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

-- 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. T o 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 T ask 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. I. INTRODUCTION Mixed Integer Linear Programs (MILPs) serve as a fundamental framework for combinatorial optimization problems, facilitating solutions across a wide range of planning and scheduling tasks in logistics [1], construction [2] and manufacturing [3].