Basic Variable Neighborhood Search Research Articles

An approximation method for the P-median problem: A bioinspired tabu search and variable neighborhood search partitioning approach

The bioinspired systems are presented as a set of models that are based on the behavior of some biological systems and how act. These models can be expressed in data mining and operations research where clustering is a recurrent technique used to solve the P-median and territorial design problems. At this point, we have solved the P-median problem with a partitioning approach with bioinspired aspects and Variable Neighborhood Search (VNS). In this work we have improved the basic VNS search strategy and we present a bioinspired partitioning algorithm with optimization by Tabu Search (TS). This clusteringpartitioning problem under a bioinspired connotation has been proposed after observing some characteristics in common between clustering and human behavior during conflict situations, where some characteristics have been modeled accordingly. Finally we present our progress from our VNS implementation to our TS proposal.

A basic variable neighborhood search heuristic for the uncapacitated multiple allocation p-hub center problem

The uncapacitated multiple allocation p-hub center problem (UMApHCP) consists of choosing p hub locations from a set of nodes with pairwise traffic demands in order to route the traffic between the origin-destination pairs such that the maximum cost between origin-destination pairs is minimum. It is assumed that transportation between non-hub nodes is possible only via chosen hub nodes. In this paper we propose a basic variable neighborhood search (VNS) heuristic for solving this NP hard problem. In addition we apply two mathematical formulations of the UMApHCP in order to detect limitations of the current state-of-the-art solver used for this problem. The heuristics are tested on benchmark instances for p-hub problems. The obtained results reveal the superiority of the proposed basic VNS over the state-of-the-art as well as over a multi-start local search heuristic developed by us in this paper.

Less is more: Basic variable neighborhood search for minimum differential dispersion problem

In this paper, we propose a basic variable neighborhood search for solving Minimum differential dispersion problem using only the swap neighborhood structure in both descent (intensification) and shaking (diversification) steps. It has become a trend in the metaheuristic literature to use hybrid metaheuristics, i.e., combination of several metaheuristic paradigms, for solving some particular optimization problem. We show that our simple method, which relies on the basic Variable neighborhood search, significantly outperforms the hybrid one that combines GRASP, Variable neighborhood search, and Exterior path relinking metaheuristics. Thus, simplicity is not only the desired user friendly property of a heuristic but can lead to more efficient and effective method than if complex hybrid metaheuristic is used: less is more.

VNS variants for the Max-Mean Dispersion Problem

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 hybridizes the previous two methods. Experimentation on previously reported instances shows that the Variable Neighborhood Search methodology is able to obtain solutions of high quality when compared with state of the art procedures.

Task Scheduling Using Two-Phase Variable Neighborhood Search Algorithm on Heterogeneous Computing and Grid Environments

Grid computing solves high-performance and high-throughput computing problems through sharing nodes ranging from personal computers to supercomputers distributed around the world. As the grid environments facilitate distributed computation, the scheduling of grid jobs has become an important issue. In this paper, an investigation on implementing Two-Phase Variable Neighborhood Search (TPVNS) algorithm for scheduling independent jobs on computational grid is carried out. The proposed algorithm consists of two modules with General Variable Neighborhood Search and Basic Variable Neighborhood Search algorithms in order to find a good mapping of grid jobs with grid nodes. The performance of the proposed algorithm has been evaluated with deterministic heuristic and evolutionary algorithms. Simulation results show that TPVNS algorithm generally performs better than the existing methods.

