A ship path planning method based on fixed and random particle population optimization

Abstract

The present invention discloses a ship path planning method based on fixed and random particle population optimization. The method first provides a fixed and random multi-particle population initialization method, generates a number of fixed particle populations and random particle populations as initial populations, wherein the particles represent the positions of ships. Secondly, the initial population is divided into multiple sub-populations according to the sub-fitness function. Then, the position and speed of each particle in the sub-population are iteratively updated, and its fitness value is calculated to obtain the individual optimal value and the sub-population global optimal value. Finally, the global optimal value is continuously updated until the maximum number of iterations is reached, and then the global optimal values ​​of all sub-populations are compared to obtain the optimal navigation position coordinates of the ship at the future moment. The present invention effectively improves the ability of the algorithm to handle complex problems, and demonstrates the effectiveness of the method in handling path planning problems, and accurately and efficiently realizes the optimal path planning of the ship.

Description

Technical Field

[0001] The present invention belongs to the field of swarm intelligence optimization, and in particular relates to a ship path planning method based on fixed and random particle population optimization. Background Art

[0002] As an important technology in the field of maritime transportation and shipping, the main task of ship path planning is to comprehensively consider a variety of complex factors and design an optimal navigation route for ships that is safe, efficient, economical and environmentally friendly. This planning process usually requires a comprehensive analysis of the geographical environment of the target sea area, established routes, and the ship's own performance to ensure that the ship can reach the destination at the optimal cost and time while avoiding risks. In recent years, with the rise of intelligent algorithms, various optimization methods have gradually been applied to ship path planning. Among them, the particle swarm optimization algorithm (PSO) has become one of the mainstream technologies for solving this problem due to its simple theoretical framework, high optimization efficiency, and easy implementation and parameter adjustment.

[0003] However, the performance of the PSO algorithm is deeply affected by its initial population configuration, and the quality of the initial population is directly related to the algorithm's ability to explore the search space. The fixed point population generation strategy can ensure that the entire search space is evenly covered, but its disadvantage is that it may reduce the diversity of the population. The random population generation strategy is the most common initialization method in the particle swarm optimization (PSO) algorithm, which can ensure the diversity of the population, but when the search space is large, it may cause particles to gather in certain specific areas and ignore other potential areas. In response to this, we introduced a population initialization method that combines fixed and random particles to ensure that the initial population is evenly distributed in the search space without losing randomness. However, its inherent limitation is that it relies on only one initial population for search. This single population search strategy often leads to limited search directions, making it difficult to fully explore the entire search space, thereby weakening the algorithm's ability to jump out of the local optimal solution. Especially when facing complex and changing problems, which are usually accompanied by multiple constraint functions and complex optimization objectives, a single population search strategy will make the algorithm less flexible. Aiming at the problem that the traditional particle swarm algorithm is prone to fall into the local optimal solution due to unreasonable population initialization, an improved method is proposed. The multi-population method is introduced to ensure that the initial population is composed of multiple sub-populations, and each sub-population is composed of particles that perform best in various aspects of the optimization problem, which improves the ability of the PSO algorithm to jump out of the local optimal solution and the optimization accuracy. Summary of the invention

[0004] In view of the shortcomings of the existing PSO algorithm population initialization, the present invention proposes a ship path planning method based on fixed and random particle population optimization. While using fixed particles and random particles to form the initial population, the method divides it into multiple sub-populations, wherein each sub-population is composed of particles that perform best in various aspects of the optimization problem, can adapt to various constraints in ship path planning, effectively improves the optimization accuracy of the PSO algorithm, and ultimately realizes the optimal path planning of the ship.

[0005] The present invention proposes a ship path planning method based on fixed and random particle population optimization, which includes the following steps:

[0006] (1) A fixed and random multi-particle population initialization method is given to generate a number of fixed particle populations and random particle populations as initial populations. The initial populations are uniformly distributed in the ship position search space without losing randomness, where the particles represent the ship positions.

[0007] (2) Divide the initial population in step (1) into multiple sub-populations according to the sub-fitness function, ensuring that the particles contained in each sub-population, that is, the navigation position coordinates of the ship at the future moment, can adapt to the various constraints of the ship path planning.

