An Iterated Greedy Heuristic for Mixed No-Wait Flowshop Problems

The mixed no-wait flowshop problem with both wait and no-wait constraints has many potential real-life applications. The problem can be regarded as a generalization of the traditional permutation flowshop and the no-wait flowshop. In this paper, we study, for the first time, this scheduling setting with makespan minimization. We first propose a mathematical model and then we design a speed-up makespan calculation procedure. By introducing a varying number of destructed jobs, a modified iterated greedy algorithm is proposed for the considered problem which consists of four components: 1) initialization solution construction; 2) destruction; 3) reconstruction; and 4) local search. To further improve the intensification and efficiency of the proposal, insertion is performed on some neighbor jobs of the best position in a sequence during the initialization, solution construction, and reconstruction phases. After calibrating parameters and components, the proposal is compared with five existing algorithms for similar problems on adapted Taillard benchmark instances. Experimental results show that the proposal always obtains the best performance among the compared methods.