Journal of Heuristics

, Volume 15, Issue 3, pp 283–312 | Cite as

Benders decomposition, Lagrangean relaxation and metaheuristic design



Large part of combinatorial optimization research has been devoted to the study of exact methods leading to a number of very diversified solution approaches. Some of those older frameworks can now be revisited in a metaheuristic perspective, as they are quite general frameworks for dealing with optimization problems. In this work, we propose to investigate the possibility of reinterpreting decompositions, with special emphasis on the related Benders and Lagrangean relaxation techniques. We show how these techniques, whose heuristic effectiveness is already testified by a wide literature, can be framed as a “master process that guides and modifies the operations of subordinate heuristics”, i.e., as metaheuristics. Obvious advantages arise from these approaches, first of all the runtime evolution of both upper and lower bounds to the optimal solution cost, thus yielding both a high-quality heuristic solution and a runtime quality certificate of that same solution.


Combinatorial optimization Lagrangean relaxation Benders’s decomposition Metaheuristic 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BolognaBolognaItaly
  2. 2.Department of Computer ScienceUniversity of BolognaBolognaItaly

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