CN112082552A - Unmanned aerial vehicle flight path planning method based on improved hybrid particle swarm optimization algorithm - Google Patents

Unmanned aerial vehicle flight path planning method based on improved hybrid particle swarm optimization algorithm Download PDF

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CN112082552A
CN112082552A CN202010665446.1A CN202010665446A CN112082552A CN 112082552 A CN112082552 A CN 112082552A CN 202010665446 A CN202010665446 A CN 202010665446A CN 112082552 A CN112082552 A CN 112082552A
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夏敏
王超群
曹林
徐安邦
徐丰
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Taicang Yangtze River Delta Research Institute of Northwestern Polytechnical University
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Abstract

The invention relates to an unmanned aerial vehicle flight path planning method based on an improved hybrid particle swarm optimization algorithm, which improves a flight path coding mode aiming at an unmanned aerial vehicle flight path constraint condition, and carries out global search on a hybrid particle swarm optimization algorithm combined with a genetic algorithm by virtue of the characteristic of strong global search capability of the particle swarm optimization algorithm, wherein when iteration times are carried out to a designated algebra and are close to a global optimal solution, the whole population enters the neighborhood of the global optimal solution; secondly, local quick search is carried out in the neighborhood of the global optimal solution by utilizing the improved genetic algorithm, the global optimal solution is finally reached, the flight path section spans a plurality of grid nodes, the complexity of hierarchical planning can be avoided, the algorithm efficiency of unmanned aerial vehicle flight path planning is improved, and the engineering application is more convenient.

Description

Unmanned aerial vehicle flight path planning method based on improved hybrid particle swarm optimization algorithm
Technical Field
The invention belongs to the technical field of flight path planning of aircrafts, and particularly relates to a flight path which can ensure safe flight of an unmanned aerial vehicle and is found on the premise of comprehensively considering the arrival time, oil consumption, threats, flight areas and other factors of the unmanned aerial vehicle. The flight path planning method can plan safe flight paths meeting various constraints in a large-scale real environment, and can be widely applied to flight path planning of various unmanned aerial vehicles.
Background
Along with the development of aviation technology, the application of unmanned aerial vehicle in military and civilian field constantly enlarges, if: enemy reconnaissance, reconnaissance-beating-evaluation, cooperative fighting, terrain exploration, geographical mapping, high-voltage inspection and the like. The tasks executed by the unmanned aerial vehicle are complex and various, and autonomous flight must be realized for improving the viability of the unmanned aerial vehicle. Flight path planning is one of the key technologies for autonomous flight of unmanned aerial vehicles.
The purpose of the flight path planning of the unmanned aerial vehicle is to find a flight path which can ensure the safety of the unmanned aerial vehicle to prevent suddenly, so that the probability of capture and destruction by enemy air defense facilities is reduced as much as possible, the probability of crash is reduced, and various constraint conditions are met. For multi-aircraft cooperative combat, in order to improve the success rate of executing tasks, cooperation and safety among multiple unmanned aerial vehicles are also important, and particularly, unmanned aerial vehicle track planning needs to consider requirements including safety, track constraint, cooperation and instantaneity.
The flight path planning is an NP problem, combined explosion is often caused when the flight path planning is directly solved, and in order to reduce the algorithm complexity, scholars at home and abroad propose various planning methods, including a planning method based on probability map search, a planning method based on grid search, a planning method based on artificial potential field and a planning method based on evolutionary computation. The invention belongs to an improved flight path planning method based on an evolutionary algorithm.
Disclosure of Invention
Aiming at the problems, the invention provides an unmanned aerial vehicle flight path planning method based on an improved hybrid particle swarm optimization algorithm, wherein a flight path section spans a plurality of grid nodes, the complexity of hierarchical planning can be avoided, the calculation efficiency of unmanned aerial vehicle flight path planning is improved, and the unmanned aerial vehicle flight path planning method is more convenient for engineering application.
The invention aims to provide an unmanned aerial vehicle flight path planning method based on an improved hybrid particle swarm optimization algorithm, which is characterized by comprising the following steps of:
(1) adopting a full real number coordinate array coding mode to construct a three-dimensional space track code for track planning:
x1y1h1d1α1…xiyihidiαi…xnynhndnαn (1)
in the formula: n is the number of track points on the track; x is the number ofi、yi、hiCoordinates and elevation values of the ith terrain grid node in the track grid map are obtained; diLength of flight path from the ith node to the (i + 1) th node, alphaiIs a direction angle;
(4) selecting one of an Alpine function, a Rastrigrin function and a Schafer function as a target function used for flight path planning, and determining a constraint condition of a flight path section;
(5) searching the constructed planning space by using a hybrid particle swarm optimization algorithm from the initial terrain grid node, and adding the searched terrain grid node into the reference track when the constraint condition of the track section is met; and circulating until the end point terrain grid node is added into the reference track.
