Adaptive optimized offshore search and rescue platform deployment method

Abstract

The application provides a self-adaptive optimization offshore search and rescue platform deployment method, which comprises the following steps: obtaining spatial position information of an object to be rescued and setting an initial deployment position of a rescue resource and an optimization algorithm parameter; in each iteration, generating an exploration target position by randomly disturbing a current optimal deployment position set, determining a main search direction and a vertical auxiliary search direction, calculating a step adjustment factor according to spatial distribution characteristics of the object to be rescued and a deviation of a current deployment scheme from an ideal distribution, calculating a moving step and updating the deployment position, and mapping back to a search area in a topological continuous manner when exceeding a boundary; according to a spatial distance minimum principle, establishing an allocation relationship, adjusting a rescue resource position to a spatial center of a service object, and iterating to convergence; calculating a total distance as an evaluation index, updating an optimal deployment position and a step adjustment factor; and iterating until termination. The method improves a convergence speed by about 45%, reduces a total rescue distance to 22.45, and improves offshore search and rescue efficiency.

Description

Technical Field

[0001] This invention relates to the field of maritime emergency rescue technology, specifically to an adaptive and optimized method for deploying a maritime search and rescue platform. Background Technology

[0002] Maritime rescue is a crucial link in ensuring maritime traffic safety and emergency response capabilities. Its efficiency directly affects the survival probability of people who have fallen overboard and the overall rescue outcome. In sudden maritime accidents, people often fall overboard. Given the complex and ever-changing sea conditions and limited rescue time windows, how to achieve rapid and rational deployment of rescue resources has become an urgent problem to be solved.

[0003] Fixed-wing aircraft have the advantages of high speed and long range, allowing them to arrive at the scene first in an emergency. By airdropping floating modular rescue platforms and emergency supplies, they can effectively extend the survival time of people who have fallen into the water, creating a window of opportunity for subsequent rescue efforts. The deployment location of the rescue platform directly affects the distance from the person in the water to the platform, thus impacting rescue efficiency.

[0004] Existing methods for deploying rescue platforms primarily employ experience-based fixed-location or random deployment approaches. In practice, these methods often deploy rescue platforms at pre-set fixed locations or randomly drop them within the accident area based on initial observations, failing to fully consider the actual spatial distribution characteristics of those in the water. Since the distribution of those in the water during maritime accidents typically exhibits both randomness and clustering, fixed-location deployment struggles to adapt to different personnel distribution patterns, resulting in some rescue platforms being too far from those in the water, leading to excessively long overall rescue distances and impacting rescue efficiency.

[0005] Another approach employs optimization algorithms to optimize the deployment location of rescue platforms. For example, swarm intelligence algorithms such as particle swarm optimization and genetic algorithms are used to iteratively search for a platform deployment scheme that minimizes the overall rescue distance. While these methods can improve deployment effectiveness to some extent, they have the following shortcomings in practical applications: First, the search step size of the optimization algorithm is usually fixed or only linearly adjusted based on the number of iterations, failing to dynamically adjust according to the spatial distribution characteristics of the people in the water and the current optimization progress. This results in insufficient global search in the early stages or slow local convergence in the later stages. Second, the boundary handling is unreasonable. When the deployment location exceeds the boundary of the search area during the search process, bounce or truncation methods are often used, limiting the continuity of the search space and affecting the discovery of the optimal solution. Furthermore, existing methods fail to effectively combine the advantages of global search and local convergence, easily getting trapped in local optima and unable to obtain a globally optimal or near-optimal deployment scheme within a limited computational time.

[0006] Therefore, a new method for deploying maritime search and rescue platforms is needed that can adaptively optimize the deployment location of rescue platforms based on the spatial distribution characteristics of people who have fallen into the water, thereby improving convergence speed and optimization accuracy while ensuring global search capabilities, thus shortening the overall rescue distance and improving the efficiency of large-scale maritime search and rescue. Summary of the Invention

[0007] The purpose of this invention is to provide an adaptive and optimized method for deploying maritime search and rescue platforms, in order to solve the following technical problems existing in the prior art:

[0008] (1) Existing rescue platform deployment methods do not fully consider the spatial distribution differences of people who have fallen into the water. They adopt fixed-location or random deployment methods, resulting in the rescue platform being too far away from the people who have fallen into the water, and the overall rescue distance being too long, which affects the rescue efficiency and the survival probability of people who have fallen into the water.

[0009] (2) The existing optimization algorithm has a fixed search step size or only relies on the number of iterations for linear adjustment. It fails to dynamically adjust according to the spatial distribution characteristics of the drowning people and the current optimization process, resulting in insufficient global search in the early stage or slow local convergence speed in the later stage, which easily leads to local optima.

[0010] (3) The boundary handling of existing methods is unreasonable. When the deployment location exceeds the boundary of the search area during the search process, the method of bouncing or truncation is often used, which restricts the continuity of the search space and affects the discovery of the optimal solution.

[0011] To achieve the above objectives, the present invention adopts the following technical solution:

[0012] This invention provides an adaptive optimization method for deploying a maritime search and rescue platform, used to adaptively optimize the deployment location of the rescue platform based on the spatial distribution of people who have fallen into the water. The method includes acquiring spatial location information of multiple individuals to be rescued and setting initial deployment locations for multiple rescue resources. The method further includes the following steps:

[0013] Step 1: Set the iteration termination condition and search control parameters for the optimization algorithm;

[0014] Step 2: In each iteration, randomly perturb the current set of optimal rescue resource deployment locations to generate a set of target locations to explore;

[0015] For each rescue resource, based on its current deployment location and the location of the corresponding exploration target, determine the main search direction toward the exploration target and the auxiliary search direction perpendicular to the main search direction;

[0016] Calculate the step size adjustment factor based on the spatial distribution characteristics of the objects to be rescued and the deviation between the current deployment plan and the ideal distribution;

[0017] Based on the main search direction, auxiliary search direction, step size adjustment factor, and the weights of the main search direction and auxiliary search direction, the movement step size of the rescue resources is calculated, and the deployment position of the rescue resources is updated. Among them, the weight of the main search direction increases with the optimization process, and the weight of the auxiliary search direction decreases with the optimization process.

