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Improving benders decomposition using a genetic algorithm

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  • Poojari, C.A.
  • Beasley, J.E.

Abstract

We develop and investigate the performance of a hybrid solution framework for solving mixed-integer linear programming problems. Benders decomposition and a genetic algorithm are combined to develop a framework to compute feasible solutions. We decompose the problem into a master problem and a subproblem. A genetic algorithm along with a heuristic are used to obtain feasible solutions to the master problem, whereas the subproblem is solved to optimality using a linear programming solver. Over successive iterations the master problem is refined by adding cutting planes that are implied by the subproblem. We compare the performance of the approach against a standard Benders decomposition approach as well as against a stand-alone solver (Cplex) on MIPLIB test problems.

Suggested Citation

  • Poojari, C.A. & Beasley, J.E., 2009. "Improving benders decomposition using a genetic algorithm," European Journal of Operational Research, Elsevier, vol. 199(1), pages 89-97, November.
    • Handle: RePEc:eee:ejores:v:199:y:2009:i:1:p:89-97
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    1. Cote, Gilles & Laughton, Michael A., 1984. "Large-scale mixed integer programming: Benders-type heuristics," European Journal of Operational Research, Elsevier, vol. 16(3), pages 327-333, June.
    2. Poojari, Chandra A. & Varghese, Boby, 2008. "Genetic Algorithm based technique for solving Chance Constrained Problems," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1128-1154, March.
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    Cited by:

    1. M. Jenabi & S. M. T. Fatemi Ghomi & S. A. Torabi & Moeen Sammak Jalali, 2022. "An accelerated Benders decomposition algorithm for stochastic power system expansion planning using sample average approximation," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1304-1336, December.
    2. Faria, Victor. A.D. & de Queiroz, Anderson Rodrigo & Lima, Luana M.M. & Lima, José W.M., 2018. "Cooperative game theory and last addition method in the allocation of firm energy rights," Applied Energy, Elsevier, vol. 226(C), pages 905-915.
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    7. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    8. Jalali, Sajjad & Seifbarghy, Mehdi & Niaki, Seyed Taghi Akhavan, 2018. "A risk-averse location-protection problem under intentional facility disruptions: A modified hybrid decomposition algorithm," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 196-219.
    9. de Sá, Elisangela Martins & de Camargo, Ricardo Saraiva & de Miranda, Gilberto, 2013. "An improved Benders decomposition algorithm for the tree of hubs location problem," European Journal of Operational Research, Elsevier, vol. 226(2), pages 185-202.
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    11. Teodor Gabriel Crainic & Mike Hewitt & Francesca Maggioni & Walter Rei, 2021. "Partial Benders Decomposition: General Methodology and Application to Stochastic Network Design," Transportation Science, INFORMS, vol. 55(2), pages 414-435, March.
    12. Reddy, K. Nageswara & Kumar, Akhilesh & Choudhary, Alok & Cheng, T. C. Edwin, 2022. "Multi-period green reverse logistics network design: An improved Benders-decomposition-based heuristic approach," European Journal of Operational Research, Elsevier, vol. 303(2), pages 735-752.
    13. Ragheb Rahmaniani & Shabbir Ahmed & Teodor Gabriel Crainic & Michel Gendreau & Walter Rei, 2020. "The Benders Dual Decomposition Method," Operations Research, INFORMS, vol. 68(3), pages 878-895, May.
    14. Kuthambalayan, Thyagaraj S. & Mehta, Peeyush & Shanker, Kripa, 2014. "Integrating operations and marketing decisions using delayed differentiation of products and guaranteed delivery time under stochastic demand," European Journal of Operational Research, Elsevier, vol. 237(2), pages 617-627.
    15. M. Jenabi & S. Fatemi Ghomi & S. Torabi & S. Hosseinian, 2015. "Acceleration strategies of Benders decomposition for the security constraints power system expansion planning," Annals of Operations Research, Springer, vol. 235(1), pages 337-369, December.
    16. Witthayapraphakorn, Aphisak & Charnsethikul, Peerayuth, 2019. "Benders decomposition with special purpose method for the sub problem in lot sizing problem under uncertain demand," Operations Research Perspectives, Elsevier, vol. 6(C).
    17. Gelareh, Shahin & Neamatian Monemi, Rahimeh & Nickel, Stefan, 2015. "Multi-period hub location problems in transportation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 75(C), pages 67-94.
    18. Soler, Edilaine Martins & de Sousa, Vanusa Alves & da Costa, Geraldo R.M., 2012. "A modified Primal–Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables," European Journal of Operational Research, Elsevier, vol. 222(3), pages 616-622.
    19. Neamatian Monemi, Rahimeh & Gelareh, Shahin & Nagih, Anass & Maculan, Nelson & Danach, Kassem, 2021. "Multi-period hub location problem with serial demands: A case study of humanitarian aids distribution in Lebanon," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 149(C).
    20. Gelareh, Shahin & Pisinger, David, 2011. "Fleet deployment, network design and hub location of liner shipping companies," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 947-964.
    21. Ashkan Fakhri & Mehdi Ghatee, 2013. "Solution of preemptive multi-objective network design problems applying Benders decomposition method," Annals of Operations Research, Springer, vol. 210(1), pages 295-307, November.
    22. N. Beheshti Asl & S. A. MirHassani, 2019. "Accelerating benders decomposition: multiple cuts via multiple solutions," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 806-826, April.

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