Skip to main content
main-content
Top

Hint

Swipe to navigate through the chapters of this book

2018 | OriginalPaper | Chapter

32. Diversity and Equity Models

Authors: Fernando Sandoya, Anna Martínez-Gavara, Ricardo Aceves, Abraham Duarte, Rafael Martí

Published in: Handbook of Heuristics

Publisher: Springer International Publishing

share
SHARE

Abstract

The challenge of maximizing the diversity of a collection of points arises in a variety of settings, and the growing interest of dealing with diversity resulted in an effort to study the management of equity. While the terms diversity and dispersion can be found in many optimization problems indistinguishable, we undertake to explore the different models behind them.
In particular, this chapter describes the mathematical models for two diversity and three equity models. Additionally, we also review two related models that have recently received special attention. This chapter also reviews heuristics and metaheuristics for finding near-optimal solutions for these problems, where constructive and local search-based methods, such as greedy randomized adaptive search procedure (GRASP) and tabu search, play an important role.
Literature
1.
go back to reference A \(\check {g}\)ca S, Eksioglu B, Ghosh JB (2000) Lagrangian solution of maximum dispersion problems. Nav Res Logist 47:97–114 A \(\check {g}\)ca S, Eksioglu B, Ghosh JB (2000) Lagrangian solution of maximum dispersion problems. Nav Res Logist 47:97–114
2.
go back to reference Aringhieri R, Cordone R (2011) Comparing local search metaheuristics for the maximum diversity problem. J Oper Res Soc 62:266–280 Aringhieri R, Cordone R (2011) Comparing local search metaheuristics for the maximum diversity problem. J Oper Res Soc 62:266–280
3.
go back to reference Aringhieri R, Cordone R, Grosso A (2015) Construction and improvement algorithms for dispersion problems. Eur J Oper Res 242:21–33 Aringhieri R, Cordone R, Grosso A (2015) Construction and improvement algorithms for dispersion problems. Eur J Oper Res 242:21–33
4.
go back to reference Asada H, Toyama F, Shoji K, Miyamichi J (2010) Genetic local search with adaptative crossover probability and its application to maximum diversity problem. IEEJ Trans Electron Inf Syst 130:529–520 Asada H, Toyama F, Shoji K, Miyamichi J (2010) Genetic local search with adaptative crossover probability and its application to maximum diversity problem. IEEJ Trans Electron Inf Syst 130:529–520
5.
go back to reference Brimberg J, Mladenovic N, Urosevic D, Ngai E (2009) Variable neighborhood search for the heaviest k-subgraph. Comput Oper Res 36:2885–2891 Brimberg J, Mladenovic N, Urosevic D, Ngai E (2009) Variable neighborhood search for the heaviest k-subgraph. Comput Oper Res 36:2885–2891
6.
go back to reference Campos V, Laguna M, Martí R (2005) Context-independient scatter and tabu search for permutation problems. INFORMS J Comput 17(1):111–122 Campos V, Laguna M, Martí R (2005) Context-independient scatter and tabu search for permutation problems. INFORMS J Comput 17(1):111–122
7.
go back to reference Carrasco R, Pham A, Gallego M, Gortázar F, Martí R, Duarte A (2015) Tabu search for the max-mean dispersion problem, Knowledge based systems 85:256–264 Carrasco R, Pham A, Gallego M, Gortázar F, Martí R, Duarte A (2015) Tabu search for the max-mean dispersion problem, Knowledge based systems 85:256–264
8.
go back to reference Castillo O, Melin P, Gamez E, Kreinovich V, Kosheleva O (2009) Intelligence techniques are needed to further enhance the advantage with diversity in problem solving. In: IEEE workshop hybrid intelligent models and applications (HIMA’09), Nashville, pp 48–55 Castillo O, Melin P, Gamez E, Kreinovich V, Kosheleva O (2009) Intelligence techniques are needed to further enhance the advantage with diversity in problem solving. In: IEEE workshop hybrid intelligent models and applications (HIMA’09), Nashville, pp 48–55