[0008] (3) Iteratively update the position and velocity of each particle in the sub-population and calculate its fitness value to obtain the individual optimal value and the global optimal value of the sub-population.

[0009] (4) Repeat the above step (3) and continuously update the global optimal value until the maximum number of iterations is reached. Then compare the global optimal values ​​of all sub-populations to finally obtain the optimal navigation position coordinates of the ship at the future moment.

[0010] Beneficial effects of the present invention:

[0011] The ship path planning method based on fixed and random particle population optimization proposed in the present invention first generates fixed particles by using a method of evenly dividing intervals, and randomly generates the remaining particles, and the two are combined to form an initial population; then, the fitness of each particle in the initial population is sorted according to multiple constraints in the ship path planning problem, and the initial population is divided into multiple sub-populations according to the sorting result, wherein each sub-population is composed of some particles that perform best in each constraint condition; it is iterated in sequence, the position and speed of each particle in the sub-population are continuously updated, its fitness value is calculated, the individual optimal value and the sub-population optimal value are obtained, and then compared with the remaining sub-populations to obtain the global optimal value, that is, the optimal position of the ship at the next moment, which effectively improves the ability of the algorithm to handle complex problems and demonstrates the effectiveness of the method in handling path planning problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 It is a flowchart of the program of the method of the present invention;

[0013] Figure 2 It is the result graph of ship path planning;

[0014] Figure 3 This is a comparison chart of experimental results. DETAILED DESCRIPTION

[0015] The ship path planning method based on fixed and random particle population optimization proposed in the present invention has a flow chart as shown in Figure 1 As shown, the final planned result path is as follows Figure 2 As shown, the planning process includes the following steps:

[0016] (1) A fixed and random multi-particle population initialization method is given to generate several fixed particle populations and random particle populations as the initial populations, and ensure that the initial populations are uniformly distributed in the ship position search space without losing randomness.

[0017] (2) Divide the initial population in step (1) into multiple sub-populations according to the sub-fitness function, ensuring that the particles contained in each sub-population, that is, the navigation position coordinates of the ship at the future moment, can adapt to the various constraints of the ship path planning.

[0018] (3) Iteratively update the position and velocity of each particle in the sub-population and calculate its fitness value to obtain the individual optimal value and the global optimal value of the sub-population.

[0019] (4) Repeat the above step (3) and continuously update the global optimal value until the maximum number of iterations is reached. Then compare the global optimal values ​​of all sub-populations to finally obtain the optimal navigation position coordinates of the ship at the future moment.

[0020] The specific steps of step (1) are as follows:

[0021] (1-1) The particle search space is divided. Specifically, the two-dimensional particle search space of the ship position is set as represents the dimension, here and Respectively represent the minimum and maximum values ​​of the search space boundary; define the particle swarm as ,in represents the particle swarm particles, of which Indicates the latitude of the ship's location, Indicates the longitude of the ship's location, and , Represents the total number of particles.

[0022] (1-2) Search space Divide evenly into intervals, the search space after division is ,in is the interval between two adjacent intervals, which can be expressed as

[0023] (1)

[0024] No. The first parameter to be optimized (longitude and latitude) Reference points It can be expressed as

[0025] (2)

[0026] (1-3) According to step (1-2), the search space of each parameter to be optimized can be evenly divided into intervals and reference point, using this Reference points can be defined

[0027] total The reference position of each particle is then adjusted each time. For a single reference point in

[0028] fixed particles; the remaining Random particles Randomly generate particles in the target search space, and combine the generated fixed particles and random particles to obtain the initial particle population.

[0029] For ease of understanding, here is an example to illustrate steps (1-1) to (1-3). The process is as follows:

[0030] Define the particle swarm as , set the two-dimensional particle search space representing the ship's position. Due to too many parameters, the position of the ship at the starting time is taken as an example: the latitude search space is , the longitude search space is

[0031] .

[0032] Divide the latitudinal search space evenly into intervals and reference points, the search space after division is [30.1759, 30.1816, 30.1873, 30.1930, 30.1988, 30.2045, 30.2102,30.2159], and the interval between two adjacent reference points is ; Similarly, the divided longitude search space is [122.6490, 122.6547, 122.6604, 122.6661, 122.6719, 122.6776, 122.6833,122.6890], with an interval of 0.0057.

