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2018 | OriginalPaper | Chapter

24. Scatter Search

Authors: Rafael Martí, Ángel Corberán, Juanjo Peiró

Published in: Handbook of Heuristics

Publisher: Springer International Publishing

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Abstract

Scatter search (SS) is a population-based metaheuristic that has been shown to yield high-quality outcomes for hard combinatorial optimization problems. It uses strategies for combining solution vectors, making limited use of randomization, that have proved effective in a variety of problem settings. The fundamental concepts and principles were first proposed in the 1960s and 1970s as an extension of mathematical relaxation techniques for combinatorial optimization problems. Its framework is flexible, allowing the development of implementations with varying degrees of sophistication.
This chapter provides a grounding in the scatter search methodology that will allow readers to create successful applications of their own. To illustrate this, we present a scatter search implementation for a \(\mathcal {NP}\)-hard variant of the classic p-hub median problem, for which we describe search elements, mechanisms, and strategies to generate, combine, and improve solutions.
Literature
1.
go back to reference Martí R (ed) (2006) Scatter search methods for optimization. Volume 169 of feature cluster of the European Journal of Operational Research. Elsevier, Amsterdam Martí R (ed) (2006) Scatter search methods for optimization. Volume 169 of feature cluster of the European Journal of Operational Research. Elsevier, Amsterdam
2.
go back to reference Alkhazaleh HA, Ayob M, Ahmad Z (2013) Scatter search for solving team orienteering problem. Res J Appl Sci 8(3):181–190 Alkhazaleh HA, Ayob M, Ahmad Z (2013) Scatter search for solving team orienteering problem. Res J Appl Sci 8(3):181–190
3.
go back to reference Bernardino AM, Bernardino EM, Sánchez-Pérez JM, Gómez-Pulido JA, Vega-Rodríguez MA (2012) Solving sonet problems using a hybrid scatter search algorithm. In: Madani K, Dourado CA, Rosa A, Filipe J (eds) Computational intelligence. Volume 399 of studies in computational intelligence. Springer, Berlin/Heidelberg, pp 81–97 Bernardino AM, Bernardino EM, Sánchez-Pérez JM, Gómez-Pulido JA, Vega-Rodríguez MA (2012) Solving sonet problems using a hybrid scatter search algorithm. In: Madani K, Dourado CA, Rosa A, Filipe J (eds) Computational intelligence. Volume 399 of studies in computational intelligence. Springer, Berlin/Heidelberg, pp 81–97
4.
go back to reference Botón-Fernández M, Vega-Rodríguez MA, Prieto-Castrillo F (2013) An efficient and self-adaptive model based on scatter search: solving the grid resources selection problem. In: Moreno-Díaz R, Pichler F, Quesada-Arencibia A (eds) Computer aided systems theory – EUROCAST 2013. Volume 8111 of lecture notes in computer science. Springer, Berlin/Heidelberg, pp 396–403 Botón-Fernández M, Vega-Rodríguez MA, Prieto-Castrillo F (2013) An efficient and self-adaptive model based on scatter search: solving the grid resources selection problem. In: Moreno-Díaz R, Pichler F, Quesada-Arencibia A (eds) Computer aided systems theory – EUROCAST 2013. Volume 8111 of lecture notes in computer science. Springer, Berlin/Heidelberg, pp 396–403
5.
go back to reference Bova N, Ibáñez Ó, Cordón Ó (2013) Image segmentation using extended topological active nets optimized by scatter search. IEEE Comput Intell Mag 8(1):16–32 CrossRef Bova N, Ibáñez Ó, Cordón Ó (2013) Image segmentation using extended topological active nets optimized by scatter search. IEEE Comput Intell Mag 8(1):16–32 CrossRef
6.
go back to reference de Athayde Costa e Silva M, Klein CE, Mariani VC, Dos Santos Coelho L (2013) Multiobjective scatter search approach with new combination scheme applied to solve environmental/economic dispatch problem. Energy 53:14–21 de Athayde Costa e Silva M, Klein CE, Mariani VC, Dos Santos Coelho L (2013) Multiobjective scatter search approach with new combination scheme applied to solve environmental/economic dispatch problem. Energy 53:14–21
7.
go back to reference Engin O, Ylmaz MK, Baysal ME, Sarucanl A (2013) Solving fuzzy job shop scheduling problems with availability constraints using a scatter search method. J Multiple-Valued Log Soft Comput 21(3–4):317–334 Engin O, Ylmaz MK, Baysal ME, Sarucanl A (2013) Solving fuzzy job shop scheduling problems with availability constraints using a scatter search method. J Multiple-Valued Log Soft Comput 21(3–4):317–334
8.
