Improvement of Optimization using Learning Based Models in Mixed Integer Linear Programming Tasks

TL;DR

This paper introduces a learning-based framework using Graph Neural Networks trained with Behavior Cloning and Reinforcement Learning to generate high-quality initial solutions, significantly reducing optimization time in large-scale MILP problems.

Contribution

It presents a novel approach combining BC and RL to train GNNs for warm-starting MILP solvers, improving efficiency in multi-agent scheduling tasks.

Findings

Reduces optimization time compared to traditional methods

Maintains solution quality and feasibility

Decreases variance in solution times

Abstract

Mixed Integer Linear Programs (MILPs) are essential tools for solving planning and scheduling problems across critical industries such as construction, manufacturing, and logistics. However, their widespread adoption is limited by long computational times, especially in large-scale, real-time scenarios. To address this, we present a learning-based framework that leverages Behavior Cloning (BC) and Reinforcement Learning (RL) to train Graph Neural Networks (GNNs), producing high-quality initial solutions for warm-starting MILP solvers in Multi-Agent Task Allocation and Scheduling Problems. Experimental results demonstrate that our method reduces optimization time and variance compared to traditional techniques while maintaining solution quality and feasibility.