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Variable Neighborhood Search

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Handbook of Metaheuristics

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 272))

Abstract

Variable neighborhood search (VNS) is a metaheuristic for solving combinatorial and global optimization problems whose basic idea is a systematic change of neighborhood both within a descent phase to find a local optimum and in a perturbation phase to get out of the corresponding valley. In this chapter we present the basic schemes of VNS and some of its extensions. We then describe recent developments, i.e., formulation space search and variable formulation search. We then present some families of applications in which VNS has proven to be very successful: (1) exact solution of large scale location problems by primal-dual VNS; (2) generation of solutions to large mixed integer linear programs, by hybridization of VNS and local branching; (3) generation of solutions to very large mixed integer programs using VNS decomposition and exact solvers (4) generation of good feasible solutions to continuous nonlinear programs; (5) adaptation of VNS for solving automatic programming problems from the Artificial Intelligence field and (6) exploration of graph theory to find conjectures, refutations and proofs or ideas of proofs.

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  1. 1.

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References

  1. D.J. Aloise, D. Aloise, C.T.M. Rocha, C.C. Ribeiro, J.C. Ribeiro, L.S.S. Moura, Scheduling work-over rigs for onshore oil production. Discrete Appl. Math. 154, 695–702 (2006)

    Google Scholar 

  2. D.V. Andrade, M.G.C. Resende, GRASP with path-relinking for network migration scheduling, in Proceedings of International Network Optimization Conference (INOC) (2007)

    Google Scholar 

  3. M. Aouchiche, P. Hansen, Recherche à voisinage variable de graphes extrèmes 13. À propos de la maille (French). RAIRO Oper. Res. 39, 275–293 (2005)

    Google Scholar 

  4. M. Aouchiche, P. Hansen, Automated results and conjectures on average distance in graphs, in Graph Theory in Paris, ed. by A. Bondy, J. Fonlupt, J.L. Fouquet, J.C. Fournier, J.L. Ramírez Alfonsń. Trends in Mathematics (Birkhäuser, Basel, 2006), pp. 21–36

    Google Scholar 

  5. M. Aouchiche, P. Hansen, On a conjecture about the Randic index. Discrete Math. 307, 262–265 (2007)

    Google Scholar 

  6. M. Aouchiche, P. Hansen, Bounding average distance using minimum degree. Graph Theory Notes N. Y. 56, 21–29 (2009)

    Google Scholar 

  7. M. Aouchiche, P. Hansen, Nordhaus-Gaddum relations for proximity and remoteness in graphs. Comput. Math. Appl. 59, 2827–2835 (2010)

    Google Scholar 

  8. M. Aouchiche, G. Caporossi, D. Cvetković, Variable neighborhood search for extremal graphs 8. Variations on Graffiti 105. Congressus Numerantium 148, 129–144 (2001)

    Google Scholar 

  9. M. Aouchiche, G. Caporossi, P. Hansen, M. Laffay, AutoGraphiX: a survey. Electron Notes Discrete Math. 22, 515–520 (2005)

    Google Scholar 

  10. M. Aouchiche, J.M. Bonnefoy, A. Fidahoussen, G. Caporossi, P. Hansen, L. Hiesse, J. Lacheré, A. Monhait, Variable neighborhood search for extremal graphs 14. The AutoGraphiX 2 system, in Global Optimization: From Theory to Implementation, ed. by L. Liberti, N. Maculan (Springer, Berlin, 2005), pp. 281–309

    Google Scholar 

  11. M. Aouchiche, P. Hansen, M. Zheng, Variable neighborhood search for extremal graphs 18. Conjectures and results about the Randic index. MATCH. Commun. Math. Comput. Chem. 56, 541–550 (2006)

    Google Scholar 

  12. M. Aouchiche, O. Favaron, P. Hansen, Recherche à voisinage variable de graphes extrèmes 26. Nouveaux résultats sur la maille (French). Les Cahiers du GERAD, G-2007-55, 2007

    Google Scholar 

  13. M. Aouchiche, G. Caporossi, P. Hansen, Variable Neighborhood search for extremal graphs 20. Automated comparison of graph invariants. MATCH. Commun. Math. Comput. Chem. 58, 365–384 (2007)

