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2021 | OriginalPaper | Chapter

Particle Swarm Optimization and Grey Wolf Optimizer to Solve Continuous p-Median Location Problems

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Abstract

The continuous p-median location problem is to locate p facilities in the Euclidean plane in such a way that the sum of distances between each demand point and its nearest median/facility is minimized. In this chapter, the continuous p-median problem is studied, and a proposed Grey Wolf Optimizer (GWO) algorithm, which has not previously been applied to solve this problem, is presented and compared to a proposed Particle Swarm Optimization (PSO) algorithm. As an experimental evidence for the NFL theorem, the experimental results showed that the no algorithm can outperformed the other in all cases, however the proposed PSO has better performance in most of the cases. The experimental results show that the two proposed algorithms have better performance than other PSO methods in the literature.

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Literature
1.
go back to reference Christofides, N.: Graph Theory, an Algorithmic Approach. Academic Press, New York (1975)MATH Christofides, N.: Graph Theory, an Algorithmic Approach. Academic Press, New York (1975)MATH
2.
go back to reference Farahani, R.Z., Hekmatfar, M.: Facility Location Concepts, Models Algorithms and Case Studies. Springer, Berlin Heidelberg (2009)CrossRef Farahani, R.Z., Hekmatfar, M.: Facility Location Concepts, Models Algorithms and Case Studies. Springer, Berlin Heidelberg (2009)CrossRef
3.
go back to reference Eiselt, H.A., Marianov, V.: Foundations of Location Analysis (International Series in Operations Research & Management Science). Springer (2011). Eiselt, H.A., Marianov, V.: Foundations of Location Analysis (International Series in Operations Research & Management Science). Springer (2011).
4.
go back to reference Farahani, R.Z., SteadieSeifi, M., Asgari, N.: Multiple criteria facility location problems: a survey. Appl. Math. Model. 34, 1689–1709 (2010)MathSciNetCrossRef Farahani, R.Z., SteadieSeifi, M., Asgari, N.: Multiple criteria facility location problems: a survey. Appl. Math. Model. 34, 1689–1709 (2010)MathSciNetCrossRef
5.
go back to reference Sule, D.R.: Logistics of Facility Location and Allocation. Marcel Dekker, Inc. (2001) Sule, D.R.: Logistics of Facility Location and Allocation. Marcel Dekker, Inc. (2001)
6.
go back to reference Drezner, Z., Hamacher, H.W.: Facility Location Applications and Theory. Springer, Berlin (2004)MATH Drezner, Z., Hamacher, H.W.: Facility Location Applications and Theory. Springer, Berlin (2004)MATH
7.
go back to reference Panteli, A., Boutsinas, B., Giannikos, I.: On solving the multiple p-median problem based on biclustering. Oper. Res. 1–25 (2019) Panteli, A., Boutsinas, B., Giannikos, I.: On solving the multiple p-median problem based on biclustering. Oper. Res. 1–25 (2019)
8.
go back to reference Megiddo, N., Supowit, K.J.: On the complexity of some common geometric location problems. SIAM J. Comput. 13(1), 182–196 (1984)MathSciNetCrossRef Megiddo, N., Supowit, K.J.: On the complexity of some common geometric location problems. SIAM J. Comput. 13(1), 182–196 (1984)MathSciNetCrossRef
9.
go back to reference Daskin, M.S.: Network and Discrete Location: Models, Algorithms, 2nd edn Wiley, New York. (2013)CrossRef Daskin, M.S.: Network and Discrete Location: Models, Algorithms, 2nd edn Wiley, New York. (2013)CrossRef
10.
go back to reference Zijm, H., Klumpp, M., Regattieri, A., Heragu, S.: Operations, Logistics and Supply Chain Management (Lecture Notes in Logistics). Springer (2019). Zijm, H., Klumpp, M., Regattieri, A., Heragu, S.: Operations, Logistics and Supply Chain Management (Lecture Notes in Logistics). Springer (2019).
