Abstract
In this chapter, a wider definition of the AROP is provided. It is extended to include problems that involve multiple objectives, which are very common in real-world design. Chapter 3 introduced AROPs with one objective function that may be sensitive to various types of uncertainties. Whenever the uncertain conditions change, a single-objective optimization problem needs to be solved in order to find the new optimal configuration. Therefore, a one-to-one mapping between the realization of the uncertain variables and the optimal configuration exists.
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Notes
- 1.
However, the dominance relations between the solutions on the curve depend on \(p_2\) as well.
- 2.
The non-dominated solutions among the optimal trade-off curve appear with symbols. Since the same eleven configurations are used for all scenarios, the symbols in Fig. 4.4a overlay at some points.
- 3.
The extreme objective vectors are either based on previous knowledge of the problem at hand, or on current understanding of the objective space.
- 4.
The normalization can express decision-maker’s preferences by setting the worst objective vector elements to values different than one.
- 5.
EAs are a popular tool for solving difficult MOPs, but other classes of multi-objective optimizers that can exploit these indicators can also be used.
- 6.
The nested optimizer can be any algorithm for multi-objective optimization.
- 7.
The number of function evaluations of the inner and outer algorithms can be either fixed or subject to variations according to the termination criteria.
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Salomon, S. (2019). Active Robust Multi-objective Optimization. In: Active Robust Optimization: Optimizing for Robustness of Changeable Products. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-15050-1_4
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