Year: 2019
Type: conference-paper
Abstract: The hypervolume (or S-metric) is a widely used quality measure employed in the assessment of multi- and many-objective evolutionary algorithms. It is also directly integrated as a component in the selection mechanism of some popular optimisers. Exact hypervolume calculation becomes prohibitively expensive in real-time applications as the number of objectives increases and/or the approximation set grows. Assuch, Monte Carlo (MC) sampling is often used to estimate its value rather than exactly calculating it. This estimation is inevitably subject to error. As standard with Monte Carlo approaches, the standard error decreases with the square root of the number of MC samples. We propose a number of real-time hypervolume estimation methods for unconstrained archives --- principally for use in real-time convergence analysis. Furthermore, we show how the number of domination comparisons can be considerably reduced by exploiting incremental properties of the approximated Pareto front. In these methods the estimation error monotonically decreases over time for (i) a capped budget of samples per algorithm generation and (ii) a fixed budget of dedicated computation time per optimiser generation for new MC samples. Results are provided using an illustrative worst-case scenario with rapid archive growth, demonstrating the orders-of-magnitude of speed-up possible.
Author: Jonathan E. Fieldsend
Institution: University of Exeter
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2949873992