Abstract
We discuss the problem of evaluating a robust solution . To this end, we first give a short primer on how to apply robustification approaches to uncertain optimization problems using the assignment problem and the knapsack problem as illustrative examples. As it is not immediately clear in practice which such robustness approach is suitable for the problem at hand, we present current approaches for evaluating and comparing robustness from the literature, and introduce the new concept of a scenario curve. Using the methods presented in this chapter, an easy guide is given to the decision maker to find, solve and compare the best robust optimization method for his purposes.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Aissi, H., Bazgan, C., Vanderpooten, D.: Min–max and min–max regret versions of combinatorial optimization problems: a survey. Eur. J. Oper. Res. 197 (2), 427–438 (2009)
Averbakh, I.: Computing and minimizing the relative regret in combinatorial optimization with interval data. Discret. Optim. 2 (4), 273–287 (2005)
Ben-Tal, A., Nemirovski, A.: Robust convex optimization. Math. Oper. Res. 23 (4), 769–805 (1998)
Ben-Tal, A., Nemirovski, A.: Robust solutions of linear programming problems contaminated with uncertain data. Math. Program. 88, 411–424 (2000)
Ben-Tal, A., Goryashko, A., Guslitzer, E., Nemirovski, A.: Robust solutions of uncertain linear programs. Oper. Res. Lett. 25, 1–13 (1999)
Ben-Tal, A., Goryashko, A., Guslitzer, E., Nemirovski, A.: Adjustable robust solutions of uncertain linear programs. Math. Program. A 99, 351–376 (2003)
Ben-Tal, A., Ghaoui, L.E., Nemirovski, A.: Robust Optimization. Princeton University Press, Princeton/Oxford (2009)
Ben-Tal, A., Bertsimas, D., Brown, D.B.: A soft robust model for optimization under ambiguity. Oper. Res. 58 (4-Part-2), 1220–1234 (2010)
Bertsimas, D., Sim, M.: Robust discrete optimization and network flows. Math. Program. B 98, 2003 (2003)
Bertsimas, D., Sim, M.: The price of robustness. Oper. Res. 52 (1), 35–53 (2004)
Bertsimas, D., Brown, D., Caramanis, C.: Theory and applications of robust optimization. SIAM Rev. 53 (3), 464–501 (2011)
Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming. Springer Science & Business Media, New York (2011)
Buhmann, J.M., Mihalák, M., Srámek, R., Widmayer, P.: Robust optimization in the presence of uncertainty. In: Proceedings of the 4th conference on Innovations in Theoretical Computer Science, pp. 505–514. ACM (2013)
Carlsson, C., Fuller, R.: Fuzzy Reasoning in Decision Making and Optimization, vol. 82. Physica, Heidelberg (2012)
Chassein, A., Goerigk, M.: A bicriteria approach to robust optimization. Comput. Oper. Res. 66, 181–189 (2015)
Fischetti, M., Monaci, M.: Light robustness. In: Ahuja, R.K., Möhring, R., Zaroliagis, C. (eds.) Robust and Online Large-Scale Optimization. Lecture Note on Computer Science, vol. 5868, pp. 61–84. Springer, Berlin (2009)
Goerigk, M., Schöbel, A.: Recovery-to-optimality: a new two-stage approach to robustness with an application to aperiodic timetabling. Comput. Oper. Res. 52, Part A(0), 1–15 (2014)
Goerigk, M., Schöbel, A.: Algorithm engineering in robust optimization. In: Kliemann, L., Sanders, P. (eds.) Algorithm Engineering: Selected Results and Surveys. Lecture Notes in Computer Science, 9220 State of the Art. Springer (2016, to appear)
Hladık, M.: Interval linear programming: a survey. In: Mann, Z.A. (ed.) Linear Programming – New Frontiers in Theory and Applications, pp. 85–120. Nova Science Publishers, New York (2012)
Kalaï, R., Lamboray, C., Vanderpooten, D.: Lexicographic α-robustness: an alternative to min–max criteria. Eur. J. Oper. Res. 220 (3), 722–728 (2012)
Kellerer, H., Pferschy, U., Pisinger, D.: Knapsack Problems. Springer, Berlin (2004)
Kouvelis, P., Yu, G.: Robust Discrete Optimization and Its Applications. Kluwer Academic Publishers, Dordrecht (1997)
Liebchen, C., Lübbecke, M., Möhring, R., Stiller, S.: The concept of recoverable robustness, linear programming recovery, and railway applications. In: Robust and Online Large-Scale Optimization. Lecture Notes in Computer Science, vol. 5868, pp. 1–27. Springer, Berlin/Heidelberg (2009)
Monaci, M., Pferschy, U.: On the robust knapsack problem. SIAM J. Optim. 23 (4), 1956–1982 (2013)
Yaman, H., Karaşan, O.E., Pınar, M.Ç.: The robust spanning tree problem with interval data. Oper. Res. Lett. 29 (1), 31–40 (2001)
Acknowledgements
Effort sponsored by the Air Force Office of Scientific Research, Air Force Material Command, USAF, under grant number FA8655-13-1-3066. The U.S Government is authorized to reproduce and distribute reprints for Governmental purpose notwithstanding any copyright notation thereon.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Chassein, A., Goerigk, M. (2016). Performance Analysis in Robust Optimization. In: Doumpos, M., Zopounidis, C., Grigoroudis, E. (eds) Robustness Analysis in Decision Aiding, Optimization, and Analytics. International Series in Operations Research & Management Science, vol 241. Springer, Cham. https://doi.org/10.1007/978-3-319-33121-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-33121-8_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-33119-5
Online ISBN: 978-3-319-33121-8
eBook Packages: Business and ManagementBusiness and Management (R0)