A Tutorial on Variable Neighborhood Search

Variable Neighborhood Search (VNS) is a recent metaheuristic, or framework for building heuristics, which exploits systematically the idea of neighborhood change, both in the descent to local minima and in the escape from the valleys which contain them. In this tutorial we first present the ingredients of VNS, i.e., Variable Neighborhood Descent (VND) and Reduced VNS (RVNS) followed by the basic and then the general scheme of VNS itself which contain both of them. Extensions are presented, in particular Skewed VNS (SVNS) which enhances exploration of far away valleys and Variable Neighborhood Decomposition Search (VNDS), a two-level scheme for solution of large instances of various problems. In each case, we present the scheme, some illustrative examples and questions to be addressed in order to obtain an efficient implementation.

[1]  Matteo Fischetti,et al.  A local branching heuristic for mixed‐integer programs with 2‐level variables, with an application to a telecommunication network design problem , 2004, Networks.

[2]  Belén Melián-Batista,et al.  The Parallel Variable Neighborhood Search for the p-Median Problem , 2002, J. Heuristics.

[3]  F. Glover,et al.  Handbook of Metaheuristics , 2019, International Series in Operations Research & Management Science.

[4]  Pierre Hansen,et al.  Variable neighborhood search for extremal graphs: 1 The AutoGraphiX system , 1997, Discret. Math..

[5]  P. Hansen,et al.  Developments of Variable Neighborhood Search , 2002 .

[6]  Alain Hertz,et al.  A variable neighborhood search for graph coloring , 2003, Eur. J. Oper. Res..

[7]  Fred W. Glover,et al.  Tabu Search , 1997, Handbook of Heuristics.

[8]  George L. Nemhauser,et al.  The uncapacitated facility location problem , 1990 .

[9]  E. Baum.  Towards practical `neural' computation for combinatorial optimization problems , 1987 .

[10]  P. Hansen.  Les Procedures D’exploration et D’optimisation par Separation Et Evaluation , 1975 .

[11]  P. Hansen,et al.  Variable neighborhood search for the p-median , 1997 .

[12]  Matteo Fischetti,et al.  Local branching , 2003, Math. Program..

[13]  P. Hansen,et al.  Variable Neighborhood Search for Extremal Graphs. 15. On Bags and Bugs , 2005 .

[14]  Pierre Hansen,et al.  Variable Neighborhood Search , 2018, Handbook of Heuristics.

[15]  Polly Bart,et al.  Heuristic Methods for Estimating the Generalized Vertex Median of a Weighted Graph , 1968, Oper. Res..

[16]  Celso C. Ribeiro,et al.  A Hybrid GRASP with Perturbations for the Steiner Problem in Graphs , 2002, INFORMS J. Comput..

[17]  Pierre Hansen,et al.  Variable Neighborhood Decomposition Search , 1998, J. Heuristics.

[18]  Pierre Hansen,et al.  Variable Neighborhood Search for Extremal Graphs: IV: Chemical Trees with Extremal Connectivity Index , 1998, Comput. Chem..

[19]  Pierre Hansen,et al.  Variable neighborhood search: Principles and applications , 1998, Eur. J. Oper. Res..

[20]  D. Cvetkovic,et al.  Variable neighborhood search for extremal graphs 3 , 2001 .

[21]  Celso C. Ribeiro,et al.  GRASP and VNS for Max-Cut , 2002 .

[22]  C. Ribeiro,et al.  Essays and Surveys in Metaheuristics , 2002, Operations Research/Computer Science Interfaces Series.

[23]  Pierre Hansen,et al.  J-MEANS: a new local search heuristic for minimum sum of squares clustering , 1999, Pattern Recognit..

[24]  Pierre Hansen,et al.  Variable Neighborhood Search for Extremal Graphs. 2. Finding Graphs with Extremal Energy , 1998, J. Chem. Inf. Comput. Sci..

[25]  Peter I. Cowling,et al.  Effective Local and Guided Variable Neighbourhood Search Methods for the Asymmetric Travelling Salesman Problem , 2001, EvoWorkshops.

[26]  Ravindra K. Ahuja,et al.  Very large-scale neighborhood search , 2000 .

[27]  C. Reeves.  Modern heuristic techniques for combinatorial problems , 1993 .

[28]  Nenad Mladenović,et al.  An Introduction to Variable Neighborhood Search , 1997 .

[29]  Jacques Desrosiers,et al.  Accelerating Strategies in Column Generation Methods for Vehicle Routing and Crew Scheduling Problems , 2002 .

[30]  Pierre Hansen,et al.  Recherche à Voisinage Variable , 2000 .

[31]  R. A. Whitaker,et al.  A Fast Algorithm For The Greedy Interchange For Large-Scale Clustering And Median Location Problems , 1983 .

[32]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[33]  A. D. Parreira,et al.  Variable Neighbourhood Search for Maximum Weight Satisfiability Problem , 2000 .

[34]  Y S Abu-Mostafa,et al.  Neural networks for computing , 1987 .

[35]  Ashish Tiwari,et al.  A greedy genetic algorithm for the quadratic assignment problem , 2000, Comput. Oper. Res..

[36]  Pierre Hansen,et al.  Programmes mathématiques en variables 0-1 , 1974 .

[37]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[38]  Pierre Hansen,et al.  Variable neighborhood search for extremal graphs. 5. Three ways to automate finding conjectures , 2000, Discret. Math..

[39]  Zvi Drezner,et al.  A New Genetic Algorithm for the Quadratic Assignment Problem , 2003, INFORMS J. Comput..

[40]  Dominique Peeters,et al.  Location on networks , 1992 .

[41]  Pierre Hansen,et al.  Variable Neighbourhood Search , 2003 .

[42]  Silvano Martello,et al.  Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization , 2012 .