[0033] Using the 8 latitude reference points and longitude reference points obtained after division, the 8 reference positions of the particles are defined as . Then, only a single reference point in the reference position is adjusted each time, and The fixed particles are shown in Table 1.

[0034] Table 1 Initial fixed particles

[0035]

[0036] Finally, randomly generate Particles, combined with the above fixed particles, constitute the initial population.

[0037] The specific steps of step (2) are as follows:

[0038] (2-1) Determine the algorithm fitness function ,in represents the first The fitness function of each child is To optimize the number of constraints in the problem, The constraints are "whether the ship passes through an obstacle", "the distance between the ship and the end of the route" and "the distance between the ship and the established route", that is, the number of sub-populations to be divided.

[0039] (2-2) Calculate the sub-fitness value of each particle in the semi-uniform initial population in step (1) , and get the sub-fitness matrix:

[0040] (3)

[0041] (2-3) The sub-fitness matrix is ​​calculated according to the first column, that is, the first sub-fitness value of the particle. Arrange in ascending order and take the first column corresponding to the arranged matrix The particles form the first subpopulation , where all particles are the best performing particles under the first constraint, and the initial population is divided into Subpopulation , each subpopulation consists of The particle composition is composed of some particles that perform best under the constraints.

[0042] For ease of understanding, an example is given here to illustrate the division process of the initial population generated in step (1):

[0043] Determine the ship's voyage Constraints: whether to pass through obstacles, the distance between the current position and the end position, and the distance between the current position and the established route, respectively, as sub-fitness functions , and , and determine the number of sub-populations to be divided to be 3.

[0044] Substitute all particles in the initial population into each sub-fitness function to calculate the fitness value, and the obtained sub-fitness matrix is ​​shown in Table 2.

[0045] Table 2 Sub-fitness matrix

[0046]

[0047] Then the sub-fitness matrix is ​​calculated according to the first column, that is, the first sub-fitness value of the particle. Sort in ascending order and take the first The particles corresponding to the rows form the first sub-population , where all particles are the 40 particles that perform best under the obstacle constraints. And so on, we get the sub-population and The initial population is divided, and each sub-population is composed of the top 40 particles that perform best under the corresponding constraints.

[0048] The specific steps of step (3) are as follows:

[0049] (3-1) Iteratively update the position and velocity of each particle in the sub-population, and define After iterations, the global optimal value of each subpopulation is , No. The optimal value of each subpopulation is ,in and Respectively represent Subpopulation The global optimal value at the iteration (marked as " ”) and The individual optimal value of each particle (marked as " ”), pp. The first Particles Represents; Particle The inertia weight is , the positive acceleration constants are , the position and velocity are and ,in and Respectively represent At the iteration, the particle In the The position and speed of the parameters to be optimized; when the At the iteration, Particles in a subpopulation Location and speed Update according to the following formula:

[0050] (4)

[0051] (5)

[0052] in, is a random number uniformly distributed in the interval [0,1].

[0053] (3-2) According to step (3-1), calculate the Particles In the The individual optimal value after iterations is , and compare it with the particle The fitness values ​​of all individuals in the iteration are compared, and the particle position corresponding to the minimum fitness value is the particle position of the Post-generation particles The individual optimal value of .

[0054] (3-3) According to step (3-2), we can obtain After the iteration In subpopulation The individual optimal value of each particle and its corresponding fitness value ; Known After the iteration The global optimal value of the subpopulation is , and compare it with Compare the optimal values ​​of all individuals in the generation, among which the minimum fitness value The corresponding particle position is The global optimal value of the population in the generation .

[0055] For ease of understanding, here is an example to illustrate steps (3-1) to (3-4). The process is as follows:

[0056] For subpopulations , set the maximum number of iterations , initial inertia weight , positive acceleration constant , , the initial global optimal value is infinite, and the speed of each particle is initialized. Due to too many parameters, only the sub-population is listed here The first particle in The operation process.

[0057] particle The starting position is , the speed is ,exist In the iteration, the position and velocity of the particle are updated using formulas (4) and (5), and the process is as follows:

[0058]

[0059]

[0060] Updated particles The parameters are: Position ,speed , individual optimal value , and its corresponding fitness value is By analogy, we can get the individual optimal values ​​of all particles, among which the minimum value is the global optimal value, which is , and the corresponding particle position is .