go back to reference Ernst AT, Krishnamoorthy M (1996) Efficient algorithms for the uncapacitated single allocation p-hub median problem. Locat Sci 4(3):139–154 CrossRef Ernst AT, Krishnamoorthy M (1996) Efficient algorithms for the uncapacitated single allocation p-hub median problem. Locat Sci 4(3):139–154 CrossRef
9.
go back to reference Everett H (1963) Generalized Lagrangean multiplier method for solving problems of optimal allocation of resources. Oper Res 11:399–417 CrossRef Everett H (1963) Generalized Lagrangean multiplier method for solving problems of optimal allocation of resources. Oper Res 11:399–417 CrossRef
11.
go back to reference Festa P, Resende MGC (2011) Grasp: basic components and enhancements. Telecommun Syst 46(3):253–271 CrossRef Festa P, Resende MGC (2011) Grasp: basic components and enhancements. Telecommun Syst 46(3):253–271 CrossRef
12.
go back to reference Glover F (1965) A multiphase-dual algorithm for the zero-one integer programming problem. Oper Res 13:879–919 CrossRef Glover F (1965) A multiphase-dual algorithm for the zero-one integer programming problem. Oper Res 13:879–919 CrossRef
13.
go back to reference Glover F (1977) Heuristics for integer programming using surrogate constraints. Decis Sci 8(7):156–166 CrossRef Glover F (1977) Heuristics for integer programming using surrogate constraints. Decis Sci 8(7):156–166 CrossRef
14.
go back to reference Glover F (1994) Tabu search for nonlinear and parametric optimization with links to genetic algorithms. Discret Appl Math 49(1–3):231–255 MathSciNetCrossRef Glover F (1994) Tabu search for nonlinear and parametric optimization with links to genetic algorithms. Discret Appl Math 49(1–3):231–255 MathSciNetCrossRef
15.
go back to reference Glover F (1998) A template for scatter search and path relinking. In Hao JK, Lutton E, Ronald E, Schoenauer M, Snyers D (eds) Artificial Evolution. Volume 1363 of Lecture Notes in Computer Science. Springer, Berlin/Heidelberg, pp 13–54. Glover F (1998) A template for scatter search and path relinking. In Hao JK, Lutton E, Ronald E, Schoenauer M, Snyers D (eds) Artificial Evolution. Volume 1363 of Lecture Notes in Computer Science. Springer, Berlin/Heidelberg, pp 13–54.
16.
go back to reference Glover F, Laguna M, Martí R (2000) Fundamentals of scatter search and path relinking. Control Cybern 29(3):652–684 MathSciNetMATH Glover F, Laguna M, Martí R (2000) Fundamentals of scatter search and path relinking. Control Cybern 29(3):652–684 MathSciNetMATH
17.
go back to reference Guo XW, Liu SX, Wang DZ (2012) Scatter search for solving multi-objective disassembly sequence optimization problems. J Northeast Univ 33(1):56–59 MATH Guo XW, Liu SX, Wang DZ (2012) Scatter search for solving multi-objective disassembly sequence optimization problems. J Northeast Univ 33(1):56–59 MATH
18.
go back to reference Habibi MR, Rashidinejad M, Zeinaddini-Meymand M, Fadainejad R (2014) An efficient scatter search algorithm to solve transmission expansion planning problem using a new load shedding index. Int Trans Electr Energy Syst 24(2):153–165 CrossRef Habibi MR, Rashidinejad M, Zeinaddini-Meymand M, Fadainejad R (2014) An efficient scatter search algorithm to solve transmission expansion planning problem using a new load shedding index. Int Trans Electr Energy Syst 24(2):153–165 CrossRef
19.
go back to reference Hariharan R, Golden Renjith Nimal RJ (2014) Solving flow shop scheduling problems using a hybrid genetic scatter search algorithm. Middle East J Sci Res 20(3):328–333 Hariharan R, Golden Renjith Nimal RJ (2014) Solving flow shop scheduling problems using a hybrid genetic scatter search algorithm. Middle East J Sci Res 20(3):328–333
20.
go back to reference Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor
21.
