Multi-target optimization method for multi-node water surface platform search formation parameters

Abstract

The invention provides a multi-target optimization method for a multi-node water surface platform formation parameter, and the method achieves the multi-dimensional decision vector and multi-target optimization of the multi-node water surface platform formation parameter optimization through employing a multi-target particle swarm algorithm on the basis of defining a region dynamic coverage evaluation index and the parameterized representation of a search formation. And the coverage speed is improved while the effective coverage rate is improved. According to the method, the target existence probability is introduced, and the efficiency evaluation of the coverage effect is realized; the formation and the platform spacing are represented by parameterization, so that the difficulty of obtaining the optimal search path is reduced; and the formation parameters are solved by adopting a multi-target particle swarm optimization algorithm, so that the optimization efficiency of the parameter optimization method is improved.

Description

Technical Field

[0001] The invention relates to the technical field of multi-node surface platform search path, and mainly relates to a multi-objective optimization method for searching formation parameters of a multi-node surface platform. Background Art

[0002] Traditional multi-node surface platform search path optimization methods for regional coverage mostly establish optimization models for a single optimization objective, facing the challenge of model mismatch in complex dynamic environments. In addition, since multi-node surface platform searches often use fixed formations to cover the search area when performing search tasks, frequent changes in speed and heading will seriously affect the detection performance of sonar equipment. Therefore, a reasonable search formation is an effective means to improve the search efficiency of multi-node surface platforms.

[0003] The closest technical solution: In the existing technology, domestic and foreign scholars mainly design the optimization of multi-node surface platform formations in combination with combat scenarios. Han Qing et al. introduced in detail the common formations and uses such as single column, single horizontal column, echelon, azimuth and V-shaped formations. Li Hao et al. established a comprehensive evaluation index system for typical formation search formations, and applied the triangular fuzzy comprehensive evaluation method to optimize the formation search formation. In addition, Guo Chuanfu et al. discussed the towed array sonar model and determined the platform configuration when the formation used the towed array sonar for search, which has a certain reference value for the study of search formation optimization.

[0004] 1. Existing technologies for multi-node surface platform search path optimization mainly focus on a single optimization goal, ignoring the search path optimization in complex dynamic environments, and cannot optimize multiple indicators at the same time;

[0005] 2. Lack of consideration of the search efficiency of multi-node surface platforms in dynamic environments, resulting in the inability to fully utilize the multi-node surface platform search sonar detection performance; Summary of the invention

[0006] The purpose of the present invention is to overcome the deficiencies of the prior art and to provide a multi-objective optimization method for searching formation parameters of a multi-node surface platform.

[0007] The object of the present invention is achieved through the following technical solution: A multi-objective optimization method for searching formation parameters of a multi-node surface platform, comprising the following steps:

[0008] Step 1: Characterize the various formations involved in the search mission planning in a parameterized form, and apply the multi-objective particle swarm optimization algorithm based on the hierarchical sequence method to the formation parameter optimization. During the optimization process, multiple objectives are optimized in sequence according to the importance order to achieve efficient optimization of the multi-objective search efficiency;

[0009] Step 2: Introduce the target existence probability to construct a search performance evaluation index, which reflects the coverage rate and coverage speed of the dynamic environment during the search process.

[0010] In step 1, a set of formation parameters is regarded as a particle, and the search mechanism of the particle swarm algorithm is used to adjust the parameters of each particle to obtain the optimal multi-objective solution; a multi-objective optimization problem with n-dimensional decision variables and m-dimensional objective variables is expressed as:

[0011]

[0012] The decision vector is X = (x1, x2, ..., x n ), the space where it is located Ω, Ω={X∈R n}; The target space is the space where the m-dimensional vector F(X) is located; sort the m targets according to their importance, assuming that the sorting result is f1(X)>f2(X)>,...,>f m (X), among which f1(X) is the most important, f m (X) is the least important; during the optimization process, multiple objectives are optimized in sequence according to the order of importance; the optimization process is: first solve the optimization problem min f1(X), where X∈Ω, and get the optimal solution X (1) and the optimal value f1 * ; Then solve the optimization problem min f2(X), where X∈Ω1=Ω∩{Xf1(X)≤f1 *}, get the optimal solution X (2) and the optimal value Repeat the above process to solve the m target optimization problems and obtain an optimal decision vector X opt .

