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