Rethinking Neural Combinatorial Optimization for Vehicle Routing Problems with Different Constraint Tightness Degrees

TL;DR

This paper analyzes how neural combinatorial optimization methods perform under different constraint tightness levels in vehicle routing problems, revealing overfitting issues and proposing a new training scheme with a multi-expert module for better adaptability.

Contribution

It introduces an efficient training scheme and a multi-expert module to improve NCO performance across varying constraint tightness degrees in vehicle routing problems.

Findings

Existing NCO methods overfit the capacity constraint.

Proposed method overcomes overfitting and adapts to various constraints.

Experimental results show superior performance on CVRP and CVRPTW.

Abstract

Recent neural combinatorial optimization (NCO) methods have shown promising problem-solving ability without requiring domain-specific expertise. Most existing NCO methods use training and testing data with a fixed constraint value and lack research on the effect of constraint tightness on the performance of NCO methods. This paper takes the capacity-constrained vehicle routing problem (CVRP) as an example to empirically analyze the NCO performance under different tightness degrees of the capacity constraint. Our analysis reveals that existing NCO methods overfit the capacity constraint, and they can only perform satisfactorily on a small range of the constraint values but poorly on other values. To tackle this drawback of existing NCO methods, we develop an efficient training scheme that explicitly considers varying degrees of constraint tightness and proposes a multi-expert module to learn a generally adaptable solving strategy. Experimental results show that the proposed method can effectively overcome the overfitting issue, demonstrating superior performances on the CVRP and CVRP with time windows (CVRPTW) with various constraint tightness degrees.