Mean value cross decomposition applied to integer programming problems

Article Abstract:

The application of the linear mean value cross decomposition method for solving linear programming problems to deriving lower bounds on the optimal objective function value of mixed and pure integer programming problems is considered. The results, which showed the method to be superior over the LP-relaxation and the Lagrangean relaxation in a branch-and-bound setting, affirmed its use for obtaining the Lagrangean dual bound, the bound of the Lagrangean dual of the LP-relaxation of the x-part and the LP-relaxation bound.

Integer programming, Decomposition method

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A Lagrangean heuristic for the facility location problem with staircase costs

Article Abstract:

A Lagrangean heuristic for solving capacitated facility location problems with staircase-like production costs is developed and compared with the ADD, convex piecewise linearization (CPL) and LAMPS heuristics. The heuristic employs Lagrangean relaxation and subgradient optimization to derive initial dual solutions as well as CPL of the staircase cost functions to derive upper and lower bounds on the optimal objective function value. It is also used as a base to build a primal heuristic.

Mathematical optimization, Optimization theory, Lagrangian functions

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Weber problems with alternative transportation systems

Article Abstract:

P-facility minsum location problems on a plane and on a network of rapid transit lines which may be utilized as a shortest-path alternative transportation system to minimize travel times and costs are considered. Specifically, the nonconvex optimization problem is reduced to Weber or multi-Weber problems which, in some cases, turn into combinatorial optimization problems or, if the gauge used to induce the metric was polyhedral, p-median problems.

Traffic estimation

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