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OR Spectrum
Erschienen in: OR Spectrum 1/2016

01.01.2016 | Regular Article

Robustness for uncertain multi-objective optimization: a survey and analysis of different concepts

verfasst von: Jonas Ide, Anita Schöbel

Erschienen in: OR Spectrum | Ausgabe 1/2016

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Abstract

In this paper, we discuss various concepts of robustness for uncertain multi-objective optimization problems. We extend the concepts of flimsily, highly, and lightly robust efficiency and we collect different versions of minmax robust efficiency and concepts based on set order relations from the literature. Altogether, we compare and analyze ten different concepts and point out their relations to each other. Furthermore, we present reduction results for the class of objective-wise uncertain multi-objective optimization problems.
Vorheriger Artikel The basic train makeup problem in shunting yards
Nächster Artikel Acknowledgement to Referees

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Literatur
Avigad G, Branke J (2008) Embedded evolutionary multi-objective optimization for worst case robustness. In: Keijzer M (ed) Proceedings of the 10th annual conference on genetic and evolutionary computation
Barrico C, Antunes C (2006) Robustness analysis in multi-objective optimization using a degree of robustness concept. In: IEEE congress on evolutionary computation. CEC 2006, pp 1887–1892. IEEE Computer Society
Ben-Tal A, Bertsimas D, Brown DB (2010) A soft robust model for optimization under ambiguity. Oper Res 58(4):1220–1234CrossRef
Ben-Tal A, Ghaoui LE, Nemirovski A (2009) Robust optimization. Princeton University Press, Princeton and OxfordCrossRef
Ben-Tal A, Goryashko A, Guslitzer E, Nemirovski A (2003) Adjustable robust solutions of uncertain linear programs. Math Program A 99:351–376CrossRef
Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Oper Res 23(4):769–805CrossRef
Ben-Tal A, Nemirovski A (1999) Robust solutions of uncertain linear programs. Oper Res Lett 25:1–13CrossRef
Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math Program A 88:411–424CrossRef
Bertsimas D, Sim M (2004) The price of robustness. Oper Res 52(1):35–53CrossRef
Birge J, Louveaux F (2011) Introduction to stochastic programming, 2nd edn., Springer series in operations research and financial engineeringSpringer, New YorkCrossRef
Bokrantz R, Fredriksson A (2013) On solutions to robust multiobjective optimization problems that are optmal under convex scalarization. arXiv preprint arXiv:​1308.​4616
Branke J (1998) Creating robust solutions by means of evolutionary algorithms. In: Eiben E, Bäck T, Schenauer M, Schwefel HP (eds) Parallel problem solving from nature-PPSNV, vol 1498. Lecture notes in computer science. Springer, Berlin, Heidelberg, pp 119–128
Chen W, Unkelbach J, Trofimov A, Madden T, Kooy H, Bortfeld T, Craft D (2012) Including robustness in multi-criteria optimization for intensity-modulated proton therapy. Phys Med Biol 57(3):591CrossRef
Deb K, Gupta H (2006) Introducing robustness in multi-objective optimization. Evol Comput 14(4):463–494CrossRef
Doolittle EK, Kerivin HLM, Wiecek MM (2012) A robust multiobjective optimization problem with application to internet routing. Department of Mathematical Sciences, Clemson University. Technical report
Ehrgott M (2005) Multicriteria optimization. Springer, Berlin, Heidelberg
Ehrgott M, Figueira JR, Greco S (eds) (2010) Trends in multiple criteria decision analysis, vol 142. International series in operations research & management. Springer, New York
Erera A, Morales J, Savelsbergh M (2009) Robust optimization for empty repositioning problems. Oper Res 57(2):468–483CrossRef
Fischetti M, Monaci M (2009) Light robustness. In: Ahuja RK, Möhring R, Zaroliagis C (eds) Robust and online large-scale optimization. Lecture note on computer science, vol 5868. Springer, pp 61–84
Goerigk M, Schöbel A (2014) Recovery-to-optimality: a new two-stage approach to robustness with an application to aperiodic timetabling. Comput Oper Res 52:1–15CrossRef
Goerigk M, Schöbel A (2015) Algorithm engineering in robust optimization. In: Kliemann L, Sanders P (eds) Algorithm engineering. arXiv:​1505.​04901. Final volume for DFG Priority Program 1307
Hites R, De Smet Y, Risse N, Salazar-Neumann M, Vincke P (2006) About the applicability of MCDA to some robustness problems. Eur J Oper Res 174:322–332CrossRef
Iancu D, Trichakis N (2014) Pareto efficiency in robust optimization. Manag Sci 60:130–147CrossRef
Ide J (2014) Concepts of robustness for uncertain multi-objective optimization. Ph.D. thesis, Universität Göttingen
Ide J, Köbis E (2014) Concepts of efficiency for uncertain multi-objective optimization problems based on set order relations. Math Methods Oper Res 80:99–127CrossRef
Ide J, Tiedemann M, Westphal S, Haiduk F (2015) An application of deterministic and robust optimization in the wood cutting industry. 4OR 13:35–57CrossRef
Khan A, Tammer C, Zalinescu C (2014) Set-valued optimization. An introduction with applications. Springer
Klamroth K, Köbis E, Schöbel A, Tammer C (2013) A unified approach for different concepts of robustness and stochastic programming via nonlinear scalarizing functionals. Optimization 62(5):649–671CrossRef
Kouvelis P, Yu G (1997) Robust discrete optimization and its applications. Kluwer Academic Publishers, BostonCrossRef
Kuhn K, Raith A, Schmidt M, Schöbel A (2013) Bicriteria robust optimization. Technical report. 2013-09. Preprint-Reihe, Institut für Numerische und Angewandte Mathematik, Georg-August Universität Göttingen
Kuroiwa D, Lee GM (2012) On robust multiobjective optimization. Vietnam J Math 40(2&3):305–317
Liebchen C, Lübbecke M, Möhring RH, Stiller S (2009) The concept of recoverable robustness, linear programming recovery, and railway applications. In: Ahuja RK, Möhring R, Zaroliagis C (eds) Robust and online large-scale optimization. Lecture note on computer science, vol 5868. Springer
Nakiboglu K (2014) On robust efficiency in the weber facility location problem. Master’s thesis, Georg August University Göttingen, Faculty of Mathematics
Perny P, Spanjaard O, Storme LX (2006) A decision-theoretic approach to robust optimization. Ann Oper Res 147:317–341CrossRef
Sayin S, Kouvelis P (2005) The multiobjective discrete optimization problem: a weighted min-max two-stage optimization approach and a bicriteria algorithm. Manag Sci 51:1572–1581CrossRef
Schöbel A (2014) Generalized light robustness and the trade-off between robustness and nominal quality. MMOR 80(2):161–191
Soyster A (1973) Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper Res 21:1154–1157CrossRef
Yu H, Liu H (2013) Robust multiple objective game theory. J Optim Theory Appl 159(1):272–280CrossRef
Metadaten
Titel
Robustness for uncertain multi-objective optimization: a survey and analysis of different concepts
verfasst von
Jonas Ide
Anita Schöbel
Publikationsdatum
01.01.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
OR Spectrum / Ausgabe 1/2016
Print ISSN: 0171-6468
Elektronische ISSN: 1436-6304
DOI
https://doi.org/10.1007/s00291-015-0418-7

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