A multi-unmanned aerial vehicle search strategy optimization method based on genetic programming

Abstract

The present application relates to a kind of genetic programming (GP) based multi-unmanned aerial vehicle search strategy optimization method, in the framework of distributed model predictive control (DMPC), each unmanned aerial vehicle (UAV) is realized by target function guide search trajectory optimization process, it is essentially to convert search strategy into mathematical logic mapping relationship.In traditional method, target function construction mainly relies on the design idea of artificial experience dominant, and this fixed search mode based on subjectivity has the limitations such as insufficient environmental adaptability, weak strategy generalization ability in complex dynamic environment.For this problem, the present application proposes a search strategy optimization method based on genetic programming algorithm, by establishing the dynamic mapping model between strategy parameter space and search performance index, realize the online dynamic evolution of search strategy and parameter adaptive adjustment.

Description

Technical Field

[0001] This invention belongs to the field of positioning accuracy measurement methods, and in particular relates to a multi-UAV search strategy optimization method based on genetic programming. Background Technology

[0002] With the rapid development of IoT technology, drones, due to their small size, flexibility, and ease of operation, have been widely used in various fields such as reconnaissance, surveillance, search and rescue, and environmental monitoring. Multi-drone cooperative search technology is an important research direction. Its core function is to help drones autonomously plan search paths in wide-area unknown environments, so that drones can quickly discover targets and provide initial information for subsequent identification, tracking, or containment algorithms.

[0003] To date, constructing a multi-UAV cooperative search system that combines flexibility, efficiency, and robustness in complex adversarial environments still faces three major technical challenges. First, existing research largely focuses on static target search scenarios. For highly random dynamic targets, existing methods suffer from significant efficiency degradation and limited target acquisition probability, primarily due to the lack of a coupled optimization mechanism for target motion prediction and dynamic adjustment of search strategies. Second, traditional cooperative search methods generally rely on centralized controllers or pre-set stable communication links, which fundamentally contradicts real-world adversarial environments. In battlefield environments with frequent electronic warfare and damaged communication infrastructure, it is difficult for UAVs to establish fast and reliable communication links, resulting in communication constraints and limited computational resources. Furthermore, existing methods are insufficient in responding to unexpected situations during missions. They lack effective dynamic threat avoidance models and group self-reconstruction strategies in the event of individual failures, making it difficult for the system to meet the robustness requirements of high-adversarial scenarios. Overcoming these bottlenecks urgently requires the development of novel distributed cooperative architectures and adaptive decision-making algorithms to achieve intelligent emergence and autonomous cooperation among multiple UAVs. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a multi-UAV search strategy optimization method based on genetic programming, as described above. The technical solution of this invention to solve the above technical problem is as follows:

[0005] A multi-UAV search strategy optimization method based on genetic programming includes the following steps:

[0006] Step 1: Initialize the population set SS using genetic programming. totalEach individual in the population is a GP tree encoded structure, and the bottom-level attribute nodes include strategies for maximizing target detection gains, maximizing region exploration gains, maximizing revisit detection gains, maximizing communication connectivity gains, and maximizing collision and obstacle avoidance gains. The upper-level attribute / functional elements are randomly configured, and the functional / attribute parameters are randomly selected when initializing each individual.

[0007] Step 2: Calculate the average probability of the target existing for each individual in the population (avg). prob and average environmental uncertainty (avg) uncer Select the average probability of the target existence (avg) prob and average environmental uncertainty (avg) uncer As the objective function f1 GP and To evaluate the fitness of GP individuals, the objective function f1 GP and The formula is as follows:

[0008]

[0009] Among them, |S train | indicates the number of individuals in the population;

[0010] Step 3: Use non-dominance relationships to stratify individuals in the population and record the stratum of each individual. Individuals in the same stratum have non-dominance relationships with each other, and individuals in the upper stratum dominate individuals in the lower stratum.

