A Reoptimization Framework for Mixed Integer Linear Programming with Dynamic Parameters

Sijia Zhang, Shuli Zeng, Fei Shang, Feng Wu, Xiangyang Li

Keywords: Mixed Integer Linear Programming; reoptimization;

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 environments often require rapid responses to slight changes in parameters, with time-critical demands for solutions. While reoptimization techniques have been explored for Linear Programming (LP) and specific MILP problems, their effectiveness in 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 the high confidence solving space for modified MILPs to contain high-quality solutions. Based on the prediction results, we fix a part of variables to apply the prediction intervals and use the Thompson Sampling algorithm to determine the set of variables to fix by updating the Beta distributions based on 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 feasible solutions under strict time limits and demonstrating faster convergence with smaller primal gaps in the early stages of solving.

Primary Area: optimization

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Submission Number: 4232