[0018] When rescue resources are deployed outside the search area boundary, they are mapped back into the search area using topological continuity.

[0019] Step 3: Based on the principle of minimum spatial distance, assign each object to be rescued to the nearest rescue resource, establishing an allocation relationship between rescue resources and objects to be rescued; adjust the deployment location of each rescue resource to the spatial center of all the objects to be rescued that it is responsible for rescuing; repeat this allocation and adjustment process until the deployment locations of rescue resources converge.

[0020] Step 4: Calculate the total distance from all objects to be rescued to their corresponding rescue resources as an evaluation index; if the current total distance is less than the historical best total distance, update the set of optimal rescue resource deployment locations; update the step size adjustment factor based on the maximum distribution distance of the objects to be rescued, the deviation between the historical average cluster center and the distribution center of the objects to be rescued, and the ratio of the weight of the main search direction to the weight of the auxiliary search direction.

[0021] Step 5: Repeat steps 2 to 4 until the iteration termination condition is met, and output the optimal set of rescue resource deployment locations.

[0022] This invention combines the global search capability of the Golden Eagle Optimization Algorithm with the local convergence capability of the KMeans clustering algorithm. It introduces an adaptive step-size adjustment factor to comprehensively consider the spatial distribution characteristics of the objects to be rescued and the deviation between the current deployment plan and the ideal distribution. This allows the rescue platform to dynamically adjust its deployment location based on the actual distribution of people in the water. The main search direction provides the primary driving force for convergence to the optimal solution, while the auxiliary search direction provides exploration capabilities perpendicular to the main direction, preventing the search path from becoming too singular. By dynamically adjusting the weights of the main search direction and the auxiliary search direction, an optimization strategy of broad-area exploration in the early stage and fine-grained convergence in the later stage is achieved.

[0023] Furthermore, the iteration termination condition is that the number of iterations reaches 50 to 200. This range of iterations ensures sufficient convergence of the algorithm while avoiding the waste of computational resources caused by excessive iteration.

[0024] Preferably, the search control parameters include an initial weight for the main search direction, a termination weight for the main search direction, an initial weight for the auxiliary search direction, and a termination weight for the auxiliary search direction; the termination weight for the main search direction is 1.5 to 2.5, and the initial weight for the main search direction is 0.3 to 0.7; the termination weight for the auxiliary search direction is 0.3 to 0.7, and the initial weight for the auxiliary search direction is 0.8 to 1.2. This parameter range ensures that the attack coefficient increases from small to large, and the cruise coefficient decreases from large to small, achieving an optimization effect of wide-area exploration in the early stage and fine-grained convergence in the later stage.

[0025] Furthermore, in step 3, the repetitive process of assigning each object to be rescued to the nearest rescue resource and adjusting the deployment location of each rescue resource to the spatial center of all the objects to be rescued under its responsibility terminates when the change in the deployment location of the rescue resources is less than a preset threshold or when a preset number of clustering iterations is reached. This convergence determination method ensures sufficient convergence of clustering while avoiding infinite iteration.

[0026] Preferably, the search area is a two-dimensional plane with rectangular boundaries. The mapping of rescue resource deployment locations exceeding the boundaries back into the search area using topological continuity specifically involves: when the coordinate of a rescue resource in the first coordinate axis direction exceeds the maximum boundary in that direction, subtracting the boundary width from the coordinate; when the coordinate of a rescue resource in the first coordinate axis direction is less than the minimum boundary in that direction, adding the boundary width to the coordinate; and applying the same processing to the second coordinate axis direction. This boundary-crossing processing method maintains the topological continuity of the search space and, combined with adaptive step size adjustment, enables a thorough exploration of the solution space.

[0027] Furthermore, in step 2, determining the auxiliary search direction perpendicular to the main search direction includes: establishing a plane equation with the main search direction as the normal and passing through the current deployment location of the rescue resources; randomly selecting a point within this plane; and calculating the vector from the current deployment location of the rescue resources to the randomly selected point, which serves as the auxiliary search direction. The cruise vector generated through this geometric constraint is strictly perpendicular to the attack vector, providing effective vertical exploration capabilities.

[0028] Preferably, the random selection of a point within the plane specifically involves: in a two-dimensional coordinate system, if the main search direction is not parallel to any coordinate axis, then a value is randomly selected within the boundary range of the second coordinate axis direction of the search area as the second coordinate axis coordinate of the randomly selected point, and the first coordinate axis coordinate of the randomly selected point is solved according to the plane equation; if the main search direction is parallel to the first coordinate axis, then a value is randomly selected within the boundary range of the second coordinate axis direction of the search area as the second coordinate axis coordinate of the randomly selected point, and the first coordinate axis coordinate of the randomly selected point is the same as the first coordinate axis coordinate of the current deployment location of the rescue resources; if the main search direction is parallel to the second coordinate axis, then a value is randomly selected within the boundary range of the first coordinate axis direction of the search area as the first coordinate axis coordinate of the randomly selected point, and the second coordinate axis coordinate of the randomly selected point is the same as the second coordinate axis coordinate of the current deployment location of the rescue resources. This random selection method ensures that the exploration range of the cruise vector is consistent with the boundary of the search area and handles the special case where the main search direction is parallel to the coordinate axis.

