A Theoretical Analysis of Curvature Based Preference Models

Various notions of preferences exist in multi-objective optimization and the decision making community. On the one hand, preferences appear as domination relations that are stronger than the classical Pareto-domination, while on the other hand, they introduce relative importance on the objective functions. In this way, preferences can appear in both domination relations and objectives. In this paper, we analyze and put together different preference models and classify them into two groups. We theoretically analyze many preference models within these groups. In particular, we are interested in curvature/ slope based models where the preferred set depend upon the curvature of efficient front. This amounts to having a direct control on trade-offs among the objective functions. A related concept of cone-based hypervolume is also theoretically investigated in this paper. Special emphasis is placed on equitable efficiency and its applications. Furthermore, we present two algorithms for finding solutions that are compatible with a given preference model.