9.
go back to reference Dell’Amico M, Trubian M (1998) Solution of large weighted equicut problems. Eur J Oper Res 106:500–521 Dell’Amico M, Trubian M (1998) Solution of large weighted equicut problems. Eur J Oper Res 106:500–521
10.
go back to reference Della Groce F, Grosso A, Locatelli M (2009) A heuristic approach for the max-min diversity problem based on max-clique. Comput Oper Res 36(8):2429–2433 Della Groce F, Grosso A, Locatelli M (2009) A heuristic approach for the max-min diversity problem based on max-clique. Comput Oper Res 36(8):2429–2433
11.
go back to reference Deng Y, Bard JF (2011) A reactive GRASP with path relinking for capacitated clustering. J Heuristics 17:119–152 Deng Y, Bard JF (2011) A reactive GRASP with path relinking for capacitated clustering. J Heuristics 17:119–152
12.
go back to reference Duarte A, Martí R (2007) Tabu search and GRASP for the maximum diversity problem. Eur J Oper Res 178:71–84 Duarte A, Martí R (2007) Tabu search and GRASP for the maximum diversity problem. Eur J Oper Res 178:71–84
13.
go back to reference Duarte A, Sánchez-Oro J, Resende M, Glover F, Martí R (2015) GRASP with exterior path relinking for differential dispersion minimization. Inf Sci 296(1):46–60 Duarte A, Sánchez-Oro J, Resende M, Glover F, Martí R (2015) GRASP with exterior path relinking for differential dispersion minimization. Inf Sci 296(1):46–60
14.
go back to reference Erkut E (1990) The discrete p-dispersion problem. Eur J Oper Res 46:48–60 Erkut E (1990) The discrete p-dispersion problem. Eur J Oper Res 46:48–60
15.
go back to reference Erkut E, Neuman S (1989) Analytical models for locating undesirable facilities. Eur J Oper Res 40:275–291 Erkut E, Neuman S (1989) Analytical models for locating undesirable facilities. Eur J Oper Res 40:275–291
16.
go back to reference Feo T, Goldschmidt O, Khellaf M (1992) One-half approximation algorithms for the k-partition problem. Oper Res 40:S170–S173 Feo T, Goldschmidt O, Khellaf M (1992) One-half approximation algorithms for the k-partition problem. Oper Res 40:S170–S173
17.
go back to reference Freitas ARR, Guimarães FG, Pedrosa Silca RC, Souza MJF (2014) Memetic self-adaptive evolution strategies applied to the maximum diversity problem. Optim Lett 8(2): 705–714 Freitas ARR, Guimarães FG, Pedrosa Silca RC, Souza MJF (2014) Memetic self-adaptive evolution strategies applied to the maximum diversity problem. Optim Lett 8(2): 705–714
18.
go back to reference French E (2005) The importance of strategic change in achieving equity in diversity. Strateg Change 14:35–44. Wiley InterScience French E (2005) The importance of strategic change in achieving equity in diversity. Strateg Change 14:35–44. Wiley InterScience
19.
go back to reference Gallego M, Laguna M, Martí R, Duarte A (2013) Tabu search with strategic oscillation for the maximally diverse grouping problem. J Oper Res Soc 64(5):724-734 Gallego M, Laguna M, Martí R, Duarte A (2013) Tabu search with strategic oscillation for the maximally diverse grouping problem. J Oper Res Soc 64(5):724-734
20.
go back to reference Ghosh JB (1996) Computational aspects of the maximum diversity problem. Oper Res Lett 19:175–181 Ghosh JB (1996) Computational aspects of the maximum diversity problem. Oper Res Lett 19:175–181
21.
go back to reference Glover F (1977) Heuristics for integer programming using surrogate constraints. Decis Sci 8(1):156–166 Glover F (1977) Heuristics for integer programming using surrogate constraints. Decis Sci 8(1):156–166