[0013] In step 2, the target existence probability is introduced to construct a multi-node surface platform coverage performance evaluation function;

[0014] Step 2.1: Single-objective evaluation indicator: area coverage

[0015] For the entire search area, in order to construct the optimization objective function, the regional coverage rate Q(k) is defined as the average probability of the target existing in the area, that is,

[0016]

[0017] Where P T (i,j,k) represents the probability of the target existing at the grid position (i,j) at time k; n x and n y Respectively represent the number of grids separated along the X-axis and Y-axis of the region, n x n y is the total number of grids in the area, and the initial existence probability of the target PT (i,j,1)=0.5, where i<n x ,j<n y ; The smaller the coverage rate Q(k) value is, the better the regional coverage performance at time k is;

[0018] Step 2.2: Multi-objective evaluation indicators: area coverage, coverage speed

[0019] According to the actual operational requirements in search path planning, the area coverage rate and coverage speed are taken as two optimization objectives of the multi-objective particle swarm algorithm and are defined as follows:

[0020]

[0021] Where k represents the detection time, K represents the total duration of the search task; when the optimization target is f1, the area coverage rate at the end of the optimization search task; when the optimization target is f2, the ratio of the duration used when the average probability of the target existence is 0.2 to the total duration of the task during the optimization search process. The smaller the value, the faster the coverage speed.

[0022] The beneficial effects of the present invention are as follows: the present invention is mainly applied to the field of search path planning for multi-node surface platforms, and proposes to use a particle swarm algorithm based on a hierarchical sequence method to simultaneously optimize two key indicators in the search process of multi-node surface platforms: area coverage and coverage speed, so as to achieve the purpose of solving the optimal search formation parameters, so as to plan a search formation for multi-node surface platforms that can better meet the coverage performance in a dynamic environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art or ordinary technicians, other drawings can be obtained based on these drawings without paying creative work.

[0024] Figure 1 It is a schematic diagram of the variation of area coverage with search time, which shows the curve of the variation of area coverage with search time during the multi-node surface platform search process and the value diagram of the two optimization objectives.

[0025] Figure 2 It is a schematic diagram of the Z-shaped round-trip transformation process, which represents the schematic diagram of the formation transformation process along with the formation parameters, and uses parameters to characterize the search formation.

[0026] Figure 3 Comparison curve of optimization objective 1: area coverage changing with the number of iterations during optimization iteration of conventional particle swarm algorithm and multi-objective particle swarm algorithm.

[0027] Figure 4Comparison curve of optimization goal 2: coverage speed changing with the number of iterations in the optimization iteration process of conventional particle swarm algorithm and multi-objective particle swarm algorithm. DETAILED DESCRIPTION

[0028] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the protection scope of the present invention.

[0029] The present invention is a multi-objective optimization method for searching formation parameters of a multi-node surface platform, and the core steps of the method include:

[0030] Step 1: Hierarchical Sequential Method

[0031] In traditional particle swarm algorithms, usually only a single objective function can be optimized. However, in the actual optimization process, it is often necessary to optimize multiple indicators at the same time. In order to meet this demand, the present invention proposes a multi-objective particle swarm algorithm, which adopts a hierarchical sequence method to achieve simultaneous optimization of multiple objectives.

[0032] The hierarchical sequence method is a commonly used method for multi-objective optimization. It sorts multiple objective functions according to priority and optimizes them layer by layer. By adopting the hierarchical sequence method, multiple objectives can be optimized simultaneously in the particle swarm algorithm. Specifically, a set of formation parameters can be regarded as a particle, and the search mechanism of the particle swarm algorithm can be used to adjust the parameters of each particle to obtain the optimal multi-objective solution. A multi-objective optimization problem with n-dimensional decision variables and m-dimensional objective variables can be expressed as:

[0033]

[0034] The decision vector is X = (x1, x2, ..., x n ), the space where it is located Ω, Ω={X∈R n}. The target space is the space where the m-dimensional vector F(X) is located. According to the idea of ​​the hierarchical sequence method, the m targets are sorted according to their importance. Assume that the sorting result is f1(X)>f2(X)>,...,>f m (X), among which f1(X) is the most important, f m (X) is the least important. During the optimization process, multiple objectives are optimized in order of importance. The optimization process is as follows: first solve the optimization problem min f1(X), where X∈Ω, and get the optimal solution X (1) and the optimal value f1 *; Then solve the optimization problem min f2(X), where X∈Ω1=Ω∩{Xf1(X)≤f1 *}, get the optimal solution X (2) and the optimal value Repeat the above process to solve the m target optimization problems and obtain an optimal decision vector X opt .

