Using Well-Understood Single-Objective Functions in Multiobjective Black-Box Optimization Test Suites
Several test function suites are being used for numerical benchmarking of multiobjective optimization algorithms. While they have some desirable properties, such as well-understood Pareto sets and Pareto fronts of various shapes, most of the currently used functions possess characteristics that are...
Saved in:
Published in | Evolutionary computation Vol. 30; no. 2; pp. 165 - 193 |
---|---|
Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
One Rogers Street, Cambridge, MA 02142-1209, USA
MIT Press
01.06.2022
MIT Press Journals, The Massachusetts Institute of Technology Press (MIT Press) |
Subjects | |
Online Access | Get full text |
ISSN | 1530-9304 1063-6560 1530-9304 |
DOI | 10.1162/evco_a_00298 |
Cover
Summary: | Several test function suites are being used for numerical benchmarking of multiobjective optimization algorithms. While they have some desirable properties, such as well-understood Pareto sets and Pareto fronts of various shapes, most of the currently used functions possess characteristics that are arguably underrepresented in real-world problems such as separability, optima located exactly at the boundary constraints, and the existence of variables that solely control the distance between a solution and the Pareto front. Via the alternative construction of combining existing single-objective problems from the literature, we describe the
test suite with 55 bi-objective functions in continuous domain, and its extended version with 92 bi-objective functions (
). Both test suites have been implemented in the
platform for black-box optimization benchmarking and various visualizations of the test functions are shown to reveal their properties. Besides providing details on the construction of these problems and presenting their (known) properties, this article also aims at giving the rationale behind our approach in terms of groups of functions with similar properties, objective space normalization, and problem instances. The latter allows us to easily compare the performance of deterministic and stochastic solvers, which is an often overlooked issue in benchmarking. |
---|---|
Bibliography: | 2022 ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 |
ISSN: | 1530-9304 1063-6560 1530-9304 |
DOI: | 10.1162/evco_a_00298 |