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41. C.D. Kolstad, L.S. Lasdon, Derivative evaluation and computational experience with large
bilevel mathematical programs. J. Optim. Theory Appl. 65(3), 485–499 (1990) [Online].
Available http://link.springer.com/10.1007/BF00939562
42. E. Aiyoshi, K. Shimizu, Hierarchical decentralized systems and its new solution
by a barrier method. IEEE Trans. Syst. Man Cybern. SMC-11(6), 444–449 (1981)
[Online]. Available https://keio.pure.elsevier.com/ja/publications/hierarchical-decentralizedsystems-and-its-new-solution-by-a-barr
43. H. Jiye, L. Guoshan, W. Shouyang, A new descent algorithm for solving quadratic bilevel
programming problems. Acta Math. Appl. Sin. 16(3), 235–244 (2000). [Online]. Available
http://link.springer.com/10.1007/BF02679888
44. S. Dempe, J. Dutta, S. Lohse, Optimality conditions for bilevel programming problems.
Optimization 55(5–6), 505–524. October 2006 [Online]. Available http://www.tandfonline.
com/doi/abs/10.1080/02331930600816189
45. A. Sinha, P. Malo, K. Deb, Evolutionary algorithm for bilevel optimization using approximations of the lower level optimal solution mapping. Eur. J. Oper. Res. 257(2), 395–411 (2017)
[Online]. Available http://www.sciencedirect.com/science/article/pii/S0377221716306634
46. R. Mathieu, L. Pittard, G. Anandalingam, Genetic algorithm based approach to bi-level linear
programming. RAIRO - Oper. Res. 28(1), 1–21 (1994) [Online]. Available http://www.rairoro.org/10.1051/ro/1994280100011
47. Y. Yafeng, Genetic-algorithms-based approach for bilevel programming models. J. Transp.
Eng. 126(2), 115–120 (2000) [Online]. Available https://ascelibrary.org/doi/abs/10.1061/
(ASCE)0733-947X(2000)126:2(115)
48. H.W. Kuhn, A.W. Tucker, Nonlinear programming, in Proceedings of the Second Berkeley
Symposium on Mathematical Statistics and Probability, 1950 (University of California Press,
Berkeley/Los Angeles, 1951), pp. 481–492
49. Y. Wang, Y.-C. Jiao, H. Li, An evolutionary algorithm for solving nonlinear bilevel programming based on a new constraint-handling scheme. IEEE Trans. Syst. Man Cybern. Part C (Appl.
Rev.) 35(2), 221–232 (2005) [Online]. Available http://ieeexplore.ieee.org/document/1424196/
50. Y. Wang, H. Li, C. Dang, A new evolutionary algorithm for a class of nonlinear bilevel
programming problems and its global convergence. INFORMS J. Comput. 23(4), 618–629
(2011) [Online]. Available http://pubsonline.informs.org/doi/abs/10.1287/ijoc.1100.0430
51. M.M. Islam, H.K. Singh, T. Ray, A surrogate assisted approach for single-objective bilevel
optimization. IEEE Trans. Evol. Comput. 21(5), 681–696 (2017)
52. A. Sinha, P. Malo, K. Deb, Solving optimistic bilevel programs by iteratively approximating
lower level optimal value function. IEEE, July 2016, pp. 1877–1884 [Online]. Available http://
ieeexplore.ieee.org/document/7744017/
53. S. Ankur, M. Pekka, D. Kalyanmoy, Efficient evolutionary algorithm for single-objective
bilevel optimization. March 2013 [Online]. arXiv:1303.3901 [cs]. Available http://arxiv.org/
abs/1303.3901
54. J.S. Angelo, E. Krempser, H.J.C. Barbosa, Differential evolution assisted by a surrogate model
for bilevel programming problems, in 2014 IEEE Congress on Evolutionary Computation
(CEC), July 2014, pp. 1784–1791
55. V. Oduguwa, R. Roy, Bi-level optimisation using genetic algorithm. IEEE Comput. Soc 322–
327 (2002) [Online]. Available: http://ieeexplore.ieee.org/document/1048121/
56. F. Legillon, A. Liefooghe, E.-G. Talbi, Cobra: a coevolutionary metaheuristic for bi-level optimization, in Metaheuristics for Bi-level Optimization. Studies in Computational Intelligence
(Springer, Berlin, Heidelberg, 2013), pp. 95–114
57. L.U. Hansen, P. Horst, Multilevel optimization in aircraft structural design evaluation. Comput. Struct. 86(1), 104–118 (2008) [Online]. Available http://www.sciencedirect.com/science/
article/pii/S0045794907001952
M. Antoniou and P. Korošec
40. A. Zhou, Q. Zhang, A surrogate-assisted evolutionary algorithm for minimax optimization, in
IEEE Congress on Evolutionary Computation, July 2010, pp. 1–7
41. C.D. Kolstad, L.S. Lasdon, Derivative evaluation and computational experience with large
bilevel mathematical programs. J. Optim. Theory Appl. 65(3), 485–499 (1990) [Online].
