## 6 Empirical Study
### Extended ZenoTravel Domain  
In order to illustrate the performance of the HQCP for high-quality plans in the partially observable environment, we extend standard ZenoTravel, one of the standard domains in the planning competition of the International Conference on AI Planning and Scheduling (AIPS-2002), into a partially observable domain. ZenoTravel is extended to verify the capabilities of the planning for high-quality plans in the partially observable domain. While numeric and temporal features are present in ZenoTravel, addressing these aspects is not the focus of this paper, and these features are treated within the framework of classical HTN planning. Given that there are no existing HTN planning approaches specifically investigating high-quality planning under partially observable conditions, we selected two cases from the ZenoTravel domain to verify and compare the planning capabilities for generating high-quality plans in such environments. In the ZenoTravel domain, an airplane transports people from city A to city C, transiting at city B. The airplane has two navigation modes: zoom and fly. Zoom, the fast movement, flies faster but consumes more fuel. The airplane must refuel when it lands at an airport if the zoom mode opens. Passengers board and debark from the airplane at the airport. Therefore, there are five actions: board, debark, fly, zoom, and refuel. Since the temporal problem is inevitable, all five actions have execution durations, and refueling can be carried out simultaneously with boarding or debarking. One key issue in the extended ZenoTravel domain is the numeric cost. The domain requires obtaining the plan with the minimum fuel consumption. Furthermore, the airplane needs to refuel when it lands at an airport, while the refueling situation is uncertain. Specifically, when the airplane lands at the airport but the oil supplier is occupied by the other planes, the airplane cannot be refueled. The occupation, however, cannot be informed in advance. Tables 1 and 2 show the different plans under the different deadlines. In Plan 1, the deadline for arriving in city C is 21:30. In order to cut the cost, the airplane uses fly mode. However, in Plan 2, the deadline for arriving in city C is 21:00. The airplane opens fly and zoom modes. The plans observe whether the oil supplier is usable when the airplane lands at an airport. As a result of assistance from the heuristic, the two plans are both the plans with the minimum costs under the temporal requirements. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Plan 1** & \\ \hline
**Actions** & **Start-Time** & **End-Time** \\ \hline (IObserve usable A) & & \\ (Iboard-passenger 20) & 16:35 & 16:55 \\ (!fly A B) & 16:55 & 19:10 \\ (!debark-passenger 10) & 19:10 & 19:25 \\ (!board-passenger 30) & 19:10 & 19:25 \\ (!fly B C) & 19:25 & 21:20 \\ (!debark-passenger 40) & 21:20 & 21:35 \\ (!Observe unusable A) & & \\ (!board-passenger 20) & 16:35 & 16:55 \\ (!fly A B) & 16:55 & 19:10 \\ (!debark-passenger 10) & 19:10 & 19:25 \\ (!board-passenger 30) & 19:10 & 19:25 \\ (!fly B C) & 19:25 & 21:20 \\ (!debark-passenger 40) & 21:20 & 21:35 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Plan 1 for the extended ZenoTravel problems. This approach significantly enhances the ability to generate high-quality plans in scenarios where environments are partially observable, a common challenge in real-world applications. By extending HTN formalisms to accommodate partial observability and incorporating quality evaluations, planners can make more informed decisions under uncertainty. The planner's demonstrated efficiency in handling partial observability and its capability for high-quality planning in such environments suggest potential applications across various industries, such as emergency decision-making, supply chain management, intelligent robots, among others. The approach generates robust plans tailored for partially observable environments, making it more practical to real-world problems.