A maritime search path planning method and device based on contrast learning

Abstract

This invention provides a method and apparatus for maritime search path planning based on contrastive learning, comprising: constructing a path-solving model including an objective function and constraints based on the searcher, the distressed target, and the area to be searched; inputting the path-solving model into a trained graph neural network to obtain the final search path output by the graph neural network; wherein the graph neural network is trained based on a contrastive learning loss function. The method provided by this invention, by constructing a path-solving model based on mixed-integer linear programming, can handle both comprehensive coverage of the search area and targeted search of distressed targets within a single optimization framework. It also incorporates survival probability decay into the distressed target search problem, prioritizing certain search areas to maximize the survival rate of early rescue. Finally, it utilizes contrastive learning to enhance the feature extraction capability of the graph neural network, thereby improving the success rate of maritime search missions.

Description

Technical Field

[0001] This invention belongs to the field of maritime search, specifically relating to a maritime search path planning method and apparatus based on comparative learning. Background Technology

[0002] With technological advancements, the maritime search environment has become increasingly complex and volatile, leading to a significant increase in the incidence of maritime accidents. Joint search for distressed targets at sea, as a crucial component of maritime operations, is finding increasingly widespread application. Joint search for distressed targets at sea, a vital part of maritime search and rescue operations, refers to the process of searching for targets encountering various dangerous situations (such as accidents, natural or man-made disasters) at sea using various sensors and platforms (such as aircraft and ships). This technological system, through a multi-source heterogeneous sensor network and cross-platform collaborative mechanisms, comprehensively utilizes high-resolution remote sensing satellites, fixed-wing patrol aircraft, shipborne UAVs, and surface vessels to dynamically search for distressed targets at sea encountering sudden events. By rationally planning target search paths, search routes can be optimized, reducing unnecessary area omissions and duplicate searches, thereby covering the most likely target areas in the shortest possible time and improving rescue efficiency and success rates.

[0003] Traditional maritime search relies too much on the subjective judgment and historical experience of decision-makers, lacks systematicity, and suffers from problems such as path redundancy, ambiguous priorities, and poor dynamic adaptability. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method and apparatus for maritime search path planning based on comparative learning.

[0005] The present invention includes a maritime search path planning method based on contrastive learning, comprising: constructing a path solving model including an objective function and constraints based on the searcher, the distressed target, and the area to be searched; wherein the objective function includes:

[0006]

[0007] in, This means maximizing the objective function. For binary decision variables, If located in the current area Searchers at time step Reaching the target movement area , If located in the current area Searchers at time step The target movement area has not been reached. , ; It is a set of discrete regions to be searched. A set of discrete time steps , The total number of time steps. The success rate of the search. For the current region The searchers in the target movement area The probability of successfully searching for a distressed target. For the target movement area The probability of a distressed target existing. Let be the survival probability decay function. and Inversely proportional; the above path solving model is input into the trained graph neural network to obtain the final search path output by the graph neural network; wherein, the above graph neural network is trained based on the contrastive learning loss function.

[0008] Optionally, the survival probability decay function mentioned above includes:

[0009] in, The attenuation rate coefficient, .

[0010] Optionally, the above constraints include: The searcher can only move from one searchable area to another adjacent searchable area between consecutive time steps; and the search path is planned starting from the searcher's preset initial search area; and the searcher can only be in one searchable area in each time step; and the searcher visits each searchable area at most once.

[0011] Optionally, before inputting the path-solving model into the trained graph neural network, the following steps are also included: A path-solving bipartite graph is constructed based on the aforementioned path-solving model; wherein the aforementioned path-solving bipartite graph includes a set of variable nodes, constraint nodes, and node edges, the aforementioned variable nodes correspond to the aforementioned binary decision variables, and the aforementioned constraint nodes correspond to the aforementioned constraint conditions; the aforementioned inputting the aforementioned path-solving model into the trained graph neural network to obtain the final search path output by the aforementioned graph neural network includes: inputting the aforementioned path-solving bipartite graph into the aforementioned graph neural network to obtain the final search path output by the aforementioned graph neural network.

[0012] Optionally, the graph neural network described above is used to: obtain the path solving bipartite graph, obtain the hidden embeddings of the variable nodes and constraint nodes in the path solving bipartite graph at layer 0 of the graph neural network, and simultaneously obtain the hidden embeddings of the node edges; utilize the constraint nodes at layer 0... Hidden embedding of the layer, the above variable nodes in the first layer The hidden embeddings of the layer and the hidden embeddings of the aforementioned node edges are updated to obtain the constrained nodes at the 1st layer. Hidden embedding of the layer; and, utilizing the above-mentioned constraint nodes in the first layer Hidden embedding of the layer, the above variable nodes in the first layer The hidden embeddings of the layer and the hidden embeddings of the aforementioned node edges are updated to obtain the variable nodes at the 1st layer. Hidden embedding of layers; where, , Let be the total number of convolutional layers in the graph neural network described above; concatenate the hidden embeddings of the variable nodes in each layer to obtain the final embeddings of the variable nodes; solve for the final search path based on the final embeddings.

[0013] Optionally, the training process of the above-mentioned graph neural network includes: obtaining an initial graph neural network and a training set including multiple historical feasible solutions; wherein each historical feasible solution includes a path to solve the bipartite graph and its corresponding final search path; training the initial graph neural network using the training set and the contrastive learning loss function to obtain the graph neural network; the contrastive learning loss function includes a multi-sample contrastive loss function. The calculation formulas include:

[0014] in, For temperature parameters, , This represents the total number of historically feasible solutions mentioned above. For the first The solution vector of a historical feasible solution. for Medium variable node The assignment, Indicates to Medium variable node Positive assignment, For the set of all variable nodes, The above graph neural network uses nodes as variables. The output logical value, The above graph neural network uses nodes as variables. The output logical value.

[0015] Optionally, the training process of the above-mentioned graph neural network includes: obtaining an initial graph neural network and a training set including multiple historical feasible solutions; wherein each historical feasible solution includes a path to solve the bipartite graph and its corresponding final search path; training the initial graph neural network using the training set and the contrastive learning loss function to obtain the graph neural network; the contrastive learning loss function includes a pairwise ranking loss function. The calculation formulas include:

[0016] in, This represents the total number of historically feasible solutions mentioned above. For the first The solution vector of a historical feasible solution. for Medium variable node The assignment, Indicates to Medium variable node Positive assignment, Indicates to Medium variable node Negative assignment, This represents the set of nodes representing positive variables. This represents the set of nodes with negative variables. Indicates belonging to variable nodes and belong to variable nodes The set, For the above graph neural network prediction pairs Medium variable node The probability of the above positive assignment. For the above graph neural network prediction pairs Medium variable node The probability of the above positive assignment. The expected interval between positive and negative samples. .

[0017] Based on the same inventive concept, this invention also provides a maritime search path planning device based on contrastive learning, comprising: a model building module, used to construct a path solving model including an objective function and constraints based on the searcher, the distressed target, and the area to be searched; wherein the objective function includes:

[0018]

[0019] in, This means maximizing the objective function. For binary decision variables, If located in the current area Searchers at time step Reaching the target movement area , If located in the current area Searchers at time step The target movement area has not been reached. , ; It is a set of discrete regions to be searched. A set of discrete time steps , The total number of time steps. The success rate of the search. For the current region The searchers in the target movement area The probability of successfully searching for a distressed target. For the target movement area The probability of a distressed target existing. Let be the survival probability decay function. and The path solving module is inversely proportional to the path solving model and inputs it into the trained graph neural network to obtain the final search path output by the graph neural network. The graph neural network is trained based on the contrastive learning loss function.

