# Efficient Task Allocation in Multi-Agent Systems Using Reinforcement Learning and Genetic Algorithm
## 4 A Learning Algorithm
### Genetic Algorithm-Enhanced Proximal Policy Optimization  
This algorithm leverages the efficiency of PPO for learning optimal policies while utilizing the evolutionary principles of the GA to select the best-performing agents, thereby enhancing decision-making in dynamic environments. The algorithm begins by initializing a population \(P\) of Actor-Critic networks, with each individual representing a distinct policy tailored for agent operations. Several key hyperparameters guide the learning process, including the learning rate lr, discount factor \(\gamma\), clip ratio \(\epsilon\), and KL divergence target KLtarget. Those values are selected based on theoretical foundations and established practices in reinforcement learning and evolutionary algorithms, ensuring a stable and efficient learning process. The specific values for these hyperparameters are chosen to align with common standards in the literature, which have been shown to perform well in similar multi-agent systems tasks. A replay buffer with a capacity of \(C\) = 10,000 is created to store observed state-action-reward sequences. This buffer facilitates experience sampling during training. Additionally, the genetic algorithm component employs a set of parameters, including mutation rates and fitness weights (\(\alpha\), \(\beta\), and \(\gamma\)), which govern the selection process and population evolution. The learning rate lr determines the step size during policy updates, with a typical value in PPO implementations chosen to ensure stable convergence. The discount factor \(\gamma\) reflects the importance of future rewards, and it is set to a commonly used value for long-term decision-making tasks. The clip ratio \(\epsilon\) is used to prevent excessive updates during the training process, ensuring stability while maintaining exploration. The KL divergence target KLtarget helps control the divergence between old and new policies, promoting gradual updates to the policy. The fitness score of each individual is computed based on cumulative reward, policy entropy, and computational resource cost, with appropriate weights (\(\alpha\), \(\beta\), and \(\gamma\)) to guide the optimization process. The selection of hyperparameters follows established guidelines in reinforcement learning and evolutionary algorithms. However, the exact values used may not be optimal across all scenarios. Specifically, the performance of the algorithm could benefit from fine-tuning the parameters to better adapt to varying environments and tasks. While the current work does not include a comprehensive optimization of these hyperparameters,future research could involve systematically varying them to assess their influence on the performance of GAPPO. During each iteration, the algorithm collects trajectories for each individual \(P_{i}\) with the population. Each agent observes the current state \(s_{t}\) and selects an action \(a_{t}\) based on its policy \(P_{i}\). The selected action is executed, resulting in a reward \(r_{t}\) and a subsequent state \(s_{t+1}\). The transition \((s_{t},a_{t},r_{t},s_{t+1})\) is appended to the trajectory \(T\), and this process continues until a terminal state is reached. The accumulated trajectories are stored in the replay buffer, allowing the PPO component to sample batches for optimization. Once the replay buffer contains a sufficient number of samples, the strategy update phase commences. A batch of transitions is sampled, and for each transition, the algorithm computes the returns \(R_{t}\) using the discount factor \(\gamma\). The advantages \(\hat{A}_{t}\) are calculated utilizing generalized advantage estimation (GAE). The action probabilities \(\pi(a_{t}|s_{t})\) and state values \(V(s_{t})\) are obtained to compute the surrogate loss \(L(\theta)\), as previously defined. This surrogate loss plays a crucial role in the GAPPO algorithm by ensuring that policy updates remain stable while allowing for effective exploration.