Minimizing Entropy to Discover Good Solutions to Recurrent Mixed Integer Programs

TL;DR

This paper introduces an entropy-based online heuristic for solving recurring mixed-integer programs efficiently, demonstrating significant speedups and improved solutions on a real-world locomotive assignment problem.

Contribution

It presents a novel entropy minimization approach that requires minimal data and tuning, enhancing solution speed and quality for recurring MIP problems.

Findings

Achieved an order of magnitude speedup over CPLEX

Found solutions with less than 2% optimality gap

Discovered better solutions than CPLEX on some instances

Abstract

Current state-of-the-art solvers for mixed-integer programming (MIP) problems are designed to perform well on a wide range of problems. However, for many real-world use cases, problem instances come from a narrow distribution. This has motivated the development of specialized methods that can exploit the information in historical datasets to guide the design of heuristics. Recent works have shown that machine learning (ML) can be integrated with an MIP solver to inject domain knowledge and efficiently close the optimality gap. This hybridization is usually done with deep learning (DL), which requires a large dataset and extensive hyperparameter tuning to perform well. This paper proposes an online heuristic that uses the notion of entropy to efficiently build a model with minimal training data and tuning. We test our method on the locomotive assignment problem (LAP), a recurring real-world problem that is challenging to solve at scale. Experimental results show a speed up of an order of magnitude compared to a general purpose solver (CPLEX) with a relative gap of less than 2%. We also observe that for some instances our method can discover better solutions than CPLEX within the time limit.