Metaheuristic approaches to solving large-scale Bilevel Uncapacitated Facility Location Problem with clients' preferences

In this study, we consider a variant of the Bilevel Uncapacitated Facility Location Problem (BLUFLP), in which the clients choose suppliers based on their own preferences. We propose and compare three metaheuristic approaches for solving this problem: Particle Swarm Optimization (PSO), Simulated Annealing (SA), and a combination of Reduced and Basic Variable Neighborhood Search Method (VNS). We used the representation of solutions and objective function calculation that are adequate for all three proposed methods. Additional strategy is implemented in order to provide significant time savings when evaluating small changes of solution's code in improvement parts. Constructive elements of each of the proposed algorithms are adapted to the problem under consideration. The results of broad computational tests on modified problem instances from the literature show good performance of all three proposed methods, even on large problem dimensions. However, the obtained results indicate that the proposed VNS-based has significantly better performance compared to SA and PSO approaches, especially when solving large-scale problem instances. Computational experiments on large scale benchmarks demonstrate that the VNS-based method is fast, competitive, and able to find high-quality solutions, even for large-scale problem instances with up to 2000 clients and 2000 potential facilities within reasonable CPU times.

Solving the minimum labelling spanning tree problem by intelligent optimization

Research on intelligent optimization is concerned with developing algorithms in which the optimization process is guided by an “intelligent agent”, whose role is to deal with algorithmic issues such as parameters tuning, adaptation, and combination of different existing optimization techniques, with the aim of improving the efficiency and robustness of the optimization process. This paper proposes an intelligent optimization approach to solve the minimum labelling spanning tree (MLST) problem. The MLST problem is a combinatorial optimization problem where, given a connected, undirected graph whose edges are labelled (or coloured), the aim is to find a spanning tree whose edges have the smallest number of distinct labels (or colours). In recent work, the MLST problem has been shown to be NP-hard and some effective metaheuristics have been proposed and analysed. The intelligent optimization algorithm proposed here integrates the basic variable neighbourhood search heuristic with other complementary approaches from machine learning, statistics and experimental soft computing, in order to produce high-quality performance and to completely automate the resulting optimization strategy. We present experimental results on randomly generated graphs with different statistical properties, and demonstrate the implementation, the robustness, and the empirical scalability of our intelligent local search. Our computational experiments show that the proposed strategy outperforms heuristics recommended in the literature and is able to obtain high quality solutions quickly.

Intelligent variable neighbourhood search for the minimum labelling spanning tree problem

Given a connected, undirected graph whose edges are labelled (or coloured), the minimum labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest number of distinct labels (or colours). In recent work, the MLST problem has been shown to be NP-hard and some effective heuristics have been proposed and analyzed. In a currently ongoing project, we investigate an intelligent optimization algorithm to solve the problem. It is obtained by the basic Variable Neighbourhood Search heuristic with the integration of other complements from machine learning, statistics and experimental algorithmics, in order to produce high-quality performance and to completely automate the resulting optimization strategy. Computational experiments show that the proposed metaheuristic has high-quality performance for the MLST problem and it is able to obtain optimal or near-optimal solutions in short computational running time.

Stochastic and semidefinite optimization for scheduling in orthogonal frequency division multiple access networks

In this paper, we propose stochastic binary quadratic programs for the scheduling resource allocation process of a wireless orthogonal frequency division multiple access network. More precisely, we formulate a two-stage stochastic model, then we further extend the two-stage model by introducing a knapsack probabilistic constrained approach, and finally we propose a multi-stage stochastic program for this problem. The models are aimed at minimizing the total power consumption of the network at each time slot of the scheduling process subject to user bit rates, sub-carrier and modulation linear constraints. In order to compute lower bounds, we derive linear and semidefinite programming relaxations for each of the proposed models. The bounds are also compared with a basic variable neighborhood search metaheuristic approach. Numerical results show tight lower bounds for the semidefinite relaxations when compared to the linear ones and with the metaheuristic. Moreover, near optimal solutions are found with the semidefinite relaxations for the two-stage model without using probabilistic constraints and for the multi-stage program as well.

