Contributed Session Mon.3.H 3503

Monday, 15:15 - 16:45 h, Room: H 3503

Cluster 20: Robust optimization [...]

Extensions of robust optimization approaches


Chair: Mohammad Mehdi Nasrabadi



Monday, 15:15 - 15:40 h, Room: H 3503, Talk 1

Phantipa Thipwiwatpotjana
Pessimistic, optimistic, and min-max regret approaches for linear programs under uncertainty

Coauthor: Weldon A. Lodwick


Uncertain data appearing as parameters in linear programs can be categorized variously. However, most theoretical approaches and models limit themselves to the analysis involving merely one kind of uncertainty within a problem. This paper presents reasonable methods for handling linear programs with mixed uncertainties which also preserve all details about uncertain data. We show how to handle mixed uncertainties which lead to optimistic, pessimistic, and minimax regret in optimization criteria.



Monday, 15:45 - 16:10 h, Room: H 3503, Talk 2

Michael Römer
Linear optimization with variable parameters: Robust and generalized linear programming and their relations


In linear programming, it is usually assumed that the problem data is certain and fixed. In many real world situations, however, the parameters are subject to variation. In a pessimistic scenario, the variation is not controllable by the decision maker: This is the case for parameters affected by measurement errors or uncertainty. One way to deal with such a situation is to employ robust linear programming to obtain a solution that is feasible for all elements of a given parameter uncertainty set.
In an optimistic scenario, the variation can be controlled: Some coefficients may represent adjustable technical parameters or can be influenced by higher-level decisions. A possible approach to model this setting is generalized linear programming. In this approach, going back to early work of Dantzig and Wolfe, a solution is sought which is feasible for at least one parameter combination from a given variation set.
In this work, we provide a unified view of robust and generalized linear programs and their compact reformulations. We discuss the dual relation of both approaches and show how this duality may contribute to a deeper understanding and a mutual stimulation of both fields.



Monday, 16:15 - 16:40 h, Room: H 3503, Talk 3

Mohammad Mehdi Nasrabadi
A fuzzy programming approach to robust optimization


A crucial feature of linear programming occurring in real-world applications is that all or some of parameters are uncertain. Robust optimization has attracted a great deal of attention to address this situation. We consider robust linear programs, where the parameters in the constraint matrix are uncertain but known to lie in a given deterministic uncertainty set. We present a fuzzy programming approach to soften the hard constraints of the robust optimization. In particular, given a feasible solution, we introduce a membership function for each constraint to indicate how much the constraint is violated in the worst-case. We characterize the three basic ingredients in fuzzy decision making, that are, fuzzy goal, fuzzy constraint, and fuzzy decision. We then present an algorithm for solving the robust linear program with softness constraints based on the well-known approach of Bellman and Zadeh (1970) in fuzzy programming. We show that the problem is efficiently solvable when the uncertain parameters are the ones considered by Bertsimas and Sim (2003).


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