[0011] For those in L l All individuals in the layer are first sorted in ascending order of their fitness values ​​corresponding to each objective function. Then, the crowding distance for each policy is calculated. The formula for calculating the crowding distance is as follows:

[0012]

[0013] Among them, Dis h Indicates in L l The crowding distance of an individual h in a layer, h∈{1,2,...,|L l |} represents the sorted individual IDs; Let h represent the fitness of the individual ranked h under the j-th objective function; and Let represent the maximum fitness value and the minimum fitness value under the j-th objective function, respectively;

[0014] Step 4: Sort individuals based on the number of non-dominated solution layers and crowding distance. First, within different non-dominated layers, individuals with lower layer numbers have higher virtual fitness. Within the same non-dominated layer, individuals with larger crowding distances have higher virtual fitness. Individuals with higher virtual fitness have higher ranking values. Calculate the virtual fitness of each individual, starting with the virtual fitness of the i-th individual. The calculation formula is:

[0015]

[0016] In the formula, N pop s represents the total number of individuals in the population. i The index of the virtual fitness value of the i-th individual;

[0017] Step 5: Based on individual virtual fitness, select P from the population using a roulette wheel selection method. s Each individual generates a subpopulation SS sub traversing subpopulations SS sub For each individual in the population, perform crossover and mutation operations sequentially to obtain an updated population. Increment the iteration count by 1, and use the method in steps 2-4 to obtain the optimal set of individuals corresponding to the updated population, which is then placed into a temporary set SS. temp ;

[0018] Step 6: Compare SS based on non-dominant relationships final and SS temp Select the better individuals and apply SS final Perform an update, then check if the maximum number of iterations has been reached. If so, proceed to step 7; otherwise, repeat the process.

[0019] Step 7: Output the final optimal set of individuals SS final The optimal individual is determined by outputting the optimal strategy, which includes the strategy for maximizing target detection gains, the strategy for maximizing area exploration gains, the strategy for maximizing revisit detection gains, the strategy for maximizing communication connectivity gains, and the strategy for maximizing collision and obstacle avoidance gains.

[0020] Furthermore, the target detection gain maximization strategy J1 represents the probability of the UAV detecting a target along its flight path from its current position to the target position. Given the search trajectory of UAV i, its detection area is A. i , t k Real-time drone target detection benefits J 1,i (t k ) is represented as:

[0021]

[0022] in, Indicates t kThe probability of the target existing in the time grid (m,n); Indicates at t k Whether UAV i detects a target at time (m,n) is calculated as follows:

[0023]

[0024] Where, η p Indicates the target detection threshold;

[0025] The strategy J2, which maximizes the area exploration gain, measures the effectiveness of the UAV in reducing environmental uncertainty during continuous search. It is characterized by maximizing the information gain of the mission area, since p mn (t k+1 The value of e will change based on the target detection results; therefore, calculating e... mn (t k+1 The expected value of ) for:

[0026]

[0027] In the formula, P mn (t k+1 ) and e′ mn (t k+1 This represents the probability of target presence and the information entropy value when a target is detected. and e″ mn (t k+1 These represent the probability of target presence and the information entropy value when no target is detected, respectively.

[0028] t k The maximum area exploration reward for drone i at time i is expressed as:

[0029]

[0030] The strategy function J3, which maximizes the revisit detection gain, represents the detection gain obtained by the UAV when repeatedly searching grids with long revisit intervals. It is represented by the total amount of pheromone in the mission area, t. k The calculation method for maximizing the revisit detection revenue strategy of drone i at time i is as follows:

[0031]

[0032] In the formula, s mn (t k ) represents t k The pheromone concentration in the time grid (m,n);

[0033] Maximizing communication connectivity gain J4 represents the gain generated by multiple UAVs maintaining global communication connectivity under limited communication distance conditions, t k The communication connectivity benefit of drone i at any time J 4,i (t k The calculation method is as follows:

[0034]

[0035] In the formula, Indicates that the drone swarm is in t k The communication link state at any given moment, 0 represents; the reciprocal of the sum of the repulsive forces acting on UAV i is used as the collision avoidance benefit J. 5,i (t k ), t k The calculation method for maximizing collision and obstacle avoidance benefits for drone i at time i is as follows:

[0036]

[0037] In the formula, ||F ij (t k The repulsive force ()|| represents the sum of the repulsive forces experienced by UAV i and UAV j, which can be calculated as:

[0038]

[0039] In the formula, dis(i,j) represents the distance between the i-th UAV and the j-th UAV and the obstacle grid cell, and d s To establish a safe distance for drones to avoid collisions.

