Multi-objective Optimisation with Multiple Preferred Regions

The typical goal in multi-objective optimization is to find a set of good and well-distributed solutions. It has become popular to focus on specific regions of the objective space, e.g., due to market demands or personal preferences. In the past, a range of different approaches has been proposed to consider preferences for regions, including reference points and weights. While the former technique requires knowledge over the true set of trade-offs (and a notion of “closeness”) in order to perform well, it is not trivial to encode a non-standard preference for the latter. With this article, we contribute to the set of algorithms that consider preferences. In particular, we propose the easy-to-use concept of “preferred regions” that can be used by laypeople, we explain algorithmic modifications of NSGAII and AGE, and we validate their effectiveness on benchmark problems and on a real-world problem.