Nenad Mladenović

Variable neighborhood search: Principles and applications

Abstract Systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization, called variable neighborhood search (VNS). We present a basic scheme for this purpose, which can easily be implemented using any local search algorithm as a subroutine. Its effectiveness is illustrated by solving several classical combinatorial or global optimization problems. Moreover, several extensions are proposed for solving large problem instances: using VNS within the successive approximation method yields a two-level VNS, called variable neighborhood decomposition search (VNDS); modifying the basic scheme to explore easily valleys far from the incumbent solution yields an efficient skewed VNS (SVNS) heuristic. Finally, we show how to stabilize column generation algorithms with help of VNS and discuss various ways to use VNS in graph theory, i.e., to suggest, disprove or give hints on how to prove conjectures, an area where metaheuristics do not appear to have been applied before.

Variable neighborhood search

Systematic change of the neighborhood in search Does not follow a single trajectory but explores increasingly distant neighbors of the incumbent solution Jumps from this solution to a new one if and only if there is an improvement In this way, keeps good (maybe optimal) variables in the incumbent and obtains promising neighbors Uses local search to get from these neighbors to local optima

Variable Neighbourhood Search

The basic idea of VNS is the change of neighbourhoods in the search for a better solution. VNS proceeds by a descent method to a local minimum exploring then, systematically or at random, increasingly distant neighbourhoods of this solution. Each time, one or several points within the current neighbourhood are used as initial solutions for a local descent. The method jumps from the current solution to a new one if and only if a better solution has been found. Therefore, VNS is not a trajectory following method (as Simulated Annealing or Tabu Search) and does not specify forbidden moves. In this work, we show how the variable neighbourhood search metaheuristic can be applied to train an artificial neural network. We define a set of nested neighbourhoods and follow the basic VNS scheme to carry out our experiments

An introduction to variable neighborhood search

In this paper we examine a relatively unexplored approach to the design of heuristics, the guided change of neighborhood in the search process. Using systematically this idea and very little more, i.e., only a local search routine, leads to a new metaheuristic, which is widely applicable. We call this approach Variable Neighborhood Search (VNS).

Variable neighborhood search for the p-median

Abstract Consider a set L of potential locations for p facilities and a set U of locations of given users. The p-median problem is to locate simultaneously the p facilities at locations of L in order to minimize the total transportation cost for satisfying the demand of the users, each supplied from its closest facility. This model is a basic one in location theory and can also be interpreted in terms of cluster analysis where locations of users are then replaced by points in a given space. We propose several new Variable Neighborhood Search heuristics for the p-median problem and compare them with Greedy plus Interchange, and two Tabu Search heuristics.

The p-Median Problem: A Survey of Metaheuristic Approaches

The p-median problem, like most location problems, is classified as NP -hard, and so, heuristic methods are usually used for solving it. The pmedian problem is a basic discrete location problem with real application that have been widely used to test heuristics. Metaheuristics are frameworks for building heuristics. In this survey, we examine the p-median, with the aim of providing an overview on advances in solving it using recent procedures based on metaheuristic rules.

J-Means: a new local search heuristic for minimum sum of squares clustering

Abstract A new local search heuristic, called J-M eans , is proposed for solving the minimum sum of squares clustering problem. The neighborhood of the current solution is defined by all possible centroid-to-entity relocations followed by corresponding changes of assignments. Moves are made in such neighborhoods until a local optimum is reached. The new heuristic is compared with two other well-known local search heuristics, K- and H-M eans as well as with H-M eans +, an improved version of the latter in which degeneracy is removed. Moreover, another heuristic, which fits into the variable neighborhood search metaheuristic framework and uses J-M eans in its local search step, is proposed too. Results on standard test problems from the literature are reported. It appears that J-M eans outperforms the other local search methods, quite substantially when many entities and clusters are considered.

Variable neighbourhood search: methods and applications

Variable neighbourhood search (VNS) is a metaheuristic, or a framework for building heuristics, based upon systematic changes of neighbourhoods both in descent phase, to find a local minimum, and in perturbation phase to emerge from the corresponding valley. It was first proposed in 1997 and has since then rapidly developed both in its methods and its applications. In the present paper, these two aspects are thoroughly reviewed and an extensive bibliography is provided. Moreover, one section is devoted to newcomers. It consists of steps for developing a heuristic for any particular problem. Those steps are common to the implementation of other metaheuristics.

Variable neighborhood search for minimum cost berth allocation

The berth allocation problem is to allocate space along the quayside to incoming ships at a container terminal in order to minimize some objective function. We consider minimization of total costs for waiting and handling as well as earliness or tardiness of completion, for all ships. We assume ships can arrive at any given time, i.e., before or after the berths become available. The resulting problem, which subsumes several previous ones, is expressed as a linear mixed 0-1 program. As it turns out to be too time-consuming for exact solution of instances of realistic size, a Variable Neighborhood Search (VNS) heuristic is proposed, and compared with Multi-Start (MS), a Genetic Search algorithm (GA) and a Memetic Search algorithm (MA). VNS provides optimal solutions for all instances solved to optimality in a previous paper of the first two authors and outperforms MS, MA and GA on large instances.

Cooperative Parallel Variable Neighborhood Search for the p -Median

We propose a cooperative multi-search method for the Variable Neighborhood Search (VNS) meta-heuristic based on the central-memory mechanism that has been successfully applied to a number of difficult combinatorial problems. In this approach, several independent VNS meta-heuristics cooperate by asynchronously exchanging information about the best solutions identified so far, thus conserving the simplicity of the original, sequential VNS ideas. The p-median problem (PM) serves as test case. Extensive experimentations have been conducted on the classical TSPLIB benchmark problem instances with up to 11948 customers and 1000 medians, without any particular calibration of the parallel method. The results indicate that, compared to sequential VNS, the cooperative strategy yields significant gains in terms of computation time without a loss in solution quality.