[0040] Furthermore, in step 5, when selecting an individual from the population using the roulette wheel method, the probability of individual i being selected is... The mathematical formula is:

[0041]

[0042] in, Let N be the virtual fitness of the i-th individual. pop Population size.

[0043] The beneficial effects of this invention are as follows:

[0044] Traditional methods rely heavily on human experience to construct objective functions. This subjective, fixed search approach suffers from limitations such as insufficient environmental adaptability and weak strategy generalization in complex dynamic environments. To address this issue, this paper proposes a search strategy optimization method based on genetic programming. By establishing a dynamic mapping model between the strategy parameter space and search performance indicators, the method enables online dynamic evolution and adaptive parameter adjustment of the search strategy. Attached Figure Description

[0045] Figure 1 This is a flowchart of the method of the present invention;

[0046] Figure 2 A tree-like coding structure diagram of the search strategy;

[0047] Figure 3 Here is a flowchart of the crossover operator operation;

[0048] Figure 4 Flowchart of subtree mutation operation;

[0049] Figure 5 Here is a flowchart of the node mutation operation;

[0050] Figure 6 To improve the mutation operation flowchart; Figure 7 A visualization analysis of the Pareto front; Figure 8 This is a schematic diagram of multi-UAV search trajectories obtained through simulation verification using different methods. Detailed Implementation

[0051] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0052] In the framework of Distributed Model Predictive Control (DMPC), the process by which each unmanned aerial vehicle (UAV) optimizes its search trajectory guided by an objective function essentially transforms the search strategy into a mathematical logical mapping relationship. Traditional methods primarily rely on human experience-driven design approaches for constructing the objective function. This subjective, fixed search pattern suffers from limitations such as insufficient environmental adaptability and weak strategy generalization ability in complex dynamic environments. To address this issue, this invention proposes a search strategy optimization method based on genetic programming. By establishing a dynamic mapping model between the strategy parameter space and search performance indicators, it enables online dynamic evolution of the search strategy and adaptive parameter adjustment.

[0053] 1. Selection of search strategy

[0054] Before applying the GP algorithm, the following underlying search strategy parameter space is designed:

[0055] (1) Target detection reward maximization strategy

[0056] The target detection reward function J1 represents the probability that the UAV will detect a target along its flight path from its current position to the target position. Given the search trajectory of UAV i, its detection area is A. i Target detection benefit J 1,i(t k This can be represented as:

[0057]

[0058] in, Indicates t k The probability of the target existing in the time grid (m,n); Indicates at t k Whether the UAV detects the target at time (m,n) is calculated as follows:

[0059]

[0060] Where, η p Indicates the target discovery threshold.

[0061] (2) Strategies to maximize the benefits of regional exploration

[0062] The area exploration benefit function J2 measures the effect of multiple UAVs on reducing environmental uncertainty during continuous search, and can be characterized by maximizing the information gain of the mission area. Since p mn (t k+1 The value of e will change based on the target detection results; therefore, calculating e... mn (t k+1 The expected value of ) for:

[0063]

[0064] In the formula, P mn (t k+1 ) and e′ mn (t k+1 This represents the probability of target presence and the information entropy value when a target is detected. and e″ mn (t k+1 ) represent the probability of target presence and the information entropy value when no target is detected, respectively.

[0065] Therefore, the benefits of regional exploration can be expressed as:

[0066]

[0067] (3) Strategies to maximize the benefits of revisiting and probing

[0068] Unexplored areas are revisited. The revisit detection benefit function J3 represents the detection benefit obtained by the UAV when repeatedly searching grids with long revisit intervals. It is represented by the total amount of pheromone in the mission area, and the calculation method is as follows:

[0069]

[0070] In the formula, s mn (t k ) represents t k The pheromone concentration in the time grid (m,n).

[0071] (4) Strategies to maximize communication connectivity benefits

[0072] The communication connectivity gain J4 represents the benefit generated by multiple UAVs maintaining global communication connectivity under limited communication distance conditions. Based on the proposed communication connectivity rate metric, the communication connectivity gain J of UAV i is... 4,i (t k The calculation method is as follows:

[0073]

[0074] In the formula, Indicates that the drone swarm is in t k The status of the communication link at any given moment.

