Multi-base cooperative detection method based on improved marine predator algorithm

Abstract

The invention relates to the field of artificial intelligence, and discloses a multi-base cooperative detection method based on an improved marine predator algorithm. The method comprises the following steps: adopting a Tent chaotic sequence to guide initialization so as to improve the global exploration capability; dynamically dividing a three-stage search process according to the effective dimension, and adaptively prolonging the global exploration time; constructing Levy disturbance vector enhanced directivity search of chaotic modulation; designing a composite fitness function containing key area weighting and spacing penalty; and an FADs effect and an elite solution library linkage mechanism are introduced to break through convergence stagnation. The system comprises a parameter input module, an environment loading module, a probability calculation module, a chaos generation module, a stage control module, a disturbance modulation module, a fitness evaluation module and the like. The convergence speed and the key sea area detection efficiency of the multi-base sonar layout scheme are improved, and experiments show that the convergence speed is improved, and the key area detection probability is improved.

Description

Technical Field

[0001] This invention belongs to the field of artificial intelligence, specifically relating to a multi-base cooperative detection method based on an improved marine predator algorithm. Background Technology

[0002] With the continuous growth of underwater target detection needs in military defense, marine resource exploration, and underwater unmanned system collaboration, multistatic sonar cooperative detection technology has become a core support for modern underwater sensing systems due to its advantages such as wide coverage, strong anti-interference capability, and high concealment. This technology constructs a spatially heterogeneous detection network by distributing multiple sonar transmitting and receiving platforms. Its effectiveness highly depends on the global optimization capability of array parameters, including the joint configuration of platform three-dimensional coordinates, heading angle, and operating frequency. However, existing optimization methods generally rely on traditional metaheuristic algorithm frameworks, which generally suffer from structural defects such as slow convergence speed, susceptibility to local optima, and insufficient solution space exploration when facing high-dimensional, nonlinear, and strongly coupled multistatic sonar parameter spaces. These shortcomings make it difficult to meet the dual requirements of detection accuracy and real-time response in complex marine environments.

[0003] Among them, the improved scheme based on the Marine Predator Algorithm (MPA) introduces general techniques such as Tent chaotic mapping, Levy flight and FADs effect optimization in initialization strategy, search phase division and perturbation mechanism, but its essence still remains at the empirical adjustment of parameters. It fails to build a customized optimization mechanism for the dynamic environmental noise, high-dimensional parameter coupling and multi-target conflict unique to multi-base sonar scenarios.

[0004] The existing three-stage search strategy divides the exploration, development and escape stages according to a fixed iteration ratio, ignoring the characteristic that the complexity of the understanding space increases exponentially with the number of platforms. This leads to a rigid search step size and a lack of environmental adaptability in the mid-to-late iterations. At the same time, the fitness function design focuses on a single indicator, such as maximizing the total detection probability, and lacks a coordinated consideration of key area protection, platform concealment constraints and overall coverage balance. As a result, the optimization results are difficult to balance tactical flexibility and survivability in actual combat deployment.

[0005] Existing technologies also have shortcomings in terms of model completeness and algorithm interpretability: the calculation of bistatic sonar detection probability lacks a unified formula, resulting in ambiguity in the fitness assessment basis; the values ​​of key parameters such as chaotic weight vector and elite matrix update coefficient lack physical or statistical basis, weakening the robustness of the algorithm; the connection logic between the Tent-Levy perturbation vector generation mechanism and the FADs effect optimization stage and the three-stage framework is not clarified, causing a break in the algorithm flow; especially without comparing with mainstream algorithms such as particle swarm optimization and gray wolf optimization in core indicators such as convergence speed and detection performance improvement, it is difficult to establish the uniqueness and advancement of its technical contribution.

[0006] Therefore, there is an urgent need for an improved marine predator algorithm that deeply integrates the dynamic characteristics of the marine environment, supports multi-objective collaborative optimization, and has the ability to adaptively reduce high-dimensional parameters, so as to overcome the technical bottlenecks in the current multi-base sonar array optimization, such as incomplete solution space coverage, low convergence efficiency, and frequent local optimum traps. Summary of the Invention

[0007] This invention provides a multi-base cooperative detection method based on an improved marine predator algorithm, including: acquiring the number of sonar platforms to be deployed, the boundary coordinates of the movable range of each platform, underwater environmental sound velocity profile data, background noise power spectral density, and a preset set of geographic coordinates of key detection areas;

[0008] Based on the bistatic sonar range model, an instantaneous detection probability calculation function for any grid point in space is established for any combination of transmitting and receiving platforms.

[0009] Perform spatial discretization operations to divide the entire operational sea area into a regular two-dimensional grid structure;

[0010] Iterate through all possible combinations of transmitting and receiving platforms and calculate the probability that each grid point will be successfully detected by the transmitting and receiving pair.

[0011] Its core lies in building a multi-platform sonar array collaborative optimization system that is oriented towards complex underwater environments and has dynamic adaptive capabilities and scenario customization mechanisms. The system has a mechanism for dynamically dividing the search phase based on effective dimensions. The effective dimension is defined as the total number of sonar platforms participating in the optimization multiplied by the spatial degrees of freedom of each platform, and then multiplied by a correction coefficient that characterizes the complexity of the environment. The correction coefficient is jointly determined by the standard deviation of underwater topographic relief and the root mean square of the sound velocity gradient.

[0012] The search phases are dynamically divided based on the effective dimensions, including: the first phase's duration algebra is set to the integer part of the quotient obtained by multiplying the total maximum number of iterations by the square root of the effective dimension and then dividing by one hundred, simulating the large-scale cruising behavior of apex predators and performing a global coarse search; the second phase's duration algebra is set to two-thirds of the remaining part after subtracting the first phase's algebra from the total maximum number of iterations, simulating the predator's encirclement and pursuit behavior after discovering prey tracks and performing a local fine search; the third phase occupies all remaining iterations, introducing a FADs effect optimization mechanism to simulate the phenomenon of oceanic floating debris accumulation areas inducing predators to change their search paths.

[0013] Preferably, the construction of the adaptive Lévy perturbation vector for Tent chaotic modulation specifically includes:

[0014] During the first phase of the global coarse search, a set of independent Lévy random numbers with the same dimension as the variable to be optimized is generated;

[0015] Simultaneously generate a set of Tent chaos numbers of the same dimension;

[0016] The adaptive Lévy perturbation vector is obtained by multiplying each Lévy random number element by the absolute value of the Tent chaos number at the corresponding position, and then multiplying it by a scaling factor that decreases linearly with the number of iterations.

