In this paper, an intensive search evolutionary algorithm is proposed to solve single machine total weighted tardiness scheduling problems. A specialised locally improved random swap mutation operator and an ordered crossover operator are used for evolution. The proposed algorithm starts with a pair of sequences: one generated by a greedy heuristic, namely, a backward phase heuristic acts as one parent, and a randomly generated sequence acts as the other. A computational experiment is conducted by applying the mutation operator on the backward phase sequence and the proposed algorithm with the same number of generations as the termination criteria. A total of 125 benchmark instances for sizes 40, 50 and 100 available in the OR library are solved and the results are compared with the available best-known results. It is observed that the proposed evolutionary algorithm provides better results than others. © Springer-Verlag London Limted 2005.