*3.3. Optimization*

Smart manufacturing based on the edge computing system has high scalability and huge IIoT devices, which is suitable based on the expansion potentiality. Data analysis and transmission are considered computational tasks. They are supposed to allocate data on an edge server or cloud to recognize the suitable task assignment for reducing the process time of the incoming task. There are *X* defined device terminals, *Y* edge nodes, and one industrial server for the cloud to design this issue in smart manufacturing. Within the manufacturing process, the requests from terminal devices are managed by a cloud or edge server. The process timing for the tasks in edge server requires two main components called computation time *θ y i*,*<sup>c</sup>*and data transmission time *θ y <sup>i</sup>*,*d*; see Equation (5).

$$
\beta\_i^y = \theta\_{i,c}^y + \theta\_{i,d}^y \tag{5}
$$

The task computation time in an edge server is evaluated based on Equation (6).

$$
\theta\_{i,c}^y = L\_i / \Sigma\_{n=1}^{n\_{max}^i} a\_{i,n}^y \tag{6}
$$

*y* is defined as the edge server, *i* represents the task computation time, and *a y i*,*<sup>n</sup>* represents the edge server's computational resources through the *n* period of maintaining tasks. *L* is defined as the length of the tasks. The task processing time in a cloud server is evaluated as it was presented in Equation (7):

$$
\beta\_i^t = \theta\_{i,c}^t + \theta\_{i,d}^y + \theta\_{i,d}^{y,t} \tag{7}
$$

The computation time in the cloud is defined as *θt i*,*c*. Data transmission between the edge and device is defined as *θ y i*,*d*. The transmission time from the edge server to cloud is defined as *θ y*,*t i*,*d* . The task assignment's presented issue is the deployment of a parallel mechanism and heterogeneous units' processing in the computational task assignment issue. Accordingly, the swarm intelligence approach is applied in this process.