    Google Scholar 

  14. M. Aouchiche, G. Caporossi, P. Hansen, Variable neighborhood search for extremal graphs 27. Families of extremal graphs. Les Cahiers du GERAD, G-2007-87, 2007

    Google Scholar 

  15. M. Aouchiche, P. Hansen, M. Zheng, Variable neighborhood search for extremal graphs 19. Further conjectures and results about the Randic index. MATCH. Commun. Math. Comput. Chem. 58, 83–102 (2007)

    Google Scholar 

  16. M. Aouchiche, F.K. Bell, D. Cvetković, P. Hansen, P. Rowlinson, S.K. Simić, D. Stevanović, Variable neighborhood search for extremal graphs 16. Some conjectures related to the largest eigenvalue of a graph. Eur. J. Oper. Res. 191, 661–676 (2008)

    Google Scholar 

  17. M. Aouchiche, G. Brinkmann, P. Hansen, Variable neighborhood search for extremal graphs 21. Conjectures and results about the independence number. Discrete Appl. Math. 156, 2530–2542 (2009)

    Google Scholar 

  18. M. Aouchiche, O. Favaron, P. Hansen, Variable neighborhood search for extremal graphs 22. Extending bounds for independence to upper irredundance. Discrete Appl. Math. 157, 3497–3510 (2009)

    Google Scholar 

  19. M. Aouchiche, P. Hansen, D. Stevanović, Variable neighborhood search for extremal graphs 17. Further conjectures and results about the index. Discussiones Mathematicae: Graph Theory 29, 15–37 (2009)

    Google Scholar 

  20. C. Audet, V. Bachard, S. Le Digabel, Nonsmooth optimization through mesh adaptive direct search and variable neighborhood search. J. Glob. Optim. 41, 299–318 (2008)

    Google Scholar 

  21. J. Beasley, OR-Library: distributing test problems by electronic mail. J. Oper. Res. Soc. 41(11), 1069–1072 (1990)

    Google Scholar 

  22. N. Belacel, P. Hansen, N. Mladenović, Fuzzy J-means: a new heuristic for fuzzy clustering. Pattern Recognit. 35, 2193–2200 (2002)

    Google Scholar 

  23. S. Belhaiza, de, N. Abreu, HanP. sen, C. Oliveira, Variable neighborhood search for extremal graphs 11. Bounds on algebraic connectivity, in Graph Theory and Combinatorial Optimization, ed. by D. Avis, A. Hertz, O. Marcotte (2007), pp. 1–16

    Google Scholar 

  24. S. Bouaziz, H. Dhahri, A.M. Alimi, A. Abraham, A hybrid learning algorithm for evolving flexible beta basis function neural tree model. Neurocomputing 117, 107–117 (2013)

    Google Scholar 

  25. J. Brimberg, N. Mladenović, A variable neighborhood algorithm for solving the continuous location-allocation problem. Stud. Locat. Anal. 10, 1–12 (1996)

    Google Scholar 

  26. J. Brimberg, P. Hansen, N. Mladenović, É. Taillard, Improvements and comparison of heuristics for solving the multisource Weber problem. Oper. Res. 48, 444–460 (2000)

    Google Scholar 

  27. S. Canuto, M. Resende, C. Ribeiro, Local search with perturbations for the prize-collecting Steiner tree problem in graphs. Networks 31, 201–206 (2001)

    Google Scholar 

  28. G. Caporossi, P. Hansen, Variable neighborhood search for extremal graphs 1. The AutoGraphiX system. Discrete Math. 212, 29–44 (2000)

    Google Scholar 

  29. G. Caporossi, P. Hansen, Variable neighborhood search for extremal graphs 5. Three ways to automate finding conjectures. Discrete Math. 276, 81–94 (2004)

    Google Scholar 

  30. G. Caporossi, A.A. Dobrynin, I. Gutman, P. Hansen, Trees with palindromic Hosoya polynomials. Graph Theory Notes N. Y. 37, 10–16 (1999)

