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Trees and Forests

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Handbook of Heuristics

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Abstract

Trees and forests have been a fascinating research topic in Operations Research (OR)/Management Science (MS) throughout the years because they are involved in numerous difficult problems, have interesting theoretical properties, and cover a large number of practical applications. A tree is a finite undirected connected simple graph with no cycles, while a set of independent trees is called a forest. A spanning tree is a tree covering all nodes of a graph. In this chapter, key components for solving difficult tree and forest problems, as well as insights to develop efficient heuristics relying on such structures, are surveyed. They are usually combined to obtain very efficient metaheuristic algorithms, hybrid methods, and matheuristics. Some emerging topics and trends in trees and forests are pointed out. This is followed by two case studies: a Lagrangian-based heuristic for the minimum degree-constrained spanning tree problem and an evolutionary algorithm for a generalization of the bounded-diameter minimum spanning tree problem. Both problems find applications in network design, telecommunication, and transportation fields, among others.

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Author information

Authors and Affiliations

  1. ICD-LOSI, UMR CNRS 6281, Université de Technologie de Troyes, Troyes Cedex, France

    Andréa Cynthia Santos

  2. LIMOS-UBP, UMR CNRS 6158, Université Blaise Pascal, Aubière Cedex, Clermont-Ferrand, France

    Christophe Duhamel

  3. Departamento de Estatística e Matemática Aplicada, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, Brazil

    Rafael Andrade

Authors
  1. Andréa Cynthia Santos
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  2. Christophe Duhamel
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  3. Rafael Andrade
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Corresponding author

Correspondence to Andréa Cynthia Santos .

Editor information

Editors and Affiliations

  1. Statistics and Operations Research Department, University of Valencia, Valencia, Spain

    Rafael Martí

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  3. Amazon.com, Inc. and University of Washington, Seattle, Washington, USA

    Mauricio G. C. Resende

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Santos, A.C., Duhamel, C., Andrade, R. (2018). Trees and Forests. In: Martí, R., Pardalos, P., Resende, M. (eds) Handbook of Heuristics. Springer, Cham. https://doi.org/10.1007/978-3-319-07124-4_49

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