An effective new heuristic algorithm for solving permutation flow shop scheduling problem

The deterministic permutation flow shop scheduling problem with makespan criterion is not solvable in polynomial time‎. ‎Therefore‎, ‎researchers have thought about heuristic algorithms‎. ‎There are many heuristic algorithms for solving it that is a very important combinatorial optimization problem‎. ‎In this paper‎, ‎a new algorithm is proposed for solving the mentioned problem‎. ‎The presented algorithm chooses the weighted path that starts from the up-left corner and reaches the down-right in the matrix of jobs processing times and calculates the biggest sum of the times in the footprints of this path‎. ‎The row with the biggest sum permutes among all the rows of the matrix for locating the minimum of makespan‎. ‎This method was run on Taillard’s standard benchmark and the solutions were compared with the optimum or the best ones as well as 14 famous heuristics‎. ‎The validity and effectiveness of the algorithm are shown with tables and statistical evaluation‎.