[0020] Based on the same inventive concept, the present invention also provides an electronic device, comprising: a processor; a memory for storing executable instructions; wherein the processor is configured to read the executable instructions from the memory and execute the executable instructions to implement any of the methods described above.

[0021] Based on the same inventive concept, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the processor performs any of the above-described methods.

[0022] The beneficial effects of this invention are as follows: The method provided by this invention, by constructing a path-solving model of mixed integer linear programming, can handle the problem of comprehensive coverage of the search area and targeted search of distressed targets within a single optimization framework. At the same time, the method provided by this invention incorporates the survival probability decay into the search problem of distressed targets, thereby prioritizing some search areas to maximize the survival rate of early rescue. Finally, it uses contrastive learning to enhance the feature extraction ability of graph neural networks on variables in the path-solving model, thereby improving the success rate of maritime search missions. Attached Figure Description

[0023] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 A flowchart illustrating a maritime search path planning method based on contrastive learning, provided as an embodiment of the present invention; Figure 2 This invention provides a summary table of experimental results in a local coverage search scenario. Figure 3 This invention provides a summary table of experimental results for a complete coverage search scenario. Figure 4 This invention provides a bar chart comparing solution time in an ablation experiment. Figure 5 This invention provides a bar chart comparing target values ​​in an ablation experiment. Figure 6 A bar chart showing the experimental results of a sensitivity analysis based on temperature parameters, provided in an embodiment of the present invention; Figure 7 A bar chart showing the experimental results of sensitivity analysis based on the ranking loss interval parameter provided in an embodiment of the present invention; Figure 8 A bar chart showing the experimental results of sensitivity analysis based on ranking loss weight coefficients provided in this embodiment of the invention; Figure 9 A parameter-based method provided in this embodiment of the invention The results of the sensitivity analysis experiment are shown in a bar chart. Figure 10 A parameter-based method provided in this embodiment of the invention The results of the sensitivity analysis experiment are shown in a bar chart. Figure 11 A parameter-based method provided in this embodiment of the invention The results of the sensitivity analysis experiment are shown in a bar chart. Figure 12 A different embodiment of the present invention Summary table of robustness test results at values; Figure 13A summary table of experimental results for different problem scales provided in this embodiment of the invention; Figure 14 A line graph showing the comparative experimental results of the TCSP model and the OSP model on weighted search success rate provided in an embodiment of the present invention; Figure 15 A line graph showing the comparative experimental results of the TCSP model and the OSP model on the cumulative weighted search success rate provided in this embodiment of the invention; Figure 16 This is a schematic diagram of the path planning experimental results of a TCSP model provided in an embodiment of the present invention; Figure 17 This is a schematic diagram of the path planning experimental results of an OSP model provided in an embodiment of the present invention; Figure 18 A schematic diagram of a maritime search path planning device based on contrastive learning provided in an embodiment of the present invention; Figure 19 This is a schematic diagram of the hardware structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0026] To better understand the above-mentioned objectives, features, and advantages of the embodiments of the present invention, the solutions of the embodiments of the present invention will be further described below. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other.

[0027] Many specific details are set forth in the following description in order to provide a full understanding of the embodiments of the present invention, but the embodiments of the present invention may also be implemented in other ways different from those described herein; obviously, the embodiments in the specification are only some embodiments of the embodiments of the present invention, and not all embodiments.

[0028] This invention provides a method for maritime search path planning based on contrastive learning, such as... Figure 1 As shown, it includes: S1. Construct a path solving model based on the searcher, the distressed target, and the area to be searched, including the objective function and constraints.

[0029] Specifically, maritime distress targets include personnel, vessels, submarines, or other living targets operating at sea that are in danger due to accidents, natural disasters, or human factors and require location and rescue through search operations. This encompasses two categories: personnel targets, including ship crews, offshore workers, passengers, and other individuals engaged in maritime activities; and vehicle targets, such as merchant ships, fishing vessels, yachts, submarines, and maritime aircraft involved in accidents. The search area can be a pre-determined area of ​​the sea surface where the distressed target may be located, determined based on the location when the distressed target issued a distress signal or the last confirmed location.

[0030] The objective function in the above embodiments includes:

[0031]

[0032] in, This means maximizing the objective function. For binary decision variables, If located in the current area Searchers at time step Reaching the target movement area , If located in the current area Searchers at time step The target movement area has not been reached. , ; It is a set of discrete regions to be searched. A set of discrete time steps , The total number of time steps. The success rate of the search. For the current region The searchers in the target movement area The probability of successfully searching for a distressed target. For the target movement area The probability of a distressed target existing. Let be the survival probability decay function. and Inversely proportional.

[0033] Specifically, as can be seen from the formula of the objective function above, the path-solving model is a mixed-integer linear programming (MILP) model. This model can accurately describe complex path planning problems, obtain the optimal solution through optimization algorithms, and possesses high flexibility, allowing for easy addition or modification of the objective function and constraints to adapt to different search scenarios. Furthermore, to improve the success rate and efficiency of the search, the survival probability of the distressed target is the core criterion for measuring search efficiency in maritime search path planning, providing a quantitative indicator for path optimization. The timeliness of the rescue response is extremely important for maritime search; arriving at the scene as early as possible to provide rescue and avoiding prolonged waiting times are crucial for effectively improving the survival rate of distressed targets—that is, the shorter the search time, the higher the survival probability.

[0034] Specifically, in the aforementioned path-finding model, using binary decision variables to represent the searcher's position decisions in the spatiotemporal domain significantly simplifies the problem's complexity. By discretizing the continuous space, binary decision variables transform the complex path planning problem into a more manageable discrete optimization problem, thereby reducing computational difficulty and improving solution efficiency. Furthermore, the use of binary decision variables allows the model to more intuitively describe the searcher's decision-making process, facilitating the construction of various logical constraints, such as mutual exclusion and order constraints, thus clearly expressing the rules and conditions of the search path and providing explicit and efficient decision support for maritime target search.

[0035] S2. Input the path-solving model into the trained graph neural network to obtain the final search path output by the graph neural network. The graph neural network is trained based on a contrastive learning loss function.

[0036] Specifically, a Graph Neural Network (GNN) is a deep learning model for processing graph-structured data. It updates node feature representations by aggregating neighborhood information, thereby learning the complex relationships between nodes and edges in the graph. GNNs learn path-solving model features through message passing mechanisms to predict path cost or feasibility. Building on this, during training, a contrastive learning loss function optimizes the model by comparing positive samples (such as known optimal paths) and negative samples (non-optimal paths). During training, the model attempts to minimize the loss for positive samples while maximizing the loss for negative samples, thus learning to distinguish between optimal and non-optimal paths. During training, the GNN continuously adjusts its network parameters and weights, and after multiple iterations, outputs the optimized final search path.

[0037] This invention proposes a comprehensive theoretical framework that combines a mixed-integer linear programming model for time-constrained search problems with a graph neural network architecture and a contrastive learning method. Specifically, the method provided by this invention constructs a path-solving model based on mixed-integer linear programming, enabling it to handle both comprehensive and targeted search for distressed targets within a single optimization framework. Furthermore, by incorporating survival probability decay into the distressed target search problem, this method prioritizes certain search areas to maximize the survival rate of early rescue efforts. Finally, contrastive learning is used to enhance the graph neural network's feature extraction capability for variables in the path-solving model, thereby improving the success rate of maritime search missions.