[0029] Further, in step 4, updating the step size adjustment factor based on the maximum distribution distance of the objects to be rescued, the deviation between the historical average cluster center and the distribution center of the objects to be rescued, and the ratio of the weight of the main search direction to the weight of the auxiliary search direction, specifically involves: the maximum distribution distance of the objects to be rescued being the maximum distance between any two objects to be rescued; the deviation between the historical average cluster center and the distribution center of the objects to be rescued being the distance between the average of the deployment locations of all rescue resources from the first iteration to the current iteration and the average of the locations of all objects to be rescued; and the step size adjustment factor being the sum of 1 plus 1, the product of the maximum distribution distance of the objects to be rescued, the deviation, and the ratio of the weight of the auxiliary search direction to the weight of the main search direction, the logarithm of the product, and then the sum of 1. This step size adjustment factor design comprehensively considers the spatial dispersion of the objects to be rescued, the deviation between the current deployment scheme and the ideal distribution, and the optimization process, achieving problem-driven adaptive step size adjustment.

[0030] Preferably, the base of the logarithm is 2. A logarithmic function with base 2 ensures the smoothness and numerical stability of the step size adjustment.

[0031] Furthermore, the number of objects to be rescued is between 100 and 300, and the number of rescue resources is between 5 and 15. This range of personnel and platform numbers represents a typical configuration for large-scale maritime search and rescue, validating the practicality of the method.

[0032] Beneficial effects

[0033] The beneficial effects of this invention are:

[0034] (1) By introducing an adaptive step size adjustment factor, taking into account the maximum distribution distance of people falling into the water, the deviation between the cluster center and the distribution center of the people, and the attack / cruise coefficient ratio, the search step size was dynamically adjusted according to the characteristics of the problem itself and the optimization process, which effectively balanced global search and local convergence. The number of convergence iterations was reduced from 74 to 41, and the convergence speed was improved by about 45%.

[0035] (2) The attack vector and cruise vector mechanism of the Golden Eagle optimization algorithm are combined with the KMeans clustering algorithm. The attack vector provides the main driving force for convergence to the optimal solution, and the cruise vector provides vertical exploration capability. By dynamically adjusting the weights of the attack coefficient and cruise coefficient, an optimization strategy of wide-area exploration in the early stage and fine convergence in the later stage is realized. The final rescue distance reaches 22.45, which is better than 24.14 of the KMeans++ method, 22.78 of the Pso-KMeans method, and 27.33 of the GMMs method.

[0036] (3) By adopting a boundary crossing strategy, when the deployment location of the rescue platform exceeds the boundary of the search area, it re-enters the search area from the opposite side, maintaining the topological continuity and integrity of the search space. Combined with adaptive step size adjustment, it achieves full exploration of the solution space, and the final rescue distance is better than 22.52 of the boundaryless processing method.

[0037] (4) By using the KMeans clustering algorithm, the person who fell into the water was assigned to the nearest rescue platform and the location of the rescue platform was adjusted to the spatial center of its service personnel. This achieved the optimal matching between rescue resources and the person to be rescued, significantly reduced the overall rescue distance, and improved the rescue efficiency and survival probability of the person who fell into the water in large-scale maritime search and rescue.

[0038] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0039] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0040] Figure 1 A schematic diagram illustrating the deployment scenario of a maritime search and rescue platform.

[0041] Figure 2 A schematic diagram illustrating the deployment results of the rescue platform.

[0042] Figure 3 A comparison chart of the convergence curves of rescue distance for different deployment methods. Detailed Implementation

[0043] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0044] It should be noted that the technical terms in the following embodiments are defined as follows:

[0045] "People who have fallen into the water" refers to people who need rescue in a maritime accident. "Rescue platform" refers to a floating modular rescue device airdropped by a fixed-wing aircraft. "Attack vector" refers to the main search direction of the rescue platform toward the target location. "Cruise vector" refers to the auxiliary search direction perpendicular to the attack vector. "Step size adjustment factor" refers to the search amplitude parameter that is dynamically adjusted according to the distribution characteristics of people who have fallen into the water and clustering bias.

[0046] The meanings of the labels in the attached diagram are as follows: Figure 1 middle Indicates the location of the i-th person who fell into the water. This indicates the deployment location of the j-th rescue platform, and the gray circles represent the personnel responsible for rescue operations on each platform. Figure 2 The red squares indicate the final deployment location of the rescue platform, the red circles indicate the location of the person who fell into the water, and the blue lines indicate the allocation relationship between the person who fell into the water and their corresponding rescue platform. Figure 3 The horizontal axis represents the number of iterations, and the vertical axis represents the total rescue distance.

[0047] Example 1:

[0048] like Figure 1 As shown, in the two-dimensional search and rescue area Within the area, based on the distribution of the people who fell into the water, a crash zone covering all personnel will be determined. The crash zone will be limited to... The rectangular region, in which , Represents the minimum and maximum boundaries on the x-axis. , This represents the minimum and maximum boundaries on the y-axis. In this embodiment, the search area is set to a 1×1 standardized region, i.e. , , , . Figure 1 People who fell into the water are represented by green circles in the image. Location of the person who fell into the water The rescue platform is indicated by a brown box in the diagram. The deployment location of each rescue platform is used The gray circles indicate the people who need to be rescued by each rescue platform.

