Distributed hybrid method to solve multiple traveling salesman problems

Abstract

The traveling salesman problem (TSP) can be defined as the process of finding the shortest path for a given set of cities, starting from base city, visiting all other cities once, and returning to the base city. However, when we consider some of the real word problems such as Routing of School bus, the methods that solve the TSP are not effective to handle these types of problems since they deal with only one salesman. On the other hand, the multiple traveling salesmen problem (mTSP), which is the generalization of the TSP, is capable of handling and using more than one salesman in real-world problems. In mTSP, m salesmen start from home city, and each one visits a particular set of cities and returns to the home city, so that all cities are visited by one salesman. The objective of mTSP is to minimize the total cost. In this paper, we proposed a distributed hybrid method to solve mTSP which use multiple machines via a web service software architecture to make sure that the result we get is the best. Fundamentally, the first step is to transform the mTSP to standard TSP then apply parallel Ant colony optimization (ACO) with different pheromone exchange (PE) policies which are without PE, with 25% of PE, and with 50% of PE. Moreover, we further enhance the result by using local search techniques. Furthermore, two techniques tested for ant to choose the next city. First technique is to choose 90% from the neighborhood based on probability and 10% from neighborhood. Second technique tested is using the probabilistic equation. In the both techniques, the three PE options have been used. Moreover, a comparison is made between the hybrid method and other methods (NMACO, MACO, and MGA) and found that the hybrid method provides a reduction in cost