11.
go back to reference Brimberg, J., Drezner, Z., Mladenovic, N., Salhi, S.: A new local search for continuous location problems. Eur. J. Oper. Res. 232, 256–265 (2014)MathSciNetCrossRef Brimberg, J., Drezner, Z., Mladenovic, N., Salhi, S.: A new local search for continuous location problems. Eur. J. Oper. Res. 232, 256–265 (2014)MathSciNetCrossRef
12.
go back to reference Love, R.F., Morris, J.G., Wesolowsky, G.O.: Facilities Location: Models & Methods. North-Holland (1988). Love, R.F., Morris, J.G., Wesolowsky, G.O.: Facilities Location: Models & Methods. North-Holland (1988).
13.
go back to reference Eiselt, H.A., Sandbiom, C.L.: Decision Analysis, Location Models, and Scheduling Problems. Springer, Berlin Heidelberg GmbH (2004)CrossRef Eiselt, H.A., Sandbiom, C.L.: Decision Analysis, Location Models, and Scheduling Problems. Springer, Berlin Heidelberg GmbH (2004)CrossRef
14.
go back to reference Ghaderi, A., Jabalameli, M.S., Barzinpour, F., Rahmaniani, R.J.N., Economics, S.: An efficient hybrid particle swarm optimization algorithm for solving the uncapacitated continuous location-allocation problem 12(3), 421–439 (2012). Ghaderi, A., Jabalameli, M.S., Barzinpour, F., Rahmaniani, R.J.N., Economics, S.: An efficient hybrid particle swarm optimization algorithm for solving the uncapacitated continuous location-allocation problem 12(3), 421–439 (2012).
15.
go back to reference Hakimi, S.L.: Optimum locations of switching centers and the absolute centers and medians of a graph. Oper. Res. 12(3), 450–459 (1964)CrossRef Hakimi, S.L.: Optimum locations of switching centers and the absolute centers and medians of a graph. Oper. Res. 12(3), 450–459 (1964)CrossRef
16.
go back to reference Hakimi, S.L.: Optimum distribution of switching centers in a communication network and some related graph theoretic problems. Oper. Res. 13(3), 462–475 (1965)MathSciNetCrossRef Hakimi, S.L.: Optimum distribution of switching centers in a communication network and some related graph theoretic problems. Oper. Res. 13(3), 462–475 (1965)MathSciNetCrossRef
19.
go back to reference Melo, M.T., Nickel, S., Saldanha-Da-Gama, F.: Facility location and supply chain management–a review. Eur. J. Oper. Res. 196(2), 401–412 (2009)MathSciNetCrossRef Melo, M.T., Nickel, S., Saldanha-Da-Gama, F.: Facility location and supply chain management–a review. Eur. J. Oper. Res. 196(2), 401–412 (2009)MathSciNetCrossRef
20.
go back to reference ReVelle, C.S., Eiselt, H.A., Daskin, M.S.: A bibliography for some fundamental problem categories in discrete location science. Eur. J. Oper. Res. 184, 817–848 (2008)MathSciNetCrossRef ReVelle, C.S., Eiselt, H.A., Daskin, M.S.: A bibliography for some fundamental problem categories in discrete location science. Eur. J. Oper. Res. 184, 817–848 (2008)MathSciNetCrossRef
21.
go back to reference Mladenovic, N., Brimberg, J., Hansen, P., Moreno-Perez, J.A.: The p-median problem: a survey of metaheuristic approaches. Eur. J. Oper. Res. 179, 927–939 (2007)MathSciNetCrossRef Mladenovic, N., Brimberg, J., Hansen, P., Moreno-Perez, J.A.: The p-median problem: a survey of metaheuristic approaches. Eur. J. Oper. Res. 179, 927–939 (2007)MathSciNetCrossRef
22.
go back to reference Church R.L., Murray, A.: Location Covering Models: History, Applications and Advancements. Springer (2018) Church R.L., Murray, A.: Location Covering Models: History, Applications and Advancements. Springer (2018)
23.
go back to reference Salhi, S., Gamal, M.: A genetic algorithm based approach for the uncapacitated continuous location–allocation problem. Ann. Oper. Res. 123(1–4), 203–222 (2003)MathSciNetCrossRef Salhi, S., Gamal, M.: A genetic algorithm based approach for the uncapacitated continuous location–allocation problem. Ann. Oper. Res. 123(1–4), 203–222 (2003)MathSciNetCrossRef
24.