[0017] Preferably, the adaptive Lévy perturbation vector retains the long-tailed jump characteristics of Lévy flight to maintain global exploration capability, while suppressing excessive random walks through nonlinear modulation of the chaotic sequence, making the search trajectory more directional.

[0018] Preferably, the establishment of the linkage mechanism between the elite library with threshold screening and the FADs effect specifically includes:

[0019] An elite solution library is set up, with a fixed capacity of 1 / 10 of the population size, and a rolling update strategy is adopted.

[0020] When the fitness of a new solution exceeds 110% of the lowest fitness value in the library, the new solution replaces the solution with the lowest fitness value in the library.

[0021] The system maintains a sliding window of length 10 to record the global optimal fitness value of the last 10 generations. After each iteration, the latest value is pushed into the window, the oldest value is popped out, and the difference between the maximum and minimum values ​​in the window is calculated.

[0022] If the difference is less than the current optimal fitness value multiplied by 0.001, then the FADs effect triggering condition is met.

[0023] This mechanism effectively injects historical high-quality solution information into the later stages of algorithm convergence, restarting the local search and breaking through the performance stagnation bottleneck.

[0024] Preferably, the binding of the physical meaning of the full-process parameters and their dynamic adaptive adjustment specifically include:

[0025] Throughout the algorithm process, all parameters are bound to physical meanings, such as binding the transmitter level to the maximum effective radiated power calibrated by the sonar equipment at the factory, and binding the receiver directivity index to the physical aperture and operating frequency of the sonar array, etc.

[0026] The search parameters at each stage are dynamically and adaptively adjusted.

[0027] The maximum number of iterations is dynamically adjusted based on factors such as the total number of sonar platforms and the level of environmental complexity.

[0028] By adopting this dynamic adaptive adjustment strategy for parameters throughout the entire process, the reliance on experience values ​​is eliminated, and the robustness and generalization ability of the algorithm in different combat scenarios are improved.

[0029] Preferably, the specific strategies and implementations of the search phase include:

[0030] In the first stage, a global coarse search is performed to simulate the large-scale cruising behavior of the top predator. The position update of each individual is guided by the current best individual and superimposed with a random step size vector that follows a Lévy distribution. The Lévy step size vector is amplitude modulated by a Tent chaotic sequence. Specifically, a set of independent Lévy random numbers with the same dimension as the variable to be optimized is generated, and a set of Tent chaotic numbers with the same dimension is generated. The Lévy random numbers are multiplied element by element by the absolute value of the Tent chaotic number at the corresponding position, and then multiplied by a scaling factor that decreases linearly with the number of iterations to obtain an adaptive Lévy perturbation vector.

[0031] In the second stage, a local fine search is performed to simulate the behavior of predators surrounding and chasing prey after discovering their tracks. The individual position update uses the difference vector between the current best individual and another randomly selected individual as the guiding direction, and an adaptive inertial weight adjustment mechanism is introduced. The scaling factor of the difference vector is dynamically determined by the ratio of the current individual fitness value to the population average fitness value.

[0032] In the third stage, an optimization mechanism based on the effect of FADs is introduced to simulate the phenomenon that marine floating debris accumulation areas induce predators to change their search paths. This mechanism is activated only when a specific trigger condition is met. The trigger condition is that the improvement of the optimal fitness value is less than 1‰ for ten consecutive generations. Once triggered, an individual is randomly selected from the current population and subjected to additional positional perturbation.

[0033] Preferably, the setting of dual termination conditions includes:

[0034] The first termination condition is reaching the preset maximum number of iterations. The maximum number of iterations is preset based on the total number of sonar platforms and the environmental complexity level. For each additional platform, the maximum number of iterations increases by 500 generations; for each increase in environmental complexity level, the maximum number of iterations increases by 300 generations.

[0035] The second termination condition is that the globally optimal fitness value does not improve for 50 consecutive generations.

[0036] When any termination condition is met, the algorithm stops running and outputs the currently recorded global optimal solution as the final multi-site sonar platform deployment scheme. This scheme includes the precise latitude and longitude coordinates or Cartesian coordinates relative to a reference point for each platform, and can be directly used by the command and control system to issue deployment commands. Preferably, the specific process for outputting the final multi-site sonar platform deployment scheme is as follows:

[0037] The global optimal solution vector is split into P groups of two-dimensional coordinates in platform order. If the input coordinate system is latitude and longitude, it is output directly.

[0038] If it is a Cartesian coordinate system, it is converted into geographic coordinates based on the latitude and longitude of the reference point and the projection parameters;

[0039] Generate a standard-format deployment instruction file, which includes fields such as the platform number, target coordinates, estimated arrival time window, and route planning suggestions for each platform.

[0040] The file is transmitted to an external command and control system through the optimal solution output interface. The interface supports multiple data formats such as JSON, XML, and CSV, and provides an API for other systems to call.

[0041] Preferably, the system includes:

[0042] The sonar platform parameter input module is used to receive hardware parameters set by the user, such as the number of platforms, maneuvering range, transmission power, and receiving sensitivity.

[0043] The environmental data loading module is used to import environmental information such as digital depth maps, sound velocity profile files, and noise maps;

[0044] The detection probability calculation engine calculates the probability of successful detection of any transceiver pair at any grid point in real time based on the bistatic sonar equations.

[0045] The chaos initialization generator is responsible for generating the Tent chaotic sequence and completing the spatial mapping of the initial population.

[0046] The dynamic stage division controller calculates the duration algebra of each stage in real time based on the effective dimensions and controls the flow jump accordingly.

[0047] An adaptive perturbation modulation unit generates perturbation vectors that meet the requirements of the current search strategy at different stages;

[0048] The FADs effect triggers a judge to monitor the convergence state and activates the elite de-perturbation mechanism when the conditions are met.

[0049] An elite solution library storage maintains a historical set of high-quality solutions and performs rolling updates.

[0050] The composite fitness evaluator calculates a comprehensive score for each candidate solution based on a weighted formula.

[0051] The optimal solution output interface exports the final layout coordinates in a standard format for external systems to use.

[0052] Preferably, the collaborative workflow of the various modules of the system is as follows:

[0053] Users first input parameters such as the number of platforms, the maximum maneuver radius of each platform, the transmitter level, and the receiver noise figure through the sonar platform parameter input module.

