Preference-based multiobjective optimization using truncated expected hypervolume improvement

The ultimate goal of multi-objective optimization is to provide potential solutions to a decision maker. Usually, what they are concerned with is a Pareto front in an interesting/preferred region, instead of the whole Pareto front. In this paper, a method for effectively approximating a preferred Pareto front, based on multiobjective efficient global optimization (EGO), is introduced. EGO uses Gaussian processes (or Kriging) to build a model of the objective function. Our variant of EGO uses truncated expected hypervolume improvement (TEHVI) as an infill criterion, which takes predictive mean, variance and preference region in the objective space into consideration. Compared to expected hypervolume improvement (EHVI), the probability density function in TEHVI follows a truncated normal distribution. This paper proposes a TEHVI method that makes it possible to set a region of interest on the Pareto front and focus search effectively on this preferred region. An expression for the exact and efficient computation of the TEHVI for truncation over a two dimensional range is derived, and benchmark results on standard bi-objective problems for small budget of evaluations are computed, confirming the effectiveness of the new approach.