[0061] exist After iterations, the particles The location is , the speed is , its fitness value , its individual optimal value for and The smallest one is 0.7376.

[0062] Similarly, we can get After the iteration, the individual optimal values ​​of all other particles will be The fitness corresponding to the global optimal value after iterations is compared with the individual optimal values ​​of all particles, where the minimum value is The global optimal value after iterations is , and the corresponding particle position is .

[0063] Similarly, for the subpopulation and The individual optimal value and the global optimal value are also continuously updated according to the above steps.

[0064] The specific steps of step (4) are as follows:

[0065] (4-1) According to step (3), we can get The global optimal value of each subpopulation at the iteration is obtained by continuous iteration until the maximum number of iterations is reached. The global optimum of the subpopulation and its corresponding fitness value .

[0066] (4-2) Compare the global optimal fitness values ​​in step (4-1), the smallest of which is the global optimal fitness value of the algorithm, and its corresponding particle position is the navigation position of the ship at the next moment.

[0067] For ease of understanding, steps (4-1) and (4-2) are described below:

[0068] According to step (3), the final sub-population is obtained by continuous iteration. The global optimum value of , and its corresponding fitness value is .

[0069] Similarly, for the subpopulation , we can get the final global optimal value , and the corresponding particle position is ; Subpopulation The global optimum value of , and the corresponding particle position is , and then take the smallest global optimal value among the three sub-populations , and its corresponding particle position [30.1759,122.6490] is the sailing position of the ship at the first moment.

[0070] The following is a detailed description of the embodiments of the method of the present invention with reference to the accompanying drawings:

[0071] First, the search space is evenly divided, and fixed particles are generated using the divided reference points. Then, the remaining particles are randomly generated to form the initial population. Secondly, the initial population is divided into multiple sub-populations according to the sub-fitness function to ensure that the particles contained in each sub-population, that is, the navigation position coordinates of the ship at the future moment, can adapt to the various constraints of the ship's path planning. Subsequently, the position and speed of each particle in the sub-population are iteratively updated, and its fitness value is calculated to obtain the individual optimal value and the sub-population optimal value, and then compared with the remaining sub-populations to obtain the global optimal value, iteratively in turn, and continuously obtain the optimal position of the ship at the next moment, so as to realize the intelligent optimization of the ship's navigation route.

[0072] The following is a detailed description of each step of this embodiment in combination with experimental data:

[0073] 1. Acquisition and processing of experimental data

[0074] (1.1) Rasterization of sea area maps

[0075] The latitude range of the target sea area is determined to be [29.8259, 30.2599], and the longitude range is [122.1389, 122.9045], and the latitude span and longitude span of each grid are defined as 0.02. The target sea area is then rasterized, which is conducive to representing subsequent location, path, obstacle and other information.

[0076] (1.2) Acquisition and processing of sea area information

[0077] First, obtain the location of obstacles in the target sea area and mark the corresponding locations in the grid network. Moment and Whether the position line at the moment passes through an obstacle is the first sub-fitness function of the particle swarm algorithm. Then, the latitude and longitude coordinates of the starting point and the end point of the ship's navigation route are determined [30.1959, 122.6690] and [29.9359, 122.3690], where the starting point is the position of the ship at the starting time, and the distance between the ship's position and the end point is the second sub-fitness function of the algorithm. Finally, the ship's scheduled route is determined. Each time the next navigation position is updated, the distance between the position and the scheduled route is the third sub-fitness function of the algorithm. .

[0078] 2. Initialize the algorithm subpopulation

[0079] (2.1) Generate the initial population

[0080] Set the number of particles , taking the position of the ship at the starting time as an example, the latitude search space is:

[0081] , the longitude search space is:

[0082] . Divide the latitudinal search space evenly into intervals and reference points, the search space after division is

[0083] [30.1759, 30.1816, 30.1873, 30.1930, 30.1988, 30.2045, 30.2102,30.2159], the interval between two adjacent reference points is ; Similarly, the longitude search space after division is [122.6490, 122.6547, 122.6604, 122.6661, 122.6719, 122.6776, 122.6833,122.6890], with an interval of It is 0.0057.

