9 Multilevel Optimisation
329
18. P. Hansen, B. Jaumard, G. Savard, New branch-and-bound rules for linear bilevel programming. SIAM J. Sci. Stat. Comput. 13(5), 1194–1217 (1992) [Online]. Available https://epubs.
siam.org/doi/abs/10.1137/0913069
19. A. Sinha, Tutorial on Bilevel Optimization - Ankur Sinha - Aalto University Wiki, 2014
[Online]. Available https://wiki.aalto.fi/display/~ansinha@aalto.fi
20. S. Ruuska, K. Miettinen, M.M. Wiecek, Connections between single-level and bilevel multiobjective optimization. J. Optim. Theory Appl. 153(1), 60–74 (2012) [Online]. Available http://
link.springer.com/10.1007/s10957-011-9943-y
21. G. Ünlü, A linear bilevel programming algorithm based on bicriteria programming. Comput.
Oper. Res. 14(2), 173–179 (1987)
22. E.-G. Talbi (ed.), Metaheuristics for Bi-level Optimization. Studies in Computational Intelligence (Springer, Berlin/Heidelberg, 2013) [Online]. Available //www.springer.com/gp/book/
9783642378379
23. G. Eichfelder, Multiobjective bilevel optimization. Math. Program. 123(2), 419–449 (2010)
24. K. Deb, A. Sinha, Solving bilevel multi-objective optimization problems using evolutionary algorithms, in International Conference on Evolutionary Multi-Criterion Optimization
(Springer, Heidelberg, 2009), pp. 110–124
25. Y. Yin, Multiobjective bilevel optimization for transportation planning and management
problems. J. Adv. Transp. 36(1), 93–105 (2002)
26. E. Roghanian, S.J. Sadjadi, M.-B. Aryanezhad, A probabilistic bi-level linear multi-objective
programming problem to supply chain planning. Appl. Math. Comput. 188(1), 786–800 (2007)
27. Y.G.A. Guangquan Zhang, J. Lu, Multi-Level Decision Making: Models, Methods and Applications. Intelligent Systems Reference Library,vol. 82 (Springer, Berlin/Heidelberg, 2015)
28. J. Lu, C. Shi, G. Zhang, On bilevel multi-follower decision making: general framework and
solutions. Inf. Sci. 176(11), 1607–1627 (2006)
29. K. Lachhwani, A. Dwivedi, Bi-level and multi-level programming problems: taxonomy of
literature review and research issues. Arch. Comput. Methods Eng. 25, 1–31 (2017)
30. F. Lin, X. Zhou, X. Lü, W. Song, Novel pre-pushing scheme for peer-assisted streaming
network based on multi-leader multi-follower Stackelberg model. Wirel. Pers. Commun. 80(1),
289–301 (2015)
31. Z. Lu, K. Deb, A. Sinha, Handling decision variable uncertainty in bilevel optimization
problems. IEEE, May 2015, pp. 1683–1690 [Online]. Available http://ieeexplore.ieee.org/
document/7257089/
32. A. Sinha, P. Malo, K. Deb, P. Korhonen, J. Wallenius, Solving bilevel multicriterion optimization problems with lower level decision uncertainty. IEEE Trans. Evol. Comput. 20(2),
199–217 (2016)
33. B.L. Gorissen, ˙
I. Yanıko˘ glu, D. den Hertog, A practical guide to robust optimization. Omega
53, 124–137 (2015)
34. A. Mucherino, M. Fuchs, X. Vasseur, S. Gratton, Variable neighborhood search for robust
optimization and applications to aerodynamics, in Large-Scale Scientific Computing, LSSC’11.
(Springer, Berlin, Heidelberg, 2012), pp. 230–237
35. I. Averbakh, Minmax regret solutions for minimax optimization problems with uncertainty.
Oper. Res. Lett. 27(2), 57–65 (2000)
36. D.-Z. Du, P.M. Pardalos, Minimax and Applications, vol. 4 (Springer Science & Business
Media, Berlin, 2013)
37. M. Vasile, On the solution of min-max problems in robust optimization, in The EVOLVE
2014 International Conference, A Bridge between Probability, Set Oriented Numerics, and
Evolutionary Computing, Jian-Guo Hotel, July 2014 [Online]. Available https://strathprints.
strath.ac.uk/52249/
38. C. Ortega, M. Vasile, New heuristics for multi-objective worst-case optimization in evidencebased robust design, in 2017 IEEE Congress on Evolutionary Computation (CEC), June 2017,
pp. 1519–1526
39. R.I. Lung, D. Dumitrescu, A new evolutionary approach to minimax problems, in 2011 IEEE
Congress of Evolutionary Computation (CEC), June 2011, pp. 1902–1905
329
18. P. Hansen, B. Jaumard, G. Savard, New branch-and-bound rules for linear bilevel programming. SIAM J. Sci. Stat. Comput. 13(5), 1194–1217 (1992) [Online]. Available https://epubs.