[0035] Step 2: Multi-node surface platform coverage performance evaluation function

[0036] Step 2.1: Single-objective evaluation indicator: area coverage

[0037] For the entire search area, in order to construct the optimization objective function, the regional coverage rate Q(k) is defined as the average probability of the target existing in the area, that is,

[0038]

[0039] Where P T (i,j,k) represents the probability of the target existing at the grid position (i,j) at time k; n x and n y Respectively represent the number of grids separated along the X-axis and Y-axis of the region, n x n y is the total number of grids in the area, and the initial existence probability of the target P T (i,j,1)=0.5, where i<n x ,j<n y The smaller the coverage rate Q(k) value is, the better the regional coverage performance at time k is.

[0040] Step 2.2: Multi-objective evaluation indicators: area coverage, coverage speed

[0041] According to the actual operational requirements in search path planning, the present invention takes the area coverage rate and coverage speed as two optimization objectives of the multi-objective particle swarm algorithm, which are defined as follows:

[0042]

[0043] In the formula, k represents the detection time, and K represents the total search task duration. When the optimization target is f1, the area coverage rate at the end of the optimization search task is optimized; when the optimization target is f2, the ratio of the time used when the average probability of the target existence is 0.2 to the total task duration is optimized. The smaller the value, the faster the coverage speed. The curve of the area coverage rate changing with the search time during the multi-node surface platform search process and the schematic diagram of the two optimization target values ​​are shown in the figure. Figure 1 shown.

[0044] Step 3: Algorithm Application and Pseudocode

[0045] Compared with the conventional particle swarm algorithm, the improved multi-objective particle swarm algorithm can select the optimization focus according to the combat requirements, adjust the optimization order of the objective function, and give the optimal combination of formation and spacing parameters that conform to the actual search process of sonar, so as to give full play to the combat capability of sonar equipment. The algorithm pseudo code is as follows:

[0046] Table 1 Pseudo code of multi-objective particle swarm algorithm

[0047]

[0048]

[0049] Embodiment: The typical specific implementation steps of this method are as follows:

[0050] Step 1: Search task modeling;

[0051] Step 1.1: Regularize the search area;

[0052] The irregular search area is simplified into a rectangular, trapezoidal or fan-shaped area. The present invention does not involve the search area simplification process.

[0053] Step 1.2: Sound propagation analysis;

[0054] The acoustic propagation law of the sonar operating frequency is analyzed for the environmental hydrological data measured historically or on-site. The present invention does not involve the acoustic propagation analysis process.

[0055] Step 1.3: Sonar detection performance analysis in the search area;

[0056] For the multi-node surface platform search mission area, the regional sonar detection performance in a complex ocean environment is analyzed. The present invention does not involve the performance analysis process.

[0057] Step 1.4: Binding of sonar working parameters;

[0058] According to the law of sound propagation, suitable sonar working parameters and sonar detection interval are bound. The present invention does not involve the binding process of sonar working parameters.

[0059] Step 2: Parametric characterization of the formation;

[0060] The various formations involved in the search mission planning are characterized in a parameterized form, mainly including straight round trip, rectangular surround, Z-shaped round trip, etc. The corresponding template parameters include direction, speed, barrier spacing, etc. The present invention does not involve the formation parameterization characterization process, but only takes the Z-shaped round trip formation parameterization as an example to describe the parameter type of particle swarm optimization.

[0061] When a multi-node surface platform implements a search task in the form of a node, it is necessary to consider the node formation and the spacing between each node. The present invention uses a Z-shaped round trip as an example to parameterize the node formation and node spacing involved in the search task, and the spacing of the nodes in the formation is determined by various parameters. The Z-shaped round-trip search formation establishes a plane rectangular coordinate system with a horizontal axis parallel to the long axis of the search area, a vertical axis parallel to the short axis of the search area, and the lower left corner of the search area as the coordinate origin.

[0062] The original Z-shaped round-trip formation is that the track of each node is composed of sides AB, BC, CD with a length of a, parallel to the Y axis, the interval between each node track is b, the departure interval is d, generally d≤a, and there are I tracks in total. First, the angle ∠BCD between the sides BC and CD in the original formation is set to 2α degrees, and then the formation is rotated clockwise by β degrees with the center of the area as the fulcrum to obtain the Z-shaped round-trip formation. The transformation process is as follows: Figure 2 As shown in the figure. After the transformation, each node route is like the letter "Z", and each node searches back and forth on the route, which is the origin of the name "Z-shaped round trip". At this time, when the search formation is a Z-shaped round trip, the tactical template parameters include length a, route interval b, route angle α, rotation angle β and node departure distance d, (x0, y0) is the center position of the search area.