[0084] Using the 8 latitude reference points and longitude reference points obtained after division, the 8 reference positions of the particles are defined as: . Then, only a single reference point in the reference position is adjusted each time, and The fixed particles are shown in Table 3.

[0085] Table 3 Initial fixed particles

[0086]

[0087] Then randomly generate the remaining Particles are added to complete the population initialization.

[0088] (2.2) Generate subpopulation

[0089] Substitute all particles in the initial population into each sub-fitness function to calculate the fitness value, and the obtained sub-fitness matrix is ​​shown in Table 4.

[0090] Table 4 Sub-fitness matrix

[0091]

[0092] Then the sub-fitness matrix is ​​calculated according to the first column, that is, the first sub-fitness value of the particle. Sort in ascending order and take the first The particles corresponding to the rows form the first sub-population , where all particles are the 40 particles that perform best under the obstacle constraints. And so on, we get the sub-population and The division of sub-populations is completed, and the particles in each sub-population can adapt well to the corresponding constraints.

[0093] 3. Update particle parameters

[0094] For subpopulations , set the maximum number of iterations , initial inertia weight , positive acceleration constant , , the initial global optimal value is infinite, and the speed of each particle is initialized. The starting position is , the speed is ,exist In the iteration, the position and velocity of the particle are updated using formulas (4) and (5), and the process is as follows:

[0095]

[0096]

[0097] Updated particles The parameters are: Position ,speed , individual optimal value , and its corresponding fitness value is By analogy, we can get the individual optimal values ​​of all particles, among which the minimum value is the global optimal value, which is , and the corresponding particle position is .

[0098] exist After iterations, the particles The location is , the speed is , its fitness value , its individual optimal value for and The smallest one is 0.7376.

[0099] Similarly, we can get After the iteration, the individual optimal values ​​of all other particles will be The fitness corresponding to the global optimal value after iterations is compared with the individual optimal values ​​of all particles, where the minimum value is The global optimal value after iterations is , and the corresponding particle position is .

[0100] Similarly, for the subpopulation and The individual optimal value and the global optimal value are also continuously updated according to the above steps.

[0101] 4. Get the best position of the ship at the next moment

[0102] As the algorithm continues to iterate, the final subpopulation is obtained The global optimum value of , and its corresponding fitness value is .

[0103] Similarly, for the subpopulation , we can get the final global optimal value , and the corresponding particle position is ; Subpopulation The global optimum value of , and the corresponding particle position is , and then take the smallest global optimal value among the three sub-populations , and its corresponding particle position [30.1759,122.6490] is the sailing position of the ship at the first moment.

[0104] According to the method of the present invention, a more reasonable ship navigation route is obtained, so that the average fitness function value of the algorithm is 0.0250, while the path planning is performed by PSO with linearly decreasing inertia weight, and its average fitness value is 0.0301. Figure 3 A comparison chart of the average fitness values ​​of the two methods is given. It can be seen from the figure that the method of the present invention is obviously better than the improved PSO in terms of convergence accuracy and can better realize ship path planning.

Claims

1. A ship path planning method based on fixed and random particle population optimization, characterized in that: The following steps are involved: S1. A fixed and random multi-particle population initialization method is given to generate a number of fixed particle populations and random particle populations as initial populations, where particles represent ship positions; S2. Divide the initial population into multiple sub-populations according to the sub-fitness function; the specific process is as follows: S2-1. Determine the fitness function F(Y) = {f k (Y)|k=1,2,...,K,K=3}, where f k (Y) represents the kth sub-fitness function in the fitness function, K is the number of constraints in the optimization problem, and the K constraints are whether the ship passes through an obstacle, the distance between the ship and the end of the route, and the distance between the ship and the established route, that is, the number of sub-populations; S2-2. Calculate the sub-fitness value f of each particle in the initial population k (Y m ),m=1,...,M, and get the sub-fitness matrix: S2-3, the sub-fitness matrix is ​​calculated according to the first column, that is, the first sub-fitness value f1(X m ) are arranged in ascending order, and the first column corresponding to the arranged matrix is ​​taken The first sub-population sub1 is composed of particles, all of which are the particles that perform best under the first constraint. The initial population is divided into K sub-populations (sub1, sub2, ..., subK) by iteration, and each sub-population is composed of the particles that perform best under the k-th constraint. S3, iteratively update the position and velocity of each particle in the sub-population, calculate its fitness value, and obtain the individual optimal value and the global optimal value of the sub-population; S4, repeat the above step S3, continuously update the global optimal value until the maximum number of iterations is reached, and then compare the global optimal values ​​of all sub-populations to obtain the optimal navigation position coordinates of the ship at the future moment; the specific implementation process is as follows: S4-1. According to step S3, the global optimal value of each subpopulation at the h+1th iteration is obtained, and the global optimal value of all K subpopulations is obtained by continuous iteration until the maximum number of iterations is reached. and its corresponding fitness value S4-2, comparing the global optimal fitness values ​​in step S4-1, the smallest one is the global optimal fitness value, and the corresponding particle position is the navigation position of the ship at the next moment.