go back to reference Hu L, Jiang Y, Zhu J, Chen Y (2013) Hybrid of the scatter search, improved adaptive genetic, and expectation maximization algorithms for phase-type distribution fitting. Appl Math Comput 219(10):5495–5515 MathSciNetMATH Hu L, Jiang Y, Zhu J, Chen Y (2013) Hybrid of the scatter search, improved adaptive genetic, and expectation maximization algorithms for phase-type distribution fitting. Appl Math Comput 219(10):5495–5515 MathSciNetMATH
22.
go back to reference Huacuja HJF, Valdez GC, Rangel RAP, Barbosa JG, Reyes LC, Valadez JMC, Soberanes HJP, Villanueva DT (2012) Scatter search with multiple improvement methods for the linear ordering problem. Malays J Comput Sci 25(2):76–89 Huacuja HJF, Valdez GC, Rangel RAP, Barbosa JG, Reyes LC, Valadez JMC, Soberanes HJP, Villanueva DT (2012) Scatter search with multiple improvement methods for the linear ordering problem. Malays J Comput Sci 25(2):76–89
23.
go back to reference Hvattum LM, Duarte A, Glover F, Martí R (2013) Designing effective improvement methods for scatter search: An experimental study on global optimization. Soft Comput 17(1):49–62 CrossRef Hvattum LM, Duarte A, Glover F, Martí R (2013) Designing effective improvement methods for scatter search: An experimental study on global optimization. Soft Comput 17(1):49–62 CrossRef
24.
go back to reference Ibáñez O, Cordón O, Damas S, Santamaría J (2012) An advanced scatter search design for skull-face overlay in craniofacial superimposition. Expert Syst Appl 39(1):1459–1473 CrossRef Ibáñez O, Cordón O, Damas S, Santamaría J (2012) An advanced scatter search design for skull-face overlay in craniofacial superimposition. Expert Syst Appl 39(1):1459–1473 CrossRef
25.
go back to reference Jabal-Ameli MS, Moshref-Javadi M (2014) Concurrent cell formation and layout design using scatter search. Int J Adv Manuf Technol 71(1–4):1–22 CrossRef Jabal-Ameli MS, Moshref-Javadi M (2014) Concurrent cell formation and layout design using scatter search. Int J Adv Manuf Technol 71(1–4):1–22 CrossRef
26.
go back to reference Jabal-Ameli MS, Moshref-Javadi M, Tabrizi BB, Mohammadi M (2013) Cell formation and layout design with alternative routing: a multi-objective scatter search approach. Int J Ind Syst Eng 14(3):269–295 Jabal-Ameli MS, Moshref-Javadi M, Tabrizi BB, Mohammadi M (2013) Cell formation and layout design with alternative routing: a multi-objective scatter search approach. Int J Ind Syst Eng 14(3):269–295
27.
go back to reference Jaradat G, Ayob M, Ahmad Z (2014) On the performance of scatter search for post-enrolment course timetabling problems. J Comb Optim 27(3):417–439 MathSciNetCrossRef Jaradat G, Ayob M, Ahmad Z (2014) On the performance of scatter search for post-enrolment course timetabling problems. J Comb Optim 27(3):417–439 MathSciNetCrossRef
28.
go back to reference Kashefi AH, Meshkin A, Zargoosh M, Zahiri J, Taheri M, Ashtiani S (2013) Scatter-search with support vector machine for prediction of relative solvent accessibility. EXCLI J 12:52–63 Kashefi AH, Meshkin A, Zargoosh M, Zahiri J, Taheri M, Ashtiani S (2013) Scatter-search with support vector machine for prediction of relative solvent accessibility. EXCLI J 12:52–63
29.
go back to reference Kothari R, Ghosh D (2014) A scatter search algorithm for the single row facility layout problem. J Heuristics 20(2):125–142 CrossRef Kothari R, Ghosh D (2014) A scatter search algorithm for the single row facility layout problem. J Heuristics 20(2):125–142 CrossRef
30.
go back to reference Krishnan M, Karthikeyan T, Chinnusamy TR, Venkatesh Raja K (2012) A novel hybrid metaheuristic scatter search-simulated annealing algorithm for solving flexible manufacturing system layout. Eur J Sci Res 73(1):52–61 Krishnan M, Karthikeyan T, Chinnusamy TR, Venkatesh Raja K (2012) A novel hybrid metaheuristic scatter search-simulated annealing algorithm for solving flexible manufacturing system layout. Eur J Sci Res 73(1):52–61
31.
