Reinforcement Learning with Combinatorial Actions: An Application to Vehicle Routing

TL;DR

This paper introduces a deep reinforcement learning framework for combinatorial action spaces, applying it to vehicle routing and achieving competitive results with traditional optimization methods.

Contribution

It formulates action selection as a mixed-integer optimization problem within deep RL, specifically addressing large combinatorial action spaces in vehicle routing.

Findings

Achieves an average gap of 1.7% on standard CVRP instances.

Framework is competitive with state-of-the-art optimization methods.

Demonstrates effectiveness of combining RL with combinatorial optimization.

Abstract

Value-function-based methods have long played an important role in reinforcement learning. However, finding the best next action given a value function of arbitrary complexity is nontrivial when the action space is too large for enumeration. We develop a framework for value-function-based deep reinforcement learning with a combinatorial action space, in which the action selection problem is explicitly formulated as a mixed-integer optimization problem. As a motivating example, we present an application of this framework to the capacitated vehicle routing problem (CVRP), a combinatorial optimization problem in which a set of locations must be covered by a single vehicle with limited capacity. On each instance, we model an action as the construction of a single route, and consider a deterministic policy which is improved through a simple policy iteration algorithm. Our approach is competitive with other reinforcement learning methods and achieves an average gap of 1.7% with state-of-the-art OR methods on standard library instances of medium size.