This page presents a collection of links and papers related to the hypervolume quality indicator, a measure often used to assess the performance of multi-objective evolutionary algorithms. It is also used directly inside EAs to provide a selection pressure rewarding convergence as well as objective-space diversity of the candidate solutions. Hypervolume has the drawback that it takes exponential time in the number of dimensions to compute. For this reason, there is an active community developing faster algorithms (in theory and in practice) for this important problem.
This is a reimplementation of the code by Fonseca et al. (Variant 3, Version 1.2) in pure Python. Some small modifications have been applied to obtain more performance on the Python interpreter.
# usage example: from hv import HyperVolume referencePoint = [2, 2, 2] hyperVolume = HyperVolume(referencePoint) front = [[1, 0, 1], [0, 1, 0]] result = hyperVolume.compute(front)
The S-Metric Selection Evolutionary Multiobjective Optmization Algorithm uses the hypervolume indicator to compute the exclusive hypervolume contribution of solutions.