A new genetic algorithm is proposed based on the careful coordination of the exploration in the solution space of the given problem and the exploitation of the information from the previous search. In the new algorithm architecture, the population in each generation consists of three sub-populations: a preserved part, a reproduced part, and a randomized part. Two parameters are incorporated into the algorithm to efficiently control the percentage of each sub-population to achieve good balance between the exploration and exploitation processes during the optimization. By modeling the algorithm as a homogeneous finite Markov chain, the new genetic algorithm is shown to converge towards the global optimum of the problem at hand. Experiments were designed to test the algorithm using the Rastrigin function, the Griewangk function, and the Schaffer function. Data analyses using the average success ratio, the average objective calculating number, the average first passage time to solution, and the standard deviation of the first passage time were compared with those of the canonical genetic algorithm, the elitist genetic algorithm, and the steady genetic algorithm. The results show strong evidence that our algorithm is superior in performance in terms of economy, robustness and efficiency.