Fast iterated local search algorithm with high order neighborhood for no-wait flowshop scheduling problem

Most of the metaheuristic algorithms for the no-wait flowshop scheduling problem with makespan criterion have adopted the O(n²) size insertion neighborhoods, and higher order (polynomial size) neighborhoods are seldom tried. However, higher order neighborhoods can improve the solution quality of metaheuristic algorithms. The paper presents a high order neighborhood with O(n⁴) size called nonadjacent job block exchange neighborhood and develops a fast search algorithms with O(n²) time complexity for it. An iterated local search algorithm is further presented for the considered problem, where the new neighborhood along with the insertion neighborhood is used in variable neighborhood decent to provide a local search procedure for iterated local search. Experimental comparison shows that the higher order neighborhood based iterated local search algorithm is both fast and effective.