Variable Formulation Search for the Cutwidth Minimization Problem

Many optimization problems are formulated as min–max problems where the objective function consist of minimizing a maximum value. In this case, it is usual that many solutions of the problem has associated the same value of the objective function. When this happens it is difficult to determine which solution is more promising to continue the search. In this paper we propose a new variant of the Variable Neighbourhood Search methodology to tackle this kind of problems. The new variant, named Variable Formulation Search, makes use of alternative formulations of the problem to determine which solution is more promising when they have the same value of the objective function in the original formulation. We do that in shaking, local search and neighbourhood change steps of the basic Variable Neighbourhood Search. We apply the new methodology to the Cutwidth Minimization Problem. Computational results show that our proposal outperforms previous algorithms in the state of the art in terms of quality and computing time.

Hybridization of harmony search with variable neighborhood search for restrictive single-machine earliness/tardiness problem

Earliness/tardiness scheduling, in connection with Just-In-Time manufacturing philosophy, is crucial in reducing the production cost while maintaining a high service level. In this article, the well-known restrictive single-machine earliness/tardiness scheduling problem (RSMETP) is addressed. A novel hybrid metaheuristic, named as PHVNS, is developed for this NP-hard problem. There are three main innovative aspects in the proposed PHVNS. First, a permutation-based harmony search (PHS) is developed in compliance with the RSMETP features and optimality properties. Secondly, in order to provide an effective balance between the global diversification and local intensification, an enhanced basic variable neighborhood search (EBVNS) is incorporated into the iterative PHS. Thirdly, several problem-dependent mechanisms are introduced to facilitate the search process of PHVNS, such as the distinctive schedule representation, specific tweaks and speed-ups to the new harmony vector, and local search strategies within a neighborhood. An extensive calibration for the main parameters in PHVNS is carried out with the aid of a carefully designed set of experiments. To evaluate and validate the fine-tuned PHVNS, computational experiments are conducted upon the test suite of 280 benchmark instances. As demonstrated in the results, the tuned PHVNS is capable of reaching the high-quality solutions in reasonable time for most of the instances. Compared with some state-of-the-art metaheuristics for RSMETP, PHVNS shows high competitiveness.

Variable neighborhood search method for optimizing the emergency service network of police special forces units

Abstract In this study we consider mathematical models that arise from the problem of establishing and optimally utilizing the network of Police Special Forces Units (PSFUs) in the Republic of Serbia. The goal is to locate certain number of PSFUs in the given network in order to minimize the maximal load of established emergency units. We have designed an efficient metaheuristic method, based on the combination of the Reduced Variable Neighborhood Search (RVNS) and the basic Variable Neighborhood Search (VNS). The proposed approach, named RVNS-VNS, involves two efficient improvement procedures: Local Search Deletion and Steepest-descent Hill Climbing, which help the algorithm converge to high-quality solutions. Computational experiments show that the proposed RVNS-VNS method quickly reaches all known optimal solutions. Furthermore, it provides solutions for the instances that CPLEX solver was unable to obtain.

Metaheuristic methods for solving the Bilevel Uncapacitated Facility Location Problem with Clients' Preferences

Abstract In this study, we consider a variant of the Bilevel Uncapacitated Facility Location Problem (BLUFLP) in which the clients choose suppliers based on their own preferences. We propose three metaheuristic methods for solving this problem: Particle Swarm Optimization (PSO), Simulated Annealing (SA) and a combination of Reduced and Basic Variable Neighborhood Search Method (RVNS-VNS). The solution encoding and constructive elements of all three proposed algorithms are adapted to the problem under consideration. The results of computational tests on problem instances with up to 2000 clients and 2000 potential facility locations show good performance of all three proposed methods, even on large problem dimensions. Finally, the obtained results indicate that the proposed RVNS-VNS method outperforms the PSO and SA methods in the sense of solutions' quality and running times.

