STK_SAMPCRIT_EHVI_EVAL computes the EHVI criterion

 CALL: EHVI = stk_sampcrit_ehvi_eval (ZP_MEAN, ZP_STD, ZI, ZR)

    computes the value EHVI of the Expected HyperVolume Improvement (EHVI) for
    a multi-objective minimization problem, with respect to the observed values
    ZI and the reference point ZR, assuming Gaussian predictive distributions
    with means ZP_MEAN and standard deviations ZP_STD.  The input arguments
    must have the following sizes:

       * ZP_MEAN    M x P,
       * ZP_STD     M x P,
       * ZI         N x P,
       * ZR         1 x P,

    where M is the number of points where the EHVI 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.

 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.

 REFERENCES

  [1] Emmerich, M. T., Giannakoglou, K. C., & Naujoks, B.  Single- and
      multiobjective evolutionary optimization assisted by gaussian random
      field metamodels. IEEE Transactions on Evolutionary Computation,
      10(4), 421-439, 2006.

 See also: stk_sampcrit_emmi_eval, stk_sampcrit_ei_eval

Package: stk