Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimization

Deep reinforcement learning (DRL)-based combinatorial optimization (CO) methods (i.e., DRL-NCO) have shown significant merit over the conventional CO solvers as DRL-NCO is capable of learning CO solvers without supervised labels attained from the verified solver. This paper presents a novel training scheme, Sym-NCO, that achieves significant performance increments to existing DRL-NCO methods. Sym-NCO is a regularizer-based training scheme that leverages universal symmetricities in various CO problems and solutions. Imposing symmetricities such as rotational and reflectional invariance can greatly improve generalization capability of DRL-NCO as symmetricities are invariant features shared by certain CO tasks. Our experimental results verify that our Sym-NCO greatly improves the performance of DRL-NCO methods in four CO tasks, including traveling salesman problem (TSP), capacitated vehicle routing problem (CVRP), prize collecting TSP (PCTSP), and orienteering problem (OP), without employing problem-specific techniques. Remarkably, Sym-NCO outperformed not only the existing DRL-NCO methods but also a competitive conventional solver, the iterative local search (ILS), in PCTSP at 240 times faster speed.