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A genetic algorithm (GA) is proposed that uses a variable population size and periodic partial reinitialization of the population in the form of a saw-tooth function. The aim is to enhance the overall performance of the algorithm relying on the dynamics of evolution of the GA and the synergy of the combined effects of population size variation and reinitialization. Preliminary parametric studies to test the validity of these assertions are performed for two categories of problems, a multimodal function and a unimodal function with different features. The proposed scheme is compared with the conventional GA and micro GA (μGA) of equal computing cost and guidelines for the selection of effective values of the involved parameters are given, which facilitate the implementation of the algorithm. The proposed algorithm is tested for a variety of benchmark problems and a problem generator from which it becomes evident that the saw-tooth scheme enhances the overall performance of GAs.