Traditional robust optimization formulations can be considered to be “passive” in the sense that they can obtain optimized design and operational solutions for a system for all realizations of uncertainty. However, flexibility in the system’s operation can be used to devise formulations that obtain solutions that are optimum for all realizations of uncertainty while operational variables are used to mitigate or eliminate the effects of uncertainty. The objective of this paper is to extend existing formulations in single-objective robust optimization to multi-objective robust optimization with or without operational flexibility under discretized uncertainty. The formulations with operational flexibility are referred to as flexible optimization. The flexible optimization formulations and corresponding solutions are demonstrated and compared with those from robust and deterministic optimization formulations using numerical examples, and an engineering example with black-box objective and constraint functions.

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