STK_SAMPCRIT_EMMI_EVAL computes the EMMI criterion
CALL: EMMI = stk_sampcrit_emmi_eval (ZP_MEAN, ZP_STD, ZI)
computes the value EMMI of the Expected MaxiMin Improvement (EMMI) for a
multi-objective minimization problem, with respect to the observed values
ZI, assuming Gaussian predictive distributions with means ZP_MEAN and
standard deviations ZP_STD. The value of the criterion is computed
approximately, using Monte Carlo simulations. The input arguments must
have the following sizes:
* ZP_MEAN M x P,
* ZP_STD M x P,
* ZI N x P,
where M is the number of points where the EMMI must be computed, P the
number of objective functions to be minimized, and N the current number of
Pareto optimal solutions. The output has size M x 1.
CALL: EMMI = stk_sampcrit_emmi_eval (ZP_MEAN, ZP_STD, ZI, NSIMU)
allows to change the number of simulations NSIMU used in the calculation of
the criterion.
NOTE
1) The result depends only on the non-dominated rows of ZI.
2) Multi-objective maximization problems, or mixed minimization/maximization
problems, can be handled by changing the sign of the corresponding
components of ZP_MEAN and ZI.
3) Objective functions should be normalized for better performances.
REFERENCES
[1] Svenson, J., & Santner, T. (2016). Multiobjective optimization of
expensive-to-evaluate deterministic computer simulator models.
Computational Statistics & Data Analysis, 94, 250-264,
DOI: 10.1016/j.csda.2015.08.011.
See also: stk_sampcrit_ehvi_eval
Package: stk