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Strengthening Relaxed Decision Diagrams for Maximum Independent Set Problem: Novel Variable Ordering and Merge Heuristics

Authors Mohsen Nafar , Michael Römer

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Author Details

Mohsen Nafar
  • Bielefeld University, Germany
Michael Römer
  • Bielefeld University, Germany

Funding

This research was funded by the Return Programme of the Federal State of North Rhine Westphalia (NRW Rückkehrprogramm).

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Mohsen Nafar and Michael Römer. Strengthening Relaxed Decision Diagrams for Maximum Independent Set Problem: Novel Variable Ordering and Merge Heuristics. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.CP.2024.21

Abstract

Finding high-quality bounds is key to devising efficient exact solution approaches for Discrete Optimization (DO) problems. To this end, Decision Diagrams (DDs) provide strong and generic bounding mechanisms. This paper focuses on so-called relaxed DDs which, by merging nodes, over-approximate the solution space of DO problems and provide dual bounds the quality of which hinges upon the ordering of the variables in the DD compilation and on the selection of the nodes to merge. Addressing the Maximum Independent Set Problem, we present a novel dynamic variable ordering strategy relying on induced subgraphs of the original graph, and a new tie-based merge heuristic. In a set of computational experiments, we show that our strategies yield much stronger bounds than the standard state-of-the-art approaches. Furthermore, implementing our heuristics in a DD-based branch-and-bound, we reduce the solution times by around 33 % on average and by more than 50 % on hard instances.

Subject Classification

ACM Subject Classification
  • Theory of computation → Discrete optimization
Keywords
  • Decision Diagram
  • Dynamic Programming
  • Maximum Independent Set Problem
  • Dual Bound

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References

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