Abstract
Bilevel multi-objective optimization problems are known to be highly complex optimization tasks which require every feasible upper-level solution to satisfy optimality of a lower-level optimization problem. Multi-objective bilevel problems are commonly found in practice and high computation cost needed to solve such problems motivates to use multi-criterion decision making ideas to efficiently handle such problems. Multi-objective bilevel problems have been previously handled using an evolutionary multi-objective optimization (EMO) algorithm where the entire Pareto set is produced. In order to save the computational expense, a progressively interactive EMO for bilevel problems has been presented where preference information from the decision maker at the upper level of the bilevel problem is used to guide the algorithm towards the most preferred solution (a single solution point). The procedure has been evaluated on a set of five DS test problems suggested by Deb and Sinha. A comparison for the number of function evaluations has been done with a recently suggested Hybrid Bilevel Evolutionary Multi-objective Optimization algorithm which produces the entire upper level Pareto-front for a bilevel problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Byrd, R.H., Nocedal, J., Waltz, R.A.: KNITRO: An integrated package for nonlinear optimization, pp. 35–59. Springer, Heidelberg (2006)
Calamai, P.H., Vicente, L.N.: Generating quadratic bilevel programming test problems. ACM Trans. Math. Software 20(1), 103–119 (1994)
Colson, B., Marcotte, P., Savard, G.: An overview of bilevel optimization. Annals of Operational Research 153, 235–256 (2007)
Deb, K.: Multi-objective optimization using evolutionary algorithms. Wiley, Chichester (2001)
Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)
Deb, K., Sinha, A.: Constructing test problems for bilevel evolutionary multi-objective optimization. In: 2009 IEEE Congress on Evolutionary Computation (CEC-2009), pp. 1153–1160. IEEE Press, Los Alamitos (2009)
Deb, K., Sinha, A.: An evolutionary approach for bilevel multi-objective problems. In: Cutting-Edge Research Topics on Multiple Criteria Decision Making, Communications in Computer and Information Science, vol. 35, pp. 17–24. Springer, Berlin (2009)
Deb, K., Sinha, A.: Solving bilevel multi-objective optimization problems using evolutionary algorithms. In: Ehrgott, M., Fonseca, C.M., Gandibleux, X., Hao, J.-K., Sevaux, M. (eds.) EMO 2009. LNCS, vol. 5467, pp. 110–124. Springer, Heidelberg (2009)
Deb, K., Sinha, A.: An efficient and accurate solution methodology for bilevel multi-objective programming problems using a hybrid evolutionary-local-search algorithm. Evolutionary Computation Journal 18(3), 403–449 (2010)
Deb, K., Sinha, A., Korhonen, P., Wallenius, J.: An interactive evolutionary multi-objective optimization method based on progressively approximated value functions. IEEE Transactions on Evolutionary Computation 14(5), 723–739 (2010)
Dempe, S., Dutta, J., Lohse, S.: Optimality conditions for bilevel programming problems. Optimization 55(5-6), 505–524 (2006)
Eichfelder, G.: Solving nonlinear multiobjective bilevel optimization problems with coupled upper level constraints. Technical Report Preprint No. 320, Preprint-Series of the Institute of Applied Mathematics, Univ. Erlangen-Närnberg, Germany (2007)
Fudenberg, D., Tirole, J.: Game theory. MIT Press, Cambridge (1993)
Geoffrion, A.M.: Proper efficiency and theory of vector maximization. Journal of Mathematical Analysis and Applications 22(3), 618–630 (1968)
Halter, W., Mostaghim, S.: Bilevel optimization of multi-component chemical systems using particle swarm optimization. In: Proceedings of World Congress on Computational Intelligence (WCCI 2006), pp. 1240–1247 (2006)
Koh, A.: Solving transportation bi-level programs with differential evolution. In: 2007 IEEE Congress on Evolutionary Computation (CEC 2007), pp. 2243–2250. IEEE Press, Los Alamitos (2007)
Mathieu, R., Pittard, L., Anandalingam, G.: Genetic algorithm based approach to bi-level linear programming. Operations Research 28(1), 1–21 (1994)
Oduguwa, V., Roy, R.: Bi-level optimization using genetic algorithm. In: Proceedings of the 2002 IEEE International Conference on Artificial Intelligence Systems (ICAIS 2002), pp. 322–327 (2002)
Sinha, A., Deb, K.: Towards understanding evolutionary bilevel multi-objective optimization algorithm. In: IFAC Workshop on Control Applications of Optimization (IFAC 2009), vol. 7. Elsevier, Amsterdam (2009)
Sinha, A., Deb, K., Korhonen, P., Wallenius, J.: Progressively interactive evolutionary multi-objective optimization method using generalized polynomial value functions. In: 2010 IEEE Congress on Evolutionary Computation (CEC 2010), pp. 1–8. IEEE Press, Los Alamitos (2010)
Vicente, L.N., Calamai, P.H.: Bilevel and multilevel programming: A bibliography review. Journal of Global Optimization 5(3), 291–306 (2004)
Wang, F.J., Periaux, J.: Multi-point optimization using gas and Nash/Stackelberg games for high lift multi-airfoil design in aerodynamics. In: Proceedings of the 2001 Congress on Evolutionary Computation (CEC 2001), pp. 552–559 (2001)
Wang, Y., Jiao, Y.-C., Li, H.: An evolutionary algorithm for solving nonlinear bilevel programming based on a new constraint-handling scheme. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews 35(2), 221–232 (2005)
Yin, Y.: Genetic algorithm based approach for bilevel programming models. Journal of Transportation Engineering 126(2), 115–120 (2000)
Zhang, G., Liu, J., Dillon, T.: Decentralized multi-objective bilevel decision making with fuzzy demands. Knowledge-Based Systems 20, 495–507 (2007)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective optimization. In: Giannakoglou, K.C., Tsahalis, D.T., Périaux, J., Papailiou, K.D., Fogarty, T. (eds.) Evolutionary Methods for Design Optimization and Control with Applications to Industrial Problems, Athens, Greece, pp. 95–100. International Center for Numerical Methods in Engineering (Cmine) (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sinha, A. (2011). Bilevel Multi-objective Optimization Problem Solving Using Progressively Interactive EMO. In: Takahashi, R.H.C., Deb, K., Wanner, E.F., Greco, S. (eds) Evolutionary Multi-Criterion Optimization. EMO 2011. Lecture Notes in Computer Science, vol 6576. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19893-9_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-19893-9_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19892-2
Online ISBN: 978-3-642-19893-9
eBook Packages: Computer ScienceComputer Science (R0)