A1 Journal article (refereed)
ANOVA-MOP : ANOVA Decomposition for Multiobjective Optimization (2018)


Tabatabaei, M., Lovison, A., Tan, M., Hartikainen, M., & Miettinen, K. (2018). ANOVA-MOP : ANOVA Decomposition for Multiobjective Optimization. SIAM Journal on Optimization, 28(4), 3260-3289. https://doi.org/10.1137/16M1096505


JYU authors or editors


Publication details

All authors or editors: Tabatabaei, Mohammad; Lovison, Alberto; Tan, Matthias; Hartikainen, Markus; Miettinen, Kaisa

Journal or series: SIAM Journal on Optimization

ISSN: 1052-6234

eISSN: 1095-7189

Publication year: 2018

Volume: 28

Issue number: 4

Pages range: 3260-3289

Publisher: Society for Industrial and Applied Mathematics

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1137/16M1096505

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/60635


Abstract


Real-world optimization problems may involve a number of computationally expensive functions with a large number of input variables. Metamodel-based optimization methods can reduce the computational costs of evaluating expensive functions, but this does not reduce the dimension of the search domain nor mitigate the curse of dimensionality effects. The dimension of the search domain can be reduced by functional anova decomposition involving Sobol' sensitivity indices. This approach allows one to rank decision variables according to their impact on the objective function values. On the basis of the sparsity of effects principle, typically only a small number of decision variables significantly affects an objective function. Therefore, neglecting the variables with the smallest impact should lead to an acceptably accurate and simpler metamodel for the original problem. This appealing strategy has been applied only to single-objective optimization problems so far. Given a high-dimensional optimization problem with multiple objectives, a method called anova-mop is proposed for defining a number of independent low-dimensional subproblems with a smaller number of objectives. The method allows one to define approximated solutions for the original problem by suitably combining the solutions of the subproblems. The quality of the approximated solutions and both practical and theoretical aspects related to decision making are discussed.


Keywords: multi-objective optimisation; Pareto efficiency; decision making

Free keywords: multiple criteria optimization; sensitivity analysis; metamodeling; dimensionality reduction; Pareto optimality


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Ministry reporting: Yes

Reporting Year: 2018

JUFO rating: 3


Last updated on 2021-17-09 at 16:50