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

Abstract

The invention relates to a multi-unmanned aerial vehicle (UAV) search strategy optimization method based on genetic programming (GP), which is characterized in that under a distributed model predictive control (DMPC) framework, each UAV is guided by a target function to realize a search trajectory optimization process, and essentially, a search strategy is converted into a mathematical logic mapping relation. In a traditional method, objective function construction mainly depends on a design thought dominated by artificial experience, and the fixed search mode based on subjectivity has the limitations of insufficient environmental adaptability, weak strategy generalization ability and the like in a complex dynamic environment. In order to solve the problem, the invention provides a search strategy optimization method based on a genetic programming algorithm, and online dynamic evolution and parameter adaptive adjustment of a search strategy are realized by establishing a dynamic mapping model between a strategy parameter space and a search performance index.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of positioning accuracy measurement methods, and particularly relates to a multi-unmanned aerial vehicle search strategy optimization method based on genetic programming. BACKGROUND

[0002] With the rapid development of Internet of Things technology, unmanned aerial vehicles are widely used in reconnaissance, surveillance, search and rescue, environmental monitoring and other fields due to their small size, flexibility and easy control. Multi-unmanned aerial vehicle cooperative search technology is an important research direction, and its core function is to help unmanned aerial vehicles autonomously plan search paths in a wide unknown environment, so that the unmanned aerial vehicles can quickly find targets and provide initial information for subsequent identification, tracking or hunting algorithms.

[0003] So far, it still faces three technical challenges to build a multi-unmanned aerial vehicle cooperative search system with flexibility, efficiency and robustness in a complex adversarial environment. First, existing researches focus on static target search scenarios, and for dynamic targets with strong randomness, existing methods have problems such as significant search efficiency decay and limited target capture probability. The core problem is the lack of coupled optimization mechanism for target motion prediction and dynamic adjustment of search strategy. Second, traditional cooperative search methods generally rely on centralized controllers or pre-set stable communication links, which fundamentally contradict the actual adversarial environment. In the battlefield environment where electronic countermeasures occur frequently and communication infrastructure is damaged, it is difficult for unmanned aerial vehicles to establish fast and reliable communication links, and there are communication constraints and limited computing resources. In addition, existing methods lack the ability to respond to sudden situations during the task, neither establishing an effective dynamic threat avoidance model nor having a group self-reconstruction strategy when an individual fails, resulting in poor system robustness that cannot meet the needs of high-adversarial scenarios. The breakthrough of the above bottleneck problems requires the development of new distributed cooperative architecture and adaptive decision-making algorithms to realize the intelligent emergence and autonomous cooperation of multi-unmanned aerial vehicles. SUMMARY

[0004] The technical problem to be solved by the application is to provide a multi-unmanned aerial vehicle search strategy optimization method based on genetic programming, which solves the above technical problems.

[0005] A multi-unmanned aerial vehicle search strategy optimization method based on genetic programming, comprising the following steps:

[0006] Step 1, initializing a population set SS using a genetic programming method 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 traverse 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 target existence probability in the time grid (m, n); The target existence probability in the time grid (m, n); k The target existence probability in the time grid (m, n);

[0023]

[0024] Wherein, η p represents the target discovery threshold;

[0025] The maximum area exploration benefit strategy J2 is used to measure the reduction effect of the UAV on the environmental uncertainty in the continuous search process, and is represented by maximizing the information gain of the task area. Since p mn (t k+1 ) value will change according to the target detection result, therefore, the mathematical expectation value of e mn (t k+1 ) is calculated as follows:

[0026]

[0027] In the formula, P mn (t k+1 ) and e′ mn (t k+1 ) represent the target existence probability and information entropy value when the target is detected, and e″ mn (t k+1 ) represent the target existence probability and information entropy value when the target is not detected;

[0028] The maximum area exploration benefit of the UAV i at time t k is represented as:

[0029]

[0030] The maximum revisit detection benefit strategy function J3 represents the detection benefit obtained by the UAV when repeatedly searching the grid with a long visited time interval. The total amount of pheromone in the task area is used to represent it, and the maximum revisit detection benefit of the UAV i at time t k is calculated as follows:

[0031]

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

[0033] ​​Maximizing the communication connectivity benefit J4 represents the benefit generated by the multi-UAVs being able to maintain a global communication connectivity state under the condition of limited communication distance, t k The communication connectivity benefit J of the UAV i at time t 4,i k The calculation method is as follows:

[0034]

[0035] In the formula, represents the communication link state of the UAV group at time t k The repulsion force received by the UAV i is represented as the obstacle avoidance benefit J 5,i k of the UAV i at time t k The calculation method of the maximum obstacle avoidance benefit strategy of the UAV i at time t

[0036]

[0037] In the formula, ||F ij k || represents the sum of the repulsion forces received by the UAV i and the UAV j, which can be calculated as:

[0038]

[0039] In the formula, dis(i,j) represents the distance between the ith UAV and the jth UAV and the obstacle grid unit, and d s is the UAV obstacle avoidance safety distance.