[0038] In practice, the above method also includes enabling searchers to search for the distressed target based on the final search path.

[0039] In one specific embodiment, the continuous search region is discretized into a regular square grid, wherein Indicates from 1 to An index is a set of discrete regions to be searched. Reachability between these regions is defined by adjacency relationships: regions From the region Reachable if and only if the edge It belongs to the reachability graph The distressed target is assumed to drift according to a discrete-time Markov model independent of the searcher's actions. The searcher maintains a track spacing. , indicating each discrete time step The search distance traveled within, of which The distance between these flight paths The edge length of the discrete search area is equal to the grid side length, ensuring that the searcher completely covers a search area at a constant speed within each time step. The goal of the pathfinding model is to find a feasible search plan that maximizes the cumulative probability of finding the distressed target within a finite time frame.

[0040] Specifically, this embodiment of the invention employs particle-based simulation to model the drifting motion of a distressed target and estimates the search area at different time periods. The search area is represented using a grid-based discretization method. The prior includes the probability of POC (i.e., region) The probability that the actual area contains distressed targets is simulated using a Gaussian distribution mixture model. For the grid-based search area, the above initial... Defined as:

[0041] in, Indicates the number of Gaussian components. and They represent the first The mean and covariance matrix of the Gaussian components, Indicates in the region The multivariate Gaussian probability density function for internal evaluation. Under the assumption that the distressed target is located within the entire search area, the initial probability distribution... Satisfy normalization constraints .

[0042] The movement of the distressed target follows a stationary Markov process described by the following characteristics. First, based on the transition probabilities... The motion model is defined as:

[0043] in, Represents regions in the reachability graph The degree, and This indicates that the distressed target remains in the current area. (i.e., target movement area) The current area The probability of ).

[0044] At the same time, the transition probability Satisfy random constraints

[0045] In one specific embodiment, the present invention provides a survival probability model for a distressed target, the expression of which is:

[0046] in, Indicates water temperature Soaking time The probability of survival of a distressed target at that time. This indicates the time delay between the occurrence of a maritime accident and the commencement of a search operation. It is a scale parameter that reflects the severity of the accident and the potential harm impact on the distressed target. It is a temperature-dependent shape parameter that determines the decay characteristics of survival rate.

[0047] In some embodiments, for simplicity, the time decay of the survival probability can also be modeled using the standard exponential decay function, which is a Weibull distribution. For special cases, simplified search survival probability decay functions include:

[0048] in, The attenuation rate coefficient, This reflects the severity of environmental conditions and the expected survival time of the distressed target.

[0049] In practice, the searcher starts from the initial position. Search and rescue operations commenced; subsequent locations were determined through an optimization process. Reachability relationships are defined using a four-connected adjacency structure in a discrete mesh: for any region... Its reachable set It is the set of its directly orthogonal neighboring regions. The reachability between regions is determined by the adjacency matrix. Depicting, among which:

[0050] For a size of Square grid, adjacency matrix Established based on Manhattan distance constraints, i.e., region reachable set Given its four-connected orthogonal neighbor set, ensure that the movement pattern matches the actual situation. The probability of detection (POD) depends on sensor efficiency and environmental conditions, and the detection pattern follows an exponential distribution.

[0051] in, The scan width, or scan width for the searcher, is an indicator of the detectability of a distressed target. The actual scan width value is easily affected by environmental conditions and can be corrected using a correction factor. Specifically, when the wind speed is 0 to 28 km / h or the waves are 0 to 1 meter, the weather correction factor is 1.0 for people in the water, on a raft, or on a boat, at a distance of less than 10 meters, and 1.0 for other search targets; when the wind speed is 28 to 46 km / h or the waves are 1 to 1.5 meters, the weather correction factor is 0.5 for people in the water, on a raft, or on a boat, at a distance of less than 10 meters, and 0.9 for other search targets; when the wind speed exceeds 46 km / h or the waves exceed 1.5 meters, the weather correction factor is 0.25 for people in the water, on a raft, or on a boat, at a distance of less than 10 meters, and 0.9 for other search targets.

[0052] In some embodiments, the constraints of the path solving model described above include: The searcher can only move from one searchable region to another adjacent searchable region between consecutive time steps; and the search path is planned starting from the searcher's initial search region; and the searcher can only be in one searchable region in each time step; and the searcher can visit each searchable region at most once.

[0053] Specifically, the constraints of the above path solving model include set partitioning constraints, path connectivity constraints, one-time visit constraints, initial position constraints, and variable domain constraints.

[0054] The set partitioning constraint ensures that the searcher can occupy only one region at each time step, i.e., it guarantees that the searcher is exactly in one region at each time step, as defined in the equation: .

[0055] Path connectivity constraints restrict the searcher to moving only between adjacent regions, i.e., regions, within consecutive time steps. At any moment Only if the searcher was in the previous moment lie in Accessible neighbors Entry is permitted only after the first time step. This constraint applies to all times after the first time step, and is defined as follows:

[0056] The one-visit constraint ensures that the searcher can only visit each region at most once during the search, thus avoiding duplicate searches in the model. The definition is as follows:

[0057] The initial position constraint requires the searcher to start from a specified initial region, defined as follows: ,in Indicates the initial region for the searcher.

[0058] Domain constraints are constraints on binary decision variables, defined as follows:

[0059] For size regional grids and Each time step, the search path includes Given the possible sequences, the aforementioned move feasibility constraints and one-time visit constraints significantly reduce the feasible solution space. Furthermore, since all the above constraints are of linear structure, the aforementioned mixed-integer linear programming model can be further constructed.

[0060] In some embodiments, the method further includes constructing a path-solving bipartite graph based on the path-solving model. The path-solving bipartite graph includes variable nodes, constraint nodes, and a set of node edges; the variable nodes correspond to binary decision variables, and the constraint nodes correspond to constraint conditions.

[0061] The above S2 includes: inputting the path-solving bipartite graph into the graph neural network to obtain the final search path output by the graph neural network.

[0062] To achieve graph neural network processing, this embodiment of the invention converts the mixed-integer linear programming model into a bipartite graph representation. This representation captures both the structural relationship between variables and constraints and reflects the inherent spatiotemporal dependencies in the time-space constraint rules.

[0063] Specifically, an embodiment of the present invention constructs a weighted bipartite graph. (i.e., the bipartite graph of the path solution mentioned above), which can depict the basic relationship between variables and constraints.

[0064] A bipartite graph consists of two disjoint sets of nodes: each constraint node... This corresponds at least to the path connectivity constraint and the one-time visit constraint in the constraints mentioned above. Each variable node... Corresponding to a binary decision variable For the sake of brevity, a single index will be used for variable nodes in the following text. If and only if the variable Under constraints When non-zero coefficients appear in the constraint nodes With variable nodes There is an edge between them .

[0065] To enrich the quantitative information of the graph, this invention associates node and edge feature vectors: firstly, it associates constraint feature vectors ( (Independent of decision variables): For each constraint node Calculate an eigenvector encoding its attributes, such as constraints (≤, =, ≥), right-hand side values, and other normalized statistics. Then associate the eigenvectors of the variable nodes ( (independent of decision variables): for each variable node Its feature vector includes objective function coefficients, variable types (binary), and other structural attributes. Finally, the associated edge features ( ): Each edge Assigned to variable Under constraints The normalized coefficients in the equation. In this problem, all coefficients are ±1, therefore... This attributed bipartite graph will serve as input for subsequent graph representation learning models.

