## 1 Introduction  
Scheduling is the construction of a timetable that encloses the plan for performing a set of operations on a limited set of non-consumable resources. Scheduling problems appear in diverse structures and exist in a wide variety of industrial and service systems [1]. The scheduling problem considered in this paper exists in maintenance and healthcare diagnostic systems in which the dynamic arrivals of jobs (maintenance requests or patients) are a common characteristic. It is referred to as the dynamic, multiprocessor open-shop scheduling problem (DMOSP). Dynamic arrivals of jobs require responsive planning for rescheduling decisions to maintain a smooth execution of schedules for both existing and arriving jobs while sustaining a high level of performance. Nowadays, responsive rescheduling is becoming a requirement for the integration of the fourth industrial revolution [2]. This paper presents the elements and processes of an efficient metaheuristic approach that can be used to provide efficient solutions to this problem. The studied problem is encountered in a system consisting of workstations that have technologically different functions. For instance, in a healthcare diagnostic system, the workstations can perform X-ray, CT scans, and ultrasound. Each workstation consists of unrelated machines working in parallel and are not necessarily identical. Therefore, they may differ in their processing times, which may also depend on the type of the job. Jobs are constituted of a set of operations. Each operation represents a task that needs to be performed on a specified workstation in which a machine needs to be selected. Jobs do not require a mandatory sequence for visiting the workstations and are not compelled to visit all of them. Machine interruptions due to sudden breakdowns or preventive maintenance activities are neglected. It is assumed that a machine can process at most one operation at a time, that operation interruption or preemption is not allowed, and that jobs cannot be split or processed on multiple machines simultaneously. Jobs differ in their priorities, which are represented as numerical values. The more important a job is, the higher its assigned priority value. A mixed-integer linear programming model for the studied problem is provided in [3]. The rescheduling management system considered herein is as explained by [PERSON] [4], and it is operated as follows. A decision-maker continuously receives jobs during the execution of a schedule and assigns a numerical value to each job, representing its priority level. Based on an initial checkup process, the processing requirements for the operations of each job are determined. Once they become known for a set of arrived jobs, the decision-maker decides on the time at which this set of jobs will be admitted, which is referred to as the job release time. At that time, if an existing job has an operation that is currently running, it is assigned a release time that equals the completion time of that operation. Its remaining not-yet-started operations are considered in the new schedule. Otherwise, the release time of the existing job is set to be equal to the release time of the arrived jobs. Accordingly, we may reasonably assume that the jobs' release times and the operations' processing times on all machines are known and certain. Meanwhile, a machine may not be ready at the beginning of a rescheduling phase due to a prior allocation of an existing job. Therefore, each machine has a ready time representing the time at which it will be available for processing jobs. Machine-ready times are assumed to be deterministic and known a priori. This paper considers a bi-objective, dynamic, multiprocessor open-shop scheduling problem (Bi-DMOSP). Since a single objective is not sufficient to cover the interests of all the stakeholders in the schedules generated for these systems, two objectives are simultaneously considered in this paper.