Comparison of the criteria for updating Kriging response surface models in multi-objective optimization

Abstract

This paper compares the criteria for updating the Kriging response surface models in multi-objective optimization: expected improvement (EI), expected hypervolume improvement (EHVI), estimation (EST), and those combination (EHVI+EST). EI has been conventionally used as the criterion considering the stochastic improvement of each objective function value individually, while EHVI has been recently proposed as the criterion considering the stochastic improvement of the front of non-dominated solutions in multi-objective optimization. EST is the value of each objective function, which is estimated non-stochastically by the Kriging model without considering its uncertainties. Numerical experiments were implemented in the welded beam design problem, and empirically showed that, in a non-constrained case, EHVI keeps a balance between accurate and wide search for non-dominated solutions on the Kriging models in multi-objective optimization. In addition, the present experiments suggested future investigation into the techniques for handling uncertain constraints to enhance the capability of EHVI in a constrained case.

Efficient multi-criteria optimization on noisy machine learning problems

“…This indicator has recently been used in design optimization under the name "Hypervolume-based Expected Improvement" (HEI), cf. [53,54].…”

Faster Exact Algorithms for Computing Expected Hypervolume Improvement

“…the variance [9]. It has been used as an infill criterion for multiobjective EGO in multiobjective optimization in various studies [3,4,5] but its application so far has been confined to the bi-objective case and the computation of the EHVI was criticized to be computationally expensive as compared to more simple generalizations of the EI [7].…”

“…Expected improvement has been studied as an infill criterion in different application fields, such as bioinformatics [15], mechanical engineering [17] and aerospace design [16]. Also the EHVI was already applied in practice for the tuning of controllers in sewage treatment plants [3], in mechanical engineering [4] and quantum control [2]. As compared to other indicators EHVI was found to have monotonicity in mean values [7] and variance [9] and yielded high accuracy optima approximations.…”

Computing 3-D Expected Hypervolume Improvement and Related Integrals in Asymptotically Optimal Time

“…Various generalizations of EI to multi-criterion optimization have been discussed in the literature, e.g., [7,[17][18][19][20]. See also [11] for an overview.…”

“…In the context of SAMCO, the Expected Hypervolume Improvement (EHVI) is frequently used as an infill or pre-selection criterion [1][2][3][4][5][6][7][8], and is a straightforward generalization of the single-objective expected improvement (EI). It is called multiple times because, in each iteration of SAMCO, either an optimum of the EI needs to be found, as in the case of Bayesian global optimization 1 [10], or, in surrogate-assisted evolutionary algorithms, it is used to pre-assess the quality of the individuals of a larger population.…”