Adaptive Constrained Optimization for Neural Vehicle Routing

Chengrui Gao, Haopu Shang, Yuyang Jiang, Ke Xue, Weiyong Yang, Chao Qian

Keywords: Neural combinatorial optimization, Reinforcement learning, Constrained optimization

Abstract: Neural solvers have shown remarkable success in tackling Vehicle Routing Problems (VRPs). However, their application to scenarios with complex real-world constraints is still at an early stage. Recent works successfully employ variants of the Lagrange multiplier method to handle such constraints, but their limitation lies in the use of a uniform multiplier across all problem instances, overlooking the fact that the difficulty of satisfying constraints varies significantly across instances. To address this limitation, we propose an instance-level adaptive constrained optimization framework that reformulates the Lagrangian dual problem by assigning each instance its own multiplier. To efficiently optimize this new problem, we design a multiplier-conditioned policy that solves instances with a controllable level of constraint awareness, which effectively decouples policy optimization from the optimization of multipliers. By leveraging this conditioned policy, we customize the optimization of multipliers for each test instance by adapting to its particular constraint violations. Experimental results on the Travelling Salesman Problem with Time Window (TSPTW), and TSP with Draft Limit (TSPDL) show that our method exhibits advantages compared to the strong solver LKH3 and significantly outperforms state-of-the-art neural methods.

Primary Area: Optimization (e.g., convex and non-convex, stochastic, robust)

Submission Number: 16560