In general, all of the hybridized evolutionary optimization algorithms use “first diversification and then intensification” routine approach. In other words, these hybridized methods all begin with a global search mode using a highly random initial search population and then switch to intense local search mode at some stage. The population initialization is still a crucial point in the hybridized evolutionary optimization algorithms since it can affect the speed of convergence and the quality of the final solution. In this study, we introduce a new approach by creating a paradigm shift that reverses the “diversification” and then “intensification” routines. Here, instead of starting from a random initial population, we firstly find a unique starting point by conducting an initial exhaustive search based on the coordinate exhaustive search local optimization algorithm only for single step iteration in order to collect a rough but some meaningful knowledge about the nature of the problem. Thus, our main assertion is that this approach will ameliorate convergence rate of any evolutionary optimization algorithms. In this study, we illustrate how one can use this unique starting point in the initialization of two evolutionary optimization algorithms, including but not limited to Big Bang-Big Crunch optimization and Particle Swarm Optimization. Experiments on a commonly used benchmark test suite, which consist of mainly rotated and shifted functions, show that the proposed initialization procedure leads to great improvement for the above-mentioned two evolutionary optimization algorithms.