[0040] Further, in step 5, when selecting individuals from the population by roulette method, the selected probability of the individual i The mathematical formula is as follows:

[0041]

[0042] Among them, is the virtual fitness of the ith individual, and N pop is the population size.

[0043] The beneficial effects of the present application are:

[0044] In the traditional method, the construction of the objective function mainly relies on the design idea dominated by artificial experience. Such a fixed search mode based on subjectivity has limitations such as insufficient environmental adaptability and weak strategy generalization ability in complex dynamic environments. To solve this problem, the present method proposes a search strategy optimization method based on genetic programming algorithm, which realizes online dynamic evolution and parameter adaptive adjustment of the search strategy by establishing a dynamic mapping model between the strategy parameter space and the search performance index. ​​​BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 Flow chart of the method of the present application;

[0046] Figure 2 Tree coding structure diagram of the search strategy;

[0047] Figure 3 Flow chart of the crossover operator operation;

[0048] Figure 4 Flow chart of the subtree mutation operation;

[0049] Figure 5 Flow chart of the node mutation operation;

[0050] Figure 6 Flow chart of the promotion mutation operation; Figure 7 Visualization analysis diagram of the Pareto front; Figure 8 Multi-UAV search trajectory schematic diagram obtained by simulation verification using different methods. DETAILED DESCRIPTION

[0051] The principles and features of the present application are described below in conjunction with the accompanying drawings, which are only used to explain the present application and are not intended to limit the scope of the present application.

[0052] Under the distributed model predictive control (DMPC) framework, each unmanned aerial vehicle (UAV) realizes the process of search trajectory optimization through the guidance of the objective function, which is essentially to convert the search strategy into a mathematical logic mapping relationship. In the traditional method, the construction of the objective function mainly relies on the design idea dominated by artificial experience. This fixed search mode based on subjectivity has limitations such as insufficient environmental adaptability and weak strategy generalization ability in complex dynamic environments. To solve this problem, the present application proposes a search strategy optimization method based on genetic programming algorithm, which realizes the online dynamic evolution and adaptive adjustment of the search strategy by establishing a dynamic mapping model between the strategy parameter space and the search performance index.

[0053] 1. Selection of search strategy

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

[0055] (1) Maximize target detection revenue strategy

[0056] The target detection revenue function J1 represents the possibility of discovering the target along the way during the flight process of the UAV from the current position to the target position. After the search trajectory of the given unmanned aerial vehicle i is given, the detection area range is A i , and the target detection revenue J 1,i(t k ) can be expressed as:

[0057]

[0058] wherein, represents the target existence probability in the grid (m, n) at time t k ; represents whether the target is detected by the UAV in the grid (m, n) at time t k , and the calculation method is as follows:

[0059]

[0060] wherein, η p represents a target discovery threshold.

[0061] (2) Strategy of maximizing regional exploration benefit

[0062] The regional exploration benefit function J2 is used to measure the effect of reducing the uncertainty of the environment in the continuous search process of multiple UAVs, which can be represented by maximizing the information gain of the task area. Since the value of p mn (t k+1 ) will change according to the target detection result, the mathematical expectation value of e mn (t k+1 ) is calculated as:

[0063]

[0064] In the formula, P mn (t k+1 ) and e′ mn (t k+1 ) represent the target existence probability and the information entropy value when the target is detected, and e″ mn (t k+1 ) represent the target existence probability and the information entropy value when the target is not detected, respectively.

