## 2 Materials and Methods
### Proposed Method
#### 2.3.4 Implementations
The baseline models included COMA, QMIX, and QTRAN. The specific information for the four scenarios used in the experiments is shown in Table 3: \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Version** \\ \hline CPU & Intel(R) Xeon(R) Gold 6330 CPU @ 2.00 GHz \\ GPU & Nvidia GeForce RTX 3090 \\ OS & Ubuntu 18.04.5 LTS \\ Language & Python 3.8.10 \\ DL Framework & PyTorch 1.7.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The hardware and software used in our experiments. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scenario** & **Alliance** & **Enemy** & **Type** & **Difficulty** \\ \hline
3m & Marine \(\times\) 3 & Marine \(\times\) 3 & Homogeneous & Easy \\
2s3z & Stalker \(\times\) 2 & Stalker \(\times\) 2 & Heterogeneous & Easy \\  & Zealot \(\times\) 3 & Zealot \(\times\) 3 & Heterogeneous & Easy \\  & Colossus \(\times\) 1 & Colossus \(\times\) 1 & & \\
1c3s5z & Stalker \(\times\) 3 & Stalker \(\times\) 3 & Heterogeneous & Medium \\  & Zealot \(\times\) 5 & Zealot \(\times\) 5 & & \\
10m\_vs\_11m & Marine \(\times\) 10 & Marine \(\times\) 11 & Homogeneous & Medium \\  & Medivac \(\times\) 1 & Medivac \(\times\) 1 & & \\ mmm & Marauder \(\times\) 2 & Marauder \(\times\) 2 & Heterogeneous & Hard \\  & Marine \(\times\) 7 & Marine \(\times\) 7 & & \\  & Medivac \(\times\) 1 & Medivac \(\times\) 1 & & \\ mmm2 & Marauder \(\times\) 2 & Marauder \(\times\) 3 & Heterogeneous & Hard \\  & Marine \(\times\) 7 & Marine \(\times\) 8 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Specific information for the SMAC scenarios. The experimental scenario settings were as follows: the SMAC game difficulty was set to 7, with an action taken every eight steps, for a total of one million training steps. The discount factor was set to \(\gamma=0.99\) and the RMS optimizer is used. Exploration was carried out using the \(\epsilon\)-greedy algorithm, where the exploration rate decay was from 1.0 to 0.05 over the first 50,000 steps and remained at 0.05 thereafter. The number of attention heads was set to 6, and the experience replay buffer size was set to 3000. The number of nearest neighbors was set to 5. The parameters of the evaluation network (evaluate net) were assigned to the target network (target net) at every 200 training steps. The reward mechanism used the default shaped reward provided by SMAC. The experimental parameters are shown in Table 4.

In terms of hyperparameter selection, while a comprehensive grid search would theoretically be ideal to determine the best settings, its computational cost was prohibitive given the scale of the experiments. Instead, we adopted a sequential tuning approach in which each hyperparameter was tuned individually while keeping the others fixed. This strategy allowed us to identify effective settings that balanced performance with computational efficiency. ### Experimental Results

Table 5 illustrates the average winning rate during the last final 100k training steps for all models across the four scenarios:

* In the 3m scenario, QTRAN performs the best, followed by QMIX-GNN and QMIX, which show similar results. COMA performs slightly worse, with a winning rate of only around 76%, indicating relatively poor performance. * In the 2s3z scenario, our QMIX-GNN has a slight decrease in winning rate compared to QMIX (a 2.6% drop). The reason for this could be that the 2s3z scenario is relatively simple, allowing agents to make good decisions based on their own observations. The introduction of information fusion increases the complexity of learning, which slows down the agent's learning process. In this scenario, QTRAN converges slowly but eventually reaches a winning rate of about 71%, while COMA struggles to converge, with a winning rate of only around 20%. * In the 1c3s5z and mmm scenarios, QTRAN performs poorly, with a winning rate of around 30%, while COMA fails to converge.