## 4 Key Enabling Technologies
### Multi-Machine Cooperative Scheduling Based on IHHO
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbols** & **Meaning** \\ \hline \(E\) & Total fuel consumption \\ \(C\) & Total scheduling cost \\ \(T\) & Task completion time \\ \(X_{ijh}\), \(X_{ig}\) & Decision variable: a binary variable indicating whether primary machines \(h\) or \\ \(d_{ij}\) & Auxiliary machines \(g\) travels from node \(i\) to node \(j\) \\ \(P_{hg}\) & Penalty cost for violating time windows \\ \(U_{h}\), \(L_{g}\) & Unloading time and loading time, where \(U_{h}=L_{g}\) \\ \(H_{v}\), \(G_{v}\) & Capacity of primary machines, capacity of auxiliary machine \\ \(q_{f}\) & The amount of farmland \(f\) to be operated \\ \(D_{i}\) & Planting density of farmland \(f\) \\ \(U_{ch}\) & Grain unloading efficiency of primary machines \(h\) \\ \(C_{w}\), \(C_{i}\) & Cost of waiting per unit of time, cost of penalization per unit of time \\ \(B_{i_{v}}\), \(E_{i}\) & Time allowed for the start of the task on the farmland \(f\) and the latest time \\ \(t_{hgf}\) & The moment the primary machines or auxiliary machines arrives on the farmland \(f\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Symbols and meaning. iary machine cannot exceed their respective capacities. Equation (5) implies that the unloading time and loading time are equal. Equation (6) represents the soft time window constraints. To improve connectivity between farmland plots, a field transfer road network is established, with path optimization carried out through the following steps:  
1. Constructing a farmland network graph, where key locations such as field entrances and exits, the agricultural machinery depot, and headland turning points are designated as network nodes. 2. Applying [PERSON]'s algorithm to determine the shortest paths between farmland plots, generating a distance matrix to support scheduling optimization [41]. 3. Dynamically adjusting transfer routes based on the real-time scheduling status of different machines and the spatial distribution of farmland plots to enhance overall efficiency. The process is shown in Figure 7.  
The improved IHHO algorithm enhances its solving capability through the following methods: First, a quasi-oppositional and quantum computing-based initialization strategy is introduced in the initialization phase to increase population diversity and optimize the quality of the initial solution, thereby improving the convergence speed [42]. Second, to enhance the global search ability of the HHO algorithm in complex problems, the multi-search mechanism of the Slime Mould Algorithm (SMA) is integrated, helping the algorithm escape local optima [43]. Additionally, a nonlinear energy factor update strategy is adopted to prevent the algorithm from falling into local optima in the later stages of convergence [44]. Finally, the mean differential mutation strategy is introduced to strengthen the optimization ability of the algorithm in complex scheduling tasks, thereby improving solution accuracy and stability [45]. The algorithm flowchart is shown in Figure 8.  
Figure 7: Field network graph and Dijkstra path optimization. Figure 9 presents Gantt charts illustrating the scheduling and operational timelines of three primary machines and four secondary machines across 20 farmland plots in a coordinated multi-field operation. The vertical axis represents machine IDs, while the horizontal axis denotes time. Different colors distinguish various task states, including transport, loading/unloading, operation, and return. The left chart displays the activities of secondary machines, while the right chart shows the primary machines' operations. Task allocation ensures that primary machines handle fieldwork, while secondary machines manage logistics and material transfer. The Gantt charts visually depict the effectiveness of the coordination strategy, highlighting how tasks are dynamically adjusted to optimize efficiency, minimize idle time, and enhance resource utilization. Figure 8: Flowchart of the Improved IIHHO Algorithm. Figure 9: Gantt chart of the IIHHO algorithm.