go back to reference Kuenne, R., Soland, R.: Exact and approximate solutions to the multisource Weber problem. Math. Program. 3, 193–209 (1972)MathSciNetCrossRef Kuenne, R., Soland, R.: Exact and approximate solutions to the multisource Weber problem. Math. Program. 3, 193–209 (1972)MathSciNetCrossRef
25.
go back to reference Ostresh, J.L.M.: Multi-exact solutions to the M-center location-allocation problem. In: Rushton, G., Goodchild M.F., Ostresh L.M. Jr. (eds.) Computer Programs for Location-Allocation Problems. Monograph No. 6, University of Iowa, IA (1973). Ostresh, J.L.M.: Multi-exact solutions to the M-center location-allocation problem. In: Rushton, G., Goodchild M.F., Ostresh L.M. Jr. (eds.) Computer Programs for Location-Allocation Problems. Monograph No. 6, University of Iowa, IA (1973).
26.
go back to reference Rosing, K.E.: An optimal method for solving the (generalized) multi-Weber problem. Eur. J. Oper. Res. 58, 414–426 (1992)CrossRef Rosing, K.E.: An optimal method for solving the (generalized) multi-Weber problem. Eur. J. Oper. Res. 58, 414–426 (1992)CrossRef
27.
go back to reference Drezner, Z., Brimberg, J., Mladenović, N., Salhi, S.: New heuristic algorithms for solving the planar p-median problem. Comput. Oper. Res. (2014) Drezner, Z., Brimberg, J., Mladenović, N., Salhi, S.: New heuristic algorithms for solving the planar p-median problem. Comput. Oper. Res. (2014)
28.
go back to reference Drezner, Z., Brimberg, J., Mladenovic, N., Salhi, S.: Solving the planar p-median problem by variable neighborhood and concentric searches. (in English), J. Glob. Optim. (2014) Drezner, Z., Brimberg, J., Mladenovic, N., Salhi, S.: Solving the planar p-median problem by variable neighborhood and concentric searches. (in English), J. Glob. Optim. (2014)
29.
go back to reference Francis, R.L., Lowe, T.J., Rayco, M.B., Tamir, A.: Aggregation error for location models: survey and analysis. Ann. Oper. Res. 167, 171–208 (2009). Francis, R.L., Lowe, T.J., Rayco, M.B., Tamir, A.: Aggregation error for location models: survey and analysis. Ann. Oper. Res. 167, 171–208 (2009).
30.
go back to reference Irawan, C.A., Salhi, S., Scaparra, M.P.: An adaptive multiphase approach for large unconditional and conditional p-median problems. Eur. J. Oper. Res. 237, 590–605 (2014)MathSciNetCrossRef Irawan, C.A., Salhi, S., Scaparra, M.P.: An adaptive multiphase approach for large unconditional and conditional p-median problems. Eur. J. Oper. Res. 237, 590–605 (2014)MathSciNetCrossRef
31.
go back to reference Rabie, H.M., El-Khodary, I.A., Tharwat, A.A.: A particle swarm optimization algorithm for the continuous absolute p-center location problem with Euclidean distance. Int. J. Adv. Comput. Sci. Appl. (IJACSA) 4(12), 101–106 (2013) Rabie, H.M., El-Khodary, I.A., Tharwat, A.A.: A particle swarm optimization algorithm for the continuous absolute p-center location problem with Euclidean distance. Int. J. Adv. Comput. Sci. Appl. (IJACSA) 4(12), 101–106 (2013)
32.
go back to reference Mirjalili, S., Mirjalili, S.M., Lewis, A.: Grey wolf optimizer. Adv. Eng. Softw. 69, 46–61 (2014)CrossRef Mirjalili, S., Mirjalili, S.M., Lewis, A.: Grey wolf optimizer. Adv. Eng. Softw. 69, 46–61 (2014)CrossRef
33.
