# Auction-Based Behavior Tree Evolution for Heterogeneous Multi-Agent Systems
## 4 Results
### Simulation Studies  
#### 4.2.1 Execute Tasks with Sufficient Energy  
In the first set of experiments, the MAS has enough energy for all tasks. Experiments end when robots mimic real-world energy conservation, meeting one of two conditions: (1) all tasks are completed or (2) the remaining energy is 5-10%. In experiment 1, there are 60 tasks randomly distributed in the environment. After a random robot receives the task information, it acts as both an auctioneer and a bidder (R1 in the experiment). According to the auction method mentioned in Section 2.2, the robots begin to individually evolve BTs after all tasks have been allocated. The design of the fitness function used in the GE process is expounded upon in Section 3.2, and the parameters involved in GE are shown in Table 1.  
Figure 5 displays the execution BTs evolved by ABTE, with nodes in dashed boxes subject to replacement. Fitness functions promote compact BTs, resulting in diverse, task-specific BTs for heterogeneous robots. R1 executes Excavation and Search without obstacle avoidance, while R2's BT includes obstacle avoidance for Communication tasks. Other robots can also evolve instinct BTs by permuting and combining these nodes. It is evident that the BTs generated by ABTE endow heterogeneous robots with diverse execution behaviors, significantly enhancing the adaptability of MASs. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Individuals in population & 100 \\ Max tree depth & 7 \\ Generations & 100 \\ Crossover & Variable\_onepoint \\ Crossover probability & 0.75 \\ Mutation probability & 0.01 \\ Selection & Tournament \\ \hline \hline \end{tabular}
\end{table} 
Table 1: GE parameters used for experiments. Figure 5: Execution BTs for all robots by ABTE. The sections outlined with dotted lines represent components that can be replaced during the evolutionary process, depending on the varying tasks that the robots are required to execute. Taking the evolutionary process of R1's BT as an example, the initial population is composed of 50 BTs, which are randomly generated based on derivation tree method [20]. Subsequent iterations involve crossover and mutation to produce succeeding generations, with a cap of 100 individuals per generation--a measure designed to curtail excessive expansion of the search space. The fitness function is tailored to foster the development of compact BTs capable of fulfilling all tasks. Following approximately 60 evolutionary rounds, the BT most suited for R1's tasks is derived. Within the ABTE framework, the most substantial computational overhead stems from the GE used to generate BTs, with the longest evolutionary duration in our experimental context being around 12 s. Notably, this overhead only exists in the stage before executing tasks and does not affect the task execution process. Furthermore, given that robots evolve their BTs in a distributed parallel mode, the cumulative computational overhead on the system is only affected by the robot with the longest evolution time. In experiment 2, the MAS consists of three groups of R1, R2, R3, and R4, which are set to complete different numbers of tasks (12-1  
The BTs evolved by GEESE operate globally, leading robots to favor closer tasks. However, in many cases, the energy consumption of executing tasks is greater than that of traveling [21]. In contrast, ABTE yields task-specific, heterogeneous BTs. Considering robotic capabilities and task priorities, each robot prioritizes high-priority tasks matching its abilities, reducing the overall energy use of the system. Figure 6 shows that the MAS controlled by ABTE outperforms GEESE in average energy consumption, with an increasing advantage as tasks rise. The standard deviation of energy consumption is also lower with the ABTE approach, ensuring more uniform resource use within the MAS. Additionally, as shown in Figure 7, we introduce resource dissipation as an evaluation metric, which elaborates on the average energy consumed by MASs to complete each task.