[0075] (5) Strategies to maximize collision and obstacle avoidance benefits

[0076] Multi-UAV collaborative search requires avoiding collisions between UAVs and those in threat zones. Inspired by the artificial potential field method, the threat zone grid and neighboring UAV grids exert repulsive forces on the UAVs. The reciprocal of the sum of the repulsive forces acting on UAV i is taken as the collision and obstacle avoidance benefit J. 5,i (t k The calculation method is as follows:

[0077]

[0078] In the formula, ||F ij (t k The repulsive force ()|| represents the sum of the repulsive forces experienced by UAV i and UAV j, which can be calculated as:

[0079]

[0080] In the formula, dis(i,j) represents the distance of the i-th UAV from other UAV positions and obstacle grid cells, and d s To establish a safe distance for drones to avoid collisions.

[0081] Since subsequent genetic programming operations require numerical calculations of the performance functions corresponding to the above search strategies, it is necessary to normalize the numerical values ​​of the performance functions to avoid the influence of different orders of magnitude on the calculation results.

[0082]

[0083] In the formula, This represents the normalized value of the i-th objective function; to avoid invalid calculations when the denominator is 0, the normalization interval is set to [f min ,f max ], f min =1,f max =100.

[0084] 2. Coding Design and Population Initialization

[0085] Genetic programming (GP) typically uses a tree structure to encode individuals, where the root node represents a function or operation, and the leaf nodes represent variables or constants. To evolve and obtain better-performing search strategies through genetic programming, this paper designs a novel tree structure to encode and represent various heuristic search strategies. This structure includes discriminant nodes, attribute nodes, and function nodes.

[0086] The discriminant node is located at the top level of the tree structure and contains two states: "Rise" and "Fall". "Rise" indicates maximizing the lower-level expression to achieve the optimal result, while "Fall" indicates minimizing the lower-level expression to achieve the optimal result. The attribute nodes include the five objective function nodes mentioned above and a constant node Const∈{0.2,0.6,0.8}. The functional nodes are shown in Table 1. In addition to basic arithmetic operators, two new types of functional nodes have been added: logarithmic functions and exponential functions. The exponential function can amplify differences through non-linear amplification, thereby amplifying weights to highlight key strategies; the logarithmic function can compress differences in input values, thereby balancing weights to balance the contributions of multiple strategies.

[0087] like Figure 2 As shown, the objective function represented by this tree structure is: Initialize the Genetic Programming (GP) population. Since all strategies use the maximum payoff function, the decision nodes are uniformly set to "ascending". The depth of the GP tree is limited to between 2 and 4 levels (excluding the top-level decision node). The population initialization process is as follows:

[0088] Step 1: Construct a full node tree: restrict attribute elements at the bottom layer, randomly configure attribute / function elements at the top layer, and clear the lower-level connections of attribute nodes;

[0089] Step 2: Parameter randomization: Randomly select function / attribute parameters from the corresponding set;

[0090] Step 3: Node Shaping: Set the top-level decision node to "ascending";

[0091] Step 4: Repeat step N above. pop This process eventually generates an initial GP tree population.

[0092] Since all heuristic strategies employ a profit-maximizing function, the discriminant node is uniformly set to "rise". The GP tree depth is defined as the number of levels excluding the top-level node. The population is initialized using the Ramped half-and-half method, with the tree depth limited to 2-4 levels. The population initialization process is as follows:

[0093] 1) Construct a full node tree: the bottom layer is limited to attribute elements, the upper layer is randomly configured with attribute / functional elements, and the lower layer connections of attribute nodes are cleared;

[0094] 2) Parameter randomization: Randomly select function / attribute parameters from the corresponding set;

[0095] 3) Node definition: Set the top-level decision node to "rise";

[0096] Repeat step N above. pop This time, the final generation size is N. pop The initial GP tree population.