[0049] Use number Number the people who fell into the water, number The location of the person who fell into the water is The location of the 200 people who fell into the water is represented as The people who fell into the water were randomly distributed within the accident area, exhibiting both randomness and clustering characteristics. (Using numbers...) Number the rescue platform, number The deployment locations of the rescue platforms are as follows: The locations of the 10 rescue platforms are collectively referred to as... ;No. The rescue platforms responsible for rescuing people who have fallen into the water are recorded as follows: All personnel who fell into the water and were under the responsibility of all platforms were recorded as follows: ,gather The elements in the set satisfy mutual exclusion and cover the entire set:

[0050]

[0051] Initialize the initial deployment location set of 10 rescue platforms And use it as the initial value of the set of optimal deployment locations for the rescue platform. The initial deployment location can be randomly generated within the search area, or the initial cluster center can be selected using the KMeans++ algorithm. The upper right subscript 0 indicates the 0th exploration of the rescue platform, i.e., the initial state. In subsequent equations, the upper right subscript indicates the number of exploration iterations for the rescue platform's location.

[0052] Step 1: Set the number of exploration iterations for the deployment location of the rescue platform. And set the attack parameters for exploration. , With cruise parameters , Attack parameters The weights of the attack vector in the movement step are controlled, and they decrease from the initial value with each iteration. Increment linearly to the termination value This achieves strong convergence towards the optimal solution in the later stages. Cruise parameters. The weights of the cruise vector in the movement step are controlled, and their values ​​change from the initial values ​​with the number of iterations. linearly decrease to the termination value This allows for extensive exploration in the early stages. The first exploration is then set. Step size adjustment factor The step size adjustment factor is dynamically updated in subsequent iterations based on the distribution characteristics of the people who fell into the water and the clustering bias.

[0053] Step 2: In the In the next iteration, firstly... The optimal deployment location set for the rescue platform obtained after the second iteration By randomly swapping the elements within the set, we obtain the target position set for the t-th iteration. Random swapping is achieved through a random permutation function. Implementation, that is ,in It is a random permutation function used for a set of indices. Perform a random rearrangement. Output the rearranged set. A value. For example, when When, it represents the k-th target position. Corresponding to the 3rd optimal position The purpose of random swapping is to increase the diversity of the search and avoid premature convergence of the algorithm.

[0054] For the A rescue platform, based on its Position after the next iteration and the target location to be explored Calculate the first Attack vectors of rescue platforms The formula for calculating the attack vector is as follows: , representing the vector pointing from the current position to the target position, provides the main driving force for convergence towards the optimal solution. The direction of the attack vector determines the main direction of movement of the rescue platform, and its length reflects the distance between the current position and the target position.

[0055] Calculate the first Cruise vector of each rescue platform The cruise vector is located at the attack vector The normal line includes the location of the rescue platform. In the plane, satisfying The cruise vector is obtained through the following process:

[0056] First, let's define the attack vector. The equation of the plane with normal is:

[0057]

[0058] in Let be the coordinates of any point in the plane. It is a constant.

[0059] Then locate the rescue platform Substituting into the equation, we obtain the constant. The value is:

[0060]

[0061] Assume the cruise vector passes through the point When the normal vector If there is a component that is 0, then the x component... Then the boundary range in the y-coordinate direction Random value within ,in In the domain A function that takes random values ​​within the plane, and then the x-coordinate is solved according to the plane equation. .

[0062] Similarly, if the y component Then the boundary range in the x-coordinate direction Random value within Solve for the y-coordinate based on the plane equation. When both x and y components are non-zero, any solution method can be chosen.

[0063] Find the point Then, calculate the cruise vector. The cruise vector provides exploration capabilities perpendicular to the attack vector, preventing the search path from becoming too singular and helping to escape local optima.

[0064] Computational rescue platform Movement step size The movement step size is determined by a weighted combination of the attack vector and the cruise vector, calculated using the following formula:

[0065]

[0066] in , Variables that take random values ​​between 0 and 1 introduce randomness to increase the exploratory power of the search; and The attack coefficient and cruise coefficient are defined as follows:

[0067]

[0068]

[0069] The attack coefficient increases linearly with the number of iterations, while the cruise coefficient decreases linearly with the number of iterations, achieving a dynamic balance between wide-area exploration in the early stage and fine convergence in the later stage. The core innovation of this invention lies in its step size adjustment factor, which is dynamically adjusted based on the distribution characteristics and clustering bias of the people who fell into the water. (Step size adjustment factor) The physical meaning of is the displacement vector of the rescue platform in the current iteration. Its direction is determined by the attack vector and the cruise vector, and its magnitude is controlled by the step size adjustment factor, random variables, and attack / cruise coefficients.

[0070] Calculate the new location of the rescue platform after it is moved. The new position is the result of moving along the direction of the movement step from the current position. Because the movement step includes randomness and a dynamic adjustment mechanism, the new position may exceed the boundary of the search area.

[0071] Perform boundary detection; if the new position is after the move... If the boundary exceeds the specified boundary, it will be processed using a boundary crossing method. The specific rules for this boundary crossing method are as follows:

[0072]

[0073]

[0074] That is when season This is equivalent to crossing from the right boundary and then re-entering from the left boundary; when season This is equivalent to crossing from the left boundary and then re-entering from the right boundary. When season ;when season Cross-boundary processing maintains the topological continuity of the search space, making the search region topologically equivalent to a torus. This avoids the disruption of search space continuity caused by traditional bounce or truncation boundary processing methods, and, together with adaptive step size adjustment, enables a full exploration of the solution space.

[0075] For each rescue platform, repeat the above process of attack vector calculation, cruise vector calculation, movement step size calculation, new position update and boundary processing until the position update of all 10 rescue platforms is completed.

[0076] Step 3: Perform KMeans clustering on the obtained rescue platform locations to obtain a clustered set of rescue platform locations. KMeans clustering uses the following iterative method:

[0077] First, for each person who has fallen into the water, assign them to the nearest rescue platform from the current rescue platform location, i.e. If and only if superscript This represents the number of internal iterations in the KMeans clustering. The allocation process is based on the Euclidean distance principle, ensuring that each person who has fallen into the water is assigned to the nearest rescue platform, which aligns with the behavior of people moving to the nearest rescue platform in real-world rescue scenarios.