A reliability/availability approach to joint production and maintenance scheduling with multiple preventive maintenance services

In classical scheduling problems, it is often assumed that the machines are available during the whole planning horizon, while in realistic environments, machines need to be maintained and therefore may become unavailable within production periods. Hence, in this paper we suggest a joint production and maintenance scheduling (JPMS) with multiple preventive maintenance services, in which the reliability/availability approach is employed to model the maintenance aspects of a problem. To cope with the suggested JPMS, a mixed integer nonlinear programming model is developed and then a population-based variable neighbourhood search (PVNS) algorithm is devised for a solution method. In order to enhance the search diversification of basic variable neighbourhood search (VNS), our PVNS uses an epitome-based mechanism in each iteration to transform a group of initial individuals into a new solution, and then multiple trial solutions are generated in the shaking stage for a given solution. At the end of the local search stage, the best obtained solution by all of the trial solutions is recorded and the worst solution in population is replaced with this new solution. The evolution procedure is continued until a predefined number of iterations is violated. To validate the effectiveness and robustness of PVNS, an extensive computational study is implemented and the simulation results reveal that our PVNS performs better than traditional algorithms, especially in large size problems.

The development and application of metaheuristics for problems in graph theory: a computational study

This is a summary of the author’s PhD thesis supervised by Kenneth DarbyDowman and defended on November 26, 2008 at Brunel University, London. The thesis is written in English and is available from Brunel University Research Archive at http://bura.brunel.ac.uk/handle/2438/3061. The researchwork reported in the thesis deals with the development and application of metaheuristics for the solution of problems in graph theory. The aim is twofold. On the one hand, the most important and efficient metaheuristics, from classical to novel approaches, are presented.Many theoretical and practical aspects ofmetaheuristics are covered, outlining their main concepts and components, similarities and differences, advantages and disadvantages. Different classes of metaheuristics are specified and, in particular, the most important single-solution and population-based metaheuristics are discussed. On the other hand, the thesis addresses some recent combinatorial optimization problems formulated on graphs, and presents appropriate metaheuristics to obtain near-optimal solutions. These problems constitute some novel research areas, and are able to represent many real-world problems. The first problem studied is the minimum labelling spanning tree (MLST) problem. Several metaheuristics for the problem are presented. Specifically, the metaheuristics recommended in the literature, the Modified Genetic Algorithm (MGA) and the Pilot Method (PILOT), are examined in detail and implemented. Some new implementations of metaheuristics are further proposed: a Greedy Randomized Adaptive Search Procedure (GRASP), a basic Variable Neighbourhood Search (VNS), and a hybrid local search method (HYBRID) obtained by combining Variable Neighbourhood Search with Simulated Annealing (SA). The nonparametric statistical tests of Friedman and Nemenyi applied to the considered algorithms on a wide range of problem instances, indicate that VNS, HYBRID, and GRASP have significantly better performance than the other methods recommended in the literature with respect to solution quality and running time. In addition, it is shown thatVNS is particularly recommended

Hybrid variable neighbourhood approaches to university exam timetabling

In this paper, we investigate variable neighbourhood search (VNS) approaches for the university examination timetabling problem. In addition to a basic VNS method, we introduce variants of the technique with different initialisation methods including a biased VNS and its hybridisation with a Genetic Algorithm. A number of different neighbourhood structures are analysed. It is demonstrated that the proposed technique is able to produce high quality solutions across a wide range of benchmark problem instances. In particular, we demonstrate that the Genetic Algorithm, which intelligently selects appropriate neighbourhoods to use within the biased VNS, produces the best known results in the literature, in terms of solution quality, on some of the benchmark instances. However, it requires relatively large amount of computational time. Possible extensions to this overall approach are also discussed.

A hybrid model of integer programming and variable neighbourhood search for highly-constrained nurse rostering problems

This paper presents a hybrid multi-objective model that combines integer programming (IP) and variable neighbourhood search (VNS) to deal with highly-constrained nurse rostering problems in modern hospital environments. An IP is first used to solve the subproblem which includes the full set of hard constraints and a subset of soft constrains. A basic VNS then follows as a postprocessing procedure to further improve the IP’s resulting solutions. The satisfaction of the excluded constraints from the preceding IP model is the major focus of the VNS. Very promising results are reported compared with a commercial genetic algorithm and a hybrid VNS approach on real instances arising in a Dutch hospital. The comparison results demonstrate that our hybrid approach combines the advantages of both the IP and the VNS to beat other approaches in solving this type of problems. We also believe that the proposed methodology can be applied to other resource allocation problems with a large number of constraints.