[0097] Table 1 Set of Functional Node Elements

[0098]

[0099] 3. Genetic manipulation

[0100] Genetic operations are a key mechanism for ensuring the global search performance of the algorithm, maintaining population diversity and passing on superior genes through genetic operators. This algorithm employs a three-stage genetic operation, including selection, crossover, and mutation operators. The specific operations are as follows:

[0101] 1) Selection Operator

[0102] In the evolutionary iteration process of genetic programming, a roulette wheel selection mechanism is first employed. Individuals are probabilistically sampled based on their fitness values, prioritizing high-fitness generalized selection (GP) individuals as parents for genetic operations. This mechanism constructs a probability distribution model by normalizing fitness values, ensuring that high-fitness individuals have a greater selection probability while preserving evolutionary opportunities for low-fitness individuals. This achieves a dynamic balance between the convergence pressure of the elite strategy and the maintenance of population diversity. The mathematical formula is:

[0103]

[0104] in, Let be the probability that individual i is selected. For its virtual fitness, N pop For population size

[0105] 2) Crossover operator: When a random number triggers the crossover probability threshold P C At that time, perform a parent-child tree replacement operation. For example... Figure 3As shown, the subtree structures of two randomly selected parent individuals are exchanged and recombinated, which preserves effective gene fragments and produces new individuals.

[0106] 3) Mutation Operator

[0107] When a random number triggers the mutation probability threshold P M At that time, a three-level mutation operation is performed on the selected individual, including subtree mutation, node mutation, and promotion mutation. For example... Figure 4 As shown, subtree mutation involves randomly selecting subtree nodes, completely removing them, and then rebuilding a completely new subtree for grafting; as... Figure 5 As shown, node mutation performs operator substitution, constant correction, and variable updates on a single node, achieving local fine-tuning; for example... Figure 6 As shown, the boost mutation selects redundant subtrees, promotes effective child nodes to the parent node position, and prunes redundant branches.

[0108] 4. Overall Algorithm Training Process

[0109] Adaptive evolution of the target search strategy is achieved based on the genetic programming algorithm. The algorithm flow is as follows: Figure 1 As shown in the pseudocode, the specific optimization process addresses the multi-factor adaptation problem (UAV parameters, environmental constraints, and target characteristics). To improve computational efficiency, a decoupled design of offline training and online planning is adopted. Dynamic evaluation is achieved through simulation based on a distributed model predictive control (DMPC) framework, avoiding real-time computation bottlenecks while ensuring the robustness of policy optimization. The average target existence probability (avg) is selected. prob and average environmental uncertainty (avg) uncer The fitness of a GP individual is evaluated as an objective function, and its calculation method is as follows:

[0110]

[0111] Among them, |S train | indicates the number of example samples in the training set. Based on this, the virtual fitness of GP individuals is calculated using the number of non-dominated solution layers and crowding distance, serving as a multi-metric evaluation criterion. The steps are as follows:

[0112] Step 1: Calculate the average value (avg) for each GP tree. prob and avg uncer For individuals i and j, they are non-dominant to each other if their fitness values ​​satisfy the following inequality:

[0113]

[0114] Individuals in the population are stratified using non-dominance relationships, and the stratum number of each individual is recorded. Individuals in the same stratum have non-dominance relationships with each other, and individuals in higher strata dominate individuals in lower strata. The expression is as follows:

[0115] Step 2: For those in L l All individuals in the layer are first sorted in ascending order according to their fitness values ​​corresponding to each objective function. Then, the crowding distance of each individual under each objective function is calculated and summed using the following formula (in the objective function f). j For individuals at minimum and maximum fitness, their crowding distance will be assigned a maximum value:

[0116]

[0117] Among them, Dis h Indicates in L l The crowding distance of an individual h in a layer, h∈{1,2,...,|L l |} represents the sorted individual IDs; Let h represent the fitness of the individual ranked h under the j-th objective function; and Let represent the maximum fitness value and the minimum fitness value under the j-th objective function, respectively.

[0118] Step 3: Calculate the virtual fitness of individuals based on the number of non-dominated solution layers and the crowding distance. First, individuals with lower layer numbers in different non-dominated layers have higher virtual fitness; within the same non-dominated layer, individuals with larger crowding distances have higher virtual fitness. Individuals with higher virtual fitness have a higher ranking value s. i The higher the virtual fitness of the i-th individual, the better. It can be calculated as

[0119]

[0120] Step 4: Based on individual virtual fitness, select P from the population using a roulette wheel selection method. s Individual-generated subpopulation SS sub traversing subpopulations SS sub Each individual in the process undergoes crossover and mutation operations in sequence.

