A Cooperative Algorithm for Energy-efficient Scheduling of Distributed No-wait Flowshop

This paper addresses an energy-efficient distributed no-wait flowshop scheduling problem (EEDNFSP) with the criteria of minimizing both the makespan and the total energy consumption. A cooperative algorithm is proposed to solve the EEDNFSP. First, a cooperative initialization method which hybridizes the modified Nawaz-Enscore-Ham (NEH) heuristic and random initialization is presented to generate good and diverse initial solutions. Second, based on the characteristics of such a bi-objective scheduling problem, three types of search operators are developed for three sub-problems, i.e., factory assignment, job sequence, and speed selection. Third, a cooperation mechanism for the search operators is designed to trade-off two criteria. Fourth, a local intensification component is used for exploiting better non-dominated solutions sufficiently. Moreover, an energy saving method is utilized to further improve the quality of the explored solutions. The effect of parameter setting on the cooperative algorithm is investigated by using the Taguchi method of design-of-experiment. Computational tests and comparisons are carried out, which verify the effectiveness of the proposed algorithm in solving the EEDNFSP.