Learning to control inexact Benders decomposition via reinforcement learning

TL;DR

This paper introduces a reinforcement learning approach to adaptively control the optimality gap in inexact generalized Benders decomposition, significantly reducing solution times for large-scale mixed-integer problems.

Contribution

It develops an RL-based policy to dynamically determine optimality gaps in inexact GBD, improving efficiency over traditional fixed-gap methods.

Findings

RL-iGBD reduces solution time substantially.

The learned policy adapts to problem features and solution progress.

In experiments, RL-iGBD outperforms standard approaches.

Abstract

Benders decomposition (BD), along with its generalized version (GBD), is a widely used algorithm for solving large-scale mixed-integer optimization problems that arise in the operation of process systems. However, the off-the-shelf application to online settings can be computationally inefficient due to the repeated solution of the master problem. An approach to reduce the solution time is to solve the master problem to local optimality. However, identifying the level of suboptimality at each iteration that minimizes the total solution time is nontrivial. In this paper, we propose the application of reinforcement learning to determine the best optimality gap at each GBD iteration. First, we show that the inexact GBD can converge to the optimal solution given a properly designed optimality gap schedule. Next, leveraging reinforcement learning, we learn a policy that minimizes the total solution time, balancing the solution time per iteration with optimality gap improvement. In the resulting RL-iGBD algorithm, the policy adapts the optimality gap at each iteration based on the features of the problem and the solution progress. In numerical experiments on a mixed-integer economic model predictive control problem, we show that the proposed RL-enhanced iGBD method achieves substantial reductions in solution time.