An algorithm for mapping the asymmetric Multiple Traveling Salesman Problem onto Colored Petri Nets

Abstract

The Multiple Traveling Salesman Problem is an extension of the famous Traveling Salesman Problem. Finding an optimal solution to the Multiple Traveling Salesman Problem (mTSP) is a difficult task as it belongs to the class of NP-hard problems. The problem becomes more complicated when the cost matrix is not symmetric. In such cases, finding even a feasible solution to the problem becomes a challenging task. In this paper, an algorithm is presented that uses Colored Petri Nets (CPN)-a mathematical modeling language-to represent the Multiple Traveling Salesman Problem. The proposed algorithm maps any given mTSP onto a CPN. The transformed model in CPN guarantees a feasible solution to the mTSP with asymmetric cost matrix. The model is simulated in CPNTools to measure two optimization objectives: the maximum time a salesman takes in a feasible solution and the collective time taken by all salesmen. The transformed model is also formally verified through reachability analysis to ensure that it is correct and is terminating.