22.
go back to reference Glover F (2014) Exterior path relinking for zero-one optimization. Int J Appl Metaheuristic Comput 5(3):1–8 Glover F (2014) Exterior path relinking for zero-one optimization. Int J Appl Metaheuristic Comput 5(3):1–8
23.
go back to reference Glover F, Laguna M (1997) Tabu Search. Kluwer Academic Publishers, Boston Glover F, Laguna M (1997) Tabu Search. Kluwer Academic Publishers, Boston
24.
go back to reference Glover F, Kuo CC, Dhir KS (1995) A discrete optimization model for preserving biological diversity. Appl Math Model 19:696–701 Glover F, Kuo CC, Dhir KS (1995) A discrete optimization model for preserving biological diversity. Appl Math Model 19:696–701
25.
go back to reference Glover F, Kuo CC, Dhir KS (1998) Heuristic algorithms for the maximum diversity problem. J Inf Optim Sci 19(1):109–132 Glover F, Kuo CC, Dhir KS (1998) Heuristic algorithms for the maximum diversity problem. J Inf Optim Sci 19(1):109–132
26.
go back to reference Hansen P, Mladenovic N (2001) Variable neighborhood search: principles and aplications. Eur J Opns Res 130:449–467 Hansen P, Mladenovic N (2001) Variable neighborhood search: principles and aplications. Eur J Opns Res 130:449–467
27.
go back to reference Hansen P, Mladenovic N (2003) Variable neighborhood search. In: Glover F, Kochenberger G (eds) Handbook in metaheuristics. Kluwer Academic Publishers, Boston Hansen P, Mladenovic N (2003) Variable neighborhood search. In: Glover F, Kochenberger G (eds) Handbook in metaheuristics. Kluwer Academic Publishers, Boston
28.
go back to reference Hassin R, Rubinstein S, Tamir A (1997) Approximation algorithms for maximum dispersion. Oper Res Lett 21:133–137 Hassin R, Rubinstein S, Tamir A (1997) Approximation algorithms for maximum dispersion. Oper Res Lett 21:133–137
29.
go back to reference Katayama K, Narihisa H (2005) An evolutionary approach for the maximum diversity problem. In: Recent advances in memetic algorithms, vol 166. Springer, Berlin/New York, pp 31–47 Katayama K, Narihisa H (2005) An evolutionary approach for the maximum diversity problem. In: Recent advances in memetic algorithms, vol 166. Springer, Berlin/New York, pp 31–47
30.
go back to reference Kincard RK (1992) Good solutions to discrete noxious location problems via metaheuristics. Ann Oper Res 40:265–281 Kincard RK (1992) Good solutions to discrete noxious location problems via metaheuristics. Ann Oper Res 40:265–281
31.
go back to reference Kuo CC, Glover F, Dhir KS (1993) Analyzing and modeling the maximum diversity problem by zero-one programming. Decis Sci 24:1171–1185 Kuo CC, Glover F, Dhir KS (1993) Analyzing and modeling the maximum diversity problem by zero-one programming. Decis Sci 24:1171–1185
32.
go back to reference Laguna M, Marí R (2003) Scatter search: methodology and implementations in C. Kluwer Academic Publishers, Dordrecht Laguna M, Marí R (2003) Scatter search: methodology and implementations in C. Kluwer Academic Publishers, Dordrecht
33.
go back to reference Martí R, Sandoya F (2013) GRASP and path relinking for the equitable dispersion problem. Comput Oper Res 40:3091–3099 Martí R, Sandoya F (2013) GRASP and path relinking for the equitable dispersion problem. Comput Oper Res 40:3091–3099
35.
go back to reference Martínez-Gavara A, Campos V, Gallego M, Laguna M, Martí R (2015) Tabu Search and GRASP for the Capacited Clustering Problem. Comput Optim Appl 62:589–607 MathSciNetCrossRef Martínez-Gavara A, Campos V, Gallego M, Laguna M, Martí R (2015) Tabu Search and GRASP for the Capacited Clustering Problem. Comput Optim Appl 62:589–607 MathSciNetCrossRef
36.