[0054] Subsequently, the environmental data loading module reads the pre-stored marine environment database and extracts data such as depth grid, sound velocity vertical profile, and background noise spectrum of the target sea area;

[0055] The detection probability calculation engine constructs a spatial grid based on the above parameters and pre-calculates the basic detection probability table of all possible transmit and receive pairs at each grid point, storing it in memory for subsequent fast querying;

[0056] The chaos initialization generator starts, generates an initial population, and passes it to the main optimization loop;

[0057] The dynamic phase division controller calculates T1, T2, and T3 and initializes the phase counter; after the main loop starts, each generation executes the following sequentially: the composite fitness evaluator calculates the fitness of all individuals in the current population;

[0058] The elite retention module selects the top 10% of individuals; the dynamic phase division controller determines the current phase.

[0059] The adaptive perturbation modulation unit, differential update module, or FADs perturbation module performs position updates based on the stage identifier;

[0060] The boundary reflection module corrects out-of-bounds coordinates; the FADs effect triggering judge checks the convergence status and decides whether to activate the perturbation.

[0061] The elite solution library memory updates the historical best solution set; the global best recorder updates the best solution information.

[0062] The termination condition judgment module checks whether the stopping criteria are met.

[0063] If the process does not terminate, it proceeds to the next generation; if it terminates, the optimal solution output interface generates a deployment plan file and transmits it to the command system.

[0064] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0065] 1. By introducing a dynamic three-stage partitioning mechanism based on effective dimensions, the problem that traditional fixed-ratio partitioning cannot adapt to changes in the number of platforms and environmental complexity is solved, enabling the algorithm to automatically extend the global exploration time when the solution space expands, thus avoiding premature convergence.

[0066] 2. By constructing an adaptive Lévy perturbation vector with Tent chaotic modulation, the low search efficiency caused by the excessive randomness of the original Lévy flight is overcome, and the search directionality is enhanced while retaining the long-distance jump capability.

[0067] 3. By designing a composite fitness function that combines weighted evaluation of key areas with penalties for platform spacing, we achieved targeted enhancement of detection effectiveness in key sea areas and rigid constraints on safe distances between platforms;

[0068] 4. By establishing an elite solution library with threshold screening and a linkage mechanism with the FADs effect, historical high-quality solution information is effectively injected in the later stage of algorithm convergence, restarting the local search vitality and breaking through the performance stagnation bottleneck.

[0069] 5. By binding the physical meaning of all parameters throughout the process and dynamically and adaptively adjusting them, the algorithm eliminates reliance on empirical values ​​and improves its robustness and generalization ability in different combat scenarios. Attached Figure Description

[0070] Figure 1 This is a schematic diagram of the overall technical architecture of a multi-base cooperative detection method based on an improved marine predator algorithm proposed in this invention;

[0071] Figure 2 This is a schematic diagram of the core principle framework of the present invention, which integrates chaotic initialization, dynamic three-stage search and adaptive Lévy perturbation modulation.

[0072] Figure 3 This is a flowchart illustrating the logical flow of sonar platform deployment parameter input and environmental data loading into the detection probability calculation engine in this invention.

[0073] Figure 4 This is a schematic diagram of the data flow and deployment instruction transmission between the global optimal solution output interface and the external command and control system in this invention; Detailed Implementation

[0074] refer to Figures 1 to 4 A multi-base cooperative detection method based on an improved marine predator algorithm is proposed. Its core lies in constructing a multi-platform sonar array cooperative optimization system that is oriented towards complex underwater environments and has dynamic adaptive capabilities and scene customization mechanisms.

[0075] This system breaks through the static parameter dependence of traditional metaheuristic algorithms in initialization strategy, search phase division and perturbation mechanism. It addresses the inherent challenges in multi-base sonar detection missions, such as the nonlinear growth of solution space dimension with the number of platforms, the differentiation of detection priorities in target areas, and the non-uniform distribution of detection probability caused by environmental noise and propagation attenuation. It proposes a complete technical solution that integrates chaotic sequence-guided initialization, dynamic proportional three-stage search architecture, adaptive Lévy perturbation modulation mechanism and composite fitness evaluation system based on key area weighting.

[0076] This invention reconstructs the core computational module of the marine predator algorithm, enabling it to autonomously adjust its search behavior based on the current iteration process and population convergence status. This ensures global exploration capabilities while enhancing local development accuracy, ultimately achieving efficient optimization of spatial deployment schemes for multi-base sonar platforms and improving the comprehensive detection coverage efficiency of specific key sea areas.

[0077] In one embodiment of the present invention, the method includes acquiring the number of sonar platforms to be deployed, the boundary coordinates of the movable range of each platform, underwater environmental sound velocity profile data, background noise power spectral density, and a preset set of geographic coordinates for key detection areas. Further, based on a bistatic sonar range model, an instantaneous detection probability calculation function is established for any combination of transmitting and receiving platforms at any grid point in space. This function takes the transmitter level, receiver directivity index, propagation loss, noise level, and detection threshold as input variables, and outputs the probability value of successful detection of that grid point by the transmitting and receiving pair. The propagation loss is quantified using a joint model of spherical spread and frequency-dependent absorption attenuation, and the absorption coefficient is calculated in real time using empirical formulas based on seawater temperature, salinity, and pressure. The detection threshold is set as a fixed signal-to-noise ratio threshold, the value of which is determined based on the hardware sensitivity calibration results of the sonar equipment.

[0078] After acquiring the aforementioned basic parameters, the system first performs a spatial discretization operation, dividing the entire operational sea area into a regular two-dimensional grid structure, with each grid cell representing a minimum detection and assessment unit. The grid resolution is determined based on the sonar system's maximum effective range and the smallest resolvable target size, and is typically set to 1 / 50 of the maximum effective range.

[0079] For each grid point, the system iterates through all possible combinations of transmitting and receiving platforms and calculates the instantaneous detection probability of the transceiver pair at that point.

[0080] In the calculation, the source power is taken as the maximum effective radiated power of the sonar equipment as specified by the manufacturer, in decibels.

[0081] The receiver directivity index is derived from the Rayleigh criterion based on the physical aperture of the sonar array and the operating frequency.

[0082] The propagation loss is composed of the geometric extension term and the medium absorption term. The geometric extension term is calculated according to the attenuation law of spherical waves, while the medium absorption term is based on the Franz formula. After inputting the current water depth, temperature and salinity parameters, the attenuation value per kilometer is output, and then multiplied by the actual propagation path length to obtain the total absorption loss.

[0083] The noise level is obtained by integrating the background noise power spectral density provided by the environmental data loading module after bandpass filtering, with the integration interval being the center frequency ±10%. The detection threshold is uniformly set to 15dB, which is derived from the statistical average of the signal-to-noise ratio decision threshold of a typical active sonar system.