[0078] For each group of people requiring rescue by a rescue platform, update the deployment location of the rescue platform as follows: ,in For the first The number of people who have fallen into the water and are to be rescued by each rescue platform. The physical meaning of the update formula is to adjust the position of the rescue platform to the arithmetic mean of the positions of all the people it is responsible for rescuing, i.e., the spatial center or centroid. This adjustment makes the position of the rescue platform tend towards the geometric center of the people it is rescuing, thereby minimizing the average distance between the rescue platform and the people it is rescuing.

[0079] Repeat the above allocation and update process until the rescue platform's location converges. The convergence criterion is that the change in the rescue platform's location is less than a preset threshold or a preset number of clustering iterations is reached. In this embodiment, the number of KMeans clustering iterations is set to V=20. Typically, after 10-15 iterations, the change in the rescue platform's location is less than 10. -4 The clustering process reaches a convergence state. After cluster convergence, the set of deployment locations of the rescue platforms is obtained. And the grouping results of the people who fell into the water The deployment locations of the rescue platform and personnel groups were updated to the clustered locations, i.e. .

[0080] Step 4: Cluster the location set of the rescue platform Calculate the distance function The magnitude of the distance. The distance function is defined as:

[0081]

[0082] This represents the sum of the Euclidean distances from all people who fell into the water to their respective rescue platforms. Distance function. This is a quantitative indicator for evaluating the effectiveness of a rescue platform deployment plan. The smaller the value, the shorter the overall rescue distance and the higher the rescue efficiency. The physical meaning of the distance function is the total distance that all people in the water need to swim to their corresponding rescue platform, which is directly related to the rescue time and the physical exertion of the people in the water.

[0083] Update the optimal deployment location for the rescue platform. The update rules are as follows:

[0084]

[0085] That is, if the current distance function Less than the historical best distance function Then let Otherwise, keep the optimal position unchanged, and let This update rule guarantees the optimal set of deployment locations. It always corresponds to the minimum distance function value that has appeared in history to prevent the optimization process from deteriorating, which reflects the greedy optimization characteristic of the algorithm.

[0086] Update step size adjustment factor The formula for calculating the step size adjustment factor is:

[0087]

[0088] in, , represents the maximum distance between any two people who have fallen into the water, reflecting the spatial dispersion of the people who have fallen into the water. The larger the value, the more dispersed the people are. , represents the Euclidean distance between the average deployment location of all rescue platforms from the first iteration to the current iteration and the average location of all people who fell into the water. It reflects the deviation between the historical average cluster center and the distribution center of people who fell into the water. The larger the value, the further the current deployment plan deviates from the ideal distribution. The ratio of the cruise coefficient to the attack coefficient reflects the balance between exploration and convergence in the current iteration, and this ratio decreases with the number of iterations.

[0089] Step size adjustment factor The study comprehensively considered the spatial distribution characteristics of people who fell into the water (α), the deviation between the current deployment plan and the ideal distribution (β), and the optimization process ( This achieves problem-driven adaptive step size adjustment. When the distribution of people who have fallen into the water is scattered (large α) or the current deployment plan deviates significantly from the ideal distribution (large β), the step size adjustment factor increases, expanding the search range; when the optimization enters the later stage ( When the step size is small, the step size adjustment factor decreases, focusing on local convergence. The introduction of the logarithmic function ensures the smoothness and numerical stability of the step size adjustment, and the base 2 ensures that the step size adjustment factor is within a reasonable range (usually between 1 and 3).

[0090] Step 5: Repeat steps 2 through 4 until 100 iterations are completed, based on the set iteration count T=100. In each iteration, the location of the rescue platform gradually approaches the optimal deployment location through the global search of the Golden Eagle algorithm and the local convergence of KMeans clustering. The optimal deployment location of the rescue platform is obtained after the last iteration. This is the optimal deployment scheme that is ultimately output, enabling adaptive optimization deployment of rescue platforms in large-scale maritime search and rescue operations.

[0091] like Figure 2As shown, 200 people who had fallen into the water were randomly distributed within a 1×1 search area. After applying the adaptive optimization deployment method of this invention, the final deployment locations of the 10 rescue platforms are marked with red squares. The figure shows that each rescue platform is located near the geometric center of the people it is responsible for rescuing. The lines connecting the people to their corresponding rescue platforms (blue straight lines) are relatively short and the distribution is relatively even. There are no instances of some rescue platforms handling too many people or some areas lacking rescue platforms. This indicates that the deployment method of this invention can adaptively adjust the positions of the rescue platforms according to the spatial distribution of the people who have fallen into the water, achieving an optimal match between rescue resources and those to be rescued.

[0092] Using the above technical solution, in the 41st iteration, the distance function The algorithm stabilized at around 22.45, indicating convergence. The overall rescue distance after convergence is 22.45, meaning the total distance from all 200 people in the water to their corresponding rescue platforms is 22.45 units (the search area side length is 1 unit). The mechanism for reducing the overall rescue distance is as follows: This invention uses an adaptive step size adjustment factor. In the early stages of optimization, when the distribution of people in the water is scattered or the cluster center deviates significantly from the distribution center, the search step size is increased, allowing the rescue platform to explore a larger area and avoid getting trapped in local optima. In the later stages of optimization, when the cluster center gradually approaches the distribution center, the search step size is decreased, allowing the rescue platform to finely adjust near the optimal position and accelerate convergence. Simultaneously, the boundary crossing process maintains the topological continuity of the search space, enabling the rescue platform to effectively explore near the boundary, avoiding the fragmentation of the search space caused by traditional boundary processing methods. The attack vector of the Golden Eagle algorithm provides the main driving force for convergence to the optimal solution, while the cruise vector provides exploration capability perpendicular to the main direction. The dynamic weighted combination of the two achieves an effective balance between global search and local convergence.