[0066] Furthermore, this invention constructs a graph neural network framework incorporating constraint-aware normalization to output the probability distribution of a binary variable, predicting the likelihood of the decision variable taking the value 1 in a high-quality initial solution set. The graph neural network architecture comprises three main components: an embedding layer, a bipartite graph convolutional layer, and an output layer. The original features of the bipartite graph are first embedded and then fed into the bipartite graph convolutional layer equipped with a constraint-aware normalization module for computation. This module mitigates structural bias by subtracting constraint-induced bias terms. Feature representations from different depths are concatenated to preserve local and global contextual information, then mapped through an output multilayer perceptron and optimized using a hybrid contrastive-ranking loss. The core of this framework lies in the integration of a constraint-aware normalization module... Layer-based bipartite graph convolution. Unlike standard convolution operations, constraint-aware normalization explicitly addresses the inherent structural biases in the interactions between constraint variables. This operation calculates a normalized bias term by aggregating constraint information and subtracting it from the variable features, effectively decoupling the influence of the variable's own characteristics on the strength of the constraints it is connected to. This design ensures that the learned embedding representation is robust to changes in constraint density. To capture hierarchical structural information, this paper employs a layered feature concatenation strategy. The initial layer (layer 0), intermediate layers (e.g., layer 2), and final layer (layer 3) are concatenated. The embedded representations of the layers are concatenated to form a comprehensive multidimensional feature vector. Finally, the fused representation is mapped to probability scores through the output multilayer perceptron and activated by the sigmoid function. The entire network is trained end-to-end using a hybrid contrastive ranking loss, which identifies high-quality solutions by optimizing the relative ranking of variables.

[0067] Specifically, in some embodiments, graph neural networks are used for: S01. Obtain the path solving bipartite graph, and obtain the hidden embeddings (i.e., initial hidden embeddings) of the variable nodes and constraint nodes in the path solving bipartite graph at layer 0 in the graph neural network. At the same time, obtain the hidden embeddings of the node edges.

[0068] Specifically, S01 also includes obtaining the original feature vectors of the bipartite graph for path solving. The original feature vectors of constraints, variables, and edges are projected onto a dimensionless perceptron by three independent multilayer perceptrons. In the common latent space, the hidden embeddings of the constraint nodes in layer 0 of the graph neural network are obtained. Hidden embeddings of variable nodes in layer 0 of a graph neural network and hidden embedding of node edges .in, , , These represent the mapping processes of three independent multilayer perceptrons.

[0069] S02, using constraint nodes in the first... Hidden embeddings of layers, variable nodes in the first layer The hidden embeddings of the layer and the hidden embeddings of the node edges are updated to obtain the constraint node at the 1st layer. Hidden embeddings of layers; and, utilizing constraint nodes in the first layer Hidden embeddings of layers, variable nodes in the first layer The hidden embeddings of the layer and the hidden embeddings of the node edges are updated to obtain the variable node at the th layer. Hidden embedding of layers; where, , This represents the total number of convolutional layers in the graph neural network.

[0070] The core of graph neural networks is a series of... Each layer consists of bipartite graph convolutional layers that iteratively update node embeddings by passing messages between variable nodes and constraint nodes. A two-phase message-passing update is performed. The first is the variable-to-constraint update: the embedding of the constraint node is updated by aggregating information from its neighboring variable nodes, expressed as follows: Then comes constraint-to-variable update: the embedding of variable nodes is updated by aggregating information from neighboring constraint nodes, expressed as follows: .in, and They are nodes and nodes The set of adjacent nodes, For aggregation functions that are invariant to substitution (e.g., summation or averaging). and These are learnable message and update functions (typically implemented using a multilayer perceptron). A specific embodiment of this invention employs a model with the following number of layers: .

[0071] S03. Concatenate the hidden embeddings of the variable nodes at each layer to obtain the final embeddings of the variable nodes.

[0072] Specifically, a key feature of the graph neural network of this invention is the use of skip connections across all layers, where the final representation of each variable is a concatenation of its embeddings from all layers, represented as follows: .

[0073] S04. Solve for the final search path based on the final embedding.

[0074] Specifically, the final concatenated variable embeddings will be input into another multilayer perceptron, and then passed through a sigmoid activation function to convert each binary variable into its own embedding. Generate a probability , ,in, This represents the set of binary variables in the mixed-integer linear programming problem. Can be interpreted as model predictor variables The probability of taking the value 1 in a relatively optimal feasible solution.

[0075] The above embodiments of the present invention employ a constraint-aware normalization mechanism, which eliminates feature bias caused by constraints through two-layer message passing, thereby achieving cross-scale generalization.

[0076] In some embodiments, the training process of the above-described graph neural network includes: Obtain an initial graph neural network and a training set including multiple historical feasible solutions; each historical feasible solution includes a path to solve the bipartite graph and its corresponding final search path. Train the initial graph neural network using the training set and a contrastive learning loss function to obtain the final graph neural network.

[0077] To train the graph neural network, embodiments of the present invention collect multiple high-quality feasible solutions for each instance in the training set, rather than relying solely on a single optimal solution. The following embodiments of the present invention also propose a hybrid contrastive-ranking loss function, which prompts the model to assign higher probabilities to variables observed in better solutions, while introducing additional ranking-based regularization terms to improve consistency among variable predictions.

[0078] The multi-sample contrastive loss acts on the embedding space, driving the positive sample variables. The whole is far away from the set of all binary variables. This achieves coarse-grained separation. Pairwise ranking loss, on the other hand, applies a margin between each pair of positive and negative sample variables. This ensures that the predicted value of the positive sample variable should at least exceed that of the negative sample variable. That concludes the above. The final hybrid loss combines the two parts mentioned above: the multi-sample contrast loss provides global contrast supervision, while the pairwise ranking loss ensures fine-grained pairwise separation.

[0079] Specifically, the multi-sample contrast loss function The calculation formulas include:

[0080] in, For temperature parameters, Minimizing the temperature parameter solves for each feasible solution in the pool. Positive variable assignments were observed on all binary variables. The weighted negative log-likelihood of ). This represents the total number of historically feasible solutions. For the first The solution vector of a historical feasible solution. for Medium variable node The assignment, Indicates to Medium variable node Positive assignment, For the set of all variable nodes, For graph neural networks, the nodes are variables. The output logical value, For graph neural networks, the nodes are variables. The output logical value. Specifically, a positive assignment indicates that the variable node... Positive assignments play a positive role in determining the final search path, even if the objective function is larger or the search path better satisfies the constraints. Negative assignments, on the other hand, indicate that the variable node... It has a negative effect on the determination of the final search path, even if the objective function is smaller or the search path deviates further from the constraints.

[0081] The multi-sample contrastive loss function implements a global discrimination mechanism, ensuring that the collective log-odds quality of path variables dominates the overall probability distribution. This guarantees that the graph neural network learns to assign high confidence to the entire optimal path rather than individual decisions. (Temperature parameter) This controls the clarity of this distinction; the lower the value, the more stringent the distinction between different sample variables.

[0082] In some embodiments, the above pairwise sorting loss function The calculation formulas include:

[0083] in, This represents the total number of historically feasible solutions. For the first The solution vector of a historical feasible solution. for Medium variable node The assignment, Indicates to Medium variable node Positive assignment, Indicates to Medium variable node Negative assignment, This represents the set of nodes representing positive variables. This represents the set of nodes with negative variables. Indicates belonging to variable nodes and belong to variable nodes The set, For graph neural network prediction pairs Medium variable node The probability of assigning a positive value. For graph neural network prediction pairs Medium variable node The probability of assigning a positive value. The expected interval between positive and negative samples. .