    Google Scholar 

  31. G. Caporossi, D. Cvetković, I. Gutman, P. Hansen, Variable neighborhood search for extremal graphs 2. Finding graphs with extremal energy. J. Chem. Inform. Comput. Sci. 39, 984–996 (1999)

    Google Scholar 

  32. G. Caporossi, I. Gutman, P. Hansen, Variable neighborhood search for extremal graphs 4. Chemical trees with extremal connectivity index. Comput. Chem. 23, 469–477 (1999)

    Google Scholar 

  33. G. Caporossi, I. Gutman, P. Hansen, L. Pavlović, Graphs with maximum connectivity index. Comput. Biol. Chem. 27, 85–90 (2003)

    Google Scholar 

  34. J. Cohoon, S. Sahni, Heuristics for backplane ordering. J. VLSI Comput. Syst. 2, 37–61 (1987)

    Google Scholar 

  35. D. Cvetkovic, S. Simic, G. Caporossi, P. Hansen, Variable neighborhood search for extremal graphs 3. On the largest eigenvalue of color-constrained trees. Linear Multilinear Algebra 49, 143–160 (2001)

    Google Scholar 

  36. W.C. Davidon, Variable metric algorithm for minimization. Argonne National Laboratory Report ANL-5990 (1959)

    Google Scholar 

  37. J. Desrosiers, N. Mladenović, D. Villeneuve, Design of balanced MBA student teams. J. Oper. Res. Soc. 56, 60–66 (2005)

    Google Scholar 

  38. H. Dhahri, A.M. Alimi, A. Abraham, Hierarchical multi-dimensional differential evolution for the design of beta basis function neural network. Neurocomputing 97, 131–140 (2012)

    Google Scholar 

  39. A. Djenic, N. Radojicic, M. Maric, N. Mladenović, Parallel VNS for bus terminal location problem. Appl. Soft Comput. 42, 448–458 (2016)

    Google Scholar 

  40. M. Dražić, V. Kovacevic-Vujcić, M. Cangalović, N. Mladenović, GLOB - a new VNS-based software for global optimization, in Global Optimization: From Theory to Implementation, ed. by L. Liberti, N. Maculan (Springer, Berlin, 2006), pp. 135–144

    Google Scholar 

  41. S. Elleuch, B. Jarboui, N. Mladenović, Reduced variable neighborhood programming for the preventive maintenance planning of railway infrastructure. GERAD Technical report, G-2016-92, Montreal (2016)

    Google Scholar 

  42. S. Elleuch, B. Jarboui, N. Mladenović, Variable neighborhood programming - A new automatic programming method in artificial intelligence. GERAD Technical report, G-2016-21, Montreal (2016)

    Google Scholar 

  43. M. Fischetti, A. Lodi, Local branching. Math. Program. 98, 23–47 (2003)

    Google Scholar 

  44. R. Fletcher, M.J.D. Powell, Rapidly convergent descent method for minimization. Comput. J. 6, 163–168 (1963)

    Google Scholar 

  45. P.W. Fowler, P. Hansen, G. Caporossi, A. Soncini, Variable neighborhood search for extremal graphs 7. Polyenes with maximum HOMO-LUMO gap. Chem. Phys. Lett. 49, 143–146 (2001)

    Google Scholar 

  46. M.R. Garey, D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, New York, 1978)

    Google Scholar 

  47. P. Gill, W. Murray, M.A. Saunders, SNOPT: an SQP algorithms for largescale constrained optimization. SIAM J. Optim. 12, 979–1006 (2002)

    Google Scholar 

  48. R.E. Griffith, R.A. Stewart, A nonlinear programming technique for the optimization of continuous processing systems. Manag. Sci. 7, 379–392 (1961)

    Google Scholar 

  49. I. Gutman, O. Miljković, G. Caporossi, P. Hansen, Alkanes with small and large Randić connectivity indices. Chem. Phys. Lett. 306, 366–372 (1999)

    Google Scholar 

  50. I. Gutman, P. Hansen, H. Mélot, Variable neighborhood search for extremal graphs 10. Comparison of irregularity indices for chemical trees. J. Chem. Inform. Model. 45, 222–230 (2005)