[0121] Step 5: Determine if the maximum number of iterations has been reached. If not, repeat steps 1 to 4. If yes, output the optimal Pareto solution set.

[0122] The pseudocode for the method of this invention is as follows:

[0123] Input: Population size N pop Maximum number of iterations max_gen, crossover rate P C Variation rate P M Attribute node set S Att Functional node set S funGP tree depth range, training example set S train ;

[0124] Output: The Pareto optimal set of individuals (SS) final

[0125]

[0126]

[0127]

[0128] Simulation verification

[0129] The search area was set to 2000m × 1000m, containing 8 dynamic targets and 7 circular threat areas, with the radius of the threat areas ranging from 30m to 50m. To simulate the random motion of the targets, three target motion modes were set in the dynamic simulation: "linear motion," "random motion," and "sine-periodic maneuver." During linear motion, the target's heading angle remained constant; during random motion, the target's velocity and heading angle changed randomly with a 10% probability; and during sinusoidal maneuver, the target's heading angle varied with a sinusoidal period. Specific target motion parameters are shown in Table 2. The UAV swarm consisted of 5 multi-rotor UAVs with different performance parameters, shown in Table 3, where the warning distance represents the UAV's advance perception distance of the threat area. The parameters of the DMPC-based distributed decision-making method and the GP algorithm are shown in Tables 4 and 5, respectively.

[0130] Table 2 Dynamic target motion parameters

[0131]

[0132]

[0133] Table 3 Performance parameters of heterogeneous UAV swarms

[0134]

[0135] Table 4 DMPC Method Parameters

[0136]

[0137] Table 5 Genetic Programming Algorithm Parameters

[0138]

[0139] To evaluate the search strategy during the genetic programming (GP) evolution process, the initial positions of the UAV and the moving target were randomly initialized based on the simulation environment parameters described above, generating 10 sets of training samples, and the maximum search time step was set to 100. The training results are as follows: Figure 7 As shown in Table 6, based on the non-dominant relationship of GP individuals, five strategies on the Pareto front are selected, and their corresponding objective functions are shown in Table 6. Analysis shows that although the objective function configurations for these five strategies are different, the weight ratios of J1 and J2 are greater than those of J3 and J5. This is because in the search task, only basic revisit detection and obstacle avoidance strategies need to be maintained. Meanwhile, the weight ratio of J4 is minimized. This is because communication connectivity easily leads to multiple UAVs clustering in the same area, which is not conducive to distributed cooperative search of moving targets. Strategy S1 from Table 6 is selected for simulation verification, and the resulting multi-UAV search trajectories are shown in Table 6. Figure 8 As shown, multiple UAVs can detect all moving targets within the specified time, thus verifying the priority of the proposed method.

[0140] Table 6. Set of Optimal Search Strategies

[0141]

[0142] The above description provides examples of the preferred embodiments of the present invention, and any parts not described in detail are common knowledge to those skilled in the art. The scope of protection of the present invention is determined by the claims, and any equivalent modifications made based on the technical teachings of the present invention are also within the scope of protection of the present invention.

