We investigate strong inequalities for mixed 0-1 integer programs derived from flow cover inequalities. Flow cover inequalities are usually not facet defining and need to be lifted to obtain stronger inequalities. However, because of the sequential nature of the standard lifting techniques and the complexity of the optimization problems that have to be solved to obtain lifting coefficients, lifting of flow cover inequalities is computationally very demanding. We present a computationally efficient way to lift flow cover inequalities based on sequence independent lifting techniques and computational results that justify the effectiveness of our lifting procedures. 1 Introduction A mixed integer program (MIP) with binary integer variables (BMIP) is the appropriate mathematical model for many practical optimization problems. This model is used, for example, for facility location problems, distribution problems, network design problems and more generally when fixed or concave costs are re...

There has been a great deal of recent work on approximation algorithms for facility location problems [9]. We consider the capacitated facility location problem with hard capacities. We are given a set of facilities, F, and a set of clients D in a common metric space. Each facility i has a facility opening cost fi and capacity

This paper advocates the use of the bionomic algorithm, a recently proposed metaheuristic technique, as an effective method to solve capacitated p-median problems (CPMP). Bionomic algorithms already proved to be an effective framework for finding good solutions to combinatorial optimization problems, when good local optimization algorithms are available. The paper also presents an effective local search technique for the CPMP. Computational results show the effectiveness of the proposed approach, when compared to the best performing heuristics so far presented in the literature. Correspondence to: Vittorio Maniezzo, Scienze Informazione, Univ. Bologna, via Sacchi 3, 47023 Cesena, Italy. 2 1 Introduction The capacitated p-median problem (CPMP) considered in this paper is the problem of partitioning a set of n weighted entities (objects, customers,...) into p disjoint clusters, so that the total dissimilarity within each cluster is minimized and constraints on maximum cluster capaciti...

We review the models for telecommunication network design where there is a location problem involved. We classify the models into three classes as uncapacitated, capacitated and dynamic models. For each class, we discuss the core problem, its generalizations and the solution methods in the literature.

The polyhedral approach is one of the most powerful techniques available for solving hard combinatorial optimization problems. The main idea behind the technique is to consider the linear relaxation of the integer combinatorial optimization problem, and try to iteratively strengthen the linear formulation by adding violated strong valid inequalities, i.e., inequalities that are violated by the current fractional solution but satisfied by all feasible solutions, and that define high-dimensional faces, preferably facets, of the convex hull of feasible solutions. If we have the complete description of the convex hull of feasible solutions all extreme points of this formulation are integral, which means that we can solve the problem as a linear programming problem. Linear programming problems are known to be computationally easy. In Part I of this article we discuss theoretical aspects of polyhedral techniques. Here we will mainly concentrate on the computational aspects. In particular we ...

Most facility location problems are computationally hard to solve. The standard technique for solving these problems is branch-and-bound. To keep the size of the branch-and-bound tree as small as possible it is important to obtain a good lower bound on the optimal solution by deriving strong linear relaxations. One way of strengthening the linear relaxation is by adding inequalities that define facets of the convex hull of feasible solutions. Here we describe some simple, but computationally very useful classes of inequalities that were originally developed for relaxations of the facility location problems. Algorithms for generating violated inequalities belonging to the described classes have been implemented as system features in various branchand -bound software packages, so as long as the software can recognize the relaxations for which the inequalities are developed, the inequalities will be generated "automatically". Here we explicitly add the variables and constraints that are n...

This survey presents cutting planes that are useful or potentially useful in solving mixed integer programs. Valid inequalities for i) general integer programs, ii) problems with local structure such as knapsack constraints,and iii) problems with 0-1 coe#cient matrices,such as set packing,are examined in turn. Finally the use of valid inequalities for classes of problems with structure,such as network design,is explored. Keywords: Mixed Integer Programming,Cutting Planes Classification: MSC(199 9991,S Research carried out with financial support of the projectTMR-DON) nr. ERB FMRX-CT98-0202 of the European Community. This text presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister's O#ce, Science Policy Programming. The scientific responsibility is assumed by the authors. 1Departmen t of Operationy ResearchLonq3 School ofEconq6qU Houghton Street,Lonet WC2A 2AE,Un,UI KinUI6I 2Kon33UyIb0qIUn trumBerlin Takustr. 7 D-14195Berlin German y. 3 Fakultat fur Mathematik, IMO Otto-vono-vUv keUnv ersitat MagdeburgUnd ersitatsplatz 2 D-39106 MagdeburgGerman y. 4 CORE,UnE ersite Catholique de Louvain 1348 Louvainbb60bUy e, Belgium. Introductiz This survey is devoted to cutting planes that are useful or potentially useful in solving mixed integer programs. This topic is important because a) strengthening formulations with cutting planes is of interest independently of the algorithm used to solve the problem, and b) linear programming based branch-and-bound with cuts added, known as branch-and-cu , is now one of the most widespread and successful tools for solving mixed integer programs. The paper is divided into four sections. First we discuss ways of generating cuts for general integer program...

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This paper presents a local search method for constraint satisfaction problems, which is guided by some learning properties derived from a probabilistic choice model. The local search algorithm randomly selects a variable in a violated constraint and another variable from the search space. Two trials are performed, each of which assigns a different value to one of the selected variables whilst keeping the other fixed. Partial constraint propagation is performed in the process. The evaluation function for these trials is based on the overall degree of constraint violation. The trial results are accumulated with respect to individual variables. When sufficient trial history has been collected for a variable, it is analysed to infer a likely optimal value for that variable to be fixed at for a number of iterations. The algorithms presented have been applied to a demand responsive container freight rail scheduling problem. In this problem, all the decision variables are binary and relatively few feasible solutions exist. This paper will report on tests using real life data from Thailand.

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