[0093] like Figure 3 As shown, the comparison data of the rescue distance convergence curves of the adaptive optimization deployment method of the present invention and existing methods further verify the above-mentioned technical effects. From Figure 3As can be seen, at the initial iteration, the rescue distance of this invention is approximately 26, comparable to other methods. This is because in the initial stage, the deployment location of the rescue platform did not adequately explore the distribution of people who had fallen into the water, resulting in a relatively large error. With increasing iterations, the rescue distance of this invention rapidly decreases, reaching approximately 23.5 by the 10th iteration, approximately 22.8 by the 20th iteration, and stabilizing at approximately 22.45 by the 41st iteration, thus achieving convergence. The converged rescue distance is superior to the KMeans++ deployment method's 24.14, the Pso-KMeans deployment method's 22.78, the GMMs deployment method's 27.33, and the Geo-optimized KMeans method without step size adjustment and boundary handling's 22.52. Compared to methods without step size adjustment and boundary handling, this invention requires only 41 convergence iterations, fewer than the required 74, resulting in a convergence speed improvement of approximately 45%. This demonstrates that the adaptive step size adjustment factor and the cross-boundary handling strategy of this invention have significant effects on accelerating convergence speed and improving optimization accuracy.

[0094] Example 2

[0095] The difference from Example 1 is that this example tests the impact of different iteration numbers and different combinations of attack / cruise parameters on the deployment effect of the rescue platform.

[0096] First, the effect of different iteration numbers T was tested. Other parameters remained consistent with Example 1 (200 people who fell into the water, 10 rescue platforms). , , , Comparative experiments were conducted with iteration counts T=50, T=100, and T=150. The results show that when T=50, the algorithm converges on the 35th iteration, with a final rescue distance of approximately 22.6, exhibiting a relatively fast convergence speed but slightly lower accuracy than Example 1. When T=100, the algorithm converges on the 41st iteration, with a final rescue distance of 22.45, consistent with Example 1. When T=150, the algorithm converges on the 42nd iteration, with a final rescue distance of approximately 22.44, achieving accuracy comparable to T=100 but increasing computation time by approximately 50%. These results validate the rationality of setting the number of iterations from 50 to 200: too few iterations (T<50) may lead to insufficient convergence and slightly lower accuracy; too many iterations (T>200) offer limited improvement in accuracy but significantly increase computational cost; T=50-200 represents a reasonable range for balancing convergence accuracy and computational efficiency.

[0097] Next, the effects of different combinations of attack / cruise parameters were tested. Keeping other parameters consistent with Example 1, the following parameter combinations were tested respectively: (1) , , , (2) , , , (Parameters of Example 1); (3) , , , Experimental results show that: the final rescue distance of parameter combination (1) is about 22.7, and the convergence speed is slow (about 55 iterations). This is because the attack coefficient is small, resulting in insufficient convergence ability in the later stage; the final rescue distance of parameter combination (2) is 22.45, and the convergence speed is moderate (41 iterations), with the best effect; the final rescue distance of parameter combination (3) is about 22.5, and the convergence speed is fast (about 35 iterations), but the accuracy is slightly lower. This is because the attack coefficient is too large, resulting in insufficient exploration in the early stage. The above results verify the rationality of the set search control parameter range: effective convergence can be achieved within the range of 1.5-2.5 for the termination value of the main search direction weight and 0.3-0.7 for the initial value, and 0.3-0.7 for the termination value of the auxiliary search direction weight and 0.8-1.2 for the initial value. However, the parameter combination of Example 1 achieves the best balance between convergence speed and accuracy.

[0098] Example 3

[0099] The difference from Example 1 is that this example tests the impact of different numbers of personnel and platforms on the deployment effectiveness of the rescue platform.

[0100] Keep other parameters consistent with Example 1 (T=100, , , , The following scale combinations were tested: (1) 100 people in the water + 5 rescue platforms; (2) 200 people in the water + 10 rescue platforms (configuration of Example 1); (3) 300 people in the water + 15 rescue platforms. The experimental results show that configuration (1) converged at the 38th iteration, with a final rescue distance of approximately 11.2 (the average distance from each person to the rescue platform is approximately 0.112); configuration (2) converged at the 41st iteration, with a final rescue distance of 22.45 (the average distance from each person to the rescue platform is approximately 0.112); and configuration (3) converged at the 45th iteration, with a final rescue distance of approximately 33.8 (the average distance from each person to the rescue platform is approximately 0.113). The above results show that the adaptive optimization deployment method of the present invention can effectively converge under different scales of personnel and platforms, and the average distance from each person to the rescue platform remains basically consistent (approximately 0.112-0.113), verifying the scalability of the method. Meanwhile, as the number of personnel increases, the number of iterations required for convergence increases slightly (from 38 to 45), but the increase is limited, indicating that the convergence speed of the algorithm is not sensitive to the problem size. The above results verify that the method of the present invention has good applicability in the range of 100 to 300 people to be rescued and 5 to 15 rescue resources.

[0101] Comparative Example 1

[0102] A comparative experiment was conducted using the KMeans++ deployment method. KMeans++ is an improved KMeans clustering algorithm that enhances clustering performance by optimizing the selection of initial cluster centers. The specific implementation is as follows: First, a location of a person who has fallen into the water is randomly selected as the initial location of the first rescue platform. Then, for each person who has not yet been selected as an initial location, the minimum distance from that location to a selected initial location is calculated, and the location of the person with the largest minimum distance is selected as the initial location of the next rescue platform. This process is repeated until 10 initial locations are selected. After the initial locations are determined, standard KMeans clustering iterations are performed: each person who has fallen into the water is assigned to the nearest rescue platform, and the location of each rescue platform is updated with the centroid of the person in charge. This process is repeated until convergence.

