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Genetic algorithms can provide good solutions for scheduling problems. In this paper we present a genetic algorithm to solve the single machine total weighted tardiness problem, a scheduling problem which is known to be NP-hard. First, we present a new concept of genetic operators for scheduling problems. Then, we present a developed software tool, called HybFlexGA, to examine the performance of various crossover and mutation operators by computing simulations of scheduling problems. Finally, the best genetic operators obtained from our computational tests are applied in the HybFlexGA. The computational results obtained with 40, 50 and 100 jobs show the good performance and the efficiency of the developed HybFlexGA.