once by a salesman. This paper presents an optimized model for the balanced Multiple-salesman Problem with time and capacity constraints, it requires that a salesman visits each vertex at least once and returns to the starting vertex within given time. The balanced MSP is more widely used than MTSP. We describe a particle swarm optimization algorithm for balanced MSP and explain its simple application in the Post Office Scheduling Problem. We demonstrate the effectiveness of the model and algorithm through a case study.