## 4 MODRL-SIA Algorithm
### Deep Reinforcement Learning  
Deep reinforcement learning is more akin to a human's mode of learning new things. Targeting the task and environment, it ultimately accomplishes the specified task by continuously learning from mistakes and refining strategies. Classic deep reinforcement learning comprises two crucial components, namely, the environment and the agent. The agent serves as the decision-maker, taking the environmental state as input and predicting the best action to modify the environment and obtain environmental rewards. The multi-objective location-routing problem is an NP-hard challenge. Additionally, the locations, quantities, and delivery times of receiving points are subject to constant change, rendering the solution more intricate [26]. Deep learning is currently a prominent field of artificial intelligence research. It operates as a data-driven machine learning technique, predicting the likelihood of future events based on existing historical data. While relatively mechanistic and static, it proves unsuitable for dynamic vehicle route scheduling in agricultural supply distribution. Reinforcement learning involves inferring the probability of an action occurring at the next moment based on the current and previous states and actions. It represents a continuously changing process enabling vehicle routing decisions. However, due to the complexity of vehicle paths and the continuous state changes, the discretized state space becomes extensive. Traditional reinforcement learning methods, such as Q-Learning, struggle to maintain a vast Q table in memory [27]. Figure 2: MODRL-SIA framework model. Deep reinforcement learning uses neural networks instead of Q tables and experience replay mechanisms to address training sample issues. Combining the decision-making ability of reinforcement learning with the perception ability of deep learning, it provides an effective approach to resolving complex perception decision-making problems. Optimizing discrete combinations using the randomness of swarm intelligence algorithms combined with deep reinforcement learning's perceptual capabilities yields enhanced solution accuracy, faster convergence speeds, and greater resilience to local optimality. DQN (Deep Q Network) [28] is the most commonly used deep reinforcement learning algorithm. We will employ the MODRL-SIA framework to tackle this issue. The MODRL-SIA algorithm integrates the trained agent with swarm intelligence algorithms, utilizing them to replace the original decision-making algorithm and enhance its optimization speed. The following section outlines the representation method of the DQNAgent's state space, action space, and reward and punishment function in the MODRL-SIA framework. **State Space:** The goal of this problem is to minimize cold chain distribution costs, minimize carbon emission indicators, and minimize product losses. Simultaneously, it is considered that dividing the receiving point into different vehicles will cause changes in the vehicle path, thus affecting the objective. Therefore, the state of the vehicle path is formally represented as the state of the environment. It mainly consists of three parts: distribution center information, receiving point information, and vehicle information. **Action space:** The task of the path planning allocator is to assign each order to the appropriate path. Assuming that the number of receiving points is \(m\), its action space is expressed as \(A=\{P_{1},\ P_{2},P_{3},\...,P_{i},\...,\ P_{m}\}\). Indicates the sequence code of all receiving points. Then, the sequence code is cut according to the constraints. For example, the first complete vehicle planning path after cutting is \([d_{1},28,15,21,14,8,d_{1}]\). The meaning is: Distribution center \(d_{1}\)>>Receipt point 28>>Receipt point 15>>Receipt point 14>>Receipt point 8>>Distribution center \(d_{1}\). In the same way, other routes will allocate vehicles for delivery in the order of sequence codes.