[0084] Pairwise ranking loss addresses the local optimization problem by ensuring sufficient margins between each positive and negative sample. In path planning problems, positive samples must not only be superior to negative samples but also maintain sufficient confidence margins with negative samples. This enhances the graph neural network's resilience to noise and prediction uncertainty in the training data, thereby guiding the construction of effective trust regions in subsequent optimization stages.

[0085] In summary, the final contrastive learning loss function in this embodiment of the invention is derived from the multi-sample contrastive loss function. With pairwise sorting loss function composition:

[0086] Among them, weight parameters The weight (which can be set to 0.01) is used to control the contribution of the ranking item to the overall loss. This hybrid loss function enables the graph neural network to effectively learn structural patterns from multiple high-quality solutions while maintaining consistent ranking behavior across variable assignments.

[0087] This hybrid loss function integrates the perspectives of contrastive and ranking learning to enhance the learning stability and generalization ability of graph neural networks. The contrastive loss term provides probabilistic supervision signals, guiding the model to assign higher probabilistic quality to variable patterns appearing in near-optimal solutions, thereby effectively capturing structural patterns among multiple feasible samples. Meanwhile, the ranking loss term explicitly applies interval-based separation between positive and negative variable assignments, mitigating the problem of overly smoothed or ambiguous logistic values ​​that may result from using only the contrastive term. Experience shows that this combination achieves faster convergence and better predictive consistency across different problem instances, especially in scenarios with high solution diversity or noisy objective functions.

[0088] After training, the graph neural network serves as a powerful guide for the original heuristic method. Instead of solving the original mixed-integer linear programming problem from scratch, it utilizes the predictions of the graph neural network to construct and solve a smaller, constrained subproblem. This method is called "primal-problem-aware subproblem" search—based on the trust region approach. This heuristic method mainly consists of three steps: variable fixation, subproblem construction, and solving.

[0089] For a new pathfinding model, its bipartite graph representation has been computed, and all binary variables are obtained using a trained graph neural network strategy. Predicted score Based on these scores, the variables to be temporarily fixed are first identified. The variables are divided into blocks (e.g., by time step), and within each block, the variable with the highest score is selected. The variable of proportion is added to the set "fixed at 1". At the same time, the lowest score The variable of proportion is added to the set that is "fixed at 0". .remember for The target value is assigned (0 or 1).

[0090] Subsequently, instead of rigidly fixing these variables, embodiments of the invention introduce a "confidence region," allowing the solver to deviate from a finite number of fixed variables. This is achieved by introducing relaxation auxiliary variables. The following constraints are used to extend the original mixed-integer linear programming problem:

[0091]

[0092] The above formula defines the deviation for each fixed variable. The global confidence region constraint limits the total deviation to the budget. Within, of which Typically set to , A relatively small tolerance parameter is used. Finally, a solver is used to solve the augmented mixed-integer linear programming problem within a specified time limit. This method reduces the risk of being misled by imperfect predictions while efficiently pruning the search space.

[0093] The embodiments of this invention also include a complexity analysis. First, the graph construction and reasoning process based on graph neural networks increases linearly with the instance size. Secondly, the computational cost of variable block sorting and confidence region linear constraint construction is... This can be completed in polynomial time. The core advantage of this method lies in the optimization of the solution phase: by introducing confidence region constraints, the search space of the original MILP problem is exponentially reduced. Cutting. Within tolerance. With a smaller setup, the search space is reduced by an order of magnitude, significantly reducing the search pressure of the branch and bound method within a given time limit. In summary, this method achieves efficient pruning of the local solution space with extremely low polynomial preprocessing cost, ensuring the timeliness of solution in complex decision-making scenarios.

[0094] This invention conducted comprehensive experiments to evaluate the effectiveness, robustness, and practical value of the method provided in the embodiments of this invention for the maritime search path planning problem. The experimental analysis is mainly divided into four parts. First, under two search scenarios—local coverage and global coverage—CRISP (i.e., the overall method provided in the embodiments of this invention) is benchmarked against advanced commercial solvers and learning-based methods to demonstrate its advantages in solution quality, computational efficiency, and scalability. Second, the generalization ability of CRISP is explored, specifically evaluating its policy transferability across different survival decay rates, as well as its cross-scale generalization performance from small-scale training instances to large-scale unseen problems. Third, rigorous ablation experiments and hyperparameter sensitivity analyses are conducted to verify the necessity of key model components and ensure the stability of the optimization process. Finally, to verify the practical significance of the proposed TCSP model (i.e., the path solving model in the above embodiments of this invention), a comparative case study with the classic OSP model is conducted to quantify the improvement in cumulative rescue probability and to visualize the policy evolution of the search path.

[0095] The experiment evaluated the method provided by the embodiments of the present invention in two key maritime search and rescue scenarios: (1) Local coverage search: This scenario focuses on maximizing the probability of survival under limited search time and capability constraints. Its goal is to strategically allocate search resources to the area with the highest target detection probability while taking into account the survival probability factor that decays over time. (2) Global coverage search: This scenario assumes that the search unit has sufficient time and energy to traverse the entire designated area. Its goal is to minimize the overall mission completion time while achieving complete coverage of all search areas, thereby discovering potential survivors as early as possible.

[0096] The experiment used a Gaussian Mixture Model (GMM) to generate an initial map containing survival probabilities, and simultaneously constructed 13 sets of maps with different parameter combinations. The benchmark instance, where Indicates the number of search units. The time domain is represented by the planning parameter. In the training set, 1,000 instances are generated for each configuration; the test set contains 50 independent instances for each configuration to validate the model's generalization ability. Multiple instances are labeled P-1 to P-7 and F-1 to F-6, simulating diverse maritime search and rescue missions with problem sizes ranging from approximately 1,200 constraints to over 23,000 constraints. This range reflects the scalability of the benchmark set and facilitates comprehensive performance evaluation across different computational scales.

[0097] To reduce the impact of randomness in the experiment, the results for each dataset were calculated as the average of the solutions obtained from 50 independent instances. This section uses five evaluation metrics to comprehensively evaluate the performance of the proposed algorithm. These metrics collectively reflect the solution quality, computational efficiency, and robustness: (1) Average objective value (Average obj) – the optimization objective value achieved within the specified time limit; a higher value indicates better performance. (2) Average solution time (Test time) – the clock time required to obtain the final solution or reach the maximum allowable time; a lower value is better. (3) Standard deviation of objective value (Std obj) – a metric that measures the stability of optimization results among benchmark instances; a lower variance indicates higher algorithm reliability. (4) Average gap (Average gap) – for Gurobi, this metric represents the standard gap relative to the original gap with respect to the known optimal upper bound; for GNN-based methods, it represents the gap within the current confidence domain, thus quantifying the prediction accuracy of the learning model; a lower value is better. (5) Failure count – The number of instances that fail to obtain a feasible solution within a given computational constraint, serving as an indicator of the robustness of the method.

