The YUKI algorithm is an optimization approach based on search space reduction, adjusting its exploration and exploitation strategies based on optimization progress. This article suggests an update to the exploration strategy to enhance its efficacy in engineering design problems and maintain the simplicity of the algorithm. Performance evaluations were conducted on challenging composite functions and engineering design problems. In addition, the metaheuristic structural binary-distribution technique is introduced, integrating the YUKI algorithm with gradient descent for topology optimization. This technique is tested on the problem of maximizing structural stiffness, based on strain energy, across low and high dimensions, and in the problem of heat dissipation. The results suggest a significant improvement in exploration performance. MATLAB and Python source codes for the YUKI algorithm are publicly accessible at https://brahimbenaissa.com/posts/Yuki-Algorithm-02/