    Google Scholar 

  51. S. Hanafi, J. Lazić, N. Mladenović, C. Wilbaut, I. Crévits, New variable neighborhood search based 0-1 MIP heuristic. Yugoslav J. Oper. Res. 25, 343–360 (2015)

    Google Scholar 

  52. P. Hansen, Computers in graph theory. Graph Theory Notes N. Y. XLIII, 20–39 (2002)

    Google Scholar 

  53. P. Hansen, How far is, should and could be conjecture-making in graph theory an automated process? in Graph and Discovery. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol.69 (American Mathematical Society, Providence, 2005), pp. 189–229

    Google Scholar 

  54. P. Hansen, H. Mélot, Computers and discovery in algebraic graph theory. Linear Algebra Appl. 356, 211–230 (2002)

    Google Scholar 

  55. P. Hansen, H. Mélot, Variable neighborhood search for extremal graphs 6. Analyzing bounds for the connectivity index. J. Chem. Inform. Comput. Sci. 43, 1–14 (2003)

    Google Scholar 

  56. P. Hansen, H. Mélot, Variable neighborhood search for extremal graphs 9. Bounding the irregularity of a graph. Graphs Discov. 69, 253–264 (2005)

    Google Scholar 

  57. P. Hansen, N. Mladenović, J-Means: a new local search heuristic for minimum sum-of-squares clustering. Pattern Recognit. 34, 405–413 (2001)

    Google Scholar 

  58. P. Hansen, N. Mladenović, Variable neighborhood search: principles and applications. Eur. J. Oper. Res. 130, 449–467 (2001)

    Google Scholar 

  59. P. Hansen, N. Mladenović, Variable neighborhood search, in Handbook of Metaheuristics, ed. by F. Glover, G. Kochenberger (Kluwer, Boston, 2003), pp. 145–184

    Google Scholar 

  60. P. Hansen, D. Stevanović, Variable neighborhood search for extremal graphs 15. On bags and bugs. Discrete Appl. Math. 156, 986–997 (2005)

    Google Scholar 

  61. P. Hansen, D. Vukičević, Variable neighborhood search for extremal graphs 23. On the Randic index and the chromatic number. Discrete Math. 309, 4228–4234 (2009)

    Google Scholar 

  62. P. Hansen, B. Jaumard, N. Mladenović, A. Parreira, Variable neighborhood search for weighted maximum satisfiability problem. Les Cahiers du GERAD, G-2000-62, 2000

    Google Scholar 

  63. P. Hansen, N. Mladenović, D. Pérez-Brito, Variable neighborhood decomposition search. J. Heuristics 7, 335–350 (2001)

    Google Scholar 

  64. P. Hansen, H. Mélot, I. Gutman, Variable neighborhood search for extremal graphs 12. A note on the variance of bounded degrees in graphs. MATCH Commun. Math. Comput. Chem. 54, 221–232 (2005)

    Google Scholar 

  65. P. Hansen, M. Aouchiche, G. Caporossi, H. Mélot, D. Stevanović, What forms do interesting conjectures have in graph theory? in Graph and Discovery. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 69 (American Mathematical Society, Providence, 2005), pp. 231–251

    Google Scholar 

  66. P. Hansen, N. Mladenović, D. Urošević, Variable neighborhood search and local branching. Comput. Oper. Res. 33, 3034–3045 (2006)

    Google Scholar 

  67. P. Hansen, J. Brimberg, D. Urošević, N. Mladenović, Primal-dual variable neighborhood search for the simple plant location problem. INFORMS J. Comput. 19, 552–564 (2007)

    Google Scholar 

  68. P. Hansen, N. Mladenović, J.A. Moreno Pérez, Variable neighborhood search. Eur. J. Oper. Res. 191, 593–595 (2008)

    Google Scholar 

  69. P. Hansen, N. Mladenović, J.A. Moreno Pérez, Variable neighborhood search: methods and applications. 4OR. Q. J. Oper. Res. 6, 319–360 (2008)