[0063] Figure 2 Assume that it consists of I nodes, and the initial position of node number i is X i (0) = (x i (0),y i (0)), i = 1, 2, ..., I. The coordinates of the four points A, B, C, and D in the Z-shaped round trip trajectory of the i-th node are (x Ai ,y Ai ), (x Bi ,y Bi ), (x Ci ,y Ci ), (x Di ,y Di ), whose expression is:

[0064]

[0065] Formula (4) provides the mathematical characterization process of parameterizing the search path of a multi-node surface platform;

[0066] When performing a search mission, each node sails along each side of the formation to complete the search mission.

[0067] Step 3: Search formation parameter optimization method based on multi-objective particle swarm algorithm

[0068] Step 3.1: Particle Swarm Optimization

[0069] The particle swarm algorithm is used to optimize the parameters of the parameterized Z-shaped round-trip formation. The present invention does not involve the principle design of the particle swarm algorithm, but only explains the principle.

[0070] Particle swarm optimization algorithm is an optimization algorithm based on population. The population is called particle swarm, and the individuals in the particle swarm are called particles. Suppose there is a group f(x)p ​​consisting of I particles i (t), (i=1,2,...,N), where the i-th particle is represented by an m-dimensional vector x i (i=1,2,...,I), which represents the particle position; the "flying" speed of the i-th particle is also an m-dimensional vector, denoted by v i . Set as the maximized optimization objective function, the particle swarm optimization algorithm updates the position and velocity of individual particles according to formula (5).

[0071]

[0072] In formula (5), w is the inertia factor; and is called the particle acceleration coefficient; r1 and r2 are random numbers between [0, 1]; is the optimal position (individual optimal value) searched by the i-th particle so far, and its update rule is as follows:

[0073]

[0074] p g (t) is the optimal position (group optimal value) searched by the entire particle swarm so far, that is:

[0075] p g (t)∈{p1(t),p2(t),...,p N (t)f(p g (t)=max{f(p1(t)),f(p2(t)),...,f(p N (t))})} (10)

[0076] In the particle swarm algorithm, each particle searches for the optimal solution in the search space individually and records it as the current individual extreme value; the individual extreme value is shared with other particles in the entire particle swarm, and the optimal individual extreme value is used as the current global optimal solution p of the entire particle swarm. g All particles in the particle swarm are based on their current individual extreme values ​​p i and the global optimal solution p shared by the entire particle swarm g To adjust your speed and position.

[0077] Implementation details of the particle swarm optimization algorithm: The pseudo code in Table 1 and formulas (5), (6), and (7) provide specific implementation details of the multi-objective particle swarm optimization algorithm in the present invention, including parameter setting, iterative process, multi-objective fitness value optimization process, etc.

[0078] Step 3.2: Formation parameter optimization

[0079] The multi-node surface platform route is calculated according to the Z-shaped round-trip formation parameters corresponding to each particle in the particle swarm optimization algorithm. The sonar detection efficiency is analyzed according to the sonar working mode. The adaptability value corresponding to each particle parameter is calculated using formula (2) and formula (3). The optimal position of the particle and the optimal adaptability value calculation are updated through the pseudo code steps shown in Table 1.

[0080] Step 3.3: Optimization results analysis

[0081] In order to verify the effectiveness of the proposed method, a simulation experiment was conducted by taking the maximum coverage area at the end of the priority optimization search task as an example. The changes of the area coverage rate and coverage speed with the search time during the optimization iteration of the formation parameters of the conventional particle swarm algorithm and the multi-objective particle swarm algorithm were analyzed and compared. The changes with the number of iterations are shown in the following figure. Figure 3 and Figure 4 shown.

[0082] exist Figure 3 In the figure, we can see that the two curves show similar trends, which indicates that during the optimization process, the effective area coverage of the two algorithms gradually decreases with the increase of the number of iterations. Under the same number of iterations, the final coverage effect of the multi-objective particle swarm algorithm is better than that of the conventional particle swarm algorithm.

[0083] exist Figure 4 In the figure, we can see that the changing trends of the two curves are different. In the optimization process of the conventional particle swarm algorithm, the regional coverage speed is not optimized. At this time, the regional coverage speed changes naturally with the increase of the effective area coverage rate, and the coverage speed of the next iteration is slower than that of the previous iteration. In the optimization process of the multi-objective particle swarm algorithm, while the regional coverage rate increases with the number of iterations, the regional coverage speed is also optimized to be faster, and the situation of the conventional particle swarm algorithm will not occur. Compared with the conventional particle swarm algorithm, its final coverage speed is also faster.