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

[0066]

[0067] (3) Strategy of maximizing revisit detection benefit

[0068] The UAV revisits the undetected area. The revisit detection benefit function J3 represents the detection benefit obtained by the UAV when repeatedly searching the grid with a long time interval. The total amount of pheromone in the task area is used to represent it, and the calculation method is as follows:

[0069] ​

[0070] where s mn (t k ) denotes the pheromone concentration in the grid (m, n) at time t. k

[0071] (4) Maximizing the communication connectivity benefit strategy

[0072] The communication connectivity benefit J4represents the benefit of maintaining global communication connectivity of multiple UAVs under the condition of limited communication distance. Based on the proposed communication connectivity rate indicator, the communication connectivity benefit J 4,i (t k ) of UAV i is calculated as follows:

[0073]

[0074] where denotes the communication link state of the UAV group at time t k

[0075] (5) Maximizing the collision avoidance and obstacle avoidance benefit strategy

[0076] Multiple UAVs need to avoid threat areas and inter-UAV collisions during cooperative search. Inspired by the artificial potential field method, the threat area grid and the adjacent UAV grid will exert a repulsive force on the UAV. The reciprocal of the total repulsive force experienced by UAV i is taken as the collision avoidance and obstacle avoidance benefit J 5,i (t k ), which is calculated as follows:

[0077]

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

[0079]

[0080] where dis(i, j) denotes the distance between the ith UAV and other UAVs and obstacle grid cells, and d s is the UAV collision avoidance safety distance.

[0081] Since numerical operations on the performance functions corresponding to the above search strategies are required in subsequent genetic programming operations, in order to avoid the influence of the different orders of magnitude of the performance functions on the calculation results, the numerical size of the performance functions needs to be normalized:

[0082]

[0083] where ​​denotes the normalized value of the ith objective function; to avoid invalid operations caused by denominator of 0, the normalization interval is set to [f min ,f max ] and f min = 1, f max = 100.

[0084] 2. Encoding design and population initialization

[0085] Genetic programming (GP) usually encodes individuals using tree structure, where the root node represents a function or operation, and the leaf node represents a variable or constant. To evolve better search strategies through genetic programming, this paper designs a new tree structure to encode and represent multiple heuristic search strategies, which includes discriminative nodes, attribute nodes, and function nodes.

[0086] The discriminative node is located at the top layer of the tree structure, containing two states of "Rise" and "Fall". Among them, "Rise" means maximizing the lower expression to achieve the optimum, and "Fall" means minimizing the lower expression to achieve the optimum. The attribute node includes the five objective function nodes mentioned above and a constant node Const ∈ {0.2, 0.6, 0.8}. The function node is shown in Table 1. In addition to basic arithmetic operators, two types of function nodes, logarithmic function and exponential function, are added. Exponential function can amplify the difference through nonlinear amplification, thereby amplifying the weight to highlight the key strategy; the logarithmic function can compress the difference of input values, thereby balancing the weight to balance the contribution of multiple strategies.

[0087] As shown in Figure 2 , the objective function represented by this tree structure is: Initialize the genetic programming (GP) population. Since all strategies use the maximum return function, the discriminative node is set to "rise". The depth of the GP tree is limited between 2 to 4 layers (not including the top layer discriminative node). The population initialization process is as follows:

[0088] Step 1: Build a full node tree: limit attribute elements at the bottom, randomly configure attribute / function elements at the upper layer, and clear the lower layer connection 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 discriminative node to "rise";

[0091] Step 4: Repeat the above steps N pop times to finally generate an initial GP tree population.

[0092] Given that all heuristic strategies maximize the reward function, the decision node is set to "rise" uniformly. The GP tree depth is defined as the number of layers excluding the top node, and the population is initialized using the Ramped half-and-half method, with the tree depth limited to 2-4 layers. The population initialization process is as follows:

[0093] 1) Construct a full node tree: limit the bottom layer to attribute elements, randomly configure attribute / function elements on the upper layer, and clear the connections under the attribute node;

[0094] 2) Randomize parameters: randomly select function / attribute parameters from the corresponding set;

[0095] 3) Node shaping: set the top decision node to "rise";

[0096] Repeat the above steps N pop times, and finally generate an initial GP tree population of size N pop .

