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Revisiting lagrange relaxation (LR) for processing large-scale mixed integer programming (MIP) problems

By C Siamitros, G Mitra and CA Poojari

Abstract

Lagrangean Relaxation has been successfully applied to process many well known\ud instances of NP-hard Mixed Integer Programming problems. In this paper we present\ud a Lagrangean Relaxation based generic solver for processing Mixed Integer\ud Programming problems. We choose the constraints, which are relaxed using a\ud constraint classification scheme. The tactical issue of updating the Lagrange\ud multiplier is addressed through sub-gradient optimisation; alternative rules for\ud updating their values are investigated. The Lagrangean relaxation provides a lower\ud bound to the original problem and the upper bound is calculated using a heuristic\ud technique. The bounds obtained by the Lagrangean Relaxation based generic solver\ud were used to warm-start the Branch and Bound algorithm; the performance of the\ud generic solver and the effect of the alternative control settings are reported for a wide\ud class of benchmark models. Finally, we present an alternative technique to calculate\ud the upper bound, using a genetic algorithm that benefits from the mathematical\ud structure of the constraints. The performance of the genetic algorithm is also\ud presented

Publisher: The Centre for the Analysis of Risk and Optimisation Modelling Applications (CARISMA), Brunel University
Year: 2004
OAI identifier: oai:bura.brunel.ac.uk:2438/750

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