Some combinatorial optimization problems with neighborhoods

  1. I. Espejo Miranda
  2. R. Páez Jiménez
  3. J. Puerto Albandoz
  4. A.M. Rodríguez Chía
Actes:
XXXIX CONGRESO NACIONAL DE ESTADÍSTICA E INVESTIGACIÓN OPERATIVA XIII JORNADAS DE ESTADÍSTICA PÚBLICA

Editorial: Departamento de Estadística e Investigación Operativa. Universidad de Granada

ISBN: 978-84-09-41628-8

Any de publicació: 2022

Pàgines: 198

Tipus: Aportació congrés

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Resum

Combinatorial optimization has important applications in real world situations. Many such applications can be formulated as optimization problems defined on graphs, this is the case of planning shortest paths, spanning trees, and matching among others. However, many often the exact location of the nodes is unknown and the assumption of modelling the nodes by points should be revised. In this sense, we propose to consider uncertainty regions or neighborhoods where the points will lie very likely. We deal with combinatorial optimization problems on graphs where nodes are represented by neighborhoods that are not necessarily convex. We will develop non-linear mixed integer programming formulations with second order cone constraints and study the structure of this kind of problem.