Graph learning assisted multi-objective integer programming

• Main Authors: WU, Yaoxin, SONG, Wen, CAO, Zhiguang, ZHANG, Jie, GUPTA, Abhishek, LIN, Mingyan Simon
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2021
• Subjects: Software Engineering
• Online Access: https://ink.library.smu.edu.sg/sis_research/8138; https://ink.library.smu.edu.sg/context/sis_research/article/9141/viewcontent/Learning_Generalizable_Models_for_Vehicle_Routing_Problems_via_Knowledge_Distillation__2_.pdf
• Institution: Singapore Management University

Objective-space decomposition algorithms (ODAs) are widely studied for solvingmulti-objective integer programs. However, they often encounter difficulties inhandling scalarized problems, which could cause infeasibility or repetitive nondominatedpoints and thus induce redundant runtime. To mitigate the issue, we presenta graph neural network (GNN) based method to learn the reduction rule in the ODA.We formulate the algorithmic procedure of generic ODAs as a Markov decisionprocess, and parameterize the policy (reduction rule) with a novel two-stage GNNto fuse information from variables, constraints and especially objectives for betterstate representation. We train our model with imitation learning and deploy it ona state-of-the-art ODA. Results show that our method significantly improves thesolving efficiency of the ODA. The learned policy generalizes fairly well to largerproblems or more objectives, and the proposed GNN outperforms existing ones forinteger programming in terms of test and generalization accuracy.