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Collaboration in Multi-Agent Systems (MASs) is crucial but challenging in robotics, especially in heterogeneous MASs where robots have different capabilities. Nowadays, the key issue in research on collaboration in MASs is to fully utilize the capabilities of heterogeneous agents. To address this issue, we propose Auction-Based Behavior Tree Evolution (ABTE), a novel two-layer framework designed to learn BTs for heterogeneous MASs. In the first layer, we call it the command layer, and robots receive their tasks through the auction algorithm, enhanced by our innovative three-way handshaking communication protocol embedded in BT implementation, ensuring more efficient task allocation. The second layer of ABTE defines the specific execution behaviors of agents and is, therefore, named the execution layer. The behaviors in this layer are automatically generated by Grammatical Evolution (GE), which has been proven to be a general and effective method for generating swarm BTs. Our experiments are conducted within a Disaster Rescue Scenario, which requires intricate collaboration among multiple robots with diverse capabilities. The results indicate that ABTE outperforms the baseline algorithm, GEESE, in terms of resource utilization. Moreover, it demonstrates robust effectiveness in covering high-priority tasks, thereby validating the efficacy of employing an auction algorithm for generating BTs tailored for heterogeneous MAS.