[0084] After substituting all parameters into the bistatic sonar equations, the output value is mapped to the 0-1 interval through the logistic compression function, which serves as the effective detection probability of the transceiver pair at that grid point.

[0085] In one embodiment of the present invention, the method abandons the random uniform sampling strategy in the initialization phase and instead uses a chaotic sequence generated based on the Tent mapping to guide the initial population position. Specifically, a one-dimensional Tent chaotic sequence with a length equal to the population size is first constructed, and its iterative formula is defined as follows: when the sequence element is less than 0.5, the next element is equal to twice the current element; when the sequence element is greater than or equal to 0.5, the next element is equal to twice one minus the current element. This sequence is then filled into a two-dimensional matrix row by row, and the number of columns is equal to the total number of variables to be optimized, i.e., the sum of the horizontal and vertical degrees of freedom of all sonar platforms.

[0086] Subsequently, each column of the matrix is ​​normalized to its minimum and maximum values, mapping it to the physical value range of the corresponding variable, thus obtaining an initial solution set that is ergodic and non-periodic. This initialization method effectively avoids the initial clustering phenomenon of the population getting trapped in local optima, improving the global exploration efficiency in the early stages of the algorithm.

[0087] The specific implementation steps of the initialization process are as follows:

[0088] The first step is to set the initial seed value X0 to 0.23, which is within the open interval of 0-1 and avoids the fixed point of 0.5;

[0089] The second step is to iteratively generate N chaotic values ​​according to the Tent mapping formula, where N is the preset population size, which is usually between 50 and 200.

[0090] The third step is to fill the generated one-dimensional sequence into rows in order. In the two-dimensional matrix, M is the total number of individuals in the population, and D is the dimension of the optimization variable, which is equal to the number of platforms multiplied by 2;

[0091] The fourth step is to perform normalization independently on each column of the matrix, calculate the maximum and minimum values ​​of that column, and then apply the linear transformation formula. The original chaotic values ​​are mapped to the physical feasible domain of the corresponding coordinates. For example, if the allowable range of the horizontal coordinate of a platform is 0 to 1000 meters, then the mapping coefficient a takes the value of 1000 and b takes the value of 0.

[0092] The fifth step is to apply boundary fine-tuning to the mapped coordinate values ​​to ensure that the initial position of all platforms is strictly within the user-specified maneuver range. If any boundary violation occurs, the nearest boundary point substitution strategy is used for correction.

[0093] The sixth step involves using the resulting M sets of coordinate vectors as the initial population input for subsequent optimization processes. Compared to traditional random sampling, this initialization mechanism achieves near-uniform coverage in low-dimensional spaces and exhibits stronger spatial filling and non-repetition in high-dimensional spaces, effectively reducing the redundancy of the initial solution set and laying a diverse foundation for subsequent searches.

[0094] In one embodiment of the present invention, the method divides the entire optimization process into three consecutive and mutually exclusive search phases. The duration algebra of each phase is no longer allocated in a fixed proportion, but is dynamically calculated based on the effective dimension of the current solution space. The effective dimension is defined as the total number of sonar platforms participating in the optimization multiplied by the spatial degrees of freedom of each platform, and then multiplied by a correction coefficient characterizing the environmental complexity. This coefficient is jointly determined by the standard deviation of underwater topographic relief and the root mean square of the sound velocity gradient.

[0095] The first-stage sustainability algebra is set to the integer part of the quotient obtained by multiplying the total maximum number of iterations by the square root of the effective dimension and then dividing by one hundred; the second-stage sustainability algebra is set to two-thirds of the remainder after subtracting the first-stage algebra from the total maximum number of iterations; the third stage occupies all remaining iterations. This dynamic partitioning mechanism ensures that when the number of platforms increases or the environmental complexity rises, causing a sharp expansion of the solution space, the algorithm automatically extends the global exploration time, preventing the loss of high-quality solution domains due to prematurely switching to local development.

[0096] The specific implementation process for dynamic phase division is as follows:

[0097] First, the system reads the total number of sonar platforms P input by the user, which typically ranges from 3 to 10.

[0098] Secondly, calculate the basic dimensions. Next, the topographic elevation data and sound velocity profile data of the current sea area are extracted from the environmental data loading module, and the standard deviation of topographic relief is calculated. With the root mean square of the sound speed gradient Both are expressed in meters and meters per second per meter; next, the environmental complexity correction factor is calculated. Then, calculate the effective dimensions. Then, the total maximum number of iterations is calculated according to the preset rules. Then, the number of iterations in the first stage is calculated. Then calculate the number of iterations in the second stage. Finally, the number of iterations in the third stage. The system maintains a global counter, which increments after each iteration and is synchronized with the current counter. , The algorithm compares data to determine its current stage and activates the corresponding search strategy module. This dynamic partitioning mechanism allows the algorithm to quickly enter a fine-grained search phase in simple scenarios such as a flat seabed or constant sound speed, while automatically extending the global exploration period in complex scenarios such as steep seamounts or environments with strong latitudinal shifts, thus improving the algorithm's adaptability to different combat environments.

[0099] In one embodiment of the invention, the method performs a global coarse search in the first phase, simulating the large-scale cruising behavior of apex predators. In this phase, the position update of each individual is guided by the current best individual and superimposed with a random step size vector following a Lévy distribution. This Lévy step size vector is not directly sampled and generated, but rather its amplitude is modulated using a Tent chaotic sequence.

[0100] The specific operation is as follows: First, generate a set of independent Lévy random numbers with the same dimension as the variable to be optimized, with a fixed scale parameter of 1.5; simultaneously, generate a set of Tent chaotic numbers with the same dimension; multiply each Lévy random number element by the absolute value of the Tent chaotic number at the corresponding position, and then multiply by a scaling factor that decreases linearly with the number of iterations, with an initial value of 0.8 and a final value of 0.1. The perturbation vector after this modulation retains the long-tailed jump characteristic of Lévy flight to maintain global exploration capability, while suppressing excessive random walks through nonlinear modulation of the chaotic sequence, making the search trajectory more directional.

[0101] The specific mathematical expression for the first-stage position update is as follows: Let the position update in the first stage be... The generation The position vectors of each individual are The current global optimal position is The dimensions to be optimized are First, generate Villevian random vector Secondly, generating 3D Tent Chaotic Vector Its generation method is the same as the initialization stage, but an independent seed sequence is used to ensure randomness; next, the modulation coefficient vector is calculated. Then, calculate the scaling factor. Next, the perturbation vector is calculated. Finally, update the location. .

