, Volume 21, Issue 1, pp 109–132 | Cite as

MIRHA: multi-start biased randomization of heuristics with adaptive local search for solving non-smooth routing problems

  • Angel A. Juan
  • Javier FaulinEmail author
  • Albert Ferrer
  • Helena R. Lourenço
  • Barry Barrios
Original Paper


This paper discusses the use of probabilistic or randomized algorithms for solving vehicle routing problems with non-smooth objective functions. Our approach employs non-uniform probability distributions to add a biased random behavior to the well-known savings heuristic. By doing so, a large set of alternative good solutions can be quickly obtained in a natural way and without complex configuration processes. Since the solution-generation process is based on the criterion of maximizing the savings, it does not need to assume any particular property of the objective function. Therefore, the procedure can be especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods—both of exact and approximate nature—may fail to reach their full potential. The results obtained so far are promising enough to suggest that the idea of using biased probability distributions to randomize classical heuristics is a powerful one that can be successfully applied in a variety of cases.


Randomized algorithms Combinatorial optimization Vehicle routing problem Biased random search Heuristics 

Mathematics Subject Classification (2000)

65K05 90C26 90C27 90C59 



This work has been partially supported by the Spanish Ministry of Science and Innovation (grants MTM2008-06695-C03-03, TRA2010-21644-C03 and ECO2009-11307), by the Working Community of the Pyrenees (grants IIQ13172.R11-CTP09-R2 and CTP09-00007), by the CYTED-IN3-HAROSA network ( and by the Jerónimo de Ayanz network (Government of Navarre, Spain).


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2011

Authors and Affiliations

  • Angel A. Juan
    • 1
  • Javier Faulin
    • 2
    Email author
  • Albert Ferrer
    • 3
  • Helena R. Lourenço
    • 4
  • Barry Barrios
    • 5
  1. 1.Computer Science Dept.Open University of CataloniaBarcelonaSpain
  2. 2.Statistics and Operations Research Dept.Public University of NavarrePamplonaSpain
  3. 3.Applied Mathematics 1 Dept.Technical University of CataloniaBarcelonaSpain
  4. 4.Economics and Business Dept.Universitat Pompeu FabraBarcelonaSpain
  5. 5.Industrial Engineering and Management Science Dept.Northwestern UniversityEvanstonUSA

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