In a preferred embodiment, in the method,
the Alpine function used in step (2) is:
Figure RE-GDA0002750785710000021
in the formula, x1,2∈[0,10]。
In a preferred embodiment, in the method,
the Rastrigrin function used in the step (2) is as follows:
Figure RE-GDA0002750785710000031
in the formula, xi∈(-10,10)，n＝2。
In a preferred embodiment, in the method,
the schafer function used in step (2) was:
Figure RE-GDA0002750785710000032
in the formula, xi∈[-10,10]。
In an optimal technical scheme, the searching the constructed planning space by using the hybrid particle swarm optimization algorithm in the step (3) of the method comprises the following steps:
(31) firstly, performing global optimization search by using a particle swarm optimization algorithm to obtain a neighborhood of a global optimal solution;
(32) and secondly, performing local quick search in the neighborhood of the global optimal solution by using a genetic algorithm, and finally reaching the global optimal solution to obtain the terrain grid nodes to be added with the reference track.
In a preferred technical solution, after the problem is modeled by a mathematical modeling method in the method step (31), the problem to be optimized is:
Figure RE-GDA0002750785710000033
formula (I) describes a problem to be optimized for multi-constraint, multi-control variables, where x ∈ RnFor controlling variables, the value space is Ω ═ { x | xi∈(mini,maxi) 1, 2.., n }; (x) represents the objective function to be optimized; n is a radical ofj≤gj(x)≤MjJ ═ 1,2,. m denotes m constraints; the optimization problem aims to find a group of n-dimensional control variables x meeting all constraint conditions by means of a specific optimization algorithm, so that the value of an objective function f (x) is maximum or minimum;
the method step (31) is specifically:
(311) generating an initial population POP consisting of m particles in an n-dimensional search space omega allowed by a control variable x0:x0＝(x1,x2,…,xm) (ii) a Wherein the population x0In (2), any one particle xiI 1, a, m; all represent a set of feasible solutions to the optimization problem and the position of the particle is represented as xi＝(xi1,xi2,…,xin) The velocity is denoted by vi＝(vi1,vi2,…,vin)；
(312) Constructing a fitness function according to the objective function to be optimized and the specific requirements of the optimization problem
Figure RE-GDA0002750785710000041
The fitness function is used for evaluating the adaptability of each particle in the population, the larger the value of the fitness function is, the stronger the adaptability of the particle is, the closer the adaptability is to the optimal solution is, otherwise, the weaker the adaptability is, the farther the adaptability is from the optimal solution;
(313) according to the position x of each particleiCalculating a fitness value
Figure RE-GDA0002750785710000042
For the current population xt， t＝1,…,N1(ii) a Performing an evaluation in which N1Finding out the optimal individual position in the contemporary population for the maximum iteration times of the particle swarm optimization algorithm
Figure RE-GDA0002750785710000043
And recording the currently obtained global optimal individual position by combining the previous iteration process
Figure RE-GDA0002750785710000044
(a) Comparing the fitness value of each particle with its historical optimal fitness value pbest, if so
Figure RE-GDA0002750785710000045
Then:
Figure RE-GDA0002750785710000046
if it is
Figure RE-GDA0002750785710000047
Then:
Figure RE-GDA0002750785710000048
(b) comparing the fitness value of each particle with the fitness value gbest of the current global optimal individual, if so
Figure RE-GDA0002750785710000049
Then:
Figure RE-GDA00027507857100000410
if it is
Figure RE-GDA00027507857100000411
Then:
Figure RE-GDA00027507857100000412
(314) updating the speed and the position of the ith particle according to the currently searched individual historical optimal fitness value:
Figure RE-GDA0002750785710000051
in the formula (9), viIs the flight velocity vector of the particle; x is the number ofiIs the position vector of the particle; t is an evolution algebra; learning factor c1、c2Is a non-negative real number; omega is the inertial weight; r is1、r2Is in the interval of [0,1 ]]Two random numbers which are uniformly distributed; t is a time flight factor, and T is d + omega;
the inertia weight omega needs to be continuously adjusted in a self-adaptive manner according to an iteration process, and the adjustment algorithm is as follows:
Figure RE-GDA0002750785710000052
in formula (18), α (x) represents the population evolution rate, β (x) represents the population polymerization degree;
Figure RE-GDA0002750785710000053
representing the fitness value of the t-th generation globally optimal particle,
Figure RE-GDA0002750785710000054
representing the average fitness value of all particles in the current population;
learning factor c1And c2The change rule is as follows:
Figure RE-GDA0002750785710000055
in the formula (20), c1sAnd c2sAre respectively a learning factor c1And c2Initial value of c1eAnd c2eAre respectively a learning factor c1And c2The end value of (d);
(315) obtaining the updated particle speed and position through (314), generating a new generation of population, and returning to (313); repeating the above process until the maximum iteration number N1At this time, the optimization problem is subjected to N by using a particle swarm optimization algorithm1The global search process of the secondary iteration is finished, and finally a global suboptimal solution and a feasible solution in a group of global optimal solution neighborhoods of the optimization problem are obtained.
