Abstract
The continuous defensive location problem (CDLP) is an NP-hard problem well investigated in the fields of competitive facility location. CDLP is a bi-level programming problem, where a decision maker locates defensive facilities with different capacities in the vertices of the network in order to avoid her/his aggressors from reaching core which is an important vertex in the network. In the present research, a hybrid method combining the imperialist competitive algorithm (ICA) and BFGS algorithm is presented to solve the CDLP. The proposed hybrid method integrates the ICA and the BFGS algorithm, providing a highly near-optimal solution. The upper-level problem solves the optimal location of defense facilities, and hybrid algorithm is applied. The lower-level problem is the shortest path problem which is solved by the Dijkstra method. The feasibility of the proposed hybrid method is demonstrated for a number of small, medium and large instances of the problem. The test results are compared with those obtained by genetic algorithm, particle swarm optimization and ICA in terms of solution accuracy and required CPU time. Simulation results reveal that the proposed hybrid method is feasible, robust and more effective in solving the CDLP than conventional metaheuristic methods.
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References
Alba E, Chicano JF (2004) Training neural networks with GA hybrid algorithms. In: Deb K (ed) Proceedings of GECCO04, Seattle, Washington, LNCS 3102, pp 852–863
Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algorithm: an algorithm for optimisation inspired by imperialistic competition. In: IEEE congress on evolutionary computation (no. 4425083), pp 4661–4667
Cormen TH, Leiserson CE, Rivest RL (1990) Introduction to algorithms. MIT Press, Cambridge
Daskin MS (1995) Network and discrete location: models, algorithms, and applications, 1st edn. Wiley, New York
Daskin MS (2013) Network and discrete location: models, algorithms, and applications, 2nd edn. Wiley, New York
Drezner Z (1982) Competitive location strategies for two facilities. Reg Sci Urban Econ 12:485–493
Drezner Z, Hamacher H (2002) Facility location: applications and theory. Springer, Berlin
Eaton BC, Lipsey RG (1975) The principle of minimum differentiation reconsidered: some new developments in the theory of spatial competition. Rev Econom Stud 42:27–49
Feng Y, Teng GF, Wang AX, Yao YM (2007) Chaotic inertia weight in particle swarm optimization. In: Second international conference on innovative computing, information and control, ICICIC’07, pp 475–478
Fletcher R (1987) Practical methods of optimization, 2nd edn. Wiley, New York
Fortuny-Amat J, McCarl B (1981) A representation and economic interpretation of a two-level programming problem. J Oper Res Soc 32:783–792
Francis RL, McGinnis LF, White JA (1992) Facility layout and location: an analytical approach, 2nd edn. Prentice Hall, NJ
Gendreau M, Potvin JY (2010) Handbook of metaheuristics. Springer, New York
Glover FW, Kochenberger GA (2003) Handbook of metaheuristics. Springer, New York
Hakimi SL (1983) On locating new facilities in a competitive environment. Eur J Oper Res 12:29–35
Hassan MY, Suharto MN, Abdullah MP, Majid MS, Hussin F (2012) Application of particle swarm optimization for solving optimal generation plant location problem. Int J Electr Electr Syst Res 5:47–56
Haupt RL, Haupt SE (2004) Practical genetic algorithms. Wiley, New York
Holland J (1992) Adaptation in natural and artificial system. MIT Press, Cambridge
Hotelling H (1929) Stability in competition. Econ J 30:41–57
Jabalameli MS, Ghaderi A (2008) Hybrid algorithms for the uncapacitated continuous location-allocation problem. Int J Adv Manuf Technol 37:202–209
Kennedy J, Eberhart R (1995) Particle swarm optimization. IEEE Int Conf Neural Netw 4:1942–1948
Khabbazi A, Atashpaz-Gargari E, Lucas C (2009) Imperialist competitive algorithm for minimum bit error rate beam forming. Int J Bio-Inspired Comput 1:125–133
Khanduzi R, Peyghami MR, Maleki HR (2015) Solving continuous single-objective defensive location problem based on hybrid directed tabu search algorithm. Int J Adv Manuf Technol 76:295–310
Li DH, Fukushima M (2001) On the global convergence of BFGS method for nonconvex unconstrained optimization problems. SIAM J Optim 11(4):1054–1064
Liu H, Abraham A (2007) An hybrid fuzzy variable neighborhood particle swarm optimization algorithm for solving quadratic assignment problems. J Univ Comput Sci 13(9):1309–1331
Liu GR, Han X, Lam KY (2002) A combined genetic algorithm and nonlinear least squares method for material characterization using elastic waves. Comput Methods Appl Mech Eng 191:1909–1921