siam.org/doi/abs/10.1137/0913069
19. A. Sinha, Tutorial on Bilevel Optimization - Ankur Sinha - Aalto University Wiki, 2014
[Online]. Available https://wiki.aalto.fi/display/~ansinha@aalto.fi
20. S. Ruuska, K. Miettinen, M.M. Wiecek, Connections between single-level and bilevel multiobjective optimization. J. Optim. Theory Appl. 153(1), 60–74 (2012) [Online]. Available http://
link.springer.com/10.1007/s10957-011-9943-y
21. G. Ünlü, A linear bilevel programming algorithm based on bicriteria programming. Comput.
Oper. Res. 14(2), 173–179 (1987)
22. E.-G. Talbi (ed.), Metaheuristics for Bi-level Optimization. Studies in Computational Intelligence (Springer, Berlin/Heidelberg, 2013) [Online]. Available //www.springer.com/gp/book/
9783642378379
23. G. Eichfelder, Multiobjective bilevel optimization. Math. Program. 123(2), 419–449 (2010)
24. K. Deb, A. Sinha, Solving bilevel multi-objective optimization problems using evolutionary algorithms, in International Conference on Evolutionary Multi-Criterion Optimization
(Springer, Heidelberg, 2009), pp. 110–124
25. Y. Yin, Multiobjective bilevel optimization for transportation planning and management
problems. J. Adv. Transp. 36(1), 93–105 (2002)
26. E. Roghanian, S.J. Sadjadi, M.-B. Aryanezhad, A probabilistic bi-level linear multi-objective
programming problem to supply chain planning. Appl. Math. Comput. 188(1), 786–800 (2007)
27. Y.G.A. Guangquan Zhang, J. Lu, Multi-Level Decision Making: Models, Methods and Applications. Intelligent Systems Reference Library,vol. 82 (Springer, Berlin/Heidelberg, 2015)
28. J. Lu, C. Shi, G. Zhang, On bilevel multi-follower decision making: general framework and
solutions. Inf. Sci. 176(11), 1607–1627 (2006)
29. K. Lachhwani, A. Dwivedi, Bi-level and multi-level programming problems: taxonomy of
literature review and research issues. Arch. Comput. Methods Eng. 25, 1–31 (2017)
30. F. Lin, X. Zhou, X. Lü, W. Song, Novel pre-pushing scheme for peer-assisted streaming
network based on multi-leader multi-follower Stackelberg model. Wirel. Pers. Commun. 80(1),
289–301 (2015)
31. Z. Lu, K. Deb, A. Sinha, Handling decision variable uncertainty in bilevel optimization
problems. IEEE, May 2015, pp. 1683–1690 [Online]. Available http://ieeexplore.ieee.org/
document/7257089/
32. A. Sinha, P. Malo, K. Deb, P. Korhonen, J. Wallenius, Solving bilevel multicriterion optimization problems with lower level decision uncertainty. IEEE Trans. Evol. Comput. 20(2),
199–217 (2016)
33. B.L. Gorissen, ˙
I. Yanıko˘ glu, D. den Hertog, A practical guide to robust optimization. Omega
53, 124–137 (2015)
34. A. Mucherino, M. Fuchs, X. Vasseur, S. Gratton, Variable neighborhood search for robust
optimization and applications to aerodynamics, in Large-Scale Scientific Computing, LSSC’11.
(Springer, Berlin, Heidelberg, 2012), pp. 230–237
35. I. Averbakh, Minmax regret solutions for minimax optimization problems with uncertainty.
Oper. Res. Lett. 27(2), 57–65 (2000)
36. D.-Z. Du, P.M. Pardalos, Minimax and Applications, vol. 4 (Springer Science & Business
Media, Berlin, 2013)
37. M. Vasile, On the solution of min-max problems in robust optimization, in The EVOLVE
2014 International Conference, A Bridge between Probability, Set Oriented Numerics, and
Evolutionary Computing, Jian-Guo Hotel, July 2014 [Online]. Available https://strathprints.
strath.ac.uk/52249/
38. C. Ortega, M. Vasile, New heuristics for multi-objective worst-case optimization in evidencebased robust design, in 2017 IEEE Congress on Evolutionary Computation (CEC), June 2017,
pp. 1519–1526
39. R.I. Lung, D. Dumitrescu, A new evolutionary approach to minimax problems, in 2011 IEEE
Congress of Evolutionary Computation (CEC), June 2011, pp. 1902–1905