Abstract
In this paper, we introduce a novel continuous bi-level programming model of an interdiction/fortification problem, referred to as partial interdiction/fortification problem with capacitated facilities and Budget constraint (PIFCB). PIFCB is modeled as a Stackelberg game between a defender (leader) and an attacker (follower). The decisions of the defender are related to find optimal allocations of defensive resources as well as customer-facility assignments. So, the total system losses and demand-weighted distance are minimized. Following this action, the attacker seeks facilities to interdict for the capacity or service reduction and maximal losses resulting from a limited offensive budget. After modeling this problem, two combined methods, entitled particle swarm optimization with CPLEX (PSO-CPLEX) and teaching learning-based optimization with CPLEX (TLBO-CPLEX), are devised as solution procedures. For this bi-level programming problem, we executed two approaches which search the solution space of the defender’s subproblem, according to PSO and TLBO principles, and corresponding attacker’s subproblem is solved using CPLEX. To investigate the suggested methods, a comprehensive computational study is conducted and the effectiveness of the methods is compared together. The experimental results show the superiority of TLBO-CPLEX against PSO-CPLEX.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aksen D, Piyade N, Aras N (2010) The budget constrained r-interdiction median problem with capacity expansion. Central Eur J Oper Res 18(3):269–291
Aksen D, Aras N, Piyade N (2013) A bilevel p-median model for the planning and protection of critical facilities. J Heuristics 19:373–398
Aksen D, Akca SS, Aras N (2014) A bilevel partial interdiction problem with capacitated facilities and demand outsourcing. Comput Oper Res 41(1):346–358
Bard JF (1998) Practical bilevel optimization: algorithms and applications. Kluwer Academic Publishers, Dordrecht
Chen D, Zou F, Wang J, Yuan W (2015) A teaching–learning-based optimization algorithm with producer–scrounger model for global optimization. Soft Comput 19:745–762
Church RL, Scaparra MP, Middleton RS (2004) Identifying critical infrastructure: the median and covering facility interdiction problems. Ann Assoc Am Geogr 94(3):491–502
Church RL, Scaparra MP (2007) Protecting critical assets: the r-interdiction median problem with fortification. Geogr Anal 39(2):129–46
Colson B, Marcotte P, Savard G (2005) Bilevel programming: a survey. 4OR Q J Oper Res 3(2):87–107
Hakimi SL (1964) Optimum locations of switching centers and the absolute centers and medians of a graph. Oper Res 12(3):450–459
Hansen P, Jaumard B, Savard G (1992) New branch-and-bound rules for linear bilevel programming. SIAM J Sci Stat Comput 13:1194–1217
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 Electron Syst Res 5:47–56
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: IEEE international conference on neural networks, vol 4, pp 1942–1948
Liberatore F, Scaparra MP, Daskin MS (2012) Hedging against disruptions with ripple effects in location analysis. Omega 40(10):21–30
Rao RV, Kalyankar VD (2013) Parameter optimization of modern machining processes using teaching–learning-based optimization algorithm. Eng Appl Artif Intell 26:524–531
Rao RV, Patel V (2012) An elitist teaching–learning-based optimization algorithm for solving complex constrained optimization problems. Int J Ind Eng Comput 3:535–560
Rao RV, Patel V (2013) Comparative performance of an elitist teaching–learning-based optimization algorithm for solving unconstrained optimization problems. Int J Ind Eng Comput 4:29–50
Rao RV, Savsani VJ, Vakharia DP (2011) Teaching-learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput Aided Des 43:303–315
Rao RV, Savsani VJ, Vakharia DP (2012) Teaching–learning-based optimization: an optimization method for continuous non-linear large scale problem. Inf Sci 183:1–15
Ren A, Wang Y, Xue X (2014) An interval programming approach for the bilevel linear programming problem under fuzzy random environments. Soft Comput 18:995–1009
Satapathy SC, Naik A (2012) Improved teaching learning based optimization for global function optimization. Decis Sci Lett 2:23–34
Scaparra MP, Church RL (2008) A bilevel mixed integer program for critical infrastructure protection planning. Comput Oper Res 35(6):1905–23
Scaparra MP, Church RL (2012) Protecting supply systems to mitigate potential disaster: a model to fortify capacitated facilities. Int Reg Sci Rev 35:188–210
Stackelberg H (1952) The theory of market economy. Oxford University Press, Oxford
Talbi EG (2013) Metaheuristics for bi-level optimization. Springer, Berlin Heidelberg
Weber A (1909) Über den Standort der Industrien. Reine Theorie des Standorts, Mohr, Tübingen, Teil
White JA, Case KE (1974) On covering problems and the central facilities location problems. Geogr Anal 6(3):281–294
Yang XS (2010) Nature-inspired metaheuristic algorithm. Luniver Press, Frome
Acknowledgements
The first author would like to thank Gonbad Kavous University for supporting this research work. The second and third authors would like to appreciate the research council of Shiraz University of Technology for supporting this research. Last but not least, the authors are very grateful to the editor and the reviewers for their valuable comments.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interests regarding the publication of this paper.
Additional information
Communicated by V. Loia.
Appendix
Appendix
Visualization of customer nodes and candidate facility locations on the \(x-y\) plane (see Figs. 3, 4, 5).
Distribution of customer and facility locations for \(m = 10\) and \(n = 100\)
Distribution of customer and facility locations for \(m = 20\) and \(n = 200\)
Distribution of customer and facility locations for \(m = 30\) and \(n = 300\)
Rights and permissions
About this article
Cite this article
Khanduzi, R., Reza Maleki, H. & Akbari, R. Two novel combined approaches based on TLBO and PSO for a partial interdiction/fortification problem using capacitated facilities and budget constraint. Soft Comput 22, 5901–5919 (2018). https://doi.org/10.1007/s00500-018-3005-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-018-3005-4