[0102] In this update formula, the Lévy distribution provides long-distance jump capability, the Tent chaotic sequence introduces nonlinear modulation to break pure randomness, and the linearly decreasing scaling factor ensures that the search step size gradually converges with the iteration process. In actual implementation, the system needs to perform boundary checks on the updated position. If any component exceeds the preset range, the mirror reflection method is used to map it back into the feasible region.

[0103] As one embodiment of the present invention, the method performs a local fine search in the second stage to simulate the encirclement and pursuit behavior of a predator after discovering the traces of its prey.

[0104] In this stage, individual position updates use the difference vector between the current best individual and another randomly selected individual as the guiding direction, and an adaptive inertia weight adjustment mechanism is introduced. The initial value of the inertia weight is set to 0.9, and it decreases linearly to 0.4 with the number of iterations. The scaling factor of the difference vector is dynamically determined by the ratio of the current individual's fitness value to the population's average fitness value. If the individual's fitness is higher than the average, the scaling factor is 0.5; if it is lower than the average, the scaling factor is 1.2. This design prompts low-fitness individuals to make large jumps to escape inferior regions, while high-fitness individuals make small-range fine adjustments to precisely approximate the optimal solution.

[0105] The specific implementation steps for the second-stage position update are as follows: First, calculate the average fitness value of the current population. The fitness of all individuals is obtained by taking the arithmetic mean of their fitness; secondly, for each individual... Calculate its fitness and ratio Secondly, based on The value determines the scaling factor. ,like If it is greater than 1, then It equals 0.5, otherwise It equals 1.2; then, randomly select a different population from the current population. individual Then, calculate the difference vector. Then calculate the inertia weight. Finally, update the location. .

[0106] In this update strategy, the inertia weight controls the degree to which historical positions are preserved. A high initial value helps maintain the stability of the search direction, while a linear decrease gradually enhances the influence of new information. The scaling factor is adaptively adjusted according to individual performance. High-performance individuals use a conservative step size for local fine-tuning, while low-performance individuals use an aggressive step size to try to jump out of the current region. Boundary reflection processing is also performed after the update to ensure the feasibility of the solution.

[0107] In addition, the system immediately calculates the fitness value of the new position after each update and compares it with the original position. If the new fitness is better, the update is accepted; otherwise, the original position is retained. This elite retention mechanism further accelerates the convergence process.

[0108] In one embodiment of the present invention, the method introduces a FADs effect optimization mechanism in the third stage to simulate the phenomenon that marine debris accumulation areas induce predators to change their search paths. This mechanism is activated only when a specific triggering condition is met: the improvement in the optimal fitness value is less than 1‰ over ten consecutive generations.

[0109] Once triggered, 20% of individuals are randomly selected from the current population and subjected to additional positional perturbations.

[0110] The direction of the perturbation is determined by the difference vector between a historical best solution randomly selected from the pre-built elite solution library and the current individual position. The perturbation amplitude follows a normal distribution with a mean of 0 and a standard deviation of 5% of the current search space side length.

[0111] The elite solution library is fixed at 1 / 10 of the population size and adopts a rolling update strategy. It is only replaced when the fitness of a new solution exceeds the lowest value in the library. The replacement threshold γ is set to 0.1, that is, the fitness of a new solution must be higher than 110% of the lowest fitness value in the library to be selected.

[0112] This mechanism effectively prevents the algorithm from stagnating in the later stages of convergence by injecting historical high-quality solution information to revitalize the local search.

[0113] The specific process of FADs effect activation and execution is as follows: The system maintains a sliding window of length 10 to record the globally optimal fitness values ​​of the last ten generations. After each iteration, the latest value is pushed into the window, the oldest value is popped out, and the difference between the maximum and minimum values ​​within the window is calculated. .like If the fitness value is less than the current optimal fitness value multiplied by 0.001, then the trigger condition is met.

[0114] Upon triggering, the system performs the following operations: First, randomly select from the current population. The first step involves treating each individual as a perturbation object, where M is the population size; the second step involves randomly selecting a solution from the elite solution pool. The third step is to process each selected individual... Calculate the perturbation direction vector Fourth step, generate obedience , Normal random numbers of a Step 5: Calculate the perturbation vector. Step 6: Update location Step 7: Perform boundary reflection processing on the new position; Step 8: Recalculate the fitness and update the global optimal record. The update rules for the elite solution library are as follows: The library is initialized to empty; whenever a new solution is generated, if the library is not full, it is added directly; if the library is full, the fitness of the new solution is calculated. With the lowest fitness in the library ratio ;like If the solution is found to be the lowest fitness in the pool, then the new solution replaces the one with the new one; otherwise, the new solution is discarded. This mechanism ensures that a diverse subset of historical best solutions is always preserved in the pool, preventing a single solution from dominating the direction of perturbation. At the same time, threshold screening prevents low-quality solutions from polluting the elite pool, thus maintaining the evolutionary vitality of the pool.

[0115] As one embodiment of the present invention, the method constructs a composite fitness function to quantitatively evaluate the comprehensive detection performance of each candidate array configuration scheme. This fitness function consists of three weighted summations: the first term is the basic coverage term, which calculates the sum of probabilities that all grid points are detected by at least one transmit / receive pair; the second term is a key area enhancement term, which calculates the detection probability only for grid points within a preset key detection area and multiplies it by a weighting coefficient of 3; the third term is a platform spacing penalty term, which applies a negative penalty to any two platforms whose distance is less than a safety threshold, with the penalty value equal to the safety threshold minus the square of the actual distance.

[0116] The three weight coefficients are 1, 3, and -5, respectively. Extensive simulation experiments have verified that this set of parameters can improve the detection probability of key areas while ensuring full coverage and effectively avoiding mutual interference between platforms. A chaotic weight vector is introduced into the fitness function to dynamically fine-tune the contribution of each factor. This vector is generated by the Tent chaotic sequence, and its element values ​​are limited to the range of 0.99 to 1.01. It is used to apply slight perturbations to the three basic weights in each evaluation to prevent the algorithm from developing path dependence on specific weight combinations.

