Feasibility-Aware Imitation Learning for Benders Decomposition

TL;DR

This paper introduces a feasibility-aware imitation learning method to predict integer variables in Benders decomposition, improving solution time while maintaining accuracy in mixed-integer optimization.

Contribution

It develops a novel imitation learning framework that accounts for feasibility, enhancing Benders decomposition efficiency without sacrificing convergence guarantees.

Findings

Reduces solution time compared to existing imitation learning methods.

Maintains finite convergence and solution accuracy.

Effective in a prototypical case study.

Abstract

Mixed-integer optimization problems arise in a wide range of control applications. Benders decomposition is a widely used algorithm for solving such problems by decomposing them into a mixed-integer master problem and a continuous subproblem. A key computational bottleneck is the repeated solution of increasingly complex master problems across iterations. In this paper, we propose a feasibility-aware imitation learning framework that predicts the values of the integer variables of the master problem at each iteration while accounting for feasibility with respect to constraints governing admissible integer assignments and the accumulated Benders feasibility cuts. The agent is trained using a two-stage procedure that combines behavioral cloning with a feasibility-based logit adjustment to bias predictions toward assignments that satisfy the evolving cut set. The agent is deployed within an agent-based Benders decomposition framework that combines explicit feasibility checks with a time-limited solver computation of a valid lower bound. The proposed approach retains finite convergence properties, as the lower bound is certified at each iteration. Application to a prototypical case study shows that the proposed method improves solution time relative to existing imitation learning approaches for accelerating Benders decomposition, while preserving solution accuracy.