[0103] Experimental results show that the KMeans++ method converges after approximately 15 clustering iterations, with a final rescue distance of 24.14. Compared to 22.45 in Example 1, the rescue distance increases by 7.5%. The larger rescue distance is due to the fact that the KMeans++ method relies solely on the optimal selection of initial cluster centers, lacking global search capability across the solution space, and is easily trapped in local optima due to the influence of initial values. Although KMeans++'s initial center selection strategy is superior to completely random selection, it still cannot guarantee that the initial centers are close to the global optimum, causing the final convergence position to deviate from the optimum.

[0104] Comparative Example 2

[0105] A comparative experiment was conducted using the Pso-KMeans deployment method. The Pso-KMeans method combines particle swarm optimization (PSO) with KMeans clustering, but does not employ adaptive step size adjustment or boundary crossing handling. Specifically, 10 particles are initialized (each particle represents a set of deployment locations for 10 rescue platforms), each with position and velocity attributes. In each iteration, KMeans clustering is performed on each particle, and the distance function is calculated as the fitness. The particle positions are updated according to the velocity and position update formulas of the PSO algorithm. Particles exceeding the boundary are truncated, i.e., their positions are set to the boundary values.

[0106] Experimental results show that the Pso-KMeans method converges after approximately 40 iterations, with a final rescue distance of 22.78. Compared to 22.45 in Example 1, the rescue distance increased by 1.5%, while the convergence speed remained comparable. The slightly larger rescue distance is due to the following: the inertia weight in the Pso-KMeans method's velocity update formula is a fixed value or linearly decreasing, failing to dynamically adjust according to the problem's characteristics (distribution of people who fell into the water and clustering bias). This results in unreasonable search step sizes in some iterations, affecting local search capabilities. Furthermore, the truncated boundary treatment disrupts the continuity of the search space, preventing the effective exploration of parts of the solution space.

[0107] Comparative Example 3

[0108] A comparative experiment was conducted using the Gaussian Mixture Models (GMMs) deployment method. GMMs are a probability distribution-based clustering algorithm that assumes the location of a person who has fallen into the water follows a mixture of multiple Gaussian distributions. The specific implementation is as follows: Initialize the mean (corresponding to the rescue platform location), covariance matrix, and mixing coefficients of 10 Gaussian distributions; iteratively optimize the parameters using the EM (Expectation-Maximization) algorithm: the E-step calculates the posterior probability of each person belonging to each Gaussian distribution, and the M-step updates the Gaussian distribution parameters based on the posterior probability; iterates until the log-likelihood function converges.

[0109] Experimental results show that the GMMs method converges after approximately 30 EM iterations, with a final rescue distance of 27.33. Compared to 22.45 in Example 1, the rescue distance increases by 21.7%, significantly worse than the present invention. The reason for the larger rescue distance is that the GMMs method assumes that the location of people in the water follows a Gaussian distribution, but in actual maritime accidents, the distribution of people in the water usually exhibits both randomness and clustering, failing to satisfy the Gaussian distribution assumption, resulting in poor clustering performance. Furthermore, the GMMs method optimizes by maximizing the log-likelihood function, rather than minimizing the overall rescue distance; these two objectives are not entirely consistent, causing the optimization result to deviate from actual needs.

[0110] Comparative Example 4

[0111] A comparative experiment was conducted using the Geo-optimized KMeans method without step size adjustment and boundary handling. This method combines the Golden Eagle algorithm with KMeans clustering, but does not use an adaptive step size adjustment factor (the step size adjustment factor is fixed at s=1) or cross-boundary handling (the positions exceeding the boundary are truncated). Other parameters are consistent with those in Example 1.

[0112] Experimental results show that the method converges after approximately 74 iterations, with a final rescue distance of 22.52. Compared to Example 1, the convergence speed is about 80% slower (from 41 iterations to 74 iterations), and the final rescue distance is slightly larger by 0.3%. These results verify the effectiveness of the adaptive step size adjustment factor and the boundary crossing processing strategy of this invention: the adaptive step size adjustment factor dynamically adjusts the search range based on the distribution characteristics of the people who have fallen into the water and clustering bias, expanding the search range in the early stages of optimization and focusing on local convergence in the later stages, significantly accelerating the convergence speed; the boundary crossing processing maintains the topological continuity of the search space, enabling the rescue platform to effectively explore near the boundary, avoiding the fragmentation of the search space caused by truncation processing, and further improving the optimization accuracy.

[0113] Based on the experimental results of Examples 1-3 and Comparative Examples 1-4, the adaptive optimization deployment method of the present invention is superior to existing methods in terms of convergence speed and optimization accuracy. It can effectively solve the technical problems of unreasonable deployment location of rescue platforms and excessively long overall rescue distance in large-scale maritime search and rescue, and significantly improve rescue efficiency and the survival probability of people who fall into the water.