[0117] The specific calculation process for fitness evaluation is as follows: Let the total number of grid points be... The key area grid point set is Its size is The total number of platforms is The safe distance threshold is This value is typically taken as five times the physical size of the sonar array. First, for each grid point... Calculate its probability of being detected. The method involves iterating through all send / receive pair combinations and calculating the detection probability for each pair. Then, the maximum value is taken as the final detection probability for that point, i.e. ;

[0118] Secondly, calculate the basic coverage items. Secondly, calculate the reinforcement items for key areas. Next, calculate the platform spacing penalty term. Traverse all platforms Calculate distance ,like Then the penalty value is accumulated. Otherwise, add 0; then, generate a three-dimensional chaotic weight vector W, whose components... , , The independent Tent sequences are linearly transformed to the interval of 0.99 to 1.01; finally, the overall fitness is calculated. .

[0119] In this fitness function design, the basic coverage term ensures global detection capability, the key area term forces the algorithm to prioritize optimization of critical sea areas with high weights, and the spacing penalty term applies heavy penalties to close-range deployments through a quadratic function, effectively preventing platform collisions or signal interference. The introduction of chaotic weights breaks the local optimum trap that fixed weights may lead to, allowing the algorithm to slightly adjust the optimization objective focus in different iterations, enhancing global robustness. Each fitness evaluation independently generates a new chaotic weight vector, ensuring the randomness and non-repetition of perturbations.

[0120] In one embodiment of the present invention, the method executes an elite retention strategy after each iteration. The top 10% of individuals in terms of fitness in the current population are directly copied to the next generation population, without participating in subsequent position updates. The remaining individuals migrate positions according to the update rules corresponding to their respective search stages. If the new position after migration exceeds a preset physical boundary, it is mapped back into the feasible region using a mirror reflection method. After all individuals have completed their position updates, their fitness values ​​are recalculated, and the global optimal solution recorder is updated. This recorder not only stores the current optimal fitness value and its corresponding solution vector, but also simultaneously records the iteration number of the first occurrence of the solution and the cumulative iteration number of times it has remained optimal, for subsequent convergence analysis and adaptive parameter adjustment.

[0121] The specific implementation details of elite retention and global recording are as follows: After each generation iteration, the system sorts all individuals in the current population in descending order of fitness value, and selects the top... Individuals, as elite individuals, directly replicate themselves in the next generation of the population. Position; Remaining Individuals migrate by calling the corresponding location update module based on their current stage identifier; after migration, boundary reflection correction is performed on all non-elite individuals.

[0122] Then, the fitness values ​​of all individuals are recalculated; next, the optimal fitness in the new population is compared. Best in history ,like Then update the global optimal solution vector. Equals the corresponding individual position, recording the first occurrence of the algebra. equal to the current algebra Reset the continuous algebra ;like ,but Increment by 1; otherwise, remain unchanged.

[0123] This recording mechanism provides convergence state feedback for the algorithm and can be used to dynamically adjust search parameters, for example, when... The FADs effect is triggered prematurely when the preset threshold is exceeded, or If it occurs early, the duration of subsequent stages should be appropriately shortened.

[0124] The elite preservation strategy ensures that high-quality solutions are not overwritten by destructive updates, accelerates the algorithm's convergence to the optimal region, and maintains population diversity to prevent premature convergence.

[0125] In one embodiment of the present invention, the method is provided with dual termination conditions. The first termination condition is reaching a preset maximum number of iterations, which is pre-set based on the total number of sonar platforms and the environmental complexity level. For every additional platform, the maximum number of iterations increases by 500 generations; for every increase in environmental complexity level, the maximum number of iterations increases by 300 generations. The second termination condition is that the globally optimal fitness value does not improve for 50 consecutive generations.

[0126] When any termination condition is met, the algorithm stops running and outputs the currently recorded global optimal solution as the final multi-base sonar platform deployment scheme.

[0127] This solution includes the precise latitude and longitude coordinates or Cartesian coordinates relative to a reference point for each platform, which can be directly used by the command and control system to issue deployment instructions.

[0128] The specific process for termination judgment and result output is as follows: After each iteration, the system checks two conditions. Condition 1: Current generation Is it ≥ ,

[0129] ;

[0130] Round down to the nearest integer. For the number of platforms, This represents the environmental complexity coefficient.

[0131] Condition 2: The global optimal solution continues to maintain an algebraic structure. Check if the value is ≥50. If either condition is true, terminate the optimization loop. After termination, the system executes the final solution output operation:

[0132] First, the global optimal solution vector X_global_best is split into P groups of two-dimensional coordinates according to platform order. Second, if the input coordinate system is latitude and longitude, it is directly output; if it is Cartesian coordinates, it is converted into geographic coordinates based on the latitude and longitude of the reference point and projection parameters. Next, a standard-format deployment instruction file is generated, containing fields such as the number of each platform, target coordinates, estimated arrival time window, and route planning suggestions. Finally, the file is transmitted to the external command and control system through the optimal solution output interface.

[0133] This interface supports various data formats such as JSON, XML, and CSV, and provides an API for other systems to call.

[0134] The dual termination condition ensures that the algorithm stops in time before resources are exhausted, avoiding invalid computation. At the same time, the convergence stagnation judgment ends the optimization process that has no room for improvement in advance, improving computational efficiency.

[0135] As one embodiment of the present invention, the system includes a sonar platform parameter input module, an environmental data loading module, a detection probability calculation engine, a chaos initialization generator, a dynamic stage division controller, an adaptive perturbation modulation unit, a FADs effect triggering judge, an elite solution library memory, a composite fitness evaluator, and an optimal solution output interface.

[0136] The sonar platform parameter input module receives hardware parameters set by the user, such as the number of platforms, maneuvering range, transmission power, and receiving sensitivity.

[0137] The environmental data loading module imports environmental information such as digital water depth maps, sound velocity profile files, and noise maps.

[0138] The detection probability calculation engine calculates the probability of successful detection of any transceiver pair at any grid point in real time based on the bistatic sonar equations.

[0139] The chaos initialization generator is responsible for generating the Tent chaotic sequence and completing the spatial mapping of the initial population.

[0140] The dynamic stage division controller calculates the duration algebra of each stage in real time based on the effective dimensions and controls the flow jump.

[0141] The adaptive perturbation modulation unit generates perturbation vectors that meet the requirements of the current search strategy at different stages.

[0142] The FADs effect triggers the judge to monitor the convergence state and activates the elite de-perturbation mechanism when conditions are met.

[0143] The elite solution library storage maintains a historical set of high-quality solutions and performs rolling updates.

[0144] The composite fitness evaluator calculates a comprehensive score for each candidate solution using a weighted formula. The optimal solution output interface exports the final layout coordinates in a standard format for use by external systems.

