A heuristic algorithm with six implementations (HA-I to HA-VI) is presented in this paper, and it is used to solve the permutation flowshop scheduling problem to minimise the total flowtime of jobs. These implementations have been evaluated by using the 90 benchmark flowshop scheduling problem instances, and the solutions yielded are compared with the solutions reported in the literature. The comparison shows that the implementations all together have produced better solutions for 28 problem instances and same solutions for 29 problem instances, out of 90 problem instances considered with respect to the solutions by Iterated Local Search algorithm proposed by Dong et al. (2009). They have also produced better solutions for 50 problem instances and the same solutions for 19 problem instances, out of 90 problem instances considered with respect to the solutions by PSOvns algorithm proposed by Tasgetiren et al. (2007), as reported in Dong et al. (2009). © 2014 Inderscience Enterprises Ltd.