go back to reference Laguna M, Gortázar F, Gallego M, Duarte A, Martí R (2014) A black-box scatter search for optimization problems with integer variables. J Glob Optim 58(3):497–516 MathSciNetCrossRef Laguna M, Gortázar F, Gallego M, Duarte A, Martí R (2014) A black-box scatter search for optimization problems with integer variables. J Glob Optim 58(3):497–516 MathSciNetCrossRef
32.
go back to reference Laguna M, Martí R (2002) Scatter search: methodology and implementations in C. Kluwer Academic, Norwell MATH Laguna M, Martí R (2002) Scatter search: methodology and implementations in C. Kluwer Academic, Norwell MATH
33.
go back to reference Le Q, Yang G, Hung W, Guo W (2012) Reliable NoC mapping based on scatter search. In: Liu B, Ma M, Chang J (eds) Information computing and applications. Volume 7473 of lecture notes in computer science. Springer, Berlin/Heidelberg, pp 640–647 Le Q, Yang G, Hung W, Guo W (2012) Reliable NoC mapping based on scatter search. In: Liu B, Ma M, Chang J (eds) Information computing and applications. Volume 7473 of lecture notes in computer science. Springer, Berlin/Heidelberg, pp 640–647
34.
go back to reference Le Q, Yang G, Hung WNN, Zhang X, Fan F (2014) A multiobjective scatter search algorithm for fault-tolerant noc mapping optimisation. Int J Electron 101(8):1056–1073 CrossRef Le Q, Yang G, Hung WNN, Zhang X, Fan F (2014) A multiobjective scatter search algorithm for fault-tolerant noc mapping optimisation. Int J Electron 101(8):1056–1073 CrossRef
35.
go back to reference Li J, Prins C, Chu F (2012) A scatter search for a multi-type transshipment point location problem with multicommodity flow. J Intell Manuf 23(4):1103–1117 CrossRef Li J, Prins C, Chu F (2012) A scatter search for a multi-type transshipment point location problem with multicommodity flow. J Intell Manuf 23(4):1103–1117 CrossRef
36.
go back to reference Li VC, Liang YC, Sun YY, Chen YS (2012) A scatter search method for the multidimensional knapsack problem with generalized upper bound constraints. J Chin Inst Ind Eng 29(8):559–571 Li VC, Liang YC, Sun YY, Chen YS (2012) A scatter search method for the multidimensional knapsack problem with generalized upper bound constraints. J Chin Inst Ind Eng 29(8):559–571
37.
go back to reference Li ZZ, Song XY, Sun JZ, Huang ZT (2012) A scatter search methodology for the aircraft conflict resolution problem. In: Huang D, Jiang C, Bevilacqua V, Figueroa JC (eds) Intelligent computing technology. Volume 7389 of lecture notes in computer science. Springer, Berlin/Heidelberg, pp 18–24 Li ZZ, Song XY, Sun JZ, Huang ZT (2012) A scatter search methodology for the aircraft conflict resolution problem. In: Huang D, Jiang C, Bevilacqua V, Figueroa JC (eds) Intelligent computing technology. Volume 7389 of lecture notes in computer science. Springer, Berlin/Heidelberg, pp 18–24
38.
go back to reference Lin SW, Chen SC (2012) Parameter determination and feature selection for c4.5 algorithm using scatter search approach. Soft Comput 16(1):63–75 CrossRef Lin SW, Chen SC (2012) Parameter determination and feature selection for c4.5 algorithm using scatter search approach. Soft Comput 16(1):63–75 CrossRef
39.
go back to reference Liu Q, Wang WX, Zhu KR, Zhang CY, Rao YQ (2014) Advanced scatter search approach and its application in a sequencing problem of mixed-model assembly lines in a case company. Eng Optim 46(11):1485–1500 MathSciNetCrossRef Liu Q, Wang WX, Zhu KR, Zhang CY, Rao YQ (2014) Advanced scatter search approach and its application in a sequencing problem of mixed-model assembly lines in a case company. Eng Optim 46(11):1485–1500 MathSciNetCrossRef
40.
go back to reference Love RF, Morris JG, Wesolowski GO (1988) Facilities location: models and methods. Elsevier, New York MATH Love RF, Morris JG, Wesolowski GO (1988) Facilities location: models and methods. Elsevier, New York MATH
41.
go back to reference Lv Y, Wang G, Tang L (2014) Scenario-based modeling approach and scatter search algorithm for the stochastic slab allocation problem in steel industry. ISIJ Int 54(6):1324–1333 CrossRef Lv Y, Wang G, Tang L (2014) Scenario-based modeling approach and scatter search algorithm for the stochastic slab allocation problem in steel industry. ISIJ Int 54(6):1324–1333 CrossRef
42.
