328
M. Antoniou and P. Korošec
Acknowledgments This work is funded by the European Commission’s H2020 programme,
through the UTOPIAE Marie Curie Innovative Training Network, H2020-MSCA-ITN-2016, Grant
agreement number 722734, and through the SYNERGY Twinning project, H2020-TWINN-2015,
Grant agreement number 692286.
References
1. K. Deb, D. Kalyanmoy, Multi-Objective Optimization Using Evolutionary Algorithms (Wiley,
New York, NY, 2001)
2. A. Sinha, Z. Lu, K. Deb, P. Malo, Bilevel Optimization based on Iterative Approximation of
Multiple Mappings. Feb. 2017 [Online]. arXiv:1702.03394 [math]. Available http://arxiv.org/
abs/1702.03394
3. J. Bracken, J.T. McGill, Mathematical programs with optimization problems in the constraints.
Oper. Res. 21(1), 37–44 (1973)
4. W. Candler, R. Norton, Multi-Level Programming and Development Policy (The World Bank,
Washington, DC, 1977)
5. A. Sinha, P. Malo, K. Deb, A review on bilevel optimization: from classical to evolutionary
approaches and applications. May 2017 [Online]. arXiv:1705.06270 [cs, math]. Available
http://arxiv.org/abs/1705.06270
6. A. Valejo, M.C. Ferreira de Oliveira, G.P.R. Filho, A.D.A. Lopes, Multilevel approach for
combinatorial optimization in bipartite network. Knowledge-Based Systems, March 2018
[Online]. Available http://www.sciencedirect.com/science/article/pii/S0950705118301539
7. W.W. Hager (ed.), Multiscale Optimization Methods and Applications. Nonconvex optimization and its applications, vol. 82 (Springer, New York, 2006)
8. P. Korošec, J. Šilc, B. Robiˇ c, Solving the mesh-partitioning problem with an ant-colony
algorithm, in Parallel Computing, vol. 30(5–6), pp. 785–801, May 2004 [Online]. Available
http://linkinghub.elsevier.com/retrieve/pii/S0167819104000432
9. M.G. Fernández-Godino, C. Park, N.-H. Kim, R.T. Haftka, Review of multi-fidelity models
(2016). Preprint. arXiv:1609.07196
10. J.A. Monschke, M.S. Eldred, Multilevel-Multifidelity Acceleration of PDE-Constrained
Optimization. American Institute of Aeronautics and Astronautics, January 2017 [Online].
Available http://arc.aiaa.org/doi/10.2514/6.2017-0132
11. I.C. Kampolis, K.C. Giannakoglou, A multilevel approach to single- and multiobjective
aerodynamic optimization. Comput. Methods Appl. Mech. Eng. 197(33), 2963–2975 (2008)
[Online]. Available http://www.sciencedirect.com/science/article/pii/S0045782508000388
12. C. Walshaw, Multilevel refinement for combinatorial optimisation problems. Ann. Oper.
Res. 131(1–4), 325–372. October 2004 [Online]. Available https://link.springer.com/article/
10.1023/B:ANOR.0000039525.80601.15
13. A. Migdalas, P.M. Pardalos, P. Värbrand, Multilevel Optimization: Algorithms and Applications
(Springer Science & Business Media, London, Heidelberg, 2013). google-Books-ID: 5pXaBwAAQBAJ
14. T. Dudás, B. Klinz, G.J. Woeginger, The computational complexity of multi-level bottleneck
programming problems, in Multilevel Optimization: Algorithms and Applications (Springer,
Boston, MA, 1998), pp. 165–179
15. H.V. Stackelberg, Theory of the market economy (1952) [Online]. Available http://agris.fao.
org/agris-search/search.do?recordID=US201300604530
16. S. Dempe, Foundations of Bilevel Programming (Springer Science & Business Media,
Berlin/Heidelberg, 2002). google-Books-ID: 1sCWQ1MLMeQC
17. J. Lu, J. Han, Y. Hu, G. Zhang, Multilevel decision-making: a survey, in Information Sciences,
vol. 346–347 (2016), pp. 463–487 [Online]. Available http://linkinghub.elsevier.com/retrieve/
pii/S0020025516300202
M. Antoniou and P. Korošec
Acknowledgments This work is funded by the European Commission’s H2020 programme,
through the UTOPIAE Marie Curie Innovative Training Network, H2020-MSCA-ITN-2016, Grant
agreement number 722734, and through the SYNERGY Twinning project, H2020-TWINN-2015,
Grant agreement number 692286.