    Google Scholar 

  70. A. Hertz, M. Plumettaz, N. Zufferey, Variable space search for graph coloring. Discrete Appl. Math. 156, 2551–2560 (2008)

    Google Scholar 

  71. ILOG CPLEX 10.1. User’s Manual (2006)

    Google Scholar 

  72. K. Jornsten, A. Lokketangen, Tabu search for weighted k-cardinality trees. Asia-Pacific J. Oper. Res. 14, 9–26 (1997)

    Google Scholar 

  73. J.R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection (MIT, Cambridge, 1992)

    Google Scholar 

  74. J. Lazić, S. Hanafi, N. Mladenović, D. Urošević, Variable neighbourhood decomposition search for 0–1 mixed integer programs. Comput. Oper. Res. 37, 1055–1067 (2010)

    Google Scholar 

  75. L. Liberti, M. Dražić, Variable neighbourhood search for the global optimization of constrained NLPs, in Proceedings of GO Workshop, Almeria, 2005

    Google Scholar 

  76. B. Melián, N. Mladenović, Editorial. IMA J. Manag. Math. 18, 99–100 (2007)

    Google Scholar 

  77. MIPLIB http://miplib.zib.de/miplib2003/

  78. N. Mladenović, A variable neighborhood algorithm – a new metaheuristic for combinatorial optimization. Abstracts of papers presented at Optimization Days, Montréal (1995), p. 112

    Google Scholar 

  79. N. Mladenović, Formulation space search – a new approach to optimization (plenary talk), in Proceedings of XXXII SYMOPIS’05, ed. by J. Vuleta (Vrnjacka Banja, Serbia, 2005)

    Google Scholar 

  80. N. Mladenović, P. Hansen, Variable neighborhood search. Comput. Oper. Res. 24, 1097–1100 (1997)

    Google Scholar 

  81. N. Mladenović, J. Petrović, V. Kovačević-Vujčić, M. Čangalović, Solving spread spectrum radar polyphase code design problem by tabu search and variable neighborhood search. Eur. J. Oper. Res. 151, 389–399 (2003)

    Google Scholar 

  82. N. Mladenović, F. Plastria, D. Urošević, Reformulation descent applied to circle packing problems. Comput. Oper. Res. 32, 2419–2434 (2005)

    Google Scholar 

  83. N. Mladenović, F. Plastria, D. Urošević, Formulation space search for circle packing problems. Lect. Notes Comput. Sci. 4638, 212–216 (2007)

    Google Scholar 

  84. N. Mladenović, M. Dražić, V. Kovačevic-Vujčić, M. Čangalović, General variable neighborhood search for the continuous optimization. Eur. J. Oper. Res. 191, 753–770 (2008)

    Google Scholar 

  85. N. Mladenović, D. Urošević, D. Pérez-Brito, C.G. García-González, Variable neighbourhood search for bandwidth reduction. Eur. J. Oper. Res. 200, 14–27 (2010)

    Google Scholar 

  86. N. Mladenovic, J. Kratica, V. Kovacevic-Vujcic, M. Cangalovic, Variable neighborhood search for metric dimension and minimal doubly resolving set problems. Eur. J. Oper. Res. 220, 328–337 (2012)

    Google Scholar 

  87. J.M. Moreno-Vega, B. Melián, Introduction to the special issue on variable neighborhood search. J. Heuristics 14, 403–404 (2008)

    Google Scholar 

  88. J.J. Pantrigo, R. Marti, A. Duarte, E.G. Pardo, Scatter search for the cutwidth minimization problem. Ann. Oper. Res. 199, 285–304 (2012)

    Google Scholar 

  89. E.G. Pardo, N. Mladenović, J.J. Pantrigo, A. Duarte, Variable formulation search for the cut-width minimization problem. Appl. Soft Comput. 13, 2242–2252 (2014)

    Google Scholar 

  90. F. Plastria, N. Mladenović, D. Urošević, Variable neighborhood formulation space search for circle packing, in 18th Mini Euro Conference VNS, Tenerife, 2005

    Google Scholar 

  91. J. Puchinger, G. Raidl, Bringing order into the neighborhoods: relaxation guided variable neighborhood search. J. Heuristics 14, 457–472 (2008)