[0145] The collaborative workflow of each module in the system is as follows: First, the user inputs parameters such as the number of platforms, the maximum maneuver radius of each platform, the transmitter level, and the receiver noise figure through the sonar platform parameter input module; then, the environmental data loading module reads the pre-stored marine environment database and extracts data such as the depth grid, sound velocity vertical profile, and background noise spectrum of the target sea area; the detection probability calculation engine constructs a spatial grid based on the above parameters and pre-calculates the basic detection probability table of all possible transmit and receive pairs at each grid point, storing it in memory for subsequent fast querying; the chaos initialization generator starts, generates the initial population and passes it to the main optimization loop; the dynamic stage division controller calculates T1, T2, and T3 and initializes the stage counter; after the main loop starts, each generation executes the following in sequence: the composite fitness evaluator calculates the fitness of all individuals in the current population; the elite retention module selects the top 10% of individuals;

[0146] The dynamic stage division controller determines the current stage; the adaptive perturbation modulation unit, differential update module, or FADs perturbation module performs position updates according to the stage identifier; the boundary reflection module corrects out-of-bounds coordinates; the FADs effect triggering judge checks the convergence state and decides whether to activate the perturbation; the elite solution library memory updates the historical best solution set; the global best recorder updates the best solution information; the termination condition judgment module checks whether the stopping criterion is met. If it has not terminated, it proceeds to the next generation;

[0147] If the process terminates, the optimal solution output interface generates a deployment plan file and transmits it to the command system. This system architecture automates the entire algorithm process, with clear responsibilities for each module, seamless data flow, and supports both real-time online optimization and offline batch processing modes to meet the needs of different operational scenarios.

[0148] Compared with the prior art, the advantages and positive effects of the present invention are as follows: by introducing a dynamic three-stage partitioning mechanism based on effective dimensions, the problem that the traditional fixed ratio partitioning cannot adapt to changes in the number of platforms and the complexity of the environment is solved, and the algorithm automatically extends the global exploration time when the solution space expands, thus avoiding premature convergence.

[0149] By constructing an adaptive Lévy perturbation vector with Tent chaotic modulation, the inefficiency caused by the excessive randomness of the original Lévy flight is overcome, and the search directionality is enhanced while retaining the long-distance jump capability.

[0150] By designing a composite fitness function that combines weighted evaluation of key areas with penalties for platform spacing, we achieved targeted enhancement of detection effectiveness in key sea areas and hard constraints on safe distances between platforms.

[0151] By establishing an elite solution library with threshold screening and a linkage mechanism with the FADs effect, historical high-quality solution information is effectively injected in the later stage of algorithm convergence, restarting the local search vitality and breaking through the performance stagnation bottleneck.

[0152] By binding the physical meaning of all parameters and dynamically and adaptively adjusting them, the algorithm is freed from dependence on empirical values, thus improving its robustness and generalization ability in different combat scenarios.

[0153] It should be noted that, in this document, relational terms such as "first" and "second" are used only 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 process, method, article, or apparatus.

[0154] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A multi-base cooperative detection method based on an improved marine predator algorithm, characterized in that, include: Acquire the number of sonar platforms to be deployed, the coordinates of the movable range boundaries of each platform, underwater environmental sound velocity profile data, background noise power spectral density, and the preset set of geographic coordinates of key detection areas; Based on the bistatic sonar range model, an instantaneous detection probability calculation function for any grid point in space is established for any combination of transmitting and receiving platforms. Perform spatial discretization operations to divide the entire operational sea area into a regular two-dimensional grid structure; Iterate through all possible combinations of transmitting and receiving platforms and calculate the probability that each grid point will be successfully detected by the transmitting and receiving pair. Its core lies in building a multi-platform sonar array collaborative optimization system that is oriented towards complex underwater environments and has dynamic adaptive capabilities and scenario customization mechanisms. The system has a mechanism for dynamically dividing the search phase based on effective dimensions. The effective dimension is defined as the total number of sonar platforms participating in the optimization multiplied by the spatial degrees of freedom of each platform, and then multiplied by a correction coefficient that characterizes the complexity of the environment. The correction coefficient is jointly determined by the standard deviation of underwater topographic relief and the root mean square of the sound velocity gradient. The search phase is dynamically divided according to the effective dimension, including: the first phase's continuous algebra is set to the integer part of the quotient obtained by multiplying the total maximum number of iterations by the square root of the effective dimension and then dividing by one hundred, simulating the large-scale cruising behavior of the top predator and performing a global coarse search. The second stage's continuous algebra is set to two-thirds of the remaining number of iterations after subtracting the first stage's algebra, simulating the predator's encirclement and pursuit behavior after discovering prey's tracks, and performing a local fine search; the third stage occupies all remaining iterations, introducing a FADs effect optimization mechanism to simulate the phenomenon of ocean floating debris accumulation areas inducing predators to change their search paths.

2. The multi-base cooperative detection method based on an improved marine predator algorithm according to claim 1, characterized in that, The construction of the adaptive Lévy perturbation vector for Tent chaotic modulation specifically includes: During the first phase of the global coarse search, a set of independent Lévy random numbers with the same dimension as the variable to be optimized is generated; Simultaneously generate a set of Tent chaos numbers of the same dimension; The adaptive Lévy perturbation vector is obtained by multiplying each Lévy random number element by the absolute value of the Tent chaos number at the corresponding position, and then multiplying it by a scaling factor that decreases linearly with the number of iterations.

3. The multi-base cooperative detection method based on an improved marine predator algorithm according to claim 2, characterized in that, The adaptive Lévy perturbation vector retains the long-tailed jump characteristics of Lévy flight to maintain global exploration capability, while suppressing excessive random walks through nonlinear modulation of the chaotic sequence, making the search trajectory more directional.

4. The multi-base cooperative detection method based on an improved marine predator algorithm according to claim 1, characterized in that, The establishment of a linkage mechanism between the elite library with threshold screening and the FADs effect specifically includes: An elite solution library is set up, with a fixed capacity of 1 / 10 of the population size, and a rolling update strategy is adopted. When the fitness of a new solution exceeds 110% of the lowest fitness value in the library, the new solution replaces the solution with the lowest fitness value in the library. The system maintains a sliding window of length 10 to record the global optimal fitness value of the last 10 generations. After each iteration, the latest value is pushed into the window, the oldest value is popped out, and the difference between the maximum and minimum values ​​in the window is calculated. If the difference is less than the current optimal fitness value multiplied by 0.001, then the FADs effect triggering condition is met. This mechanism effectively injects historical high-quality solution information into the later stages of algorithm convergence, restarting the local search and breaking through the performance stagnation bottleneck.

