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Non Delayed Relax-and-Cut Algorithms

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  • Abilio Lucena

Abstract

Attempts to allow exponentially many inequalities to be candidates to Lagrangian dualization date from the early 1980's. In this paper, the term Relax-and-Cut, introduced elsewhere, is used to denote the whole class of Lagrangian Relaxation algorithms where Lagrangian bounds are attempted to be improved by dynamically strengthening relaxations with the introduction of valid constraints. An algorithm in that class, denoted here Non Delayed Relax-and-Cut, is described in detail, together with a general framework to obtain feasible integral solutions. Specific implementations of NDRC are presented for the Steiner Tree Problem and for a Cardinality Constrained Set Partitioning Problem. Copyright Springer Science + Business Media, Inc. 2005

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  • Abilio Lucena, 2005. "Non Delayed Relax-and-Cut Algorithms," Annals of Operations Research, Springer, vol. 140(1), pages 375-410, November.
    • Handle: RePEc:spr:annopr:v:140:y:2005:i:1:p:375-410:10.1007/s10479-005-3977-1
    DOI: 10.1007/s10479-005-3977-1
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    Cited by:

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    2. Jesus Cunha & Luidi Simonetti & Abilio Lucena, 2016. "Lagrangian heuristics for the Quadratic Knapsack Problem," Computational Optimization and Applications, Springer, vol. 63(1), pages 97-120, January.
    3. Chagas, Rosklin Juliano & Valle, Cristiano Arbex & da Cunha, Alexandre Salles, 2018. "Exact solution approaches for the Multi-period Degree Constrained Minimum Spanning Tree Problem," European Journal of Operational Research, Elsevier, vol. 271(1), pages 57-71.
    4. Pereira, Dilson Lucas & Salles da Cunha, Alexandre, 2020. "Dynamic intersection of multiple implicit Dantzig–Wolfe decompositions applied to the adjacent only quadratic minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 284(2), pages 413-426.

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