A diversity metric based on Gaussian process model for diverse and competitive design

With the consideration that the single global optimum may be invalid because of some uncertainties, multiple designs with diversity, and competitiveness are usually desired. In this work, the uncertainty from a latent constraint is considered. A so-called latent constraint is a constraint unknown during the optimization problem formulation and solution, and its impact on feasibility of design is only recognized in the later stage. Based on the Gaussian process model and a rough assumption, a metric named trD is proposed which maintains several desired properties for measuring the diversity, and it is nearly consistent monotonicity with the probability that all the designs fail the latent constraint. By checking various Diversity Metric (DM) in literature for different purposes against the desired properties for a proper DM in line with latent constraint, the DM proposed in this work is justified. With the developed trD, three optimization models for diverse and competitive design are investigated with the numerical tests, including mathematical function, truss structure design, and topology optimization. The results show that with the same diversity, more optimal diverse designs result in better competitiveness but with a limit.

Automated summary

This study considers the uncertainty caused by latent constraints and develops a metric named trD for optimizing diverse and competitive designs. The results demonstrate that more optimal diverse designs lead to better competitiveness, but with limitations.