Balancing diversity and performance in global optimization

This paper studies the problem of balancing diversity and performance in surrogate-based global optimization when we look for two diverse competitive designs. A previous formulation that maximizes the average performance of the two designs with constraint on diversity is compared to a new formulation that maximizes diversity for a given loss in performance with respect to a single global optimum. The loss in performance is estimated using the surrogate. Three test functions are used to compare the curves of diversity vs. performance obtained from the two formulations. Significantly, for the examples, the search for the two diverse designs produced also designs much closer in performance to the global optimum than the two designs satisfying the diversity constraint or goal. Therefore, if three designs are accepted as the outcome of the search, the loss of performance may be drastically reduced.