Platinum ratio search versus golden ratio search

In this simulation study, we examine the traditional golden ratio search in view of cost minimization and search risk, and propose an alternative search plan with what we call “platinum ratio”. The golden ratio search has been thought the best for unimodal optimization. However, our study shows that the golden ratio search is the best only in the sense of zero variation, but not in the sense of minimum cost. In the sense of cost minimization without considering search risk, the best sectioning ratio is around 0.55 (we name it as platinum ratio), rather than the golden ratio, 0.618.