Available http://link.springer.com/10.1007/BF00939562
42. E. Aiyoshi, K. Shimizu, Hierarchical decentralized systems and its new solution
by a barrier method. IEEE Trans. Syst. Man Cybern. SMC-11(6), 444–449 (1981)
[Online]. Available https://keio.pure.elsevier.com/ja/publications/hierarchical-decentralizedsystems-and-its-new-solution-by-a-barr
43. H. Jiye, L. Guoshan, W. Shouyang, A new descent algorithm for solving quadratic bilevel
programming problems. Acta Math. Appl. Sin. 16(3), 235–244 (2000). [Online]. Available
http://link.springer.com/10.1007/BF02679888
44. S. Dempe, J. Dutta, S. Lohse, Optimality conditions for bilevel programming problems.
Optimization 55(5–6), 505–524. October 2006 [Online]. Available http://www.tandfonline.
com/doi/abs/10.1080/02331930600816189
45. A. Sinha, P. Malo, K. Deb, Evolutionary algorithm for bilevel optimization using approximations of the lower level optimal solution mapping. Eur. J. Oper. Res. 257(2), 395–411 (2017)
[Online]. Available http://www.sciencedirect.com/science/article/pii/S0377221716306634
46. R. Mathieu, L. Pittard, G. Anandalingam, Genetic algorithm based approach to bi-level linear
programming. RAIRO - Oper. Res. 28(1), 1–21 (1994) [Online]. Available http://www.rairoro.org/10.1051/ro/1994280100011
47. Y. Yafeng, Genetic-algorithms-based approach for bilevel programming models. J. Transp.
Eng. 126(2), 115–120 (2000) [Online]. Available https://ascelibrary.org/doi/abs/10.1061/
(ASCE)0733-947X(2000)126:2(115)
48. H.W. Kuhn, A.W. Tucker, Nonlinear programming, in Proceedings of the Second Berkeley
Symposium on Mathematical Statistics and Probability, 1950 (University of California Press,
Berkeley/Los Angeles, 1951), pp. 481–492
49. Y. Wang, Y.-C. Jiao, H. Li, An evolutionary algorithm for solving nonlinear bilevel programming based on a new constraint-handling scheme. IEEE Trans. Syst. Man Cybern. Part C (Appl.
Rev.) 35(2), 221–232 (2005) [Online]. Available http://ieeexplore.ieee.org/document/1424196/
50. Y. Wang, H. Li, C. Dang, A new evolutionary algorithm for a class of nonlinear bilevel
programming problems and its global convergence. INFORMS J. Comput. 23(4), 618–629
(2011) [Online]. Available http://pubsonline.informs.org/doi/abs/10.1287/ijoc.1100.0430
51. M.M. Islam, H.K. Singh, T. Ray, A surrogate assisted approach for single-objective bilevel
optimization. IEEE Trans. Evol. Comput. 21(5), 681–696 (2017)
52. A. Sinha, P. Malo, K. Deb, Solving optimistic bilevel programs by iteratively approximating
lower level optimal value function. IEEE, July 2016, pp. 1877–1884 [Online]. Available http://
ieeexplore.ieee.org/document/7744017/
53. S. Ankur, M. Pekka, D. Kalyanmoy, Efficient evolutionary algorithm for single-objective
bilevel optimization. March 2013 [Online]. arXiv:1303.3901 [cs]. Available http://arxiv.org/
abs/1303.3901
54. J.S. Angelo, E. Krempser, H.J.C. Barbosa, Differential evolution assisted by a surrogate model
for bilevel programming problems, in 2014 IEEE Congress on Evolutionary Computation
(CEC), July 2014, pp. 1784–1791
55. V. Oduguwa, R. Roy, Bi-level optimisation using genetic algorithm. IEEE Comput. Soc 322–
327 (2002) [Online]. Available: http://ieeexplore.ieee.org/document/1048121/
56. F. Legillon, A. Liefooghe, E.-G. Talbi, Cobra: a coevolutionary metaheuristic for bi-level optimization, in Metaheuristics for Bi-level Optimization. Studies in Computational Intelligence
(Springer, Berlin, Heidelberg, 2013), pp. 95–114
57. L.U. Hansen, P. Horst, Multilevel optimization in aircraft structural design evaluation. Comput. Struct. 86(1), 104–118 (2008) [Online]. Available http://www.sciencedirect.com/science/
article/pii/S0045794907001952