Solving Robust Variants of Integer Flow Problems with Uncertain Arc Capacities

Bazaraa MS, Jarvis JJ, Sherali HD. Linear Programming and Network Flows. Fourth Edition. Hoboken NJ: Wiley; 2010.

Jungnickel D. Graphs, Networks and Algorithms. Fourth Edition. Springer, Berlin; 2013.

Papadimitriou CH, Steiglitz K. Combinatorial Optimization – Algorithms and Complexity. Mineola NY: Dover Publications; 1998.

Ben-Tal A, El Ghaoui L, Nemirovski A. Robust Optimization. Princeton NJ: Princeton University Press; 2009.

Bertsimas D, Sim M. Robust discrete optimization and network flows. Mathematical Programming. 2003;98: 49-71.

Bertsimas D, Sim M. The price of robustness. Operations Research. 2004;52: 35-53.

Kouvelis P, Yu G. Robust Discrete Optimization and Its Applications. Berlin: Springer; 1997.

Aissi H, Bazgan C, Vanderpooten D. Min-max and min-max regret versions of combinatorial optimization problems: A survey. European Journal of Operational Research. 2009;197: 427-438.

Aissi H, Bazgan C, Vanderpooten D. General approximation schemes for min-max (regret) versions of some (pseudo-)polynomial problems. Discrete Optimizaton. 2010;7: 136-148.

Bertsimas D, Brown DB, Caramanis C. Theory and applications of robust optimization. SIAM Review. 2011;53: 464-501.

Kasperski A, Zielinski P. Robust discrete optimization under discrete and interval uncertainty: A survey. In: Doumpos M, Zopounidis C, Grigoroudis E. (eds.) Robustness Analysis in Decision Aiding, Optimization, and Analytics. Cham CH: Springer; 2016. p. 113-143.

Aissi H, Vanderpooten D. Robust capacity expansion of a network under demand uncertainty: A bi-objective approach. Networks. 2016;68: 185-199.

Atamtürk A, Zhang M. Two-stage robust network flow and design under demand uncertainty. Operations Research. 2007;55: 662-673.

Bertsimas D, Nasrabadi E, Stiller S. Robust and adaptive network flows. Operations Research. 2013;61: 1218-1242.

Boginski VL, Commander CW, Turko T. Polynomial-time identification of robust network flows under uncertain arc failures. Optimization Letters. 2009;3: 461-473.

Minoux M. On robust maximum flow with polyhedral uncertainty sets. Optimization Letters. 2009;3: 367-376.

Minoux M. Robust network optimization under polyhedral demand uncertainty is NP-hard. Discrete Applied Mathematics. 2010;158: 597-603.

Ordoñez F, Zhao J. Robust capacity expansion of network flows. Networks. 2007;50: 136-145.

Poss M. A comparison of routing sets for robust network design. Optimization Letters. 2014;8: 1619-1635.

Righetto GM, Morabito R, Alem D. A robust optimization approach for cash flow management in stationery companies. Computers and Industrial Engineering. 2016;99: 137-152.

Rui M, Jinfu Z. Robust discrete optimization for the minimum cost flow problem. In: Wang C, Ye Z. (eds.) Proceedings of the International Workshop on Intelligent Systems and Applications – ISA 2009. Wuhan, China, 23-24 May 2009. Piscataway NJ: IEEE; 2009. p. 1-4.

Špoljarec M, Manger R. Heuristic solutions to robust variants of the minimum-cost integer flow problem. Journal of Heuristics. 2020;26: 531-559.

Eiben AE, Smith JE. Introduction to Evolutionary Computing. Second edition. Berlin: Springer; 2015.

Talbi EG. Metaheuristics – From Design to Implementation. Hoboken NJ: Wiley; 2009.

Korte B, Vygen J. Combinatorial Optimization – Theory and Algorithms. Fifth Edition. Berlin: Springer; 2012.

Carre B. Graphs and Networks. Oxford UK: Oxford University Press; 1979.

IBM Corporation. IBM ILOG CPLEX Optimization Studio, CPLEX User's Manual, Version 12, Release 8. IBM Knowledge Center; 2017. Available from: https://www.ibm.com/support/knowledgecenter/SSSA5P_12.8.0 [Accessed 17 Dec 2018].

Troelsen A, Japikse P. C# 6.0 and the .NET 4.6 Framework. 7th Edition. New York NY: Apress; 2016.

Beasley JE. OR-Library. Brunel University London; 2018. Available from: http://people.brunel.ac.uk/~mastjjb/jeb/info.html [Accessed 17 Dec 2018].

DIMACS – Center for Discrete Mathematics and Theoretical Computer Science. DIMACS Implementation Challenges. Piscataway NJ: Rutgers University; 2017. Available from: http://archive.dimacs.rutgers.edu/Challenges [Accessed 17 Dec 2018].