This work presents an optimization method combined with evolutionary space search algorithm (ESSA) for solving numerical optimization problems. The main strategy of the ESSA is to divide the feasible solution space into many subspaces and search for the solution by finding the optimal subspace. To facilitate the global exploration property, the subspace is characterized in terms of quantum bit representation and selected based on selection probabilities. As differences in fitness are evaluated with each generation, the quantum bits also evolve gradually. This process increases the probability of selecting subspaces that generate better fitness and enables the algorithm to exploit good subspaces, which then promotes local exploitation capability. An overlapping strategy is developed to prevent the subspace search from being trapped at a local optimum. Applying the ESSA to ten benchmark functions of diverse complexities shows that the quantum evolution substantially enhances the search for an optimal solution by finding the subspace in which the optimal solution resides. Performance comparisons with other evolutionary algorithms (EAs) under the same termination condition are also presented to confirm the superiority and effectiveness of the ESSA.