Heuristics and Learning Models for Dubins MinMax Traveling Salesman Problem

Abstract

This paper addresses a MinMax variant of the Dubins multiple traveling salesman problem (mTSP). This routing problem arises naturally in mission planning applications involving fixed-wing unmanned vehicles and ground robots. We first formulate the routing problem, referred to as the one-in-a-set Dubins mTSP problem (MD-GmTSP), as a mixed-integer linear program (MILP). We then develop heuristic-based search methods for the MD-GmTSP using tour construction algorithms to generate initial feasible solutions relatively fast and then improve on these solutions using variants of the variable neighborhood search (VNS) metaheuristic. Finally, we also explore a graph neural network to implicitly learn policies for the MD-GmTSP using a learning-based approach; specifically, we employ an S-sample batch reinforcement learning method on a shared graph neural network architecture and distributed policy networks to solve the MD-GMTSP. All the proposed algorithms are implemented on modified TSPLIB instances, and the performance of all the proposed algorithms is corroborated. The results show that learning based approaches work well for smaller sized instances, while the VNS based heuristics find the best solutions for larger instances.

Path Planning Technique for Mobile Robots: A Review

“…Path planning remains a central concern in the field of robotics [223], and in Table 15, we undertake a comparative analysis to elucidate the distinctions and commonalities between this paper and other review articles, based on this we obtained the analysis in Figure 12. This paper distinguishes itself with its contemporaneity, as it incorporates recent literature for 60.9% and 86.6% of the 254 sources within the last 5 and 10 years, respectively.…”