## 4 Multi-Objective Optimization for Edible Oil Transportation Scheduling Method
### Pipeline Cost Function  
During the digitization of the pipeline system, special attention must be given to the unique nature of edible oil transport, particularly the need to prevent edible oil cross-contamination. In this study, directional indicators were assigned to each node to reflect its functional role, as illustrated in Figure 7. Arrows pointing outward indicate edible oil outflow, whereas those pointing inward denote edible oil inflow. To quantify the scheduling significance of each node, we define the \"node connectivity number\" as the total count of its outward connections. This number serves as an indicator of the node's potential for flow distribution. Nodes with higher connectivity are more likely to be frequently utilized in edible oil transfer operations and may become bottlenecks, leading to congestion of pipeline resources. Accordingly, node connectivity is incorporated as a weighted parameter in the scheduling algorithm. In practical applications, critical nodes are often cross-type junctions with four outlets. Therefore, the upper bound of node weight \(w_{cost}\) is set to 4 in this study, serving as a reference for prioritizing scheduling decisions. In the proposed system design, the shortest path for each edible oil transfer task is first computed using a path planning algorithm. The total cost is then obtained by summing the weight values of all nodes, such as valves and pipes, encountered along the path. Node  
Figure 7: Localized view of the digitized pipeline network. A close-up view of the digitized pipeline layout, illustrating the interconnections between valves, tanks, and transport lines used in the edible oil distribution system. weights are assigned based on their connectivity (i.e., the number of links to other nodes) to control their frequency of usage during scheduling. Nodes with higher connectivity are assigned to a lower scheduling priority, which helps reduce resource congestion at highly connected junctions. This strategy promotes balanced utilization of pipeline resources and enhances the system's ability to handle dynamic and highly variable operational demands. Due to differences in node position and function, the number of links varies between nodes, influencing their assigned cost weight. To prevent high-flexibility nodes, such as multi-directional valves or frequently used pipe junctions from becoming over utilized by a single task, a node weight-limiting mechanism is introduced. As illustrated in the A* path planning example in Figure 8, the specific valve and pipeline resources used during the routing process are analyzed. The connectivity and weight of each node are summarized in Table 2, with different node types visually distinguished using color coding. Furthermore, as shown in Table 2, the parameters for pipeline resources required by each task are relatively well-defined. The factory's oil transportation task planning is conducted based on customer order requirements, with task contents generally being quite explicit. Moreover, the complexity of the oil pipeline environment is significantly lower compared to the movement paths and environments encountered by robots or autonomous mobile robots (AMRs). The proposed cost function is calculated based on the number of nodes traversed by each task and their associated weights. This function serves as the basis for determining \begin{table}
\begin{tabular}{c c} \hline \hline
**Node Items** & **Number of Connected Modes (Weight)** \\ \hline T5004\_OUT & 4 \\ Valve02\_T5004\_Pi06 & 1 \\ Pipe06\_T5004\_T5005 & 4 \\ Pipe06\_T5001\_T5002 & 4 \\ Pump\_Big\_PiPackage05 & 2 \\ Pipe\_PiPackage06 & 3 \\ Valve05\_Pa & 1 \\ Pipe\_Pa\_v05v25 & 4 \\ T0201\_IN & 0 \\
**Total Weight** & **23** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Node weight for the shortest path. Figure 8: Simulation of the shortest path. Visualization of the computed shortest path for a given transport task, highlighting the sequence of utilized pipeline and valve nodes. the execution priority of individual edible oil transfer tasks.