[0098] Figure 2 The tables in the table provide detailed empirical results for the local cover search scenario. These results clearly demonstrate that the CRISP framework proposed in this invention has significant advantages over existing benchmarks, including the commercial solver Gurobi and other learning-assisted methods (Neural Diving and P&S). CRISP consistently achieves a better balance between solution quality and computational efficiency across all test cases. Analysis shows that CRISP not only achieves the highest average objective value in all scenarios but also achieves a better average optimality gap. This indicates that CRISP can guide the search process towards provably better solutions. This superior solution quality is directly related to the higher prediction accuracy of the graph representation learning model, which is quantified by the average gap metric based on the GNN method. This metric reflects the model's gap within its confidence region and measures the model's prediction accuracy for the quality of local search decisions; a smaller value indicates higher prediction fidelity. On larger-scale tests, CRISP demonstrates significantly higher prediction accuracy than other learning-based methods. For example, on the P-3 instance, CRISP's average gap is 0.7111, which is 29.6% lower than the P&S method and 41.3% lower than the neural stealth method. Similar advantages can be observed on the P-5 instance. This superior predictive accuracy provides the solver with more reliable guidance, enabling it to explore the search space more effectively and ultimately converge to a solution with a higher objective value, as evidenced by CRISP's leading performance in the average objective value column.

[0099] While significantly improving solution quality, CRISP also drastically reduces computation time. Compared to Gurobi, CRISP reduces the average solution time by 34.2% on instance P-1, 21.3% on P-2, 21.0% on P-3, and 18.2% on P-4. This sustained speedup fully demonstrates the efficiency of the learned strategy in pruning search trees and accelerating the discovery of high-quality integer feasible solutions.

[0100] Furthermore, CRISP's superior robustness is a key feature. This is particularly evident in the P-2 instance, where the neural stealth heuristic exhibited a catastrophic performance degradation: despite a shorter average run time, its objective value was negligible (31.14 vs. CRISP's 314.82), with a reported average gap exceeding 92%, and it failed in all 46 test runs. In stark contrast, CRISP demonstrated perfect reliability across all experiments, with zero failures. Its objective value consistently maintained a low standard deviation, further confirming its stable and predictable performance—a crucial property for real-world deployments. In conclusion, the experimental results demonstrate that CRISP not only accelerates the search process but also finds higher-quality solutions more efficiently with smaller, certified optimality gaps. Compared to standalone commercial solvers and other hybrid techniques, CRISP exhibits significantly superior and more robust performance characteristics.

[0101] Figure 3 Experimental results are presented across a complete search scenario, highlighting the scalability and robustness of the CRISP framework, with its advantages becoming increasingly significant as problem complexity increases. On smaller instances F-1 to F-3, all methods successfully yielded high-quality solutions, where CRISP's main advantage lies in its superior computational efficiency. It consistently produces solutions of equal quality to the benchmark methods, with significantly shorter computation times. For example, on instances F-1 and F-2, compared to the benchmark solver Gurobi, its solution time is reduced by 35.3% and 35.8%, respectively, without sacrificing solution quality.

[0102] CRISP's true advantage is fully demonstrated on the most challenging instances F-4 through F-6, where other methods begin to falter. On the largest instance, F-6 (where all methods meet the time limit), CRISP achieves a remarkable 39.5% improvement in average objective value compared to Gurobi (285.53 vs. 204.73), while also significantly outperforming the suboptimal method P&S. Crucially, CRISP exhibits exceptional robustness. It is the only method to successfully solve all instances with zero failures. This contrasts sharply with Gurobi and neural stealth methods, which failed 8 to 14 times on the most difficult problems (F-5, F-6). This reliability is further supported by a significantly smaller standard deviation of objective values ​​on these instances, indicating that CRISP's performance is not only superior on average but also more consistent and predictable. This dominant performance stems from the model's higher predictive fidelity at the most critical moments. For these complex problems (F-4, F-5, F-6), effective heuristic guidance is crucial, and the model learned by CRISP consistently maintains the lowest mean gap, meaning its predictions are the most accurate. This allows it to more intelligently explore a wide search space and converge to regions of high-quality solutions that other methods cannot obtain within time constraints.

[0103] In summary, the full coverage experiments demonstrate that CRISP is not merely an accelerator for simple problems, but also a robust and scalable approach. It performs exceptionally well when traditional solvers and other hybrid methods underperform, providing higher quality and more reliable solutions.

[0104] To evaluate the contribution of each component in the CRISP framework, an ablation study was conducted on a P-2 instance. Figure 4 The solution time of the complete CRISP model was compared with that of two variants with critical components removed, as well as that of Gurobi. Figure 5 The full CRISP model was compared with two variants that removed key components, along with the Gurobi objective. The two variants included a variant that removed the pairwise ranking loss component (CRISP w / o Ranking) and a variant that removed the self-contrast learning component (CRISP w / o MSCL). The results in the figure confirm that both the ranking loss and self-contrast learning components are indispensable for achieving optimal performance. Removing either component, while maintaining competitive solution quality, leads to a decrease in computational efficiency. To further explore the behavioral characteristics of CRISP and verify the robustness of the proposed method, a systematic sensitivity analysis was conducted on three key hyperparameters of the contrastive loss between control variables, including the temperature parameter in the multi-sample contrastive loss (MSCL). The interval parameter in the sorting loss and the weighting coefficients used to balance the two losses. All experiments were conducted on an 11g × 40t sample, and the results are as follows: Figures 6 to 8 As shown.

[0105] like Figure 6 As shown (blue represents the target value, orange represents time), the softmax temperature parameter... It exhibits U-shaped sensitivity, and its best performance occurs when This result indicates a key trade-off: excessively low temperatures ( Training instability may result from over-focusing on indistinguishable negative samples; while excessively high temperatures ( This may result in an overly smoothed distribution, making it impossible to adequately distinguish between different samples.

[0106] like Figure 7 As shown (blue represents the target value, orange represents time), when the sorting loss interval... Increasing the margin to 0.8 resulted in a monotonically improving model performance. This confirms the hypothesis that a larger, well-defined margin enhances the reliability of decisions by more clearly distinguishing the logistic values ​​of variables. However, excessively large margins may hinder optimization convergence, thus a practical upper bound exists.

[0107] Figure 8 The analysis shows (blue represents the target value, orange represents time), a smaller coefficient This is optimal, and performance decreases as this value increases. While the ranking loss is crucial, overemphasizing it seems counterproductive. Therefore, it's speculated that this might be because excessive focus on inter-class separation amplifies the impact of outliers, ultimately harming the overall accuracy of the model.

[0108] In addition to training the hyperparameters, the experiment also analyzed the sensitivity of the inference parameters controlling the prediction-search process. For example... Figures 9 to 11 As shown ( Figure 9 The parameters are shown. Sensitivity analysis, Figure 10 The parameters are shown. Sensitivity analysis, Figure 11 The parameters are shown. Sensitivity analysis (blue represents the target value, orange represents time), the parameters selected for the variables are... It exhibits optimal performance at this point, with a target value of 314.78, while maintaining a reasonable computation time of 74.14 seconds. Parameters in The optimal result (target value: 314.81) was obtained, indicating that a suitable candidate set size can effectively balance solution quality and search efficiency. Confidence region radius exist It achieves optimal performance with a higher objective value (314.78) and the fastest solution time (74.14 seconds). These results confirm that, compared to the baseline method, CRISP's high-quality predictions require only a smaller search neighborhood, thereby reducing computational overhead while maintaining solution quality.

[0109] The experiment also evaluated the robustness of CRISP under different time decay factors, which are key parameters affecting the change of survival probability over time in maritime search and rescue scenarios. Figure 12 The table shows the results for the P-2 instance as the decay factor changes from 0.065 to 0.10. CRISP consistently reduces the solution time across all decay values, demonstrating strong generalization ability.