Lust T, Tuyttens D (2014) Variable and large neighborhood search to solve the multiobjective set covering problem. J Heuristics 20:165–188
Malek M, Guruswamy M, Owens H, Pandya M (1989) A hybrid algorithm technique. Technical report, Department of Computer Sciences, The University of Texas at Austin, TR-89-06
Maniezzo V, Stutzle T, Vob S (2009) Hybridizing metaheuristics and mathematical programming. Springer, New York
Martinez-Salazar IA, Molina J, Angel-Bello F, Gomez T, Caballero R (2014) Solving a bi-objective transportation location routing problem by metaheuristic algorithms. Eur J Oper Res 234(1):25–36
Moadi S, Mohaymany AS, Babaei M (2011) Application of imperialist competitive algorithm to the emergency medical services location problem. Int J Artif Intell Appl 2(4):137–147
Mohammadi M, Tavakkoli-Moghaddam R, Rostami H (2011) A multiobjective imperialist competitive algorithm for a capacitated hub covering location problem. Int J Ind Eng Comput 2:671–688
Molla-Alizadeh-Zavardehi S, Sadi Nezhad S, Tavakkoli-Moghaddam R, Yazdani M (2013) Solving a fuzzy fixed charge solid transportation problem by metaheuristics. Math Comput Model 57:1543–1558
Montana DJ, Davis L (1989) Training feed forward neural networks using genetic algorithms. In: Proceedings of the international joint conference on artificial intelligence, New York
Moreno Perez JA, Marcos Moreno Vega J, Verdegay JL (2004) Fuzzy location problems on networks. Fuzzy Sets Syst 142(3):393–405
Nekooghadirli N, Tavakkoli-Moghaddam R, Ghezavati VR, Javanmard S (2014) Solving a new bi-objective location-routing-inventory problem in a distribution network by metaheuristics. Comput Ind Eng 76:204–221
Niknam T, Taherian Fard E, Pourjafarian N, Rousta A (2011) An efficient hybrid algorithm based on modified imperialist competitive algorithm and K-means for data clustering. Eng Appl Artif Intell 24:306–317
Osman IH (1995) An introduction to meta-heuristics. In: Wilsdon C, Lawrence M (eds) Operational research tutorial papers. Operational Research Society Press, Birmingham, pp 92–122
Peyghami MR, Khanduzi R (2012) Predictability and forecasting automotive price based on a hybrid train algorithm of MLP neural network. Neural Comput Appl 21:125–132
Pradeepmon TG, Paul B (2011) A hybrid algorithm for uncapacitated facility location problems. Int J Serv Econ Manag 3(2):197–206
Rambod M, Rezaeian J (2014) Robust meta-heuristics implementation for unrelated parallel machines scheduling problem with rework processes and machine eligibility restrictions. Comput Ind Eng 77:15–28
Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: Evolutionary computation proceedings, 1998. IEEE world congress on computational intelligence, the 1998 IEEE international conference, pp 69–73
Talbi N, Belarbi K (2011) Fast hybrid PSO and tabu search approach for optimization of a fuzzy controller. IJCSI Int J Comput Sci Issues 8(2):215–219
Tavakkoli-Moghaddam R, Gholipour-Kanani Y, Shahramifar M (2013) A multiobjective imperialist competitive algorithm for a capacitated single-allocation hub location problem. Int J Eng 26(6):605–620
Uno T, Katagiri H (2008) Single and multiobjective defensive location problems on a network. Eur J Oper Res 188:76–84
Weber A (1909) Ber den Standort der Industrienl. Reine Theory des Standorts Mohr, Tbingen, Teil
White JA, Case KE (1974) On covering problems and the central facilities location problems. Geogr Anal 6(3):281–294
Wendell RE, McKelvey RD (1981) New perspective in competitive location theory. Eur J Oper Res 6:174–182
Yang XS (2008) Introduction to mathematical optimization from linear programming to metaheuristics. Cambridge International Science Publishing, Cambridge
Zanjirani Farahani R, Hekmatfar M (2009) Facility location concepts, models, algorithms and case studies. Springer, Berlin
Zhang G, Shao X, Li P, Gao L (2009) An effective hybrid particle swarm optimization algorithm for multiobjective flexible job-shop scheduling problem. Comput Ind Eng 56:1309–1318
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The authors would like to thank the research council of Shiraz University of Technology for supporting this research.
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Maleki, H.R., Khanduzi, R. & Akbari, R. A novel hybrid algorithm for solving continuous single-objective defensive location problem. Neural Comput & Applic 28, 3323–3340 (2017). https://doi.org/10.1007/s00521-016-2254-3
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DOI: https://doi.org/10.1007/s00521-016-2254-3