References
1. K. Deb, D. Kalyanmoy, Multi-Objective Optimization Using Evolutionary Algorithms (Wiley,
New York, NY, 2001)
2. A. Sinha, Z. Lu, K. Deb, P. Malo, Bilevel Optimization based on Iterative Approximation of
Multiple Mappings. Feb. 2017 [Online]. arXiv:1702.03394 [math]. Available http://arxiv.org/
abs/1702.03394
3. J. Bracken, J.T. McGill, Mathematical programs with optimization problems in the constraints.
Oper. Res. 21(1), 37–44 (1973)
4. W. Candler, R. Norton, Multi-Level Programming and Development Policy (The World Bank,
Washington, DC, 1977)
5. A. Sinha, P. Malo, K. Deb, A review on bilevel optimization: from classical to evolutionary
approaches and applications. May 2017 [Online]. arXiv:1705.06270 [cs, math]. Available
http://arxiv.org/abs/1705.06270
6. A. Valejo, M.C. Ferreira de Oliveira, G.P.R. Filho, A.D.A. Lopes, Multilevel approach for
combinatorial optimization in bipartite network. Knowledge-Based Systems, March 2018
[Online]. Available http://www.sciencedirect.com/science/article/pii/S0950705118301539
7. W.W. Hager (ed.), Multiscale Optimization Methods and Applications. Nonconvex optimization and its applications, vol. 82 (Springer, New York, 2006)
8. P. Korošec, J. Šilc, B. Robiˇ c, Solving the mesh-partitioning problem with an ant-colony
algorithm, in Parallel Computing, vol. 30(5–6), pp. 785–801, May 2004 [Online]. Available
http://linkinghub.elsevier.com/retrieve/pii/S0167819104000432
9. M.G. Fernández-Godino, C. Park, N.-H. Kim, R.T. Haftka, Review of multi-fidelity models
(2016). Preprint. arXiv:1609.07196
10. J.A. Monschke, M.S. Eldred, Multilevel-Multifidelity Acceleration of PDE-Constrained
Optimization. American Institute of Aeronautics and Astronautics, January 2017 [Online].
Available http://arc.aiaa.org/doi/10.2514/6.2017-0132
11. I.C. Kampolis, K.C. Giannakoglou, A multilevel approach to single- and multiobjective
aerodynamic optimization. Comput. Methods Appl. Mech. Eng. 197(33), 2963–2975 (2008)
[Online]. Available http://www.sciencedirect.com/science/article/pii/S0045782508000388
12. C. Walshaw, Multilevel refinement for combinatorial optimisation problems. Ann. Oper.
Res. 131(1–4), 325–372. October 2004 [Online]. Available https://link.springer.com/article/
10.1023/B:ANOR.0000039525.80601.15
13. A. Migdalas, P.M. Pardalos, P. Värbrand, Multilevel Optimization: Algorithms and Applications
(Springer Science & Business Media, London, Heidelberg, 2013). google-Books-ID: 5pXaBwAAQBAJ
14. T. Dudás, B. Klinz, G.J. Woeginger, The computational complexity of multi-level bottleneck
programming problems, in Multilevel Optimization: Algorithms and Applications (Springer,
Boston, MA, 1998), pp. 165–179
15. H.V. Stackelberg, Theory of the market economy (1952) [Online]. Available http://agris.fao.
org/agris-search/search.do?recordID=US201300604530
16. S. Dempe, Foundations of Bilevel Programming (Springer Science & Business Media,
Berlin/Heidelberg, 2002). google-Books-ID: 1sCWQ1MLMeQC
17. J. Lu, J. Han, Y. Hu, G. Zhang, Multilevel decision-making: a survey, in Information Sciences,
vol. 346–347 (2016), pp. 463–487 [Online]. Available http://linkinghub.elsevier.com/retrieve/
pii/S0020025516300202