[0110] The experiment further evaluated the generalization performance of the same model on different problem sizes, which was trained based on P-2 instances. Figure 13 The table below shows the results on instances ranging from P-5 to P-7. Both methods ran under a time limit close to 360 seconds, but CRISP consistently yielded higher quality solutions. This advantage became increasingly significant as the problem size increased. On the P-5 instance, the improvement in average objective value was not yet noticeable; however, for the largest P-7 instance, CRISP achieved a significantly higher objective value (249.13 vs. 247.87) and a better final optimality gap (0.0397 vs. 0.0449). This trend suggests that the policy learned from smaller instances (P-2) has effective generalization capabilities, demonstrating increasingly superior performance on larger and more complex problems.

[0111] The primary objective of time-sensitive maritime search and rescue operations is to maximize the probability of a successful rescue, which depends not only on the discovery of the target but also on its discovery while it is still alive. To this end, the experiment introduces a "weighted success coefficient" as a key performance indicator to quantify search and rescue effectiveness per unit time. This indicator combines the detection probability within a given area with the target's survival probability over time. Figure 14As shown, the two models exhibit a stark contrast in the temporal distribution of search and rescue effectiveness. The TCSP model demonstrates a significantly higher weighted success coefficient gain in the initial phase of the search (approximately 0-20 time steps). This indicates that the TCSP model strategically prioritizes accessing areas that generate the highest immediate reward—defined as the product of the detection probability and the current survival probability. As these high-value areas are covered, the gain naturally decays. In contrast, the OSP model shows a more uniform gain distribution, which remains consistently low in the early stages, reflecting that its systematic coverage strategy fails to adequately consider the urgency arising from the decaying survival probability. This strategic difference is directly reflected in the cumulative weighted success (CWS), such as... Figure 15 As shown, the CWS curve of the TCSP model exhibits a rapid initial rise and maintains a leading advantage throughout the simulation. At the end of the simulation, the final CWS of the TCSP model reached 0.2308, while that of the OSP model was 0.1831. This indicates a significant improvement of approximately 26% in the overall success rate of the rescue, fully demonstrating the superior performance of the TCSP model in maximizing the final success rate under realistic time constraints.

[0112] The performance difference between the two models stems from their fundamentally different path planning logic, which is evident in... Figure 16 and Figure 17 The visual path shown provides an intuitive representation of this. Figure 16 The path generated by the TCSP model exhibits a dynamic, non-uniform, and opportunistic pattern. It initially concentrates its search efforts on core regions with the highest initial containment probability (e.g., waypoints 1-20). This "preload" strategy is a direct mathematical interpretation of the "time is life" principle: early searches in these high-value regions maximize the chance of success before the survival probability significantly diminishes. Only after covering the most promising areas does the path expand to peripheral, lower-probability regions. In contrast, the path generated by OSP (… Figure 17 This approach follows a classic, systematic "lawnmower" or "reciprocating scan" pattern. While this path ensures geometrical complete coverage of the search area, its planning logic is static and highly insensitive to the dynamic decay of the target's survival probability. For example, it might schedule a cell with a high initial POC for later access, by which time the prospect of a successful rescue has significantly decreased. This results in low marginal utility for later search efforts, explaining its poor performance on the CWS metric.

[0113] In summary, the TCSP model achieves intelligent and dynamic allocation of search resources by internalizing the time dimension into its decision-making core. Its strategy of prioritizing access to regions with high immediate expected returns ensures that search efforts are most effective in the critical initial phase when the probability of target survival is highest.

[0114] It should be noted that the method of this embodiment can be executed by a single device, such as a computer or server. The method of this embodiment can also be applied to a distributed scenario, where multiple devices cooperate to complete the task. In such a distributed scenario, one of these devices may execute only one or more steps of the method of this embodiment, and the multiple devices will interact with each other to complete the above method.

[0115] It should be noted that the above description describes some embodiments of the present invention. Other embodiments are within the scope of the appended specification. In some cases, the actions or steps described in the specification may be performed in a different order than those in the above embodiments and still achieve the desired results. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0116] Based on the same inventive concept, corresponding to any of the methods in the above embodiments, the present invention also provides a maritime search path planning device based on contrastive learning, such as... Figure 18 As shown, it includes: The model building module is used to construct a path-solving model based on the searcher, the distressed target, and the area to be searched, including an objective function and constraints; the objective function includes:

[0117]

[0118] in, This means maximizing the objective function. For binary decision variables, If located in the current area Searchers at time step Reaching the target movement area , If located in the current area Searchers at time step The target movement area has not been reached. , ; It is a set of discrete regions to be searched. A set of discrete time steps , The total number of time steps. The success rate of the search. For the current region The searchers in the target movement area The probability of successfully searching for a distressed target. For the target movement area The probability of a distressed target existing. Let be the survival probability decay function. and Inversely proportional.

[0119] The solution module is used to input the path solving model into the trained graph neural network to obtain the final search path output by the graph neural network; the graph neural network is trained based on the contrastive learning loss function.

[0120] This invention proposes a comprehensive theoretical framework that combines a mixed-integer linear programming model for time-constrained search problems with a graph neural network architecture and a contrastive learning method. Specifically, the device provided in this invention constructs a path-solving model based on mixed-integer linear programming, enabling it to handle both comprehensive and targeted search problems for distressed targets within a single optimization framework. Furthermore, by incorporating survival probability decay into the distressed target search problem, the device prioritizes certain search areas to maximize the survival rate of early rescue efforts. Finally, contrastive learning is used to enhance the graph neural network's feature extraction capability for variables in the path-solving model, thereby improving the success rate of maritime search missions.

[0121] For ease of description, the above apparatus is described in terms of its functions, divided into various modules. Of course, in implementing this invention, the functions of each module can be implemented in one or more software and / or hardware components.

[0122] The apparatus of the above embodiments is used to implement the corresponding maritime search path planning method based on contrastive learning in any of the foregoing embodiments, and has the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0123] Figure 19 A schematic diagram of the structure of an electronic device provided by an embodiment of the present invention is shown.

[0124] like Figure 19 As shown, the electronic device may include a processor and a memory storing computer program instructions.

[0125] Specifically, the processor may include a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement embodiments of the present invention.

[0126] The memory may include a large-capacity storage device for information or instructions. For example, and not limitingly, the memory may include a hard disk drive (HDD), a floppy disk drive, flash memory, an optical disk drive, a magneto-optical disk drive, magnetic tape, or a Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, the memory may include removable or non-removable (or fixed) media. Where appropriate, the memory may be internal or external to the integrated gateway device. In a particular embodiment, the memory is a non-volatile solid-state memory. In a particular embodiment, the memory includes read-only memory (ROM). Where appropriate, the ROM may be a mask-programmed ROM, a programmable ROM (PROM), an erasable PROM (Electrically Programmable ROM, EPROM), an electrically erasable programmable ROM (EEPROM), an electrically alterable ROM (EAROM), or flash memory, or a combination of two or more of these.

[0127] The processor reads and executes computer program instructions stored in memory to perform the steps of the maritime search path planning method based on contrastive learning provided in the embodiments of the present invention.

[0128] In one example, the electronic device may also include a transceiver and a bus. For example, Figure 19 As shown, the processor, memory, and transceiver are connected via a bus and communicate with each other.

[0129] A bus may be hardware, software, or both. For example, and not limitingly, a bus may include an Accelerated Graphics Port (AGP) or other graphics bus, an Extended Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), a Hyper Transport (HT) interconnect, an Industrial Standard Architecture (ISA) bus, an Infinite Bandwidth Interconnect, a Low Pin Count (LPC) bus, a memory bus, a MicroChannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local Bus (VLB) bus, or other suitable buses, or a combination of two or more of these. Where appropriate, a bus may include one or more buses. Although specific buses are described and illustrated in embodiments of the invention, the invention contemplates any suitable bus or interconnect.

