A Collaborative Multiobjective Fruit Fly Optimization Algorithm for the Resource Constrained Unrelated Parallel Machine Green Scheduling Problem

Due to the development of the green economy, green manufacturing has been a hot topic. This paper proposes a new problem, i.e., the resource constrained unrelated parallel machine green manufacturing scheduling problem RCUPMGSP) with the criteria of minimizing the makespan and the total carbon emission. To solve the problem, a collaborative multiobjective fruit fly optimization algorithm CMFOA) is proposed. First, a job-speed pair-based solution representation is presented, and an effective decoding method is designed. Second, a heuristic for initialization of the population is proposed. Third, three collaborative search operators are designed to handle three subproblems in the smell-based search phase, i.e., job-to-machine assignment, job sequence, and processing speed selection. The technique for order preference by similarity to an ideal solution and the fast nondominated sorting methods are both employed for multiobjective evaluation in the vision-based search phase. Moreover, a critical-path-based carbon saving technique is designed according to the problem analysis to further improve the nondominated solutions explored in the fruit fly optimization algorithm-based evolution. In addition, the effect of parameter setting is investigated and the suitable parameter values are recommended. Finally, numerical tests and comparisons are carried out using the randomly generated instances, which show that the CMFOA is able to obtain more and better nondominated solutions than other algorithms. The comparisons also demonstrate the effectiveness of the collaborative scheme and the carbon saving technique as well as the CMFOA in solving the RCUPMGSP.