564127c03caab942e503ee6f810f54fd-Supplemental.pdf

This paper solves three NP-hard routing problems, traveling salesman problem (TSP), prize collecting TSP (PCTSP), and capacitated vehicle routing problem (CVRP). This section provides detailed descriptions of PCTSP and CVRP (for TSP, see section 3). The PCTSP is similar to TSP, while there are differences in that we do not have to visit all the nodes and that the destination is not the first node but the depot node, i.e., a tour is not a cycle. Let N be the number of nodes. The problem instance of PCTSP is s = {(xi,λi,µi)}N+1i=1, where the xi R2 is in 2D euclidean coordinates, λi R is the penalty of unvisited node, and µi R is the prize of visited node. The L(π|s) is the tour length, and λ(π|s) is the total penalty of the unvisited nodes.