go back to reference Mladenović N, Todosijević R, Urosević D (2016) Less is more: basic variable neighborhood search for minimum differential dispersion problem. Inf Sci 326:160171 CrossRef Mladenović N, Todosijević R, Urosević D (2016) Less is more: basic variable neighborhood search for minimum differential dispersion problem. Inf Sci 326:160171 CrossRef
37.
go back to reference Morán-Mirabal LF, González-Velarde JL, Resende MGC, Silva RMA (2013) Randomized heuristics for handover minimization in mobility networks. J Heuristics 19:845–880 CrossRef Morán-Mirabal LF, González-Velarde JL, Resende MGC, Silva RMA (2013) Randomized heuristics for handover minimization in mobility networks. J Heuristics 19:845–880 CrossRef
38.
go back to reference O’Brien FA, Mingers J (1995) The equitable partitioning problem: a heuristic algorithm applied to the allocation of university student accommodation. Warwick Business School, Research Paper no. 187 O’Brien FA, Mingers J (1995) The equitable partitioning problem: a heuristic algorithm applied to the allocation of university student accommodation. Warwick Business School, Research Paper no. 187
39.
go back to reference Page SE (2007) The difference: how the power of diversity creates better groups, firms, schools, and societies. Princeton University Press, Princeton Page SE (2007) The difference: how the power of diversity creates better groups, firms, schools, and societies. Princeton University Press, Princeton
40.
go back to reference Palubeckis G (2007) Iterated tabu search for the maximum diversity problem. Appl Math Comput 189(1):371–383 MathSciNetMATH Palubeckis G (2007) Iterated tabu search for the maximum diversity problem. Appl Math Comput 189(1):371–383 MathSciNetMATH
41.
go back to reference Pisinger D (2006) Upper bounds and exact algorithms for p-dispersion problems. Comput Oper Res 33:1380–1398 CrossRef Pisinger D (2006) Upper bounds and exact algorithms for p-dispersion problems. Comput Oper Res 33:1380–1398 CrossRef
42.
go back to reference Porumbel D, Hao J, Glover F (2011) A simple and effective algorithm for the MaxMin diversity problem. Ann Oper Res 186(1):275–293 CrossRef Porumbel D, Hao J, Glover F (2011) A simple and effective algorithm for the MaxMin diversity problem. Ann Oper Res 186(1):275–293 CrossRef
43.
44.
go back to reference Ravi SS, Rosenkrantz DJ, Tayi GK (1994) Heuristic and special case algorithms for dispersion problems. Oper Res 42:299–310 CrossRef Ravi SS, Rosenkrantz DJ, Tayi GK (1994) Heuristic and special case algorithms for dispersion problems. Oper Res 42:299–310 CrossRef
45.
go back to reference Resende MGC, Werneck R (2004) A hybrid heuristic for the p-median problem. J Heuristics 10(1):59–88 CrossRef Resende MGC, Werneck R (2004) A hybrid heuristic for the p-median problem. J Heuristics 10(1):59–88 CrossRef
46.
go back to reference Resende MGC, Martí R, Gallego M, Duarte A (2010) GRASP and path relinking for the max−min diversity problem. Comput Oper Res 37(3):498–508 MathSciNetCrossRef Resende MGC, Martí R, Gallego M, Duarte A (2010) GRASP and path relinking for the max−min diversity problem. Comput Oper Res 37(3):498–508 MathSciNetCrossRef
47.
go back to reference Wang J, Zhou Y, Cai Y, Yin J (2012) Learnable tabu search guided by estimation of distribution for maximum diversity problems. Soft Comput 16(4):711–728 CrossRef Wang J, Zhou Y, Cai Y, Yin J (2012) Learnable tabu search guided by estimation of distribution for maximum diversity problems. Soft Comput 16(4):711–728 CrossRef
Metadata
Title
Diversity and Equity Models
Authors
Fernando Sandoya
Anna Martínez-Gavara
Ricardo Aceves
Abraham Duarte
Rafael Martí
Copyright Year
2018
DOI
https://doi.org/10.1007/978-3-319-07124-4_61

Premium Partner