This paper proposes a new multi-start scheme that generates guided random bits in selecting initial search points for global optimization with univariate dynamic encoding algorithm for searches (uDEAS). The proposed method counts the number of 1 in each bit position from all the previously generated initial search matrices and, based on this information, generates 0 in proportion with the probability of selecting 1. This rule is simple and effective for improving diversity of initial search points. The performance improvement of the proposed multi-start is validated through implementation in uDEAS and function optimization experiments.