Statistical optimization of expensive multi-response black-box functions
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Assume that a set of P process parameters p_i, i=1,…,P, determines the outcome of a set of D descriptor variables d_j, j=1,…,D, via an unknown functional relationship ϕ: 𝐩↦𝐝, ℝ^P→ℝ^D, where 𝐩=(p_1,…,p_P), 𝐝=(d_1,…,d_D). It is desired to find appropriate values 𝐩̂ = (p̂_1,…, p̂_P) for the process parameters such that the corresponding values of the descriptor variables ϕ (𝐩̂) are close to a given target 𝐝^*=(d^*_1,…,d^*_D), assuming that at least one exact solution exists. A sequential approach using dimension reduction techniques has been developed to achieve this. In a simulation study, results of the suggested approach and the algorithms NSGA-II, SMS-EMOA and MOEA/D are compared.
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