Light-MILPopt: Solving Large-scale Mixed Integer Linear Programs with Lightweight Optimizer and Small-scale Training Dataset

Published: 16 Jan 2024, Last Modified: 21 Apr 2024ICLR 2024 posterEveryoneRevisionsBibTeX
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Keywords: Large-scale MILP, Learning for Optimization, Lightweight Optimization Framework
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TL;DR: This paper proposes Light-MILPopt that only uses a lightweight optimizer and small-scale training dataset to solve large-scale MILPs.
Abstract: Machine Learning (ML)-based optimization approaches emerge as a promising technique for solving large-scale Mixed Integer Linear Programs (MILPs). However, existing ML-based frameworks suffer from high model computation complexity, weak problem reduction, and reliance on large-scale optimizers and large training datasets, resulting in performance bottlenecks for large-scale MILPs. This paper proposes Light-MILPopt, a lightweight large-scale optimization framework that only uses a lightweight optimizer and small training dataset to solve large-scale MILPs. Specifically, Light-MILPopt can be divided into four stages: Problem Formulation for problem division to reduce model computational costs, Model-based Initial Solution Prediction for predicting and constructing the initial solution using a small-scale training dataset, Problem Reduction for both variable and constraint reduction, and Data-driven Optimization for current solution improvement employing a lightweight optimizer. Experimental evaluations on four large-scale benchmark MILPs and a real-world case study demonstrate that Light-MILPopt, leveraging a lightweight optimizer and small training dataset, outperforms the state-of-the-art ML-based optimization framework and advanced large-scale solvers (e.g. Gurobi, SCIP). The results and further analyses substantiate the ML-based framework's feasibility and effectiveness in solving large-scale MILPs.
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Primary Area: optimization
Submission Number: 2674