Solving Medium to Large Sized Euclidean Generalized Minimum Spanning Tree Problems

The generalized minimum spanning tree problem is a generalization of the minimum spanning tree problem. This network design problems finds several practical applications, especially when one considers the design of a large-capacity backbone network connecting several individual networks. In this paper we study the performance of six neighborhood search heuristics based on tabu search and variable neighborhood search on this problem domain. Our principal finding is that a tabu search heuristic almost always provides the best quality solution for small to medium sized instances within short execution times while variable neighborhood decomposition search provides the best quality solutions for most large instances.

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

Linear Programming by Solving Systems of Differential Equations Using Game Theory

In this paper we will solve some linear programming problems by solving systems of differential equations using game theory. The linear programming problem must be a classical constraints problem or a classical menu problem, i.e. a maximization/minimization problem in the canonical form with all the coefficients (from objective function, constraints matrix and right sides) positive. Firstly we will transform the linear programming problem such that the new problem and its dual have to be solved in order to find the Nash equilibrium of a matriceal game. Next we find the Nash equilibrium by solving a system of differential equations as we know from evolutionary game theory, and we express the solution of the obtained linear programming problem (by the above transformation of the initial problem) using the Nash equilibrium and the corresponding mixed optimal strategies. Finally, we transform the solution of the obtained problem to obtain the solution of the initial problem. We make also a program to implement the algorithm presented in the paper.Linear programming, evolutionary game theory, Nash equilibrium.

Solving the p -Median Problem with a Semi-Lagrangian Relaxation

Lagrangian relaxation is commonly used in combinatorial optimization to generate lower bounds for a minimization problem. We study a modified Lagrangian relaxation which generates an optimal integer solution. We call it semi-Lagrangian relaxation and illustrate its practical value by solving large-scale instances of the p-median proble

Hybrid resolution approaches for dynamic assignment problem of reusable containers

In this study, we are interested in the reusing activities of reverse logistics. We focus on the dynamic assignment of reusable containers problem (e.g. gas bottles, beverages, pallets, maritime containers, etc.). The objective is to minimize the collect, reloading, storage and redistribution operations costs over a fixed planning horizon taking into account the greenhouse gas emissions. We present a new generic Mixed Integer Programming (MIP) model for the problem. The proposed model was solved using the IBM ILOG CPLEX optimization software; this method yield exact solutions, but it is very time consuming. So we adapted two hybrid approaches using a genetic algorithm to solve the problem at a reduced time (The second hybrid approach is enhanced with a local search procedure based on the Variable Neighborhood Search VNS). The numerical results show that both developed hybrid approaches generate high-quality solutions in a moderate computational time, especially the second hybrid method

A dissimilarity-based approach for Classification

The Nearest Neighbor classifier has shown to be a powerful tool for multiclass classification. In this note we explore both theoretical properties and empirical behavior of a variant of such method, in which the Nearest Neighbor rule is applied after selecting a set of so-called prototypes, whose cardinality is fixed in advance, by minimizing the empirical mis-classification cost. With this we alleviate the two serious drawbacks of the Nearest Neighbor method: high storage requirements and time-consuming queries. The problem is shown to be NP-Hard. Mixed Integer Programming (MIP) programs are formulated, theoretically compared and solved by a standard MIP solver for problem instances of small size. Large sized problem instances are solved by a metaheuristic yielding good classification rules in reasonable time.operations research and management science;