Compact Integer Programs for Depot-Free Multiple Traveling Salesperson Problems

Multiple traveling salesperson problems (mTSP) are a collection of that generalize the classical problem (TSP). In nutshell, an mTSP variant seeks minimum cost m paths visit all vertices given weighted complete graph. This paper introduces novel compact integer programs for depot-free (DFmTSP). fundamental models real scenarios where depots unknown or unnecessary. The proposed adapted to main variants DFmTSP, such as closed paths, open bounding constraints (also known load balance), and minsum minmax objective functions. Some these have O(n2m) binary variables O(n2) constraints, is number salespersons n=|V(G)|. Furthermore, we introduce more with same most its variants. Without losing their compactness, fixed-destination multiple-depots (FD-MmTSP) combination FD-MmTSP fewer than part input, but solution still consists paths. We used off-the-shelf optimization software empirically test over benchmark dataset; tests show meet desirable theoretical properties practical advantages state art.