# Efficient Task Allocation in Multi-Agent Systems Using Reinforcement Learning and Genetic Algorithm
## 4 A Learning Algorithm
### Genetic Algorithm-Enhanced Proximal Policy Optimization
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1:Initialize: Population of Actor-Critic networks \(P=\{P_{1},P_{2},\ldots,P_{N}\}\)
2:Set hyperparameters: learning rate \(lr\), discount factor \(\gamma\), clip ratio \(\epsilon\), and KL divergence target \(KL_{target}\)
3:Initialize replay buffer with capacity \(C=10,000\)
4:Set generation counter \(g=0\)
5:while training do
6:for each individual \(P_{i}\in P\)do
7: Initialize trajectory \(T\) and observe initial state \(s_{0}\)
8:for each time step \(t=0\) to \(T_{max}\)do
9: Select action \(a_{t}\) using policy \(P_{i}\) based on \(s_{t}\)
10: Execute \(a_{t}\), observe reward \(r_{t}\) and next state \(s_{t+1}\)
11: Append transition \((s_{t},a_{t},r_{t},s_{t+1})\) to trajectory \(T\)
12:if terminal state reached then
13: Break
14:endif
15:endfor
16: Store trajectory \(T\) in replay buffer
17:endfor
18:if len(replay buffer) \(\geq\) BATCH_SIZE then
19: Sample a batch of transitions from replay buffer
20:for each transition in the batch do
21: Compute returns \(R_{t}\) using \(\gamma\)
22: Compute advantages \(\hat{A}_{t}\) using Generalized Advantage Estimation (GAE)
23: Get action probabilities \(\pi(a_{t}|s_{t})\) and state values \(V(s_{t})\)
24: Calculate surrogate loss \(L(\theta)\) from (13)
25: Calculate value loss from (15)
26: Compute total loss \(L=L(\theta)+L_{V}\)
27: Update network parameters \(\theta\) using gradient descent
28:endfor
29:endif
30:endwhile
31:while\(g<\) max_generations do
32:for each individual \(P_{i}\in P\)do
33: Evaluate \(P_{i}\) in the environment to obtain fitness score \(F_{i}\)
34:endfor
35: Select individuals based on fitness using a selection strategy (e.g., tournament selection)
36: Generate new population \(P^{\prime}=\{P^{\prime}_{1},P^{\prime}_{2},\ldots,P^{\prime}_{N}\}\) via crossover and mutation
37: Update population \(P\gets P^{\prime}\) and increment generation counter \(g\)
38:endwhile
39:Periodically: Update target networks to stabilize training This optimization framework leverages genetic operations--selection, mutation, and recombination--enabling agents to evolve strategies that better adapt to dynamic task environments. By integrating the genetic algorithm with the Actor-Critic network, agents are equipped to refine their strategies through both gradient-based and evolutionary search, enhancing adaptability and ensuring efficient coverage and resource allocation in complex and variable environments. This section provides a comprehensive overview of the enhanced PPO agent with the genetic algorithm, detailing its initialization, iterative interactions between agents and the environment, and the strategy update phase. The distinctive features of this algorithm in the context of multi-agent task allocation are emphasized, highlighting its potential for improving operational efficiency. ### Robustness Under Failure Conditions

GAPPO is designed to operate reliably in dynamic environments and addresses potential failure conditions inherent in multi-agent systems. In the event of communication breakdowns, GAPPO's decentralized architecture enables each agent to rely on local observations and previously learned policies. This design ensures that task execution can continue even when global communication is unavailable. These design choices are based on well-established principles of decentralized control, which support system resilience under adverse conditions. Although our current experimental evaluation focuses on standard operating scenarios, the theoretical foundation of GAPPO provides a promising basis for robustness in real-world applications. ## 5 Experimental Results

In this section, we evaluate the established model alongside the proposed GAPPO algorithm through numerical simulations under varying experimental configurations. Specifically, four experiments were conducted to assess the performance of GAPPO in task allocation, considering scenarios with different numbers of agents and tasks.