A new meta-heuristic evolutionary algorithm, named a memetic algorithm, for solving single machine total weighted tardiness scheduling problems is presented in this paper. Scheduling problems are proved to be NP-hard (Non-deterministic polynomial-time hard) types of problems and they are not easily or exactly solved for larger sizes. Therefore, application of the meta-heuristic technique to solve such NP hard problems is pursued by many researchers. The memetic algorithm is a marriage between population-based global searches with local improvement for each individual. The algorithm is tested with benchmark problems available in the OR (operations research) library. The results of the proposed algorithm are compared with the best available results and were found to be nearer to optimal. The memetic algorithm performs better than the heuristics like earliest due date and modified due date. © Springer-Verlag London Limited 2004.