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Integrated integer programming and decision diagram search tree with an application to the maximum independent set problem

Abstract

We propose an optimization framework which integrates decision diagrams (DDs) and integer linear programming (ILP) to solve combinatorial optimization problems. The hybrid DD-ILP approach explores the solution space based on a recursive compilation of relaxed DDs and incorporates ILP calls to solve subproblems associated with DD nodes. The selection of DD nodes to be explored by ILP technology is a significant component of the approach. We show how supervised machine learning can be useful to detect, on-the-fly, a subproblem structure for ILP technology. We use the maximum independent set problem as a case study. Computational experiments show that, in presence of suitable problem structure, the integrated DD-ILP approach can exploit complementary strengths and improve upon the performance of both a stand-alone DD solver and an ILP solver in terms of solution time and number of solved instances.

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Notes

  1. 1.

    This set of instances is available at https://github.com/jaimegonzalezj/Instances-MISP-DDILP-paper.git

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Acknowledgements

We thank the anonymous referees for providing thoughtful, constructive and detailed comments which helped to improve this work.

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Correspondence to Jaime E. González.

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González, J.E., Cire, A.A., Lodi, A. et al. Integrated integer programming and decision diagram search tree with an application to the maximum independent set problem. Constraints (2020). https://doi.org/10.1007/s10601-019-09306-w

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Keywords

  • Decision diagrams
  • Integrated methods
  • Integer linear programming
  • Hybrid optimization
  • Supervised learning