[0097] Table 1 Set of function node elements

[0098]

[0099] 3. Genetic operations

[0100] Genetic operations are the key mechanism to ensure the global search efficiency of the algorithm, and the population diversity maintenance and high-quality gene inheritance are achieved through genetic operators. This algorithm uses three-stage genetic operation operators, including selection operator, crossover operator and mutation operator. The specific operations are as follows

[0101] 1) Selection operator

[0102] In the evolutionary iteration process of genetic programming, first, the roulette selection mechanism is used to sample individuals probabilistically based on fitness values, and GP individuals with high fitness are preferentially selected as parent individuals for genetic operations. This mechanism builds a probability distribution model by normalizing fitness values, so that individuals with high fitness have a higher selection probability, while individuals with low fitness are given the opportunity to evolve, thereby achieving a dynamic balance between the convergence pressure of elitist strategy and the maintenance of population diversity. The mathematical formula is:

[0103]

[0104] where, is the probability of individual i being selected, is its virtual fitness, N pop is the population size

[0105] 2) Crossover operator When the random number triggers the crossover probability threshold P C , perform 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 all individuals in L l , sort them by the fitness value of each objective function from small to large. Then calculate the crowding distance of each individual under each objective function and sum them up (in the objective function f j , the crowding distance of the individual with the minimum fitness and the maximum fitness will be assigned a maximum value):

[0116]

[0117] Where Dis h represents the crowding distance of individual h in L l , h∈{1,2,...,|L l |} is the individual number after sorting; represents the fitness of the individual ranked as h under the jth objective function; and represent the maximum fitness value and the minimum fitness value under the jth objective function, respectively.

[0118] Step 3: based on the number of non-dominated solution layers and the crowding distance, calculate the virtual fitness of the individual. First, the individual with a lower layer number in different non-dominated layers has a higher virtual fitness; in the same non-dominated layer, the individual with a larger crowding distance has a higher virtual fitness. The individual with a higher virtual fitness has a higher sorting value s i , the virtual fitness of the ith individual can be calculated as

[0119]

[0120] Step 4: based on the virtual fitness of the individual, select P s individuals from the population to generate a sub-population SS sub by roulette method, traverse each individual in the sub-population SS sub , and perform crossover and mutation operations in turn.

[0121] Step 5: determine whether the maximum number of iterations is reached. If not, repeat steps 1 to 4. If yes, output the optimal Pareto solution set.

[0122] The pseudo code of the method of the application is as follows:

[0123] Input: population size N pop , maximum number of iterations max_gen, crossover rate P C , mutation rate P M , attribute node set S Att , function node set S fun ​, GP tree depth range, training example set S train ;

[0124] Output: Pareto-optimal individual set SS final

[0125]

[0126]

[0127]

[0128] Simulation verification

[0129] The search task area is set to 2000m x 1000m, which contains 8 dynamic targets and 7 circular threat areas with a radius of 30m-50m. In order to simulate the random motion state of the target, 3 kinds of target motion modes are set in the dynamic simulation, which are "straight line motion", "random motion" and "sinusoidal periodic maneuver". Among them, the target heading angle remains unchanged in straight line motion, the target speed and heading angle change randomly with 10% probability in random motion, and the target heading angle changes with sinusoidal period in sinusoidal periodic maneuver. The specific motion parameters of the target are shown in Table 2. The unmanned aerial vehicle cluster is composed of 5 multi-rotor unmanned aerial vehicles with different performance parameters, and the performance parameters are shown in Table 3, in which the early warning distance represents the advance perception distance of the unmanned aerial vehicle to the threat area. The parameters of the distributed decision-making method based on DMPC and the parameters of 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 unmanned aerial vehicle cluster