[0130] The following are embodiments of a computer-readable storage medium provided in this invention. This computer-readable storage medium belongs to the same inventive concept as the maritime search path planning method based on contrastive learning in the above embodiments. For details not described in detail in the embodiments of the computer-readable storage medium, please refer to the embodiments of the maritime search path planning method based on contrastive learning described above.

[0131] This embodiment provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform a comparative learning-based maritime search path planning method.

[0132] Of course, the computer-executable instructions provided in the embodiments of the present invention are not limited to the above-described method operations, but can also execute related operations in the maritime search path planning method based on contrastive learning provided in any embodiment of the present invention.

[0133] Based on the above description of the implementation methods, those skilled in the art can clearly understand that the present invention can be implemented using software and necessary general-purpose hardware, and of course, it can also be implemented using hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk, or optical disk, etc., including several instructions to cause a computer cloud platform (which can be a personal computer, server, or network cloud platform, etc.) to execute the maritime search path planning method based on contrastive learning provided in the various embodiments of the present invention.

[0134] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the aforementioned element.

[0135] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments described above, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A maritime search path planning method based on contrastive learning, characterized in that, include: A pathfinding model is constructed based on the searcher, the distressed target, and the area to be searched, including an objective function and constraints; wherein, the objective function includes: in, This means maximizing the objective function. For binary decision variables, If located in the current area Searchers at time step Reaching the target movement area , If located in the current area Searchers at time step The target movement area has not been reached. , ; It is a set of discrete regions to be searched. A set of discrete time steps , The total number of time steps. The success rate of the search. For the current region The searchers in the target movement area The probability of successfully searching for the distressed target. For the target movement area The probability of the presence of the distressed target. Let be the survival probability decay function. and Inversely proportional; The path solving model is input into a trained graph neural network to obtain the final search path output by the graph neural network; wherein the graph neural network is trained based on a contrastive learning loss function. The survival probability decay function includes: in, The attenuation rate coefficient, ; The constraints include: The searcher can only move from one searchable area to another adjacent searchable area between consecutive time steps; and the search path is planned starting from the searcher's preset initial search area; and the searcher can only be in one searchable area in each time step; and the searcher visits each searchable area at most once. Before inputting the path solving model into the trained graph neural network, the method further includes: A path-solving bipartite graph is constructed based on the path-solving model; wherein, the path-solving bipartite graph includes a set of variable nodes, constraint nodes, and node edges, the variable nodes correspond to the binary decision variables, and the constraint nodes correspond to the constraint conditions; The step of inputting the path solving model into a trained graph neural network to obtain the final search path output by the graph neural network includes: The bipartite graph of the path solving is input into the graph neural network to obtain the final search path output by the graph neural network.

2. The maritime search path planning method based on contrastive learning as described in claim 1, characterized in that, The graph neural network is used for: Obtain the path solving bipartite graph, and obtain the hidden embeddings of the variable nodes and the constraint nodes in the path solving bipartite graph at layer 0 of the graph neural network, and at the same time obtain the hidden embeddings of the node edges; Using the constraint node in the first Hidden embedding of the layer, the variable node in the first layer The hidden embedding of the layer and the hidden embedding update of the node edges are used to obtain the constraint node at the 1st layer. Hidden embedding of layers; And, using the constraint node in the first Hidden embedding of the layer, the variable node in the first layer The hidden embedding of the layer and the hidden embedding of the node edges are updated to obtain the variable node at the 1st layer. Hidden embedding of layers; where, , The total number of convolutional layers in the graph neural network; By concatenating the hidden embeddings of the variable nodes at each layer, the final embedding of the variable nodes is obtained; The final search path is solved based on the final embedding.

3. The maritime search path planning method based on contrastive learning as described in claim 1, characterized in that, The training process of the graph neural network includes: Obtain an initial graph neural network and a training set including multiple historical feasible solutions; wherein each historical feasible solution includes a path to solve the bipartite graph and its corresponding final search path; The initial graph neural network is trained using the training set and the contrastive learning loss function to obtain the graph neural network; The contrastive learning loss function includes a multi-sample contrastive loss function. The calculation formulas include: in, For temperature parameters, , Let be the total number of historical feasible solutions. For the first The solution vector of a historical feasible solution. for Medium variable node The assignment, Indicates to Medium variable node Positive assignment, For the set of all variable nodes, The graph neural network is used as the variable node. The output logical value, The graph neural network is used as the variable node. The output logical value.

4. The maritime search path planning method based on contrastive learning as described in claim 1, characterized in that, The training process of the graph neural network includes: Obtain an initial graph neural network and a training set including multiple historical feasible solutions; wherein each historical feasible solution includes a path to solve the bipartite graph and its corresponding final search path; The initial graph neural network is trained using the training set and the contrastive learning loss function to obtain the graph neural network; The contrastive learning loss function includes a pairwise ranking loss function. The calculation formulas include: in, Let be the total number of historical feasible solutions. For the first The solution vector of a historical feasible solution. for Medium variable node The assignment, Indicates to Medium variable node Positive assignment, Indicates to Medium variable node Negative assignment, This represents the set of nodes representing positive variables. This represents the set of nodes with negative variables. Indicates belonging to variable nodes and belong to variable nodes The set, The graph neural network predicts the pairs Medium variable node The probability of the positive assignment. The graph neural network predicts the pairs Medium variable node The probability of the positive assignment. The expected interval between positive and negative samples. .

5. A maritime search path planning device based on contrastive learning, characterized in that, include: The model building module is used to construct a path-solving model, including an objective function and constraints, based on the searcher, the distressed target, and the area to be searched; wherein the objective function includes: in, This means maximizing the objective function. For binary decision variables, If located in the current area Searchers at time step Reaching the target movement area , If located in the current area Searchers at time step The target movement area has not been reached. , ; It is a set of discrete regions to be searched. A set of discrete time steps , The total number of time steps. The success rate of the search. For the current region The searchers in the target movement area The probability of successfully searching for the distressed target. For the target movement area The probability of the presence of the distressed target. Let be the survival probability decay function. and Inversely proportional; The solution module is used to input the path solving model into the trained graph neural network to obtain the final search path output by the graph neural network; wherein, the graph neural network is trained based on the contrastive learning loss function; The survival probability decay function includes: in, The attenuation rate coefficient, ; The constraints include: The searcher can only move from one searchable area to another adjacent searchable area between consecutive time steps; and the search path is planned starting from the searcher's preset initial search area; and the searcher can only be in one searchable area in each time step; and the searcher visits each searchable area at most once. Before inputting the path-solving model into the trained graph neural network, the device is further configured to: A path-solving bipartite graph is constructed based on the path-solving model; wherein, the path-solving bipartite graph includes a set of variable nodes, constraint nodes, and node edges, the variable nodes correspond to the binary decision variables, and the constraint nodes correspond to the constraint conditions; The solution module is also used for: The bipartite graph of the path solving is input into the graph neural network to obtain the final search path output by the graph neural network.

6. An electronic device, characterized in that, include: processor; A memory for storing executable instructions; wherein the processor is configured to read the executable instructions from the memory and execute the executable instructions to implement the maritime search path planning method based on contrastive learning as described in any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, The storage medium stores a computer program that, when executed by a processor, causes the processor to implement the maritime search path planning method based on contrastive learning as described in any one of claims 1 to 4.

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