A Combinatorial Branch and Bound for the Min-Max Regret Spanning Tree Problem

  • Noé GodinhoEmail author
  • Luís Paquete
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11544)


Uncertainty in optimization can be modeled with the concept of scenarios, each of which corresponds to possible values for each parameter of the problem. The min-max regret criterion aims at obtaining a solution minimizing the maximum deviation, over all possible scenarios, from the optimal value of each scenario. Well-known problems, such as the shortest path problem and the minimum spanning tree, become NP-hard under a min-max regret criterion. This work reports the development of a branch and bound approach to solve the Minimum Spanning Tree problem under a min-max regret criterion in the discrete scenario case. The approach is tested in a wide range of test instances and compared with a generic pseudo-polynomial algorithm.


Min-max regret criterion Multi-objective optimization Minimum Spanning Tree Branch and bound 



This work was carried out in the scope of the MobiWise project: From mobile sensing to mobility advising (P2020 SAICTPAC/0011/2015), co-financed by COMPETE 2020, Portugal 2020 - POCI, European Union’s ERDF.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.CISUC, Department of Informatics EngineeringUniversity of Coimbra, Pólo IICoimbraPortugal

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