In this research, a detailed study of the permutation flowshop scheduling problem with the objective of minimizing total tardiness is presented and a steady-state genetic algorithm solution procedure is developed for such problems. Also, using problem-specific knowledge, a very efficient elite guided solution improvement scheme and an appropriate crossover operator have been developed and integrated into the proposed method. Using benchmark problems, the algorithm has been compared with heuristic algorithms having the best performance in the literature. The performance of the developed algorithm is shown to be superior using a simulation study. (C) 2009 Elsevier Ltd. All rights reserved.