A population-based variable neighborhood search for the single machine total weighted tardiness problem

This paper investigates the single machine total weighted tardiness problem, in which a set of independent jobs with distinct processing times, weights, and due dates are to be scheduled on a single machine to minimize the sum of weighted tardiness of all jobs. This problem is known to be strongly NP-hard, and thus provides a challenging area for metaheuristics. A population-based variable neighborhood search (PVNS) algorithm is developed to solve it. This algorithm differs from the basic variable neighborhood search (VNS). First, the PVNS consists of a number of iterations of the basic VNS, and in each iteration a population of solutions is used to simultaneously generate multiple trial solutions in a neighborhood so as to improve the search diversification. Second, the PVNS adopts a combination of path-relinking, variable depth search and tabu search to act as the local search procedure so as to improve the search intensification. Computational experiments show that the proposed PVNS algorithm can obtain the optimal or best known solutions within a reasonable computation time for all standard benchmark problem instances from the literature.

Introduction to the special issue on variable neighborhood search

Variable Neighborhood Search (VNS) is a metaheuristic for solving optimization problems based on systematic changes of structure within a search that may be performed in a deterministic way (Variable Neighborhood Descent, VND) or randomly (reduced VNS). Basic VNS combines random selection of a point in a shaking or perturbation step followed by a deterministic local search from that point. There are several extensions and hybrids of the basic VNS scheme suggested in the literature: if VND is used instead of local search, we have general VNS; the variable neighbourhood decomposition search (VNDS) method extends the basic VNS into a two-level VNS scheme based upon decomposition of the problem; the skewed VNS allows moves to a slightly worse but far solutions, etc. VNS has been successfully applied to a wide range of combinatorial and global optimization problems. In this special issue of Journal of Heuristics we collect several new successful applications of VNS as well as studies of advanced characteristics of VNS. Most of them were presented at the XVIII Mini EURO Conference (MEC), which was held at Tenerife, Spain, in November 2005. On that meeting, 61 VNS contributions by researches from 14 different countries and 4 continents were presented. The papers that make up this special issue on Variable Neighborhood Search illustrate breadth and depth of research in variable neighborhood search since they show some advanced features of the metaheuristic. Michael Polacek, Karl F. Doerner, Richard F. Hartl and Vittorio Maniezzo develop a basic variable neighborhood search algorithm to solve the Capacitated Arc Routing Problem with Intermediate Facilities that outperforms all known heuristics on four benchmark sets. The method uses only one exchange operator, the CROSS-exchange,

PERMUTATION-BASED GENETIC, TABU, AND VARIABLE NEIGHBORHOOD SEARCH HEURISTICS FOR MULTIPROCESSOR SCHEDULING WITH COMMUNICATION DELAYS

The multiprocessor scheduling problem with communication delays that we consider in this paper consists of finding a static schedule of an arbitrary task graph onto a homogeneous multiprocessor system, such that the total execution time (i.e. the time when all tasks are completed) is minimum. The task graph contains precedence relations as well as communication delays (or data transferring time) between tasks if they are executed on different processors. The multiprocessor architecture is assumed to contain identical processors connected in an arbitrary way, which is defined by a symmetric matrix containing minimum distances between every two processors. The solution is represented by a feasible permutation of tasks. In order to obtain the objective function value (i.e. schedule length, makespan), the feasible permutation has to be transformed into the actual schedule by the use of some heuristic method. For solving this NP-hard problem, we develop basic tabu search and variable neighborhood search heuristics, where various types of reduced Or-opt-like neighborhood structures are used for local search. A genetic search approach based on the same solution space is also developed. Comparative computational results on random graphs with up to 500 tasks and 8 processors are reported. On average, it appears that variable neighborhood search outperforms the other metaheuristics. In addition, a detailed performance analysis of both the proposed solution representation and heuristic methods is presented.