Graph learning assisted multi-objective integer programming
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 t...
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| Main Authors: | , , , , , |
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| Format: | text |
| Language: | English |
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Institutional Knowledge at Singapore Management University
2021
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| 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 |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | 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. |
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