2. The ship path planning method based on fixed and random particle population optimization according to claim 1 is characterized in that: The specific implementation process of step S1 is as follows: S1-1, set the two-dimensional particle search space of the ship position to [y n,min ,y n,max ], n=1,...,N, N=2 represents the dimension, y n,min and n,max Respectively represent the minimum and maximum values ​​of the search space boundary; define the particle swarm as S p ={p i |i=1,2,...,M},p i =(y 1,i ,y 2,i ) is the i-th particle in the particle group, y 1,i Indicates the latitude of the ship's location, y 2,i Indicates the longitude of the ship's location, y n,i ∈[y n,min ,y n,max ], M represents the total number of particles; S1-2, the search space [y n,min ,y n,max ] is evenly divided into J intervals, then the search space after division is [y n,min ,y n,min +T n ,...,y n,min +(J+1)T n ,y n,max ], T n is the interval between two adjacent intervals, expressed as: T n =(y n,max -y n,min ) / J (2) The jth reference point y of the nth parameter to be optimized n,j It is expressed as: S1-3, according to step S1-2, the search space of each parameter to be optimized is evenly divided into J intervals and (J+1) reference points, and the (J+1) reference points are used to define Y1=(y 1,min ,y 2,min ),Y2=(y 1,min +T1,y 2,min +T2),...,Y J+1 =(y 1,max ,y 2,max ) The reference position of a total of (J+1) particles, and then only adjust the reference position Y each time j A single reference point in the equation gives M1 = (J + 1) N fixed particles; the remaining M2 = M-M1 random particles (Y J+2 ,Y J+3 ,...,Y J+1+M2 ) are randomly generated in the target search space, and the generated fixed particles and random particles are combined to obtain the initial particle population.

3. The ship path planning method based on fixed and random particle population optimization according to claim 2 is characterized in that: The specific implementation process of step S3 is as follows: S3-1, iteratively update the position and velocity of each particle in the sub-population, and define the global optimal value of each sub-population after h iterations as The optimal value of individuals in the kth subpopulation is in and They represent the global optimal value of the k-th subpopulation at the h-th iteration and the individual optimal value of the m-th particle, respectively. The m-th particle in the k-th subpopulation is represented by p m,subk Represents; particle p m,subk The inertia weight is The positive acceleration constants are The position and velocity are and in and They represent the particle p at the hth iteration. m,subk The position and velocity of the particle p in the kth subpopulation at the nth parameter to be optimized; when the h+1th iteration is performed, m,subk Location and speed Update according to the following formula: Among them, r1 and r2 are random numbers uniformly distributed in the interval [0,1]; S3-2, calculate the mth particle p according to step S3-1 m,subk The individual optimal value after the h+1th iteration corresponds to the fitness value Compare it with all individual fitness values ​​of the particle in the previous h iterations, where the particle position corresponding to the minimum fitness value is the particle p after the h+1th generation. m,subk The individual optimal value of S3-3, according to step S3-2, obtain the kth subpopulation after the h+1th iteration The individual optimal value of each particle and its corresponding fitness value It is known that the global optimal value of the kth subpopulation after the hth iteration is Compare it with the optimal values ​​of all individuals in the h+1th generation, where the minimum fitness value The corresponding particle position is the global optimal value of the population in the h+1th generation

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