A Local Search Algorithm for Large Maximum Weight Independent Set Problems

Authors Yuanyuan Dong , Andrew V. Goldberg, Alexander Noe , Nikos Parotsidis, Mauricio G.C. Resende , Quico Spaen

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Author Details

Yuanyuan Dong
  • Dallas, TX, USA
Andrew V. Goldberg
  • Amazon.com, Santa Clara, CA, USA
Alexander Noe
  • Amazon.com, Bellevue, WA, USA
Nikos Parotsidis
  • Department of Computer Science, University of Copenhagen, Denmark
Mauricio G.C. Resende
  • Amazon.com, Bellevue, WA, USA
  • Industrial & Systems Engineering, University of Washington, Seattle, WA, USA
Quico Spaen
  • Amazon.com, Santa Clara, CA, USA

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Yuanyuan Dong, Andrew V. Goldberg, Alexander Noe, Nikos Parotsidis, Mauricio G.C. Resende, and Quico Spaen. A Local Search Algorithm for Large Maximum Weight Independent Set Problems. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 45:1-45:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Motivated by a real-world vehicle routing application, we consider the maximum-weight independent set problem: Given a node-weighted graph, find a set of independent (mutually nonadjacent) nodes whose node-weight sum is maximum. Some of the graphs arising in the vehicle routing application are large, having hundreds of thousands of nodes and hundreds of millions of edges. To solve instances of this size, we develop a new local search algorithm, which is a metaheuristic based on the greedy randomized adaptive search (GRASP) framework. This algorithm, named METAMIS, uses a wider range of simple local search operations than previously described in the literature. We introduce data structures that make these operations efficient. A new variant of path-relinking is introduced to escape local optima and so is a new alternating augmenting-path local search move that improves algorithm performance. We compare an implementation of our algorithm with a state-of-the-art publicly available code on public benchmark sets, including some large instances. Our algorithm is, in general, competitive and outperforms this openly available code on large vehicle routing instances of the maximum weight independent set problem. We hope that our results will lead to even better maximum-weight independent set algorithms.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • local search
  • maximum-weight independent set
  • path-relinking
  • heuristic
  • metaheuristic


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