go back to reference Martí R, Corberán Á, Peiró J (2015) Scatter search for an uncapacitated p-hub median problem. Comput Oper Res 58(0):53–66 MathSciNetCrossRef Martí R, Corberán Á, Peiró J (2015) Scatter search for an uncapacitated p-hub median problem. Comput Oper Res 58(0):53–66 MathSciNetCrossRef
43.
go back to reference Meymand MZ, Rashidinejad M, Khorasani H, Rahmani M, Mahmoudabadi A (2012) An implementation of modified scatter search algorithm to transmission expansion planning. Turk J Electr Eng Comput Sci 20(Suppl.1):1206–1219 Meymand MZ, Rashidinejad M, Khorasani H, Rahmani M, Mahmoudabadi A (2012) An implementation of modified scatter search algorithm to transmission expansion planning. Turk J Electr Eng Comput Sci 20(Suppl.1):1206–1219
44.
go back to reference Naderi B, Ruiz R (2014) A scatter search algorithm for the distributed permutation flowshop scheduling problem. Eur J Oper Res 239(2):323–334 MathSciNetCrossRef Naderi B, Ruiz R (2014) A scatter search algorithm for the distributed permutation flowshop scheduling problem. Eur J Oper Res 239(2):323–334 MathSciNetCrossRef
45.
go back to reference O’Kelly ME (1987) A quadratic integer program for the location of interacting hub facilities. Eur J Oper Res 32(3):393–404 MathSciNetCrossRef O’Kelly ME (1987) A quadratic integer program for the location of interacting hub facilities. Eur J Oper Res 32(3):393–404 MathSciNetCrossRef
46.
go back to reference Pantrigo JJ, Duarte A (2013) Low-level hybridization of scatter search and particle filter for dynamic TSP solving. In: Alba E, Nakib A, Siarry P (eds) Metaheuristics for dynamic optimization. Volume 433 of studies in computational intelligence. Springer, Berlin/Heidelberg, pp 291–308 Pantrigo JJ, Duarte A (2013) Low-level hybridization of scatter search and particle filter for dynamic TSP solving. In: Alba E, Nakib A, Siarry P (eds) Metaheuristics for dynamic optimization. Volume 433 of studies in computational intelligence. Springer, Berlin/Heidelberg, pp 291–308
47.
go back to reference Pantrigo JJ, Martí R, Duarte A, Pardo EG (2012) Scatter search for the cutwidth minimization problem. Ann Oper Res 199(1):285–304 MathSciNetCrossRef Pantrigo JJ, Martí R, Duarte A, Pardo EG (2012) Scatter search for the cutwidth minimization problem. Ann Oper Res 199(1):285–304 MathSciNetCrossRef
48.
go back to reference Peiró J, Corberán A, Martí R (2014) GRASP for the uncapacitated r-allocation p-hub median problem. Comput Oper Res 43(1):50–60 MathSciNetCrossRef Peiró J, Corberán A, Martí R (2014) GRASP for the uncapacitated r-allocation p-hub median problem. Comput Oper Res 43(1):50–60 MathSciNetCrossRef
49.
go back to reference Pendharkar PC (2013) Scatter search based interactive multi-criteria optimization of fuzzy objectives for coal production planning. Eng Appl Artif Intell 26(5–6):1503–1511 CrossRef Pendharkar PC (2013) Scatter search based interactive multi-criteria optimization of fuzzy objectives for coal production planning. Eng Appl Artif Intell 26(5–6):1503–1511 CrossRef
50.
go back to reference Resende MGC, Ribeiro CC, Glover F, Martí R (2010) Scatter search and path-relinking: fundamentals, advances, and applications. In: Gendreau M, Potvin JY (eds) Handbook of metaheuristics. International series in operations research & management science, vol 146. Springer, New York, pp 87–107 CrossRef Resende MGC, Ribeiro CC, Glover F, Martí R (2010) Scatter search and path-relinking: fundamentals, advances, and applications. In: Gendreau M, Potvin JY (eds) Handbook of metaheuristics. International series in operations research & management science, vol 146. Springer, New York, pp 87–107 CrossRef
51.
go back to reference Sadiq AT, Sagheer AM, Ibrahim MS (2012) Improved scatter search for 4-colour mapping problem. Int J Reasoning-based Intell Syst 4(4):221–226 CrossRef Sadiq AT, Sagheer AM, Ibrahim MS (2012) Improved scatter search for 4-colour mapping problem. Int J Reasoning-based Intell Syst 4(4):221–226 CrossRef
52.