[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. Parts not detailed herein are common knowledge to those skilled in the art. The scope of protection of the present invention is determined by the claims. Any equivalent modifications 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, The method comprises the following steps: Step 1, initialize the population set SS by using genetic programming method total Each individual in the population is a GP tree coding structure, and the bottom attribute nodes include the strategies of maximizing target detection benefit, maximizing area exploration benefit, maximizing revisit detection benefit, maximizing communication connectivity benefit, and maximizing collision avoidance and obstacle avoidance benefit, and the upper random configuration attribute / function elements, and the function / attribute parameters are randomly selected when each individual is initialized; Step 2, calculate the average target existence probability avg of each individual in the population prob and the average environmental uncertainty avg uncer , select the average target existence probability avg prob and the average environmental uncertainty avg uncer as the objective function f1 GP and f2 GP to evaluate the GP individual fitness, the formula of the objective function f1 GP and f2 GP is as follows: where |S train | represents the number of individuals in the population; Step 3, stratifying individuals in the population by using non-dominant relations, and recording the layer where the individual is located, the individuals in the same layer are in non-dominant relations with each other, and the upper-layer individuals dominate the lower-layer individuals; All individuals in L l For all individuals in L, sort them by the fitness value of each objective function from small to large, and then calculate the crowding distance of each strategy. The formula for calculating the crowding distance is as follows: where Dis h denotes the crowding distance of individual h in L l h∈{1,2,...,|L l |} is the individual number after sorting; denotes the fitness of individual h ranked as h under the jth objective function; and denote the maximum fitness value and the minimum fitness value under the jth objective function, respectively; Step 4, sort the individuals based on the non-dominated solution layer number and the crowding distance, first, in different non-dominated layers, the lower the layer number of the individual, the higher the virtual fitness; in the same non-dominated layer, the larger the crowding distance of the individual, the higher the virtual fitness, the higher the virtual fitness of the individual, the higher the sorting value, calculate the virtual fitness of each individual, the virtual fitness of the i-th individual The calculation formula is: where N is the total number of individuals in the population, s is the number of individuals in the selected subset, and i is the rank of the virtual fitness value of the ith individual. pop where N is the total number of individuals in the population, s is the number of individuals in the selected subset, and i is the rank of the virtual fitness value of the ith individual. i where N Step 5, select P individuals from the population by roulette method based on individual virtual fitness s Generate a sub-population SS of individuals sub , traverse each individual in the sub-population SS sub , perform cross and mutation operations in turn to obtain an updated population, increment the iteration number by 1, and obtain the optimal individual set corresponding to the updated population by the method of steps 2-4 and put it into a temporary set SS temp ; Step 6, compare SS based on non-dominance relation final and SS temp ; select better individual and update SS final , judge whether the maximum iteration number is reached, yes, go to step 7, otherwise, go back to step 1 Step 7, output the final optimal individual set SS final The optimal individual in the set corresponds to the maximum target detection benefit strategy, the maximum area exploration benefit strategy, the maximum revisit detection benefit strategy, the maximum communication connectivity benefit strategy and the maximum collision avoidance and obstacle avoidance benefit strategy as the optimal strategy output.

2. The genetic programming based multi-UAV search strategy optimization method of claim 1, wherein, The maximization target detection yield strategy J1 represents the possibility of the UAV discovering the target along the way in the flight process from the current position to the target position, and after the search trajectory of the unmanned aerial vehicle i is given, the detection area range is A i , t k The target detection yield J 1,i of the unmanned aerial vehicle i at the moment t k is represented as: wherein, represents t k the target existence probability in the time grid (m, n); represents whether the target is detected by the UAV i in the grid (m, n) at time t k the time grid (m, n); wherein η p represents a target discovery threshold, 1 represents that a target is detected, and 0 represents that a target is not detected; The maximum area exploration reward strategy J2 is used to measure the reduction effect of the UAV on the environmental uncertainty in the continuous search process, which is represented by maximizing the information gain of the task area. Since the value of p mn (t k+1 ) will change according to the target detection result, the mathematical expectation value of e mn (t k+1 ) is calculated as follows: ​ where P mn (t k+1 ) and e' mn (t k+1 ) represent the target existence probability and the information entropy value when the target is detected, and e" mn (t k+1 ) represent the target existence probability and the information entropy value, respectively, when the target is not detected. t k The maximized area exploration benefit of the drone i at the moment is represented as: The maximum revisit detection benefit strategy function J3 represents the detection benefit obtained by the UAV when repeatedly searching the grid with a long visited time interval, and the total amount of pheromone in the task area is used to represent t k The maximum revisit detection benefit strategy calculation method of the UAV at the moment i is as follows: where s mn (t k ) denotes the pheromone concentration in the grid (m, n) at time t k . Maximizing the communication connectivity benefit J4 represents the benefit generated by the multi-UAVs being able to maintain a globally connected communication state under the condition of limited communication distance, t k The communication connectivity benefit J of the UAV i at time t 4,i (t k ) is calculated as follows: In the formula, represents the communication link state of the UAV group at time t k 0 represents; the reciprocal of the total repulsive force suffered by the UAV i as the collision avoidance and obstacle avoidance benefit t k The maximum collision avoidance and obstacle avoidance benefit strategy calculation method of the UAV i at time t where ||F ij (t k represents the sum of repulsive forces experienced by UAV i and UAV j, which can be calculated as: In the formula, dis(i, j) represents the distance between the i unmanned aerial vehicle and the j unmanned aerial vehicle and the obstacle grid cell, d s is the safety distance of the unmanned aerial vehicle collision avoidance.

3. The genetic programming based multi-UAV search strategy optimization method of claim 1, wherein, In step 5, the probability of selection of individual i is given by roulette wheel selection from the population The mathematical formula is: wherein, is the virtual fitness of the ith individual, N pop is the population size.

Images