A1 Journal article (refereed)
On the Extension of the DIRECT Algorithm to Multiple Objectives (2021)
Lovison, A., & Miettinen, K. (2021). On the Extension of the DIRECT Algorithm to Multiple Objectives. Journal of Global Optimization, 79(2), 387-412. https://doi.org/10.1007/s10898-020-00942-8
JYU authors or editors
Publication details
All authors or editors: Lovison, Alberto; Miettinen, Kaisa
Journal or series: Journal of Global Optimization
ISSN: 0925-5001
eISSN: 1573-2916
Publication year: 2021
Publication date: 05/09/2020
Volume: 79
Issue number: 2
Pages range: 387-412
Publisher: Springer Science and Business Media LLC
Publication country: Netherlands
Publication language: English
DOI: https://doi.org/10.1007/s10898-020-00942-8
Publication open access: Openly available
Publication channel open access: Partially open access channel
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/71664
Abstract
Deterministic global optimization algorithms like Piyavskii–Shubert, DIRECT, EGO and many more, have a recognized standing, for problems with many local optima. Although many single objective optimization algorithms have been extended to multiple objectives, completely deterministic algorithms for nonlinear problems with guarantees of convergence to global Pareto optimality are still missing. For instance, deterministic algorithms usually make use of some form of scalarization, which may lead to incomplete representations of the Pareto optimal set. Thus, all global Pareto optima may not be obtained, especially in nonconvex cases. On the other hand, algorithms attempting to produce representations of the globally Pareto optimal set are usually based on heuristics. We analyze the concept of global convergence for multiobjective optimization algorithms and propose a convergence criterion based on the Hausdorff distance in the decision space. Under this light, we consider the well-known global optimization algorithm DIRECT, analyze the available algorithms in the literature that extend DIRECT to multiple objectives and discuss possible alternatives. In particular, we propose a novel definition for the notion of potential Pareto optimality extending the notion of potential optimality defined in DIRECT. We also discuss its advantages and disadvantages when compared with algorithms existing in the literature.
Keywords: multi-objective optimisation; optimisation; algorithms; determinants; multivariable methods
Free keywords: global convergence; multiobjective optimization; multiple criteria optimization; DIRECT algorithm; deterministic optimization algorithms
Contributing organizations
Related projects
- Decision Support for Computationally Demanding Optimization Problems
- Miettinen, Kaisa
- Academy of Finland
Ministry reporting: Yes
Reporting Year: 2021
Preliminary JUFO rating: 2