Exact procedures for solving the discrete ordered median problem

The Discrete Ordered Median Problem (DOMP) generalizes classical discrete location problems, such as the N-median, N-center and Uncapacitated Facility Location problems. It was introduced by Nickel [S. Nickel. Discrete Ordered Weber problems. In B. Fleischmann, R. Lasch, U. Derigs, W. Domschke, and U. Rieder, editors, Operations Research Proceedings 2000, pages 71–76. Springer, 2001], who formulated it as both a nonlinear and a linear integer program. We propose an alternative integer linear programming formulation for the DOMP, discuss relationships between both integer linear programming formulations, and show how properties of optimal solutions can be used to strengthen these formulations. Moreover, we present a specific branch and bound procedure to solve the DOMP more efficiently. We test the integer linear programming formulations and this branch and bound method computationally on randomly generated test problems.Ministerio de Ciencia y Tecnologí

A Genetic Algorithm for solving the Discrete Ordered Median Problem with Induced Order

The Discrete Ordered Median Problem with Induced Ordered (DOMP+IO) is a multi-facility version of the classical discrete ordered median problem (DOMP), which has been widely studied. Several exact methods have been proposed to solve the DOMP, however these methods could only solve small-scale problems, which are far of real-life problems. In this work, a DOMP+IO with two kinds of facilities is considered and a heuristic method is proposed for its solving. The proposed procedure is based on a genetic algorithm and the preliminary results show the efficiency and capability to obtain good solutions for large-scale problems.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Solving Discrete Ordered Median Problems with Induced Order

Ordered median functions have been developed to model flexible discrete location problems. A weight is associated to the distance from a customer to its closest facility, depending on the position of that distance relative to the distances of all the customers. In this paper, the above idea is extended by adding a second type of facility and, consequently, a second weight, whose values are based on the position of the first weights. An integer programming formulation is provided in this work for solving this kind of models

Advances in Learning Bayesian Networks of Bounded Treewidth

This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure learning and treewidth computation. The approximate method consists in uniformly sampling $k$-trees (maximal graphs of treewidth $k$), and subsequently selecting, exactly or approximately, the best structure whose moral graph is a subgraph of that $k$-tree. Some properties of these methods are discussed and proven. The approaches are empirically compared to each other and to a state-of-the-art method for learning bounded treewidth structures on a collection of public data sets with up to 100 variables. The experiments show that our exact algorithm outperforms the state of the art, and that the approximate approach is fairly accurate.Comment: 23 pages, 2 figures, 3 table

Primal-dual variable neighborhood search for the simple plant-location problem

Copyright @ 2007 INFORMSThe variable neighborhood search metaheuristic is applied to the primal simple plant-location problem and to a reduced dual obtained by exploiting the complementary slackness conditions. This leads to (i) heuristic resolution of (metric) instances with uniform fixed costs, up to n = 15,000 users, and m = n potential locations for facilities with an error not exceeding 0.04%; (ii) exact solution of such instances with up to m = n = 7,000; and (iii) exact solutions of instances with variable fixed costs and up to m = n = 15, 000.This work is supported by NSERC Grant 105574-02; NSERC Grant OGP205041; and partly by the Serbian Ministry of Science, Project 1583