# Auction-Based Behavior Tree Evolution for Heterogeneous Multi-Agent Systems
## 4 Results
### Simulation Studies
#### 4.2.2 Ability to Cover High-Priory Tasks  
In the second set of experiments, the initial energy of MASs may be insufficient for all tasks. Robots start at (50, 50), with stopping conditions the same as those of the first set. The aim is to compare the high-priority task coverage ratio between methods when energy is limited. Excavation, Communication, and Transportation tasks have time constraints, making them high-priority compared to Search tasks. If tasks are performed outside the time limit, they are counted as unfinished tasks. The high-priority task coverage ratio is calculated by dividing the number of high-priority tasks completed by the total number of high-priority tasks.  
Figure 8 presents the results of experiment 1 from the second set. The x-axis indicates total tasks, while the y-axis shows the coverage ratio of high-priority tasks. The MAS comprises three groups of R1, R2, R3, and R4, with tasks increasing from 12 to 120 in increments of 4. ABTE fully covers high-priority tasks up to 60, whereas GEESE cannot complete all high-priority tasks beyond 28, reaching only 50% of ABTE's coverage at 60 tasks. With 120 tasks, ABTE maintains a 50% coverage ratio and GEESE drops to 24.4%. After 60 tasks, the coverage ratio of ABTE declines sharply due to the saturation of MASs at 45 high-priority tasks; beyond this, the system can complete only 45 within the time limit. At 72 tasks, GEESE peaks at 26 high-priority tasks, marking a significant gap from the saturation point of ABTE.  
Figure 8: A comparison of the coverage ratio with an increasing number of tasks.  
In experiment 2 of the second set of experiments, the number of tasks is constant at 120. We start with the MAS consisting of three groups of R1, R2, R3, and R4 and add one group of robots to the cluster at a time until both GEESE and ABTE can cover all the high-priority tasks. The result is shown in Figure 9. Overall, ABTE already has a 100% coverage ratio when seven groups of robots are included in the cluster, while GEESE will not be able to fully cover high-priority tasks until twelve groups are included.  
The outcomes of ABTE are influenced by execution time and remaining energy, favoring robots with matching capabilities or idle tasks. This enables heterogeneous MASs (robots with diverse task-specific traits) to rapidly complete high-priority tasks, a benefit particularly evident in systems with limited initial energy. Since the total energy of MASs is insufficient for all tasks, the collaboration mechanism provided by ABTE tends to guide the cluster to maximize high-priority task completion before reaching the energy threshold. Consequently, ABTE outperforms GEESE in terms of high-priority task coverage ratio.  
The above two sets of results show that ABTE allows robots to process a relatively large number of tasks with less energy consumption, and to complete more high-priority tasks. In addition, ABTE tries not only to allocate as many tasks as possible to robots that are good at executing them but also to evolve more efficient and customized BTs to control robots based on the task allocation. This makes the BTs of MASs not need to be hand-coded by experts in advance so that the MAS has stronger adaptability and flexibility to face the changes and challenges in the environment.