## 2 Related Work  
The studied problem is a generalization of the OSP, which has received much attention in the literature since it is encountered in several real-life applications. For the objective of minimizing the makespan, recently developed construction heuristics are provided in [11], and many heuristic and metaheuristic approaches are available in the literature [12]. On the other hand, a few approaches have been proposed for the mean flow time or the total completion time minimization objective. Construction heuristics were developed by [PERSON] et al. [13] and [PERSON] [14]. Metaheuristic approaches include simulated annealing by [PERSON] et al. [15] and a hybrid discrete differential evolution algorithm by [PERSON] et al. [16]. Little attention has been given to the multi-objective OSP in the literature. Only one paper has been found to deal with the makespan and the total completion-time minimization objectives by [PERSON] et al. [17]. A third objective related to minimizing the total machine idle time has also been considered. Yet, there is a correlation between the third objective and the makespan minimization objective. They proposed a metaheuristic approach based on particle swarm optimization. It is noticeable that researchers have paid more attention to the minimization of due date-related objectives, along with a completion time-basedobjective. [PERSON] et al. [18] and [PERSON] and [PERSON] [19] studied the OSP while simultaneously minimizing the total tardiness and the makespan. A solution approach was proposed based on ant colony optimization, hybridized with simulated annealing. The results were compared with those of NSGA-II. [PERSON] et al. [20] studied the OSP with the objective of minimizing total tardiness and the mean completion time simultaneously. Using a mixed-integer linear programming (MILP) model, a fuzzy programming method was proposed to find efficient solutions compared with a tabu search approach. A hybrid immune algorithm was proposed later by [PERSON] et al. [21] for the total tardiness and the total completion-time minimization objectives. The multiprocessor open-shop scheduling problem (MOSP) is a special case of the DMOSP in which identical parallel machines constitute the workstations. In addition, all machines are ready at the beginning of the schedule, at which time all jobs are released. Furthermore, each job must visit all workstations [22]. Different construction heuristics are proposed for minimizing the makespan of the MOSP in [23; 24; 25]. Those heuristics are linear-time approximation algorithms with proven bounds on their gaps from the optimal solution. [PERSON] et al. [26] provided a MILP model and developed a metaheuristic approach based on a hybrid memetic algorithm with simulated annealing to minimize the total completion time. In the literature, the MOSP is sometimes referred to as the hybrid open-shop scheduling problem. Recent algorithmic developments for its multi-objective, stochastic variant include [27; 28]. A more general case of the MOSP was studied by [PERSON] [29]; in it, machines in a workstation need not be identical, and jobs do not have to visit all workstations. He developed an MILP model and proposed a scatter search with a path-relinking metaheuristic, which generates optimal or near-optimal solutions to minimize the makespan. Recently, [PERSON] et al. [30] proposed a scatter-search metaheuristic for the MOSP with sequence-independent setup times. They considered two objectives simultaneously--the minimization of both the total tardiness and the makespan. Computational experiments revealed that their metaheuristic has better performance than a non-dominated-sorting genetic algorithm approach. Another related specialization of the MOSP is the proportionate multiprocessor open-shop scheduling problem (PMOSP), in which the processing times on the workstations do not vary among jobs. Mathematical programming models and a genetic algorithm (GA) approach were developed by [PERSON] [31]. [PERSON] et al.