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Multiobjective Optimization Under Uncertainty: A Multiobjective Robust (Relative) Regret Approach

Patrick Groetzner(patrick.groetzner***at***math.uni-augsburg.de)
Ralf Werner(ralf.werner***at***math.uni-augsburg.de)

Abstract: Consider a multiobjective decision problem with uncertainty given as a set of scenarios. In the single criteria case, robust optimization methodology helps to identify solutions which remain feasible and of good quality for all possible scenarios. An alternative method is to compare the possible decisions under uncertainty against the optimal decision with the benefit of hindsight, i.e.\ to minimize the (possibly scaled) regret of not having chosen the optimal decision. In this exposition, we extend the concept of regret to the multiobjective setting and introduce a proper definition of multivariate (relative) regret. All early attempts in such a setting mix scalarization and optimization, whereas we first model regret and then solve the resulting problem separately. Moreover, in contrast to the existing approaches, we are not limited to a finite uncertainty sets or interval uncertainty and further, computations remain tractable in most common special cases.

Keywords: multiobjective optimization, robust optimization, minmax regret, scalarization, semi-infinite optimization

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Robust Optimization

Category 3: Infinite Dimensional Optimization (Semi-infinite Programming )

Citation: P. Groetzner and R. Werner, Multiobjective Optimization Under Uncertainty: A Multiobjective Robust (Relative) Regret Approach. Preprint, 2020.

Download: [PDF]

Entry Submitted: 01/14/2020
Entry Accepted: 01/14/2020
Entry Last Modified: 01/14/2020

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