Exploiting Instance and Variable Similarity to Improve Learning-Enhanced Branching

TL;DR

This paper improves learning-enhanced branching in MILP problems by training separate models for similar variables, leveraging instance and variable similarities to achieve faster, more accurate solutions in operational settings.

Contribution

It introduces a novel approach of training multiple ML models for different variable groups based on similarity, enhancing solution quality and efficiency in MILP problems.

Findings

Significantly better gap closures on large-scale SCUC instances.

Improved solution quality with the same training data.

Effective utilization of instance and variable similarity.

Abstract

In many operational applications, it is necessary to routinely find, within a very limited time window, provably good solutions to challenging mixed-integer linear programming (MILP) problems. An example is the Security-Constrained Unit Commitment (SCUC) problem, solved daily to clear the day-ahead electricity markets. Previous research demonstrated that machine learning (ML) methods can produce high-quality heuristic solutions to combinatorial problems, but proving the optimality of these solutions, even with recently-proposed learning-enhanced branching methods, can still be time-consuming. In this paper, we propose a simple modification to improve the performance of learning-enhanced branching methods based on the key observation that, in such operational applications, instances are significantly similar to each other. Specifically, instances typically share the same size and problem structure, with slight differences only on matrix coefficients, right-hand sides and objective function. In addition, certain groups of variables within a given instance are also typically similar to each other. Therefore, unlike previous works in the literature which predicted all branching scores with a single ML model, we propose training separate ML models per variable or per groups of variables, based on their similarity. We evaluate this enhancement on realistic large-scale SCUC instances and we obtain significantly better gap closures than previous works with the same amount of training data.