1. Yasel José COSTA SALAS, 2. Norge COELLO MACHADO, 3. Elke GLISTAU, 4. Carlos MACHADO OSES A NEW ALGORITHM FOR FACILITY LOCATION PROBLEM BASED ON DYNAMIC MESH OPTIMIZATION ABSTRACT: This paper proposes Dynamic Mesh Optimization for the classical Facility Location Problem, we introduce this meta-heuristic which is a technique of evolutionary computation. A set of nodes that represent potential location solutions conform a mesh; it grows and moves dynamically throughout the search space. The algorithm performance has been compared with data set from literature. Computational results confirm the efficiency of the strategy we propose. KEYWORDS: Algoritm, location problem, Dynamic Mesh Optimization INTRODUCTION One of the most important decisions in the logistical planning is to establish where the locations have to be (whether factories, warehouse, markets, etc). The Facility Location Problem (FLP) has been widely studied by different authors, often specialists from Operation Research and Logistic areas. This kind of problem is a well-known NP-Hard combinatorial optimization problem which is encountered frequently in decision making process, beside in logistics system. In FLP there is a set of locations at which we may build a facility (such as a warehouse), where the cost of building dependents of each location; furthermore, there is a set of client locations (such as stores, markets) that require to be serviced by a facility, and if a client at location j is assigned to a facility at location i, a cost of c ij is incurred that is proportional to the distance between i and j. The objective is to determine a set of locations at which to open facilities so as to minimize the total facility and assignment costs. 19 An abundant literature on facility location problem is available. Beside, there are several type of them, such as uncapacitated facility location problem introduced by [4], [1] and capacitated facility location problem (CFLP) reported in [3] and [5]. In this paper we focus in the CFLP. Moreover, various researches have shown the effective use of meta-heuristic in CFLP [10], [6]. This paper proposes to examine the capacitated facility location problem based on DMO, which is classifying as evolutionary computation techniques. Multiple types of nodes are generated in order to conform a mesh, which dynamically expands itself and moves across the search space. This meta-heuristic was created by [7], however all work deals with the optimization process in continuous approach; we modify the algorithm for optimization process in discrete context, such as CFLP. The paper is structured as follows: In Section 2 is formulated the capacitated facility location problem, description of meta-heuristic and the algorithm steps are defined at Section 3. Computational results and the algorithm performance can be found in Section 4. Conclusions and future researches are outlined in Section 5. PROBLEM DESCRIPTION The CFLP is define on a graph G (V, E) where |V| = n, vertices (customer to meet) and “E” indicates the Euclidian distance by which the vertices are connected “V”. The decision variable can be described as Xij = (0, 1): where (0) that vertex “j” is not assigned to the facility “i” and (1) otherwise. There is a set M(i) which represents the number of arcs that affect the vertex “i”. In addition to each arcs poses a d(i,j) representing the minimum distances between “i” and “j”. It is expressed therefore an integer value m i , which represents nodes, allocated to an installation “i”, where i = (1…k). For the capacitated facility location problem are established usually the following constrains: