Multi-target vehicle path optimization method based on enhanced self-attention mechanism

Abstract

The invention relates to the technical field of intelligent logistics and path optimization, and particularly discloses a multi-target vehicle path optimization method based on an enhanced self-attention mechanism. The method comprises the following steps: S1, constructing an enhanced self-attention encoder, and carrying out deep fusion encoding on input node features and preference vectors through a self-attention module integrating channel attention, SwiGLU activation and adaptive scaling; s2, constructing a path generation network based on a problem scale perception decoder, embedding problem scale information injection nodes, and generating a path sequence in an autoregression mode; and S3, based on a reinforcement learning framework, carrying out model training in combination with a random preference strategy, and generating a Pareto frontier approximate solution of a multi-target vehicle path problem. Through the collaborative design, the model expression ability, the generalization ability and the solving precision are improved, and an efficient and reliable solution is provided for the multi-target vehicle path problem.

Description

Technical Field

[0001] This invention belongs to the field of neural combinatorial optimization and intelligent logistics path planning technology, specifically relating to a multi-objective vehicle path optimization method based on an enhanced self-attention mechanism. In particular, this invention provides a model that integrates an enhanced self-attention encoder and a problem-scale-aware decoder for efficient solving of Pareto fronts. Background Technology

[0002] The Vehicle Routing Problem (VRP) is a core optimization problem in logistics and distribution. In practical applications, decision-makers often need to consider multiple conflicting objectives simultaneously, such as minimizing total transportation costs, minimizing the longest single route length, and maximizing customer satisfaction, thus forming the Multi-Objective Vehicle Routing Problem (MOVRP). The goal of MOVRP is no longer to find a single optimal solution, but rather to find a set of Pareto optimal solutions that reflect the trade-offs between different objectives.

[0003] Traditional methods for solving MOVRP problems are mainly divided into exact algorithms and metaheuristic algorithms. Exact algorithms (such as branch and bound) can guarantee finding all Pareto optimal solutions, but their computational complexity increases exponentially with the problem size, making them difficult to apply in real-world scenarios. Metaheuristic algorithms (such as multi-objective evolutionary algorithms MOEA / D and NSGA-II) can find approximate Pareto fronts within an acceptable timeframe through population evolution, but they typically require a large number of function evaluations, resulting in low computational efficiency, and their performance is heavily dependent on parameter tuning.

[0004] In recent years, neuroheuristic methods based on Deep Reinforcement Learning (DRL) have provided a new paradigm for solving Virtual Reality Problems (VRPs). These methods can quickly generate high-quality solutions for new problem instances by training a neural network policy. However, existing neuroheuristic methods have significant shortcomings when dealing with MOVRPs: First, they typically treat preferences (weight vectors) and instance context (node ​​coordinates, requirements, etc.) independently, failing to fully exploit the complex joint effects between preferences and instances, resulting in insufficient accuracy of the generated Pareto front approximation; second, existing models are usually trained for specific problem scales, and their performance degrades significantly when generalizing to instances of unknown scale; finally, there is still room for improvement in the model's feature interaction capabilities and nonlinear representation capabilities.

[0005] Therefore, there is an urgent need for a neuro-heuristic method that can deeply integrate heterogeneous information, has strong generalization ability and powerful expressive ability, in order to meet the complex and ever-changing multi-objective path planning needs in modern logistics. Summary of the Invention

[0006] The purpose of this invention is to overcome the three major bottlenecks of existing neuroheuristic methods in solving the Multi-Objective Capacitated Vehicle Routing Problem (MOCVRP):

[0007] Insufficient feature interaction: Traditional attention mechanisms provide a shallow model of the interaction between node features, location features, and user preferences, failing to fully capture the complex impact of their combined effect on path planning.

[0008] Limited model expressive power: Standard feedforward networks and activation functions struggle to fit the complex nonlinear relationships in combinatorial optimization, limiting the model's ability to find high-quality solutions.

[0009] Weak dynamic adaptability: The model is not sensitive to dynamic context information such as problem size and remaining capacity, which leads to a decrease in its decision-making accuracy when dealing with instances of different sizes and in the process of path construction.

[0010] To achieve the above objectives, the technical solution adopted in this invention is executed in sequence according to the following three core steps:

[0011] S1. Construct an enhanced self-attention encoder by integrating channel attention, SwiGLU activation, and adaptive scaling self-attention modules to perform deep fusion encoding of the input node features and preference vectors:

[0012] In this step, an innovative encoder is constructed, the core of which is an enhanced self-attention module integrating three advanced mechanisms. This module encodes the input node features (coordinates, requirements) and user preference vectors, and sequentially performs the following operations to generate deeply fused high-dimensional node embeddings: first, query, key, and value projections are performed, and an initial attention score is calculated; then, the input node and preference embedding sequence is linearly transformed to generate a query matrix, key matrix, and value matrix, and an initial attention score is calculated.

[0013]

[0014] Then perform adaptive scaling: multiply the initial attention score by a dynamic scaling factor. Where n is the number of nodes in the current problem instance, and B is a learnable baseline size parameter. The operation aims to dynamically adjust the sharpness of the Softmax function input distribution according to the problem size, enhancing the model's adaptability to problems of different sizes.

[0015] The scaled scores are masked and normalized using Softmax. Then, a mask is applied to the scaled scores (such as masking invalid nodes), and the scores are normalized using the Softmax function to obtain the final attention weights.

[0016] Next, channel attention recalibration is performed: the output after multiplying the attention weights with the value matrix is ​​reweighted at the channel level using a squeeze-excitation network (SENet). Specifically, this includes:

[0017] Compression: Channel descriptors are generated through global average pooling;

[0018] Activation: The activation weights for each channel are generated through a two-layer neural network (the first layer reduces dimensionality and uses ReLU activation, and the second layer restores dimensionality and uses the Sigmoid function).

[0019] Reweighting: Multiply the incentive weights by the original features channel by channel to enhance important feature channels and suppress minor channels.

[0020] Perform a SwiGLU nonlinear transformation: Input the reweighted result into a feedforward sub-layer using the SwiGLU activation function. The transformation formula for this sub-layer is: FFN SwiGLU (X) = (XW1⊙Swish(XW2))W3, where W1, W2, and W3 are trainable parameters, and ⊙ represents element-wise multiplication. This significantly improves the model's nonlinear fitting capability.

[0021] S2. Construct a path generation network based on a problem-scale-aware decoder, inject problem-scale information into node embeddings, and generate path sequences in an autoregressive manner:

[0022] This step constructs a decoder responsible for converting the embeddings output by the encoder into specific path sequences. Its core lies in explicitly introducing problem-scale information and dynamically sensing the path construction status.

[0023] First, scalable problem-size embeddings are generated: a scalable encoder maps the problem size k (number of nodes) to a fixed-dimensional embedding vector. This encoder is based on a sinusoidal coding function and introduces a learnable scaling factor, scale, calculated as follows:

[0024]

[0025] The problem size information is then injected into the node embedding. Specifically, the generated problem size embedding is added to the node embedding output by the encoder to form a size-aware node embedding, which serves as the key and value of the decoder's attention mechanism.

[0026] Finally, the decoder operates in an autoregressive manner: at each step *t* of path generation, a query vector is dynamically constructed, which is obtained by projecting the encoding of the previous node and the remaining capacity information of the current vehicle. Based on this query vector and scale-aware node embeddings (key, value), the probability distribution of all unvisited nodes is calculated through an attention mechanism. The next node to be visited is selected based on this probability distribution (sampled during training, greedily selected during inference), and the path state and remaining capacity are updated. This process is repeated until a complete path sequence is generated.

[0027] S3. Based on a reinforcement learning framework and combined with a stochastic preference strategy, the model is trained to generate a Pareto front approximate solution to the multi-objective vehicle routing problem:

[0028] This step defines the training paradigm for the entire model, aiming to optimize model parameters to approximate the Pareto front of the multi-objective problem: Defining the reward function: A reward function based on the Tchebycheff scalarization method is adopted, defined as follows:

[0029]

[0030] This function provides optimization signals for each subproblem defined by preference λ, guiding the model to generate high-quality solutions. Then, a stochastic preference strategy is implemented: specifically, during model training, a preference vector λ is randomly generated for each training instance or training batch. Each component of λ is independently and uniformly sampled from the interval [0,1] and normalized. This strategy forces the model to learn to generalize over a continuous preference space. Next, reinforcement learning training is performed: the REINFORCE algorithm is used to optimize the parameters of the encoder-decoder network constructed in steps S1 and S2, aiming to maximize the expected cumulative reward. During training, the size of each batch of problem instances is randomly sampled from a predefined set to further improve the model's generalization ability. After training, for a new problem instance, given a set of user-interested preference vectors, the model can generate a path for each preference in parallel. The set of all these paths constitutes the Pareto front approximate solution for the multi-objective vehicle pathing problem. Attached Figure Description

[0031] Figure 1 This is a flowchart of a multi-objective vehicle path optimization method based on an enhanced self-attention mechanism;

[0032] Figure 2 This is an architecture diagram of a multi-objective vehicle path optimization method based on an enhanced self-attention mechanism;

[0033] Figure 3 This is an encoder architecture diagram for a multi-objective vehicle path optimization method based on an enhanced self-attention mechanism. Detailed Implementation

[0034] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments:

[0035] The specific implementation process is as follows:

[0036] like Figure 1 As shown, a multi-objective vehicle path optimization method based on an enhanced self-attention mechanism includes the following steps:

[0037] S1. Construct an enhanced self-attention encoder, which performs deep fusion encoding on the input node features and preference vector by integrating channel attention, SwiGLU activation and adaptive scaling self-attention modules;

[0038] First, an enhanced self-attention encoder is constructed to deeply fuse and encode the input node features and preference vectors. In this step, node attribute features (including coordinates, requirements, etc.) are linearly projected through a trainable matrix to generate high-dimensional node feature embeddings. Specifically, for node i, its node features... pass Projection yields h i =x i W node , where the embedding dimension d h =128. Meanwhile, the user preference vector λ∈R m (m is the target quantity) passed Mapping to preference embedding h λ =λW pref These embeddings are combined into an input sequence. Then, it is input into the enhanced self-attention encoder for processing.

[0039] The enhanced self-attention module executes a series of sophisticated computational processes in a strict sequence. First, it performs query, key-value projection, and initial attention calculations, using a trainable matrix. Project the input sequence into a query, key, and value matrix, i.e., Q = HW. Q K = HW K V = HW V And calculate the initial attention score. Next, adaptive scaling is performed, multiplying the initial attention score by a dynamic scaling factor. Where n is the number of nodes and B is the learnable baseline scale parameter. This design allows the model to adaptively adjust the sharpness of the attention distribution according to the problem size, maintaining stable performance when handling problems of different sizes. Subsequently, masking and Softmax normalization operations are performed, and a mask matrix M is applied to the scaled score to mask invalid attention connections, yielding the final score. masked =scorescaled +M, then normalize using the Softmax function to obtain the attention weights A = Softmax(score). masked ).

[0040] Next, channel attention recalibration is performed. First, the initial attention output V is calculated. attn =AV, and then apply a compression-excitation network for fine-grained channel-level reweighting. This process includes three sub-steps: compression to obtain z through global average pooling. c =GAP(V attn ); Excitation calculation s = σ(W2δ(W1z) is performed using a two-layer neural network. c ), where δ is the ReLU activation function and σ is the Sigmoid function; finally, a reweighting operation is performed. This enables the enhancement of important feature channels and the suppression of secondary channels.

[0041] After channel attention recalibration is completed, the process proceeds to the SwiGLU nonlinear transformation stage. The reweighted features are input into the SwiGLU feedforward sublayer for nonlinear transformation, specifically calculated as follows:

[0042]

[0043] Where Swish(x) = x·sigmoid(x), and W1, W2, W3 are trainable parameters. This gating mechanism significantly enhances the model's nonlinear expressive power, enabling it to better learn complex patterns in combinatorial optimization problems. The entire enhanced self-attention module is stacked with L=6 layers, and residual connections and instance normalization are used after each layer to stabilize the training process, ultimately outputting a deeply fused node embedding.

[0044] After the encoder is built, proceed to S2. Build a path generation network based on the problem size-aware decoder, inject problem size information into the node embedding, and generate path sequences in an autoregressive manner.

[0045] This decoder is responsible for converting the high-dimensional embeddings output by the encoder into specific path sequences. Its core innovation lies in explicitly introducing problem-scale information and closely combining it with the dynamic state of path construction.

[0046] First, the problem size κ is mapped to a size embedding with rich semantic information using a scalable size encoder. The specific calculation formula is as follows:

[0047]

[0048] Here, `scale` is a learnable scaling factor, and `base = 100` is the frequency base. This design allows the model to dynamically adjust the frequency response of the scale encoding, thus better adapting to larger or smaller problem sizes not seen in the training data. After obtaining the scale embedding, it is combined with the node embedding output by the encoder through a simple addition operation to obtain the scale-aware node embedding. These scale-aware node embeddings serve as keys and values ​​in the decoder's attention mechanism, providing rich contextual information for subsequent path generation. The decoder employs an autoregressive approach, performing sophisticated computations at each step t of path generation. First, the query vector is dynamically constructed. in It is the encoding of the previously visited node, l t This refers to the remaining capacity of the current vehicle. This design allows the decoder to consider both path history information and real-time resource constraints in each decision step. Then, based on this query vector and scale-aware node embeddings, an attention mechanism is used to calculate the probability distribution of all unvisited nodes. The next node to be visited is selected based on this distribution (a sampling strategy is used during training to enhance exploration, and a greedy selection strategy is used during inference to improve efficiency), and the path state and remaining capacity are updated. This process is repeated until a complete path sequence is generated.

[0049] S3. Based on the reinforcement learning framework, the model is trained by combining a stochastic preference strategy to generate a Pareto front approximate solution for the multi-objective vehicle path problem.

[0050] In this step, the reward function based on Tchebycheff decomposition is first designed. in For the ideal value estimation of each objective, dynamic estimation is performed through a small batch rollout, ∈=10 -6 A small constant is used to prevent numerical instability. This reward function provides an accurate optimization signal for each subproblem defined by the preference λ, effectively guiding the model to generate high-quality solutions in the Tchebycheff sense.

[0051] To enhance the model's generalization ability and facilitate learning in a continuous preference space, a random preference strategy is employed during training, randomly generating a preference vector λ ~ Uniform[0,1] for each training batch. m And perform normalization processing to ensure This strategy is equivalent to densely sampling a continuous preference space, forcing the model to learn to generalize across the entire preference space, rather than overfitting to just a set of discrete preference points. Furthermore, to further enhance the model's cross-scale generalization ability, problem instances in each training batch are randomly sampled from their size set. This works in conjunction with a scalable-scale encoder, forcing a single model to learn to solve problems of multiple different sizes simultaneously.

[0052] Regarding the optimization algorithm, the REINFORCE algorithm is used to optimize the policy network parameters, and the gradient calculation formula is as follows: The baseline value b is estimated using a separate Critic network, which employs a structure similar to the encoder to accurately evaluate state values, thereby effectively reducing the variance of gradient estimation. The training process uses the Adam optimizer with a learning rate of 1×10⁻⁶. -4 The weight decays to 1×10 -6 A total of 200 training cycles were conducted, with 100,000 dynamically generated instances processed in each cycle.

[0053] To verify the technical effects of this invention, performance evaluation and verification were conducted through the following two types of experiments:

[0054] Experiment 1: Model Performance Verification

[0055] The experiment was conducted on randomly generated instances of the Multi-Objective Vehicle Routing Problem with Capacity Constraints (MO-CVRP), with sizes including 100, 150, 200, 250, and 300 instances. The objective function simultaneously considered minimizing the total path length and the longest single route length to balance logistics operating costs and service efficiency.

[0056] In terms of data generation, following standard protocols, all node coordinates are uniformly and randomly sampled within a unit square [0,1]×[0,1], and customer node requirements are uniformly sampled from the set {1,2,…,9}. During training, the model dynamically generates 100,000 problem instances per epoch to ensure sufficient diversity in the training data. During the testing phase, a fixed random seed is used to generate a test set containing a sufficient number of instances to guarantee the statistical reliability of the evaluation results.

[0057] Experimental hardware environment: A server equipped with an NVIDIA RTX A4000 GPU and an Intel Xeon W-2265 CPU@3.50GHz.

[0058] Model hyperparameter settings: Embedding dimension set to d h =128, encoder layers L=6, attention heads H=8, dimension d of each attention head k =d v=16. The hidden dimension of the feedforward network is set to d. ff =512, the scale encoder uses a sinusoidal coding function, the frequency base is 100, and a learnable scaling factor is introduced to enhance generalization ability.

[0059] In terms of the reinforcement learning framework, the REINFORCE algorithm is used for policy optimization, and the reward function is designed based on the Tchebycheff scalarization method and dynamically calculated through mini-batch rollout, ∈=10. -6 Numerical stability is ensured. Baseline values ​​are estimated using an independent Critic network, effectively reducing gradient variance.

[0060] Performance evaluation uses three core metrics: hypervolume (HV) measures the convergence and diversity of the Pareto front, and the optimality gap (Gap) is calculated as Gap = (HV) / (HV). best -HV method ) / HV best ×100%, of which HV best The optimal supervolume value among all comparison methods is recorded, along with the average time taken for a single inference run.

[0061] Table 1: Comparison of benchmark models on Bi-CVRP

[0062]

[0063] Based on the Bi-CVRP experimental results shown in Table 1, the performance of each benchmark model under different problem scales is systematically analyzed. The experimental results show that the method of this invention exhibits significant advantages in both solution accuracy and technological evolution.

[0064] In terms of solution accuracy, the method of this invention achieves state-of-the-art performance across all three problem scales. Specifically, on the Bi-CVRP100 problem, the enhanced method of this invention (ours-Aug) achieves a hypervolume value of 0.251 with an optimality gap of 0.00%, demonstrating an improvement in accuracy compared to the current state-of-the-art CNH-Aug method (HV = 0.250, Gap = 0.40%). As the problem scale expands to Bi-CVRP150 and Bi-CVRP200, the advantage of the method of this invention further increases, achieving hypervolume values ​​of 0.273 and 0.286 respectively, both maintaining an optimality gap of 0.00%. Particularly noteworthy is that even on the base version (ours) without the enhancement technique, the method outperforms CNH-Aug on Bi-CVRP150 and Bi-CVRP200, fully demonstrating the inherent advantages of the core architecture of this invention. Compared with traditional methods, the method of this invention reduces the gap on Bi-CVRP200 from 16.78% to 0.00% compared with the best-performing traditional algorithm MOGLS, achieving an accuracy improvement of 16.78 percentage points.

[0065] From a technological evolution perspective, the performance comparison of various algorithm types reveals clear patterns. Traditional multi-objective evolutionary algorithms (MOEA / D, NSGA-II, NSGA-III), while robust across different problems, suffer from low computational efficiency and limited solution accuracy. Early neuroheuristic methods (DRL-MOA, ML-DAM) improved efficiency, but their solution quality remained largely unchanged compared to traditional methods. Current advanced neuroheuristic methods (PMOCO, CNH) achieve a good balance between accuracy and efficiency, and the method presented in this invention represents a further breakthrough, particularly with the support of an enhanced version, achieving optimal performance across all metrics.

[0066] Experiment 2: Verification of Generalization Ability

[0067] To evaluate the generalization ability of the proposed method in scenarios outside the training distribution, we conducted zero-shot generalization tests on unseen, larger-scale problems (Bi-CVRP250, Bi-CVRP300). Experimental results show that the proposed method exhibits excellent cross-scale generalization performance and computational efficiency while maintaining high accuracy.

[0068] On the Bi-CVRP250 problem, the enhanced method of this invention (ours-Aug) achieved the best hypervolume value of 0.284, tied with CNH-Aug, with an optimality gap of 0.00%, indicating that both state-of-the-art methods maintain excellent solution accuracy at moderate generalization scales. However, in the comparison with the basic version, the method of this invention (ours) significantly outperforms the basic CNH version (HV = 0.280, Gap = 1.41%) with a hypervolume value of 0.282 and an optimality gap of 0.70%, achieving an accuracy improvement of 0.71 percentage points.

[0069] On the more challenging Bi-CVRP300 problem, the advantages of the method of this invention are even more pronounced. The enhanced method of this invention (ours-Aug) achieved a hypervolume value of 0.284 while maintaining an optimality gap of 0.00%, while the CNH-Aug achieved a hypervolume value of 0.282 and an optimality gap of 0.70%, indicating that the method of this invention has better generalization ability on more difficult problems. Of particular note is that the performance of the CNH base version drops significantly at this scale, with the hypervolume value decreasing to 0.251 and the optimality gap as high as 11.62%, while the base version of this invention still maintains a hypervolume value of 0.281 and an optimality gap of 1.06%, demonstrating a very significant difference in generalization performance.

[0070] Table 2: Generalization Results

[0071]

[0072] The above descriptions are merely embodiments of the present invention, and common knowledge such as specific technical solutions and / or characteristics are not described in detail here. It should be noted that those skilled in the art can make various modifications and improvements without departing from the technical solutions of the present invention, and these should also be considered within the scope of protection of the present invention. These modifications and improvements will not affect the effectiveness of the implementation of the present invention or the practicality of the patent. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A multi-objective vehicle path optimization method based on an enhanced self-attention mechanism, characterized in that, Includes the following steps: S1. Construct an enhanced self-attention encoder, which performs deep fusion encoding on the input node features and preference vector by integrating channel attention, SwiGLU activation and adaptive scaling self-attention modules; S2. Construct a path generation network based on a problem-scale-aware decoder, inject problem-scale information into node embeddings, and generate path sequences in an autoregressive manner; S3. Based on the reinforcement learning framework, the model is trained by combining a stochastic preference strategy to generate a Pareto front approximate solution for the multi-objective vehicle path problem.

2. The method according to claim 1, characterized in that, The "self-attention module integrating channel attention, SwiGLU activation, and adaptive scaling" in step S1 performs the following operations in sequence: First, the input is queried, key-value projected to calculate an initial attention score; then, the initial attention score is adaptively scaled, including multiplying by a dynamic scaling factor related to the problem size, which includes the number of nodes and the baseline size parameter; then, the adaptively scaled score is masked and Softmax normalized to obtain attention weights, and the attention weights are multiplied by the value vector; and the output after multiplication is recalibrated for channel attention, including channel-level reweighting using a compression-excitation network; finally, the result after channel attention recalibration is subjected to a SwiGLU nonlinear transformation, including inputting it to a feedforward sub-layer using a SwiGLU activation function.

3. The method according to claim 2, characterized in that, The baseline scale parameter in the above steps is a learnable parameter.

4. The method according to claim 2, characterized in that, The channel attention recalibration step specifically includes: Compression: Channel descriptors are generated through global average pooling; Activation: A two-layer neural network is used, where the first layer uses the ReLU activation function and compresses the dimensions, and the second layer uses the Sigmoid function to restore the dimensions and output the activation weights; Reweighting: Multiply the incentive weights by the input features channel by channel.

5. The method according to claim 2, characterized in that, The transformation formula for the feedforward sublayer of the SwiGLU activation function in the above step is: FFN SwiGLU (X)=(XW1⊙Swish(XW2))W3 where W1, W2, W3 are trainable parameters, ⊙ denotes element-wise multiplication, and Swish(x)=x·sigmoid(x).

6. The method according to claim 1, characterized in that, The "injecting problem scale information into node embedding" in step S2 is achieved through a scalable scaling encoder, which is based on a sinusoidal coding function and introduces a learnable scaling factor, scale.

7. The method according to claim 1 or 6, characterized in that, In step S2, at each step of generating the path sequence, the decoder's query vector is obtained by projecting the encoding of the previous node and the remaining capacity information of the current vehicle.

8. The method according to claim 1, characterized in that, The "combined random preference strategy" in step S3 refers to randomly generating a preference vector λ for each training instance or each training batch during the model training process, where each component of λ is independently sampled from the interval [0,1] and normalized.

9. The method according to claim 1, characterized in that, The "combining random preference strategy" in step S3 refers to the process of training the model. The method according to claim 1, characterized in that, The reinforcement learning framework in step S3 adopts the REINFORCE algorithm, and its reward function R is designed based on the Tchebycheff scalarization method.

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