Hyperfast hypervolumes for Multi-objective optimization

by Krzysztof Nowak for PaGMO / PyGMO

Project involves computation of hypervolume in higher dimensional spaces for a set of hypercubes sharing one common point (reference point that strictly dominates the whole set). It is a geometrical interpretation of quality measure for a Pareto set. It can be used as a comparison between two population of individuals, and as a fitness function during the evolution phase in the genetic algorithm. First scenario allows for exact computation, since time is not as crucial of a factor, as it is in second case (executing hypervolume computation during the algorithm). This requires implementation of both exact and approximated methods. Additionally, few methods have been proposed that use hypervolume as a input for the fitness measure. I intend to implement at least one of them during the GSoC as well.