Abstract
Robust optimization considers uncertainty in the decision variables while noisy optimization concerns with uncertainty in the evaluation of objective and constraint functions. Although many evolutionary algorithms have been proposed to deal with robust or noisy optimization problems, the research question approached here is whether these methods can deal with both types of uncertainties at the same time. In order to answer this question, we extend a test function generator available in the literature for multi-objective optimization to incorporate uncertainties in the decision variables and in the objective functions. It allows the creation of scalable and customizable problems for any number of objectives. Three evolutionary algorithms specifically designed for robust or noisy optimization were selected: RNSGA-II and RMOEA/D, which utilize Monte Carlo sampling, and the C-RMOEA/D, which is a coevolutionary MOEA/D that uses a deterministic robustness measure. We did experiments with these algorithms on multi-objective problems with (i) uncertainty in the decision variables, (ii) noise in the output, and (iii) with both robust and noisy problems. The results show that these algorithms are not able to deal with simultaneous uncertainties (noise and perturbation). Therefore, there is a need for designing algorithms to deal with simultaneously robust and noisy environments.
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Notes
- 1.
For Gaussian noise: moderate intensity considers \(\beta = 0.01\), which corresponds to a variation of up to 3\(\%\) (either multiplying the function by 1.03 or multiplying the function by 0.97); severe intensity considers \(\beta = 1\), resulting in a variation of up to 20 times (either multiplying the function by 20 or dividing the function by 20). For uniform noise: moderate intensity considers \(\beta = 0.01\) and \(\alpha = 0.01(0.49 + 1/D)\), where D represents the number of decision variables (always considered as 24 in this work), resulting in a variation of up to 12\(\%\); severe intensity considers \(\beta = 1\) and \(\alpha = 0.49 + 1/D\), resulting in a variation of up to tens of thousands. For Cauchy noise: moderate intensity considers \(\alpha = 0.01\) and \(p = 0.05\); severe intensity considers \(\alpha = 1\) and \(p = 0.2\).
- 2.
Further details on the decomposition algorithm and methods can be found in [23].
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Acknowledgment
This work has been supported by the Brazilian agencies (i) National Council for Scientific and Technological Development (CNPq), Grant no. 312991/2020-7; (ii) Coordination for the Improvement of Higher Education Personnel (CAPES) through the Academic Excellence Program (PROEX) and (iii) Foundation for Research of the State of Minas Gerais (FAPEMIG, in Portuguese), Grant no. APQ-01779-21. MINDS Laboratory – https://minds.eng.ufmg.br/
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de Sousa, M.C., Meneghini, I.R., Guimarães, F.G. (2023). Assessment of Robust Multi-objective Evolutionary Algorithms on Robust and Noisy Environments. In: Naldi, M.C., Bianchi, R.A.C. (eds) Intelligent Systems. BRACIS 2023. Lecture Notes in Computer Science(), vol 14197. Springer, Cham. https://doi.org/10.1007/978-3-031-45392-2_3
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