[0143] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-UAV search strategy optimization method based on genetic programming, characterized in that, Includes the following steps: Step 1: Initialize the population set using genetic programming. Each individual in the population is a GP tree encoded structure, and the bottom-level attribute nodes include strategies for maximizing target detection gains, maximizing region exploration gains, maximizing revisit detection gains, maximizing communication connectivity gains, and maximizing collision and obstacle avoidance gains. Upper-level attributes / functional elements are randomly configured, and functional / attribute parameters are randomly selected during the initialization of each individual; the strategy for maximizing target detection gains... This represents the probability that a UAV will detect a target along its flight path from its current position to the target position, given a given UAV. After tracking the search trajectory, its detection area range is: , drones at all times Target detection benefits Represented as: ； in, express Time Grid The probability of the target existing in the middle; Indicates in Time Drone In the grid Whether a target was detected is calculated as follows: ； in, This indicates the target detection threshold; 1 indicates that the target has been detected, and 0 indicates that the target has not been detected. Strategies to maximize area exploration revenue This measure assesses the effectiveness of UAVs in reducing environmental uncertainty during continuous search operations, and is characterized by maximizing the information gain over the mission area. The value will change based on the target detection results; therefore, the calculation... Mathematical expectation for: ； In the formula, and This represents the probability of target presence and the information entropy value when a target is detected. and These represent the probability of target presence and the information entropy value when no target is detected, respectively. drones at all times The maximum area exploration benefit is expressed as: ； Maximize revisit probe reward strategy function This represents the detection gain obtained by a UAV when repeatedly searching grids with long visit intervals, expressed as the total amount of pheromone in the mission area. drones at all times The calculation method for maximizing the return on exploration benefits is as follows: ； In the formula, express Time Grid Pheromone concentration in the middle; Maximize communication connectivity benefits This indicates the benefits of multiple drones maintaining global communication connectivity under conditions of limited communication distance. Communication connectivity benefits of drones at any time The calculation method is as follows: ； In the formula, Indicates drone swarms in The status of the communication link at any given moment; The reciprocal of the sum of the repulsive forces acting on drone i is used as the collision and obstacle avoidance benefit. , drones at all times The calculation method for maximizing collision and obstacle avoidance benefits is as follows: ； In the formula, The sum of the repulsive forces acting on UAV i and UAV j can be calculated as follows: ； In the formula, Indicates the first The drone and the first The distance between the drone's position and the obstacle grid cells. To establish a safe distance for drones to avoid collisions; Step 2: Calculate the average probability of the target existing for each individual in the population. and average environmental uncertainty Select the average probability of the target's existence. and average environmental uncertainty As the objective function and To evaluate the fitness of individual GPs, the objective function is... and The formula is as follows: ； in, Indicates the number of individuals in a population; Step 3: Use non-dominance relationships to stratify individuals in the population and record the stratum of each individual. Individuals in the same stratum have non-dominance relationships with each other, and individuals in the upper stratum dominate individuals in the lower stratum. For those in All individuals in the layer are first sorted in ascending order of their fitness values ​​corresponding to each objective function. Then, the crowding distance for each policy is calculated. The formula for calculating the crowding distance is as follows: ； in, Indicates in Individuals in the layer Crowded distance, Individual numbers after sorting; Indicates the first The objective functions are sorted as follows: Individual fitness; and They represent the first Maximum and minimum fitness values ​​under each objective function; Step 4: Sort individuals based on the number of non-dominated solution layers and crowding distance. First, within different non-dominated layers, individuals with lower layer numbers have higher virtual fitness. Within the same non-dominated layer, individuals with larger crowding distances have higher virtual fitness. Individuals with higher virtual fitness have higher ranking values. Calculate the virtual fitness of each individual, starting with the virtual fitness of the i-th individual. The calculation formula is: ； In the formula, This represents the total number of individuals in the population. The index of the virtual fitness value of the i-th individual; Step 5: Based on individual virtual fitness, select from the population using a roulette wheel method. Each individual generates a subpopulation. traverse subpopulations For each individual in the population, perform crossover and mutation operations sequentially to obtain an updated population. Increment the iteration count by 1, and use the method in steps 2-4 to obtain the optimal set of individuals corresponding to the updated population and put it into a temporary set. ; Step 6: Compare based on non-dominant relationships and Selecting better individuals and... Perform an update and determine if the maximum number of iterations has been reached. If yes, proceed to step 7; otherwise, repeat step 6. Step 7: Output the final optimal set of individuals. The optimal individual is determined by outputting the optimal strategy, which includes the strategy for maximizing target detection gains, the strategy for maximizing area exploration gains, the strategy for maximizing revisit detection gains, the strategy for maximizing communication connectivity gains, and the strategy for maximizing collision and obstacle avoidance gains.

2. The multi-UAV search strategy optimization method based on genetic programming according to claim 1, characterized in that, In step 5, when selecting individuals from the population using the roulette wheel method, the individual... The probability of being selected The mathematical formula is: ； in, Let be the virtual fitness of the i-th individual. Population size.

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