This paper considers the VRP Problem with Soft Time-Windows (VRPSTW), a challenging routing problem due to its combination of hard time windows and a lexicographic objective function minimizing the number of vehicles, the violations of the soft time windows, and the total travel distance. The paper presents a multi-stage, variable neighborhood search algorithm for the VRPSTW, which uses the sam...

The simplicity of the maximum satisfiability problem (MAX-SAT) combined with its applicability in many areas of artificial intelligence and computing science made it one of the fundamental optimization problems. This NP-complete problem refers to the task of finding a variable assignment that satisfies the maximum number of clauses (or the sum of weights of satisfied clauses) in a Boolean formu...

Variable neighborhood search (VNS) is a recent metaheuristic for solving combinatorial and global optimization problems whose basic idea is systematic change of neighborhood within a local search. In this survey paper we present basic rules of VNS and some of its extensions. Moreover, applications are briefly summarized. They comprise heuristic solution of a variety of optimization problems, wa...

The recent Variable Neighborhood Search (VNS) metaheuristic combines local search with systematic changes of neighborhood in the descent and escape from local optimum phases. When solving large instances of various problems, its efficiency may be enhanced through decomposition. The resulting two level VNS, called Variable Neighborhood Decomposition Search (VNDS), is presented and illustrated on...

An uncapacitated facility location problem considers a set of n warehouses W and a set of m stores S. Each warehouse w has a fixed cost fw, and the transportation cost from warehouse w to store s is given by cws. The problem is to find a subset of warehouses and an assignment of warehouses to stores in order to minimize the fixed and transportation costs. Observe that once the warehouses are se...

In this paper we propose three different VNS variants to solve the Max-Mean Dispersion Problem. This problem consists of selecting a set of elements in such a way that the average distance between them is maximized. To tackle this problem, we propose a Basic Variable Neighborhood Search (BVNS), a Variable Neighborhood Descent (VND) and a Generalized Variable Neighborhood Search (GVNS) that hybr...

In this issue we present a peer-reviewed selection of short papers that were accepted for presentation in the 4th International Conference on Variable Neighborhood Search (ICVNS’16) which was held in Málaga, Spain, during October 3-5, 2016. This conference is devoted to the Variable Neighborhood Search metaheuristic which was originally proposed by Nenad Mladenović and Pierre Hansen. This metho...

We are presenting in this volume selected, peer-reviewed, short papers that were presented at the EURO Mini Conference XXVIII on Variable Neighborhood Search (MEC XXVIII VNS) which was held during October 4-7, 2012, in Herceg Novi, Montenegro.

Ant algorithms were first written about in 1991 and since then they have been applied to many problems with great success. During these years the algorithms themselves have been modified for improved performance and also been influenced by research in other fields. Since the earliest Ant algorithms, heuristics and local search have been the primary knowledge sources. This thesis asks the questi...

This paper presents a variable neighborhood search (VNS) algorithm for solving bandwidth coloring problem (BCP) and bandwidth multicoloring problem (BMCP). BCP and BMCP are generalizations of the well known vertex coloring problem and they are of a great interest from both theoretical and practical points of view. Presented VNS combines a shaking procedure which perturbs the colors for an incre...