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The objective of this paper is to find the generation scheduling such that the total operating cost can be minimized, when subjected to a variety of constraints. This also means that it is desirable to find the optimal generating unit commitment in the power system for the next H hours. Genetic Algorithms (GA's) are general-purpose optimization techniques based on principles inspired from the biological evolution using metaphors of mechanisms such as neural section, genetic recombination and survival of the fittest. In this, the unit commitment schedule is coded as a string of symbols. An initial population of parent solutions is generated at random. Here, each schedule is formed by committing all the units according to their initial status (“flat start”). Here the parents are obtained from a pre-defined set of solution's i.e. each and every solution is adjusted to meet the requirements. Then, a random recommitment is carried out with respect to the unit's minimum down times. And SA improves the status. A 66-bus utility power system with twelve generating units in India demonstrates the effectiveness of the proposed approach. Numerical results are shown comparing the cost solutions and computation time obtained by using the Genetic Algorithm method and other conventional methods.