ANOVA-MOP : ANOVA Decomposition for Multiobjective Optimization
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
Published inSIAM Journal on Optimization
© 2018, Society for Industrial and Applied Mathematics.
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. ...
PublisherSociety for Industrial and Applied Mathematics
Publication in research information system
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Related funder(s)Academy of Finland
Funding program(s)Academy Project, AoF
Additional information about fundingThis work was partly funded by the Academy of Finland Project 287496, Early Career Scheme (ECS) Project 21201414, the General Research Fund Project 11226716, and sponsored by the Research Grants Council of Hong Kong and the KAUTE Foundation.
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