5. A multi-base cooperative detection method based on an improved marine predator algorithm according to claim 1, characterized in that, The physical meaning binding and dynamic adaptive adjustment of the entire process parameters specifically include: Throughout the algorithm process, all parameters are bound to physical meanings, such as binding the transmitter level to the maximum effective radiated power calibrated by the sonar equipment at the factory, and binding the receiver directivity index to the physical aperture and operating frequency of the sonar array, etc. The search parameters at each stage are dynamically and adaptively adjusted. The maximum number of iterations is dynamically adjusted based on factors such as the total number of sonar platforms and the level of environmental complexity. By adopting this dynamic adaptive adjustment strategy for parameters throughout the entire process, the reliance on experience values ​​is eliminated, and the robustness and generalization ability of the algorithm in different combat scenarios are improved.

6. A multi-base cooperative detection method based on an improved marine predator algorithm according to claim 1, characterized in that, The specific strategies and implementation of the search phase include: In the first stage, a global coarse search is performed to simulate the large-scale cruising behavior of the top predator. The position update of each individual is guided by the current best individual and superimposed with a random step size vector that follows a Lévy distribution. The Lévy step size vector is amplitude modulated by a Tent chaotic sequence. Specifically, a set of independent Lévy random numbers with the same dimension as the variable to be optimized is generated, and a set of Tent chaotic numbers with the same dimension is generated. The Lévy random numbers are multiplied element by element by the absolute value of the Tent chaotic number at the corresponding position, and then multiplied by a scaling factor that decreases linearly with the number of iterations to obtain an adaptive Lévy perturbation vector. In the second stage, a local fine search is performed to simulate the behavior of predators surrounding and chasing prey after discovering their tracks. The individual position update uses the difference vector between the current best individual and another randomly selected individual as the guiding direction, and an adaptive inertial weight adjustment mechanism is introduced. The scaling factor of the difference vector is dynamically determined by the ratio of the current individual fitness value to the population average fitness value. In the third stage, an optimization mechanism based on the effect of FADs is introduced to simulate the phenomenon that marine floating debris accumulation areas induce predators to change their search paths. This mechanism is activated only when a specific trigger condition is met. The trigger condition is that the improvement of the optimal fitness value is less than 1‰ for ten consecutive generations. Once triggered, an individual is randomly selected from the current population and subjected to additional positional perturbation.

7. A multi-base cooperative detection method based on an improved marine predator algorithm according to claim 1, characterized in that, The setting of dual termination conditions includes: The first termination condition is reaching the preset maximum number of iterations. The maximum number of iterations is preset based on the total number of sonar platforms and the environmental complexity level. For each additional platform, the maximum number of iterations increases by 500 generations; for each increase in environmental complexity level, the maximum number of iterations increases by 300 generations. The second termination condition is that the globally optimal fitness value does not improve for 50 consecutive generations. When any termination condition is met, the algorithm stops running and outputs the currently recorded global optimal solution as the final multi-base sonar platform deployment scheme. The scheme includes the precise latitude and longitude coordinates of each platform or the plane rectangular coordinates relative to the reference point, which can be directly used by the command and control system to issue deployment instructions.

8. A multi-base cooperative detection method based on an improved marine predator algorithm according to claim 7, characterized in that, The specific process for outputting the final multi-base sonar platform deployment scheme is as follows: The global optimal solution vector is split into P groups of two-dimensional coordinates in platform order. If the input coordinate system is latitude and longitude, it is output directly. If it is a Cartesian coordinate system, it is converted into geographic coordinates based on the latitude and longitude of the reference point and the projection parameters; Generate a standard-format deployment instruction file, which includes fields such as the platform number, target coordinates, estimated arrival time window, and route planning suggestions for each platform. The file is transmitted to an external command and control system through the optimal solution output interface. The interface supports multiple data formats such as JSON, XML, and CSV, and provides an API for other systems to call.

9. A multi-base cooperative detection method based on an improved marine predator algorithm according to claim 1, characterized in that, The system includes: The sonar platform parameter input module is used to receive hardware parameters set by the user, such as the number of platforms, maneuvering range, transmission power, and receiving sensitivity. The environmental data loading module is used to import environmental information such as digital depth maps, sound velocity profile files, and noise maps; The detection probability calculation engine calculates the probability of successful detection of any transceiver pair at any grid point in real time based on the bistatic sonar equations. The chaos initialization generator is responsible for generating the Tent chaotic sequence and completing the spatial mapping of the initial population. The dynamic stage division controller calculates the duration algebra of each stage in real time based on the effective dimensions and controls the flow jump accordingly. An adaptive perturbation modulation unit generates perturbation vectors that meet the requirements of the current search strategy at different stages; The FADs effect triggers a judge to monitor the convergence state and activates the elite de-perturbation mechanism when the conditions are met. An elite solution library storage maintains a set of historical high-quality solutions and performs rolling updates. The composite fitness evaluator calculates a comprehensive score for each candidate solution based on a weighted formula. The optimal solution output interface exports the final layout coordinates in a standard format for external systems to use.

10. A multi-base cooperative detection method based on an improved marine predator algorithm according to claim 9, characterized in that, The collaborative workflow of each module in the system is as follows: Users first input parameters such as the number of platforms, the maximum maneuver radius of each platform, the transmitter level, and the receiver noise figure through the sonar platform parameter input module. Subsequently, the environmental data loading module reads the pre-stored marine environment database and extracts data such as depth grid, sound velocity vertical profile, and background noise spectrum of the target sea area; The detection probability calculation engine constructs a spatial grid based on the above parameters and pre-calculates the basic detection probability table of all possible transmit and receive pairs at each grid point, storing it in memory for subsequent fast querying; The chaos initialization generator starts, generates an initial population, and passes it to the main optimization loop; The dynamic phase division controller calculates T1, T2, and T3 and initializes the phase counter; after the main loop starts, each generation executes the following sequentially: the composite fitness evaluator calculates the fitness of all individuals in the current population; The elite retention module selects the top 10% of individuals; the dynamic phase division controller determines the current phase. The adaptive perturbation modulation unit, differential update module, or FADs perturbation module performs position updates based on the stage identifier; The boundary reflection module corrects out-of-bounds coordinates; the FADs effect triggering judge checks the convergence status and decides whether to activate the perturbation. The elite solution library memory updates the historical best solution set; the global best recorder updates the best solution information. The termination condition judgment module checks whether the stopping criteria are met. If it does not end, it proceeds to the next generation; If the process terminates, the optimal solution output interface generates a deployment plan file and transmits it to the command system.

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