[0084] Based on the definition of regional dynamic coverage evaluation indicators and search formation parameterization, the present invention uses a multi-objective particle swarm algorithm to solve the multi-dimensional decision vector and multi-objective optimization problem of multi-node surface platform formation parameter optimization, thereby improving the effective coverage rate and the coverage speed. The present invention introduces the probability of target existence to achieve the performance evaluation of the coverage effect; uses parameterization to characterize the formation and platform spacing to reduce the difficulty of obtaining the optimal search path; and uses a multi-objective particle swarm optimization algorithm to solve the formation parameters, thereby improving the optimization efficiency of the parameter optimization method. The simulation results show that the search formation given by the formation parameter optimization method can meet the regional coverage requirements in a complex dynamic environment, ensure that there is enough time to re-search the searched area, reduce the target loss problem caused by target movement, and improve the target discovery probability.

[0085] Glossary of relevant technical terms

[0086] 1. Target existence probability: The probability that the target exists in a specific location, used to evaluate search effectiveness;

[0087] 2. Parametric representation: The characteristics of a complex system or model are represented by a set of parameters to facilitate mathematical modeling and optimization;

[0088] 3. Particle Swarm Optimization Algorithm: An optimization algorithm based on swarm intelligence that seeks the optimal solution by simulating the social behavior of bird flocks or fish schools.

[0089] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A multi-objective optimization method for searching formation parameters of a multi-node surface platform, characterized by: The steps include: Step 1: Characterize the various formations involved in the search mission planning in a parameterized form, and apply the multi-objective particle swarm optimization algorithm based on the hierarchical sequence method to the formation parameter optimization. During the optimization process, multiple objectives are optimized in sequence according to the importance order to achieve efficient optimization of the multi-objective search efficiency; Step 2: Introduce the target existence probability to construct a search performance evaluation index, which reflects the coverage rate and coverage speed of the dynamic environment during the search process.

2. The multi-objective optimization method for searching formation parameters of a multi-node surface platform according to claim 1 is characterized by: In step 1, a set of formation parameters is regarded as a particle, and the search mechanism of the particle swarm algorithm is used to adjust the parameters of each particle to obtain the optimal multi-objective solution; a multi-objective optimization problem with n-dimensional decision variables and m-dimensional objective variables is expressed as: min F(X)=(f1(X),f2(X),...,f m (X)) (1) stX∈Ω The decision vector is X = (x1, x2, ..., x n ), the space where it is located Ω, Ω={X∈R n }; The target space is the space where the m-dimensional vector F(X) is located; sort the m targets according to their importance, assuming that the sorting result is f1(X)>f2(X)>,...,>f m (X), among which f1(X) is the most important, f m (X) is the least important; during the optimization process, multiple objectives are optimized in sequence according to the order of importance; the optimization process is: first solve the optimization problem min f1(X), where X∈Ω, and get the optimal solution X (1) and the optimal value Then solve the optimization problem min f2(X), where Get the optimal solution X (2) and the optimal value Repeat the above process to solve the m target optimization problems and obtain an optimal decision vector X opt .

3. The multi-objective optimization method for searching formation parameters of a multi-node surface platform according to claim 2 is characterized by: In step 2, the target existence probability is introduced to construct a multi-node surface platform coverage performance evaluation function; Step 2.1: Single-objective evaluation indicator: area coverage For the entire search area, in order to construct the optimization objective function, the regional coverage rate Q(k) is defined as the average probability of the target existing in the area, that is, Where P T (i,j,k) represents the probability of the target existing at the grid position (i,j) at time k; n x and n y Respectively represent the number of grids separated along the X-axis and Y-axis of the region, n x n y is the total number of grids in the area, and the initial existence probability of the target P T (i,j,1)=0.5, where i<n x ,j<n y ; The smaller the coverage rate Q(k) value is, the better the regional coverage performance at time k is; Step 2.2: Multi-objective evaluation indicators: area coverage, coverage speed According to the actual operational requirements in search path planning, the area coverage rate and coverage speed are taken as two optimization objectives of the multi-objective particle swarm algorithm and are defined as follows: Where k represents the detection time, K represents the total duration of the search task; when the optimization target is f1, the area coverage rate at the end of the optimization search task; when the optimization target is f2, the ratio of the duration used when the average probability of the target existence is 0.2 to the total duration of the task during the optimization search process. The smaller the value, the faster the coverage speed.

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