The Hypervolume Indicator

The hypervolume indicator is one of the most used set-quality indicators for assessment stochastic multiobjective optimizers, as well selection in evolutionary optimization algorithms. Its theoretical properties justify its wide acceptance, particularly strict monotonicity with respect to set dominance which still unique hypervolume-based indicators. This paper discusses computation hypervolume-related problems, highlighting relations between them, providing an overview paradigms and techniques used, a description main algorithms each problem, rundown fastest regarding asymptotic complexity runtime. By complete computational problems associated indicator, this serves starting point development new algorithms, supports users identification appropriate implementations available problem.