    Google Scholar 

  92. C.C. Ribeiro, M.C. de Souza, Variable neighborhood search for the degree-constrained minimum spanning tree problem. Discrete Appl. Math. 118, 43–54 (2002)

    Google Scholar 

  93. C.C. Ribeiro, E. Uchoa, R. Werneck, A hybrid GRASP with perturbations for the Steiner problem in graphs. INFORMS J. Comput. 14, 228–246 (2002)

    Google Scholar 

  94. J. Rolim, O. Sýkora, I. Vrt’o, Optimal cutwidths and bisection widths of 2- and 3-dimensional meshes, in Graph-Theoretic Concepts in Computer Science. Lecture Notes in Computer Science, vol. 1017 (1995), pp. 252–264

    Google Scholar 

  95. J. Sedlar, D. Vukicevic, M. Aouchiche, P. Hansen, Variable neighborhood search for extremal graphs 24. Conjectures and results about the clique number. Les Cahiers du GERAD G-2007-33, 2007

    Google Scholar 

  96. J. Sedlar, D. Vukicevic, M. Aouchiche, P. Hansen, Variable neighborhood search for extremal graphs 25. Products of connectivity and distance measures. Les Cahiers du GERAD, G-2007-47, 2007

    Google Scholar 

  97. D. Stevanovic, M. Aouchiche, P. Hansen, On the spectral radius of graphs with a given domination number. Linear Algebra Appl. 428, 1854–1864 (2008)

    Google Scholar 

  98. B. Subudhi, D. Jena, A differential evolution based neural network approach to nonlinear system identification. Appl. Soft Comput. 11, 861–871 (2011)

    Google Scholar 

  99. A.D. Toksari, E. Güner, Solving the unconstrained optimization problem by a variable neighborhood search. J. Math. Anal. Appl. 328, 1178–1187 (2007)

    Google Scholar 

  100. D. Urošević, J. Brimberg, N. Mladenović, Variable neighborhood decomposition search for the edge weighted k-cardinality tree problem. Comput. Oper. Res. 31, 1205–1213 (2004)

    Google Scholar 

  101. Y. Vimont, S. Boussier, M. Vasquez, Reduced costs propagation in an efficient implicit enumeration for the 01 multidimensional knapsack problem. J. Comb. Optim. 15, 165–178 (2008)

    Google Scholar 

  102. R. Whitaker, A fast algorithm for the greedy interchange of large-scale clustering and median location problems. INFOR 21, 95–108 (1983)

    Google Scholar 

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Acknowledgements

The work of Nenad Mladenović was conducted at the National Research University Higher School of Economics, Nizhni Novgorod, Russia, and supported by RSF grant 14-41-00039. The fourth author is partially funded by Ministerio de Economía y Competitividad (Spanish Government) with FEDER funds, grant TIN2015-70226-R, and by Fundación Cajacanarias, grant 2016TUR19.

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Authors and Affiliations

  1. École des Hautes Études Commerciales, Montréal, QC, Canada

    Pierre Hansen

  2. GERAD, Montréal, QC, Canada

    Pierre Hansen

  3. Mathematical Institute, SANU, Belgrade, Serbia

    Nenad Mladenović

  4. Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, ON, Canada

    Jack Brimberg

  5. IUDR and Department of Informatics and Systems Engineering, Universidad de La Laguna, Tenerife, Spain

    José A. Moreno Pérez

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  1. Pierre Hansen
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Correspondence to Nenad Mladenović .

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  1. Department of Mathematics and Industrial Engineering, Polytechnique Montréal, Montreal, QC, Canada

    Michel Gendreau

  2. Département d’informatique et de recherche opérationnelle, Université de Montréal, Montreal, QC, Canada

    Jean-Yves Potvin

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Hansen, P., Mladenović, N., Brimberg, J., Pérez, J.A.M. (2019). Variable Neighborhood Search. In: Gendreau, M., Potvin, JY. (eds) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol 272. Springer, Cham. https://doi.org/10.1007/978-3-319-91086-4_3

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