[0114] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. An adaptive optimization method for deploying a maritime search and rescue platform, comprising acquiring spatial location information of multiple objects to be rescued, and setting initial deployment locations for multiple rescue resources, characterized in that, It also includes the following steps: Step 1: Set the iteration termination condition and search control parameters for the optimization algorithm; Step 2: In each iteration, randomly perturb the current set of optimal rescue resource deployment locations to generate a set of target locations to explore; For each rescue resource, based on its current deployment location and the location of the corresponding exploration target, determine the main search direction toward the exploration target and the auxiliary search direction perpendicular to the main search direction; Calculate the step size adjustment factor based on the spatial distribution characteristics of the objects to be rescued and the deviation between the current deployment plan and the ideal distribution; Based on the main search direction, auxiliary search direction, step size adjustment factor, and the weights of the main search direction and auxiliary search direction, the movement step size of the rescue resources is calculated, and the deployment position of the rescue resources is updated. Among them, the weight of the main search direction increases with the optimization process, and the weight of the auxiliary search direction decreases with the optimization process. When rescue resources are deployed outside the search area boundary, they are mapped back into the search area using topological continuity. Step 3: Based on the principle of minimum spatial distance, assign each object to be rescued to the nearest rescue resource, establishing an allocation relationship between rescue resources and objects to be rescued; adjust the deployment location of each rescue resource to the spatial center of all the objects to be rescued that it is responsible for rescuing; repeat this allocation and adjustment process until the deployment locations of rescue resources converge. Step 4: Calculate the total distance from all objects to be rescued to their corresponding rescue resources as an evaluation index; if the current total distance is less than the historical best total distance, update the set of optimal rescue resource deployment locations; update the step size adjustment factor based on the maximum distribution distance of the objects to be rescued, the deviation between the historical average cluster center and the distribution center of the objects to be rescued, and the ratio of the weight of the main search direction to the weight of the auxiliary search direction. Step 5: Repeat steps 2 to 4 until the iteration termination condition is met, and output the optimal set of rescue resource deployment locations.

2. The adaptive optimization method for deploying a maritime search and rescue platform according to claim 1, characterized in that, The iteration termination condition is when the number of iterations reaches 50 to 200.

3. The adaptive optimization method for deploying a maritime search and rescue platform according to claim 1, characterized in that, The search control parameters include the initial weight of the main search direction, the termination weight of the main search direction, the initial weight of the auxiliary search direction, and the termination weight of the auxiliary search direction. The termination weight of the main search direction is 1.5 to 2.5, and the initial weight of the main search direction is 0.3 to 0.7; the termination weight of the auxiliary search direction is 0.3 to 0.7, and the initial weight of the auxiliary search direction is 0.8 to 1.

2.

4. The adaptive optimization method for deploying a maritime search and rescue platform according to claim 1, characterized in that, In step 3, the repeated process of assigning each object to be rescued to the nearest rescue resource and adjusting the deployment location of each rescue resource to the spatial center of all the objects to be rescued under its responsibility terminates when the change in the deployment location of the rescue resource is less than a preset threshold or when a preset number of clustering iterations is reached.

5. The adaptive optimization method for deploying a maritime search and rescue platform according to claim 1, characterized in that, The search area is a two-dimensional plane with rectangular boundaries. The method of mapping the deployment locations of rescue resources that exceed the boundaries back into the search area through topological continuity is as follows: when the coordinate of a rescue resource in the first coordinate axis direction exceeds the maximum boundary in the first coordinate axis direction, the coordinate is subtracted from the boundary width in the first coordinate axis direction; when the coordinate of a rescue resource in the first coordinate axis direction is less than the minimum boundary in the first coordinate axis direction, the coordinate is added to the boundary width in the first coordinate axis direction; the same processing is performed on the second coordinate axis direction.

6. The adaptive optimization method for deploying a maritime search and rescue platform according to claim 1, characterized in that, In step 2, determining the auxiliary search direction perpendicular to the main search direction includes: establishing a plane equation with the main search direction as the normal and passing through the current deployment location of the rescue resources; randomly selecting a point in the plane; and calculating the vector from the current deployment location of the rescue resources to the randomly selected point as the auxiliary search direction.

7. The adaptive optimization method for deploying a maritime search and rescue platform according to claim 6, characterized in that, The process of randomly selecting a point within the plane specifically involves the following steps: In a two-dimensional coordinate system, if the main search direction is not parallel to any coordinate axis, a value is randomly selected within the boundary range of the second coordinate axis direction of the search area as the second coordinate axis coordinate of the randomly selected point, and the first coordinate axis coordinate of the randomly selected point is solved according to the plane equation; if the main search direction is parallel to the first coordinate axis, a value is randomly selected within the boundary range of the second coordinate axis direction of the search area as the second coordinate axis coordinate of the randomly selected point, and the first coordinate axis coordinate of the randomly selected point is the same as the first coordinate axis coordinate of the current deployment location of the rescue resources; if the main search direction is parallel to the second coordinate axis, a value is randomly selected within the boundary range of the first coordinate axis direction of the search area as the first coordinate axis coordinate of the randomly selected point, and the second coordinate axis coordinate of the randomly selected point is the same as the second coordinate axis coordinate of the current deployment location of the rescue resources.

8. The adaptive optimization method for deploying a maritime search and rescue platform according to claim 1, characterized in that, In step 4, updating the step size adjustment factor based on the maximum distribution distance of the objects to be rescued, the deviation between the historical average cluster center and the distribution center of the objects to be rescued, and the ratio of the weight of the main search direction to the weight of the auxiliary search direction specifically involves: the maximum distribution distance of the objects to be rescued being the maximum distance between any two objects to be rescued; the deviation between the historical average cluster center and the distribution center of the objects to be rescued being the distance between the average of the deployment locations of all rescue resources from the first iteration to the current iteration and the average of the locations of all objects to be rescued; and the step size adjustment factor being the sum of 1, the product of the maximum distribution distance of the objects to be rescued, the deviation, and the ratio of the weight of the auxiliary search direction to the weight of the main search direction, plus 1, taking the logarithm, and then adding 1.

9. The adaptive optimization method for deploying a maritime search and rescue platform according to claim 8, characterized in that, The base of the logarithm is 2.

10. The adaptive optimization method for deploying a maritime search and rescue platform according to claim 1, characterized in that, The number of people to be rescued is between 100 and 300, and the number of rescue resources is between 5 and 15.

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