Edge Matters: A Predict-and-Search Framework for MILP based on Sinkhorn-Nomalized Edge Attention Networks and Adaptive Regret-Greedy Search
Keywords: MILP; EGAT; Sinkhorn; Adaptive Trust Region
TL;DR: We introduce EGAT, using node and edge features with Sinkhorn normalization and an adaptive trust-region algorithm, achieving better accuracy and efficiency than Gurobi and SCIP in COP.
Abstract: Predict-and-search is increasingly becoming the predominant framework for solving Mixed-Integer Linear Programming (MILP) problems through the application of ML algorithms. Traditionally, MILP problems are represented as bipartite graphs, wherein nodes and edges encapsulate critical information pertaining to the objectives and constraints. However, existing ML approaches have primarily concentrated on extracting features from nodes while largely ignoring those associated with edges. To bridge this gap, we propose a novel framework named \model{} which leverages a graph neural network SKEGAT that integrates both node and edge features. Furthermore, we design an adaptive Regret-Greedy algorithm to break the barriers of the problem scale and hand-crafted tuning. Experiments across a variety of combinatorial optimization problems show that \model{} surpasses current SOTA algorithms, delivering notable enhancements in both solution accuracy and computational efficiency.
Primary Area: optimization
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Submission Number: 13150
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