Summary
Uncrowded hypervolume improvement (UHVI) extends hypervolume improvement to provide selection pressure for dominated solutions in multi-objective optimization. For a point that improves the Pareto front, UHVI equals its positive hypervolume improvement; for a dominated point, it assigns a negative value based on distance to the front instead of the flat value of zero returned by ordinary HVI (1).
This makes the objective informative on both sides of the Pareto frontier.
1.
Maree SC, Alderliesten T, Bosman PAN. Uncrowded Hypervolume-based Multi-objective Optimization with Gene-pool Optimal Mixing. 2020; Available from: https://arxiv.org/abs/2004.05068