An Improved Heuristic for Permutation Flowshop Scheduling

Flowshop scheduling deals with determination of optimum sequence of jobs to be processed on some machines in a fixed order so as to satisfy certain scheduling criteria. The general problem of scheduling has been shown to be NP-complete. Exact algorithms, such as integer programming and branch-and-bound, guarantee optimality but do not yield the optimum solution in polynomial time even for problems of small size. Heuristics have been shown to yield good working solutions (not necessarily optimal) in reasonable time. Although much research on the flowshop problem has been done over several decades starting from Johnson's lgorithm, only a few good algorithms exist. The Nawaz-Enscore-Ham heuristic, used for minimisation of makespan, continues to be the most popular algorithm because of its simplicity, solution quality and time-complexity. In the present paper we have modified the NEH algorithm, achieving significant improvement in the quality of the solution while maintaining the same algorithmic complexity. The proposed approach derives its strength from the use of a population-based technique. Experimental comparisons have been made on a large number of randomly generated test problems of varying problem sizes. Our approach is shown to outperform both the original NEH and NEH's best-known competitor to date, the HFC heuristic. Statistical tests of significance are performed to substantiate the claims of improvement.