In a preferred technical scheme, the method step (32) specifically comprises the following steps:
(321) after global search is finished by utilizing particle swarm optimization algorithm, a new population X is generatedN1As an initial population for local search of genetic algorithm, each particle in the particle swarm optimization algorithmOne-to-one correspondence becomes chromosome x in genetic algorithm populationi(i ═ 1.., m), and n-dimensional chromosome xiIndicates that the staining has n genes;
(322) calculating each chromosome x in the populationiCorresponding fitness function value
Figure RE-GDA0002750785710000061
For the current population Xt(t＝N1,N1+1,…,N1+N2) Performing an evaluation in which N2The maximum iteration number of the genetic algorithm;
(323) and calculating the probability of each chromosome being selected as a parent according to the calculation result of the individual fitness in the whole population, wherein the calculation method comprises the following steps:
Figure RE-GDA0002750785710000062
in the formula, PiIs chromosome xiThe probability of selection of (a) is,
Figure RE-GDA0002750785710000063
is the minimum fitness value in the population;
then, according to the roulette game rule, selecting the whole population;
(324) performing pairwise crossing operation on the parent combination generated by the selection operation in the step (323) to generate a child individual;
(325) comparing the fitness values of all the parent individuals and all the offspring individuals, selecting n individuals with the maximum fitness values from the fitness values to form a new population, and turning to the step (322); repeating the above process until the maximum iteration number N2(ii) a At this time, after local optimization through a genetic algorithm, an optimal solution closest to the global optimal solution is obtained.
In a preferred technical scheme, in the step (323), according to roulette game rules, the whole population is selected as follows:
(a) generating a random number rand over the interval (0, 1);
(b) calculating the ith chromosome xiThe calculation method of (2) is as follows:
Figure RE-GDA0002750785710000064
(c) if sumP is greater than or equal to rand, then the chromosome xiAre selected as parent individuals. If mp<And (d) repeating the steps (a) and (b) until m/2 groups of parent combinations are selected.
In a preferred embodiment, the hybridization operation in step (324) of the method is specifically as follows:
(a) generating a random number rand over the interval (0, 1);
(b) comparison of hybridization probability pcrossAnd the size of the random number rand, determining whether the parent combination is subjected to hybridization operation. If p iscrossIf the number of the offspring individuals is more than or equal to rand, performing hybridization operation on the parent combination to generate two new offspring individuals; otherwise, the hybridization operation is not carried out;
(c) repeating the processes (a) and (b) until all the parents are combined to complete the hybridization operation.
In a preferred technical scheme, when the hybridization operation is performed in the step (32), a preset reconstruction operator and a disturbance operator perform constraint operation on the mutation, wherein the reconstruction operator operation is to randomly select a node from a flight path as a starting node of the mutation, and then find a flight path which is different from the original flight path and meets the flight path constraint condition from the starting node to a target point;
and the disturbance operator operation is to randomly select a node on the variant track as a disturbance node, and when the disturbance operator moves to the disturbance node after disturbance, the track still meets the track constraint condition, and then the variant operation is successful.
The invention aims to provide an improved hybrid particle swarm optimization algorithm aiming at the problem that the traditional optimization algorithm is poor in optimization effect when solving the problem of complex optimization, the algorithm can be ingeniously combined with the advantages of a genetic algorithm and a particle swarm optimization algorithm, and the algorithm is hereinafter referred to as the hybrid particle swarm optimization algorithm combined with the genetic algorithm.
The invention has the beneficial effects that: aiming at the complex optimization problems of multiple control variables, multiple constraint conditions and multiple extreme points, the optimization method can efficiently and quickly realize optimization calculation. Compared with the traditional genetic algorithm and particle swarm optimization algorithm, the optimization algorithm provided by the invention has higher global search capability and local convergence rate.
Compared with the traditional unmanned aerial vehicle track planning method, the unmanned aerial vehicle track planning method has the advantages that:
an unmanned aerial vehicle flight path planning method based on an improved hybrid particle swarm optimization algorithm is characterized in that: the unmanned aerial vehicle track planning method improves a track coding mode and improves a crossover operator and a mutation operator of a genetic algorithm aiming at a track constraint condition of the unmanned aerial vehicle, particularly, the mutation operator adopts an operation mode of combining a reconstruction operator and a disturbance operator, and a track section spans a plurality of grid nodes, so that the complexity of hierarchical planning can be avoided, the calculation efficiency of unmanned aerial vehicle track planning is improved, and the engineering application is more convenient.