go back to reference Ahmed H., Glasgow, J.: Swarm intelligence: concepts, models and applications. In: Technical Report 2012–585 School of Computing, Queen's University, Kingston, Ontario, Canada 2012, vol. K7L3N6 Ahmed H., Glasgow, J.: Swarm intelligence: concepts, models and applications. In: Technical Report 2012–585 School of Computing, Queen's University, Kingston, Ontario, Canada 2012, vol. K7L3N6
34.
go back to reference Tharwat, A., Ella Hassanien, A., Elnaghi, B.E.: A BA-based algorithm for parameter optimization of support vector machine. Pattern Recognit. Lett. 93, 13–22 (2017) Tharwat, A., Ella Hassanien, A., Elnaghi, B.E.: A BA-based algorithm for parameter optimization of support vector machine. Pattern Recognit. Lett. 93, 13–22 (2017)
35.
go back to reference Sumathi, S., Paneerselvam, S.: Computational Intelligence Paradigms: Theory & Applications using MATLAB. Taylor and Francis Group LLC (2010) Sumathi, S., Paneerselvam, S.: Computational Intelligence Paradigms: Theory & Applications using MATLAB. Taylor and Francis Group LLC (2010)
37.
go back to reference Hassanien A.E., Emary, E.: Swarm Intelligence: Principles, Advances, and Applications. CRC Press (2018) Hassanien A.E., Emary, E.: Swarm Intelligence: Principles, Advances, and Applications. CRC Press (2018)
38.
go back to reference Martinez, W.L., Martinez, A.R., Solka, J.: Exploratory data analysis with MATLAB. Chapman and Hall/CRC (2017). Martinez, W.L., Martinez, A.R., Solka, J.: Exploratory data analysis with MATLAB. Chapman and Hall/CRC (2017).
39.
go back to reference Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neutral Networks, pp. 1942–1948 (1995). Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neutral Networks, pp. 1942–1948 (1995).
40.
go back to reference Yang, X.-S.: Nature-Inspired Optimization Algorithms. Elsevier (2014) Yang, X.-S.: Nature-Inspired Optimization Algorithms. Elsevier (2014)
41.
go back to reference Shelokar, P.S., Siarry, P., Jayaraman, V.K., Kulkarni, B.D.: Particle swarm and ant colony algorithms hybridized for improved continuous optimization. Appl. Math. Comput. 188, 129–142 (2007)MathSciNetMATH Shelokar, P.S., Siarry, P., Jayaraman, V.K., Kulkarni, B.D.: Particle swarm and ant colony algorithms hybridized for improved continuous optimization. Appl. Math. Comput. 188, 129–142 (2007)MathSciNetMATH
42.
go back to reference Reinelt, G.: TSLIB—a traveling salesman library. ORSA J. Comput 3, 376–384 (1991)CrossRef Reinelt, G.: TSLIB—a traveling salesman library. ORSA J. Comput 3, 376–384 (1991)CrossRef
43.
go back to reference Brimberg, J., Hansen, P., Mladenovi, N., Taillard, E.D.: Improvements and comparison of heuristics for solving the uncapacitated multisource weber problem. Oper. Res. 48(3), 444–460 (2000)CrossRef Brimberg, J., Hansen, P., Mladenovi, N., Taillard, E.D.: Improvements and comparison of heuristics for solving the uncapacitated multisource weber problem. Oper. Res. 48(3), 444–460 (2000)CrossRef
44.
go back to reference Brito, J., Martínez, F.J., Moreno, J.A.: Particle swarm optimization for the continuous p-median problem. In: 6th WSEAS International Conference on Computational Intelligence, Man-Machine Systems and Cybernetics, CIMMACS, pp. 14–16 (2007). Brito, J., Martínez, F.J., Moreno, J.A.: Particle swarm optimization for the continuous p-median problem. In: 6th WSEAS International Conference on Computational Intelligence, Man-Machine Systems and Cybernetics, CIMMACS, pp. 14–16 (2007).
Metadata
Title
Particle Swarm Optimization and Grey Wolf Optimizer to Solve Continuous p-Median Location Problems
Author
Hassan Mohamed Rabie
Copyright Year
2021
DOI
https://doi.org/10.1007/978-3-030-59338-4_21

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