In this paper, a constrained genetic algorithm (CGA) is proposed to solve the single machine total weighted tardiness problem. The proposed CGA incorporates dominance rules for the problem under consideration into the GA operators. This incorporation should enable the proposed CGA to obtain close to optimal solutions with much less deviation and much less computational effort than the conventional GA (UGA). Several experiments were performed to compare the quality of solutions obtained by the three versions of both the CGA and the UGA with the results obtained by a dynamic programming approach. The computational results showed that the CGA was better than the UGA in both quality of solutions obtained and the CPU time needed to obtain the close to optimal solutions. The three versions of the CGA reduced the percentage deviation by 15.6%, 61.95%, and 25% respectively and obtained close to optimal solutions with 59% lower CPU time than what the three versions of the UGA demanded. The CGA performed better than the UGA in terms of quality of solutions and computational effort when the population size and the number of generations are smaller. In this paper, a constrained genetic algorithm (CGA) is proposed to solve the single machine total weighted tardiness problem. The proposed CGA incorporates dominance rules for the problem under consideration into the GA operators. This incorporation should enable the proposed CGA to obtain close to optimal solutions with much less deviation and much less computational effort than the conventional GA (UGA). Several experiments were performed to compare the quality of solutions obtained by the three versions of both the CGA and the UGA with the results obtained by a dynamic programming approach . The computational results showed that the CGA was the more than the UGA in both quality of solutions obtained and the CPU time needed to obtain the close to optimal solutions. The three versions of the CGA reduced the percentage deviation by 15.6%, 61.95%, and 25% respectively and obtained close to optimal solutions with 59% lower CPU time than what the three versions of the UGA demanded. The CGA performed better than the UGA in terms of quality of solutions and computational effort when the population size and the number of generations are smaller.