Unified Neural Solvers for General TSP and Multiple Combinatorial Optimization Tasks via Problem Reduction and Matrix Encoding
Keywords: Travelling Salesman Problem, Neural Combinatorial Optimization
Abstract: Various neural solvers have been devised for combinatorial optimization (CO), which are often tailored for specific problem types, ranging from TSP, CVRP to SAT, etc. Yet, it remains an open question how to achieve universality regarding problem representing and learning with a general framework. This paper first proposes RedCO, to unify a set of CO problems by reducing them into the general TSP form featured by distance matrices. The applicability of this strategy is dependent on the efficiency of the problem reduction and solution transition procedures, which we show that at least ATSP, HCP, and SAT are readily feasible. The hope is to allow for the effective and even simultaneous use of as many types of CO instances as possible to train a neural TSP solver, and optionally finetune it for specific problem types. In particular, unlike the prevalent TSP benchmarks based on Euclidean instances with 2-D coordinates, our focused domain of general TSP could involve non-metric, asymmetric or discrete distances without explicit node coordinates, which is much less explored in TSP literature while poses new intellectual challenges. Along this direction, we devise two neural TSP solvers with and without supervision to conquer such matrix-formulated input, respectively: 1) MatPOENet and 2) MatDIFFNet. The former is a reinforcement learning-based sequential model with pseudo one-hot embedding (POE) scheme; and the latter is a Diffusion-based generative model with the mix-noised reference mapping scheme. Extensive experiments on ATSP, 2DTSP, HCP- and SAT-distributed general TSPs demonstrate the strong ability of our approaches towards arbitrary matrix-encoded TSP with structure and size variation. Source code and data will be made public.
Primary Area: learning on graphs and other geometries & topologies
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Submission Number: 4469
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