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A new simulated annealing (SA) algorithm combined with a dynamic economic dispatch method has been developed for solving the short-term unit commitment (UC) problem. SA is used for the scheduling of the generating units, while a dynamic economic dispatch method is applied incorporating the ramp rate constraints in the solution of the UC problem. New rules concerning the tuning of the control parameters of the SA algorithm are proposed. Three alternative mechanisms for generating feasible trial solutions in the neighborhood of the current one, contributing to the reduction of the required CPU time, are also presented. The ramp rates are taken into account by performing either a backward or a forward sequence of conventional economic dispatches with modified limits on the generating units. The proposed algorithm is considerably fast and provides feasible near-optimal solutions. Numerical simulations have proved the effectiveness of the proposed algorithm in solving large UC problems within a reasonable execution time.