Graph-Based Imitation and Reinforcement Learning for Efficient Benders Decomposition

TL;DR

This paper presents a graph neural network-based agent that accelerates Benders Decomposition by combining imitation learning and reinforcement learning, achieving significant computational time reductions in case studies.

Contribution

Introduces a novel graph-based agent trained with IL and RL to improve Benders Decomposition efficiency, incorporating a verification mechanism for solution quality.

Findings

Reduces solution time by 42% in a mixed-integer nonlinear program.

Achieves 23% time reduction in irrigation scheduling without losing water efficiency.

Demonstrates effectiveness across two diverse case studies.

Abstract

This work introduces an end-to-end graph-based agent for accelerating the computational efficiency of Benders Decomposition. The agent's policy is parameterized by a graph neural network which takes as input a bipartite graph representation of the master problem and proposes a candidate solution. The agent is trained using a two-stage approach that combines imitation (IL) and reinforcement learning (RL). IL is used to mimic a solver and obtain a warm-start policy which is then finetuned using RL with a reward signal that balances feasibility and computational efficiency. We augment the agent with a verification mechanism that checks the agent's prediction for feasibility and solution quality. The framework is evaluated in two case studies: (i) an illustrative mixed-integer nonlinear program, where it reduces the solution time by 42% without loss of solution quality, and (ii) a closed-loop irrigation scheduling problem, where it achieves a 23% time reduction without compromising water use efficiency.