Abstract
In this paper, we propose an enhanced genetic algorithm and chaos search for solving bilevel programming problem (BLPP). Enhanced genetic algorithm based on new effective selection technique. Effective selection technique enables the upper level decision maker to choose an appropriate solution in anticipation of the lower level’s decision. Firstly, the upper level problem is solved using genetic algorithm based on new effective selection technique. Secondly, another search based on chaos theory is applied on the obtained solution. The performance of the algorithm has been evaluated on different sets of test problems. Also, comparison between the proposed algorithm results and other best known solutions is introduced to show the effectiveness and efficiency of our proposed algorithm.
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References
Kalashnikov, V., Dempe, S., Pérez-Valdés, A., Kalashnykova, I., Camacho-Vallejo, J.: Bilevel programming and applications. Math. Probl. Eng. 1–16 (2015)
Ruusk, S., Miettinen, K., Wiecek, M.: Connections between single-level and bilevel multiobjective optimization. J. Optimiz. Theory App. 153, 60–74 (2012)
Shuang, M.: A nonlinear bilevel programming approach for product portfolio management. Plus 5(1), 1–18 (2016)
Gaspar, I., Benavente, J., Bordagaray, M., Jose, B., Moura, L., Ibeas, A.: A bilevel mathematical programming model to optimize the design of cycle paths. Transport Res. Procedia 10, 423–443 (2015)
Aihong, R., Yuping, W., Xingsi, X.: A novel approach based on preference-based index for interval bilevel linear programming problem. J. Inequal. Appl. 1–16 (2017)
Birla, R., Agarwal, V., Khan, I., Mishra, V.: An alternative approach for solving bi-level programming problems. Am. J. Oper. Res. 7, 239–247 (2017)
Osman, M., Emam, M., Elsayed, M.: Interactive approach for multi-level multi-objective fractional programming problems with fuzzy parameters. J. Basic Appl. Sci. 7(1), 139–149 (2018)
Migdalas, M., Pardalos, M., Värbrand, P.: Multilevel Optimization: Algorithms and Applications, 1st Edn. pp. 149–164. Kluwer, U.S.A (1998)
Bard, J.: Some properties of the bilevel programming problem. J. Optimiz. Theory App. 68(2), 371–378 (1991)
Bard, J., Moore, J.: A Branch and Bound Algorithm for the Bi-level Programming Problem Siam. J. Sci. Stat. Comp. 11(2), 281–292 (1990)
Bard, J., Falk, J.: An explicit solution to the multi-level programming problem. Comput. Oper. Res. 9(1), 77–100 (1982)
Jie, L., Jialin, H., Yaoguang, H., Guangquan, Z.: Multilevel decision-making: a survey. Inform. Sci. 346–347, 463–487 (2016)
Wang, G., Wan, Z., Wang, X., Yibing, L.: Genetic algorithm based on simplex method for solving linear-quadratic bilevel programming problem. Comput. Math. Appl. 56, 2550–2555 (2008)
El-Desoky, I., El-Shorbagy, M., Nasr, S., Hendawy, Z., Mousa, A.: A hybrid genetic algorithm for job shop scheduling problem. Int. J. Adv. Eng. Technol. Comput. Sci. 3(1), 6–17 (2016)
Hosseini, E.: Solving linear tri-level programming problem using heuristic method based on bi-section algorithm. Asian J. Sci. Res. 10, 227–235 (2017)
Carrasqueira, P., Alves, M., Antunes, C.: Bi-level particle swarm optimization and evolutionary algorithm approaches for residential demand response with different user profiles. Inform. Sci. 418, 405–420 (2017)
Wang, L., Zheng, D., Lin, Q.: Survey on chaotic optimization methods. Comput. Technol. Automat. 20(1), 1–5 (2001)
Sinha, A., Malo, P., Kalyanmoy, D.: Test problem construction for single-objective bilevel optimization. Evol. Comput. 22(3) (2014)
Sinha, A., Malo, P., Deb, K.: Unconstrained scalable test problems for single-objective bilevel optimization. In: Proceedings of the 2012 IEEE Congress on Evolutionary Computation, Brisbane, Australia, June 2012
Zhongping, W., Guangmin, W., Bin, S.: A hybrid intelligent algorithm by combining particle swarm optimization with chaos searching technique for solving nonlinear bi-level programming problems. Swarm Evol. Comput. 8, 26–32 (2013)
Nasr, S., El-Shorbagy, M., El-Desoky, I., Hendawy, I., Mousa, A.: Hybrid genetic algorithm for constrained nonlinear optimization problems. Brit. J. Math. Comp. Sci. 7(6), 466–480 (2015)
El-Shorbagy, M., Mousa, A., Nasr, S.: A chaos-based evolutionary algorithm for general nonlinear programming problems. Chaos Soliton Fract. 85, 8–21 (2016)
Mousa, A., El-Shorbagy, M., Abd-El-Wahed, W.: Local search based hybrid particle swarm optimization algorithm for multiobjective optimization. Swarm Evol. Comput. 3, 1–14 (2012)
Mousa, A., Abd-El-Wahed, W., Rizk-Allah, R.: A hybrid ant optimization approach based local search scheme for multiobjective design optimizations. Elec. Power Sys. Res. 81, 1014–1023 (2011)
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Abo-Elnaga, Y., Nasr, S.M., El-Desoky, I.M., Hendawy, Z.M., Mousa, A.A. (2020). Enhanced Genetic Algorithm and Chaos Search for Bilevel Programming Problems. In: Hassanien, A., Azar, A., Gaber, T., Bhatnagar, R., F. Tolba, M. (eds) The International Conference on Advanced Machine Learning Technologies and Applications (AMLTA2019). AMLTA 2019. Advances in Intelligent Systems and Computing, vol 921. Springer, Cham. https://doi.org/10.1007/978-3-030-14118-9_48
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DOI: https://doi.org/10.1007/978-3-030-14118-9_48
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