Neural Deconstruction Search for Vehicle Routing Problems

Autoregressive construction approaches generate solutions to vehicle routing problems in a step-by-step fashion, leading to high-quality solutions that are nearing the performance achieved by handcrafted, operations research techniques. In this work, we challenge the conventional paradigm of sequential solution construction and introduce an iterative search framework where solutions are instead deconstructed by a neural policy. Throughout the search, the neural policy collaborates with a simple greedy insertion algorithm to rebuild the deconstructed solutions. Methods that can learn to solve complex optimization problems have the potential to transform decision-making processes across virtually all domains. It is therefore unsurprising that learningbased optimization approaches have garnered significant attention and yielded substantial advancements (Bello et al., 2016; Kool et al., 2019; Kwon et al., 2020). Notably, reinforcement learning (RL) approaches are particularly promising because they do not rely on a pre-defined training set of representative solutions and can develop new strategies from scratch for novel optimization problems. These methods generally construct solutions incrementally through a sequential decision-making process and have been successfully applied to various vehicle routing problems. Despite recent progress, learning-based methods for combinatorial optimization (CO) problems usually fall short of outperforming the state-of-the-art techniques from the operations research (OR) community. For instance, while some new construction approaches for the capacitated vehicle routing problem (CVRP) have surpassed the LKH3 solver (Helsgaun, 2000), they still struggle to match the performance of the state-of-the-art HGS solver (Vidal et al., 2012), particularly for larger instances with over 100 nodes. One reason for this is their inability to explore as many solutions as traditional approaches within the same amount of time.