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Non Delayed Relax-and-Cut Algorithms

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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.

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  1. Departamento de Administração, Universidade Federal do Rio de Janeiro, Rio de Janeiro

    Abilio Lucena

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  1. Abilio Lucena
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Correspondence to Abilio Lucena.

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Lucena, A. Non Delayed Relax-and-Cut Algorithms. Ann Oper Res 140, 375–410 (2005). https://doi.org/10.1007/s10479-005-3977-1

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