TY - JOUR

T1 - Minmax robustness for multi-objective optimization problems

AU - Ehrgott, Matthias

AU - Ide, Jonas

AU - Schoebel, Anita

PY - 2014/11/16

Y1 - 2014/11/16

N2 - In real-world applications of optimization, optimal solutions are often of limited value, because disturbances of or changes to input data may diminish the quality of an optimal solution or even render it infeasible. One way to deal with uncertain input data is robust optimization, the aim of which is to find solutions which remain feasible and of good quality for all possible scenarios, i.e., realizations of the uncertain data. For single objective optimization, several definitions of robustness have been thoroughly analyzed and robust optimization methods have been developed. In this paper, we extend the concept of minmax robustness (Ben-Tal, Ghaoui, & Nemirovski, 2009) to multi-objective optimization and call this extension robust efficiency for uncertain multi-objective optimization problems. We use ingredients from robust (single objective) and (deterministic) multi-objective optimization to gain insight into the new area of robust multi-objective optimization. We analyze the new concept and discuss how robust solutions of multi-objective optimization problems may be computed. To this end, we use techniques from both robust (single objective) and (deterministic) multi-objective optimization. The new concepts are illustrated with some linear and quadratic programming instances.

AB - In real-world applications of optimization, optimal solutions are often of limited value, because disturbances of or changes to input data may diminish the quality of an optimal solution or even render it infeasible. One way to deal with uncertain input data is robust optimization, the aim of which is to find solutions which remain feasible and of good quality for all possible scenarios, i.e., realizations of the uncertain data. For single objective optimization, several definitions of robustness have been thoroughly analyzed and robust optimization methods have been developed. In this paper, we extend the concept of minmax robustness (Ben-Tal, Ghaoui, & Nemirovski, 2009) to multi-objective optimization and call this extension robust efficiency for uncertain multi-objective optimization problems. We use ingredients from robust (single objective) and (deterministic) multi-objective optimization to gain insight into the new area of robust multi-objective optimization. We analyze the new concept and discuss how robust solutions of multi-objective optimization problems may be computed. To this end, we use techniques from both robust (single objective) and (deterministic) multi-objective optimization. The new concepts are illustrated with some linear and quadratic programming instances.

KW - Multi-objective optimization

KW - Robustness and sensitivity analysis

KW - Scenarios

KW - Uncertainty modelling

U2 - 10.1016/j.ejor.2014.03.013

DO - 10.1016/j.ejor.2014.03.013

M3 - Journal article

VL - 239

SP - 17

EP - 31

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 1

ER -