go back to reference Salazar-Aguilar MA, Ríos-Mercado RZ, González-Velarde JL, Molina J (2012) Multiobjective scatter search for a commercial territory design problem. Ann Oper Res 199(1):343–360 MathSciNetCrossRef Salazar-Aguilar MA, Ríos-Mercado RZ, González-Velarde JL, Molina J (2012) Multiobjective scatter search for a commercial territory design problem. Ann Oper Res 199(1):343–360 MathSciNetCrossRef
53.
go back to reference Shen Z, Zou H, Sun H (2012) Task scheduling for imaging reconnaissance satellites using multiobjective scatter search algorithm. In: Li Z, Li X, Liu Y, Cai Z (eds) Computational intelligence and intelligent systems. Communications in computer and information science. Springer, Berlin/Heidelberg, pp 240–249 Shen Z, Zou H, Sun H (2012) Task scheduling for imaging reconnaissance satellites using multiobjective scatter search algorithm. In: Li Z, Li X, Liu Y, Cai Z (eds) Computational intelligence and intelligent systems. Communications in computer and information science. Springer, Berlin/Heidelberg, pp 240–249
54.
go back to reference Tan Y, Cheng TCE, Ji M (2014) A multi-objective scatter search for the ladle scheduling problem. Int J Prod Res 52(24):7513–7528 CrossRef Tan Y, Cheng TCE, Ji M (2014) A multi-objective scatter search for the ladle scheduling problem. Int J Prod Res 52(24):7513–7528 CrossRef
55.
go back to reference Tang J, Zhang G, Zhang B, Cen H (2012) Resource-constrained project scheduling using electromagnetism-based scatter search. J Comput Inf Syst 8(12):5219–5227 Tang J, Zhang G, Zhang B, Cen H (2012) Resource-constrained project scheduling using electromagnetism-based scatter search. J Comput Inf Syst 8(12):5219–5227
56.
go back to reference Tavakkoli-Moghaddam R, Ranjbar-Bourani M, Amin GR, Siadat A (2012) A cell formation problem considering machine utilization and alternative process routes by scatter search. J Intell Manuf 23(4):1127–1139 CrossRef Tavakkoli-Moghaddam R, Ranjbar-Bourani M, Amin GR, Siadat A (2012) A cell formation problem considering machine utilization and alternative process routes by scatter search. J Intell Manuf 23(4):1127–1139 CrossRef
57.
go back to reference Valsecchi A, Damas S, Santamaría J, Marrakchi-Kacem L (2014) Intensity-based image registration using scatter search. Artif Intell Med 60(3):151–163 CrossRef Valsecchi A, Damas S, Santamaría J, Marrakchi-Kacem L (2014) Intensity-based image registration using scatter search. Artif Intell Med 60(3):151–163 CrossRef
58.
go back to reference Wang J, Hedar AR, Wang S, Ma J (2012) Rough set and scatter search metaheuristic based feature selection for credit scoring. Expert Syst Appl 39(6):6123–6128 CrossRef Wang J, Hedar AR, Wang S, Ma J (2012) Rough set and scatter search metaheuristic based feature selection for credit scoring. Expert Syst Appl 39(6):6123–6128 CrossRef
59.
go back to reference Xu Y, Qu R (2012) A hybrid scatter search meta-heuristic for delay-constrained multicast routing problems. Appl Intell 36(1):229–241 CrossRef Xu Y, Qu R (2012) A hybrid scatter search meta-heuristic for delay-constrained multicast routing problems. Appl Intell 36(1):229–241 CrossRef
61.
go back to reference Zhang T, Chaovalitwongse WA, Zhang Y (2012) Scatter search for the stochastic travel-time vehicle routing problem with simultaneous pick-ups and deliveries. Comput Oper Res 39(10):2277–2290 MathSciNetCrossRef Zhang T, Chaovalitwongse WA, Zhang Y (2012) Scatter search for the stochastic travel-time vehicle routing problem with simultaneous pick-ups and deliveries. Comput Oper Res 39(10):2277–2290 MathSciNetCrossRef
Metadata
Title
Scatter Search
Authors
Rafael Martí
Ángel Corberán
Juanjo Peiró
Copyright Year
2018
DOI
https://doi.org/10.1007/978-3-319-07124-4_20

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