Don't Restart, Just Reuse: Reoptimizing MILPs with Dynamic Parameters

Sijia Zhang, Shuli Zeng, Shaoang Li, Feng Wu, Shaojie Tang, Xiangyang Li

TL;DR: This paper introduces VP-OR, a two-stage reoptimization framework for MILP with dynamic parameters. It uses GNN for variable prediction and Thompson Sampling for refining solutions, finding better solutions under strict time limits.

Abstract:

Many real-world applications, such as logistics, routing, scheduling, and production planning, involve dynamic systems that require continuous updates to solutions for new Mixed Integer Linear Programming (MILP) problems.
These systems often require rapid updates to their solutions to accommodate slight modifications in constraints or objectives introduced by evolving conditions.
While reoptimization techniques have been explored for Linear Programming (LP) and certain specific MILP problems, their effectiveness in addressing general MILP is limited. In this work, we propose a two-stage reoptimization framework for efficiently identifying high-quality feasible solutions. Specifically, we first utilize the historical solving process information to predict a high confidence solution space for modified MILPs, which is likely to contain high-quality solutions. Building on the prediction results, we fix a part of variables within the predicted intervals and apply the Thompson Sampling algorithm to determine which variables to fix. This is done by updating the Beta distributions based on the solutions obtained from the solver. Extensive experiments across nine reoptimization datasets show that our VP-OR outperforms the state-of-the-art methods, achieving higher-quality solutions under strict time limits.

Lay Summary: Dynamic planning systems (e.g., delivery routing or factory scheduling) often require immediate updates when conditions change. Traditional methods respond too slowly to disruptions like traffic jams or new orders. Our approach has two key steps: First, it predicts promising solution areas by learning from historical decision patterns. Second, it intelligently tests critical choices through adaptive trial-and-error. Validated across logistics and manufacturing scenarios, our method generates high-quality plans faster than state-of-the-art techniques. This enables minute-level production rescheduling, and faster emergency response routing.

Primary Area: Optimization->Discrete and Combinatorial Optimization

Keywords: Mixed Integer Linear Programming; reoptimization;

Submission Number: 6142