We propose a problem space genetic algorithm to solve single machine total weighted tardiness scheduling problems. The proposed algorithm utilizes global and time-dependent local dominance rules to improve the neighborhood structure of the search space. They are also a powerful exploitation (intensifying) tool since the global optimum is one of the local optimum solutions. Furthermore, the problem space search method significantly enhances the exploration (diversification) capability of the genetic algorithm. In summary, we can improve both solution quality and robustness over the other local search algorithms reported in the literature.