Drawings
The invention is further described with reference to the following figures and examples:
FIG. 1 is a general flow chart of the flight path planning method based on the hybrid particle swarm optimization of the present invention;
FIG. 2 is a schematic diagram of the principle of the hybrid particle swarm optimization algorithm based on the combination of the genetic algorithm. In the figure, Ω is the search space for a control variable x, x0Representing the initial value, x, of the control variableoptRepresents the global optimal solution of the optimization problem, and U represents a neighborhood of the global optimal solution. The PSO algorithm is an optimized particle swarm algorithm; the GA algorithm is a modified genetic algorithm.
FIG. 3 is a flow chart of the hybrid particle swarm optimization algorithm based on the combination of the genetic algorithm.
FIG. 4 is a schematic diagram of the crossover and mutation operations of the genetic algorithm in the hybrid particle swarm optimization algorithm based on the combination of the genetic algorithm;
fig. 5 is a schematic diagram of a specific flow of the unmanned aerial vehicle flight path planning method based on the hybrid particle swarm optimization.
Detailed Description
The above-described scheme is further illustrated below with reference to specific examples. It should be understood that these examples are for illustrative purposes and are not intended to limit the scope of the present invention. The conditions used in the examples may be further adjusted according to the conditions of the particular manufacturer, and the conditions not specified are generally the conditions in routine experiments.
The unmanned aerial vehicle flight path planning method provided by the invention can plan a flight path meeting the requirements, avoids the complexity of hierarchical planning, and improves the efficiency of unmanned aerial vehicle flight path planning and the engineering practicability.
Examples
The general flow of the unmanned aerial vehicle flight path planning method provided by the invention is as follows:
first, track coding
The track coding mode adopts a full real number coordinate array coding mode:
x1y1h1d1α1…xiyihidiαi…xnynhndnαn (1)
in the formula: n is the number of track points on the track; x is the number ofi、yi、h1Coordinates and elevation values of the ith node in the grid graph are obtained; diLength of flight path from the ith node to the (i + 1) th node, alphaiIs the direction angle.
Second, flight path planning content based on hybrid particle swarm optimization
As shown in fig. 2, track points satisfying constraints (i.e., topographical grid nodes to be added with a reference track) are first sought through a hybrid particle swarm algorithm, and then search and selection are performed by adopting an improved genetic algorithm, wherein the specific operations include (3) selection and hybridization, (4) mutation, and (5) elite preservation strategy (rollback).
The general flow of the hybrid particle swarm optimization algorithm combined with the genetic algorithm provided by the invention is as follows:
(1) a general optimization problem is described by a mathematical modeling method in the form of the following mathematical expression:
Figure RE-GDA0002750785710000091
equation (1) describes a general optimization problem for multi-constraint, multi-control variables, where x ∈ RnFor controlling variables, the value space is Ω ═ { x | xi∈(mini,maxi) 1, 2.., n }; (x) represents the objective function to be optimized; n is a radical ofj≤gj(x)≤MjJ ═ 1,2,. m denotes m constraints. The objective of the optimization problem is to find a set of n-dimensional control variables x satisfying all constraints by means of a specific optimization algorithm, so that the value of the objective function f (x) is maximum or minimum.
(2) And (3) carrying out global optimization search on the optimization problem described by the formula (1) by utilizing a particle swarm optimization algorithm. In order to improve the global search capability of the traditional particle swarm optimization algorithm, the following four improvements are carried out:
(a) homogenizing the initial population to ensure that the values of all individuals in the randomly generated initial population are uniformly distributed in a search space of a control variable as much as possible, so that the diversity of the initial population is ensured;
(b) the inertial weight is adjusted in a self-adaptive mode, the inertial weight is adjusted in real time by using the population evolution speed and the population polymerization degree based on the self-adaptive inertial weight adjusting method of the Sigmoid function, the probability that the algorithm falls into local optimum is effectively reduced, and the diversity of the population in the iteration process is kept;
(c) the learning factor changes asynchronously, namely the learning factor changes asynchronously according to the current population evolution state, and the iteration starting stage has strong self-learning capacity, is convenient for realizing rapid search and enhances the global search capacity; in the later iteration stage, the strong social learning ability is beneficial to local fine search so as to improve the ability of the population to converge to the global optimum;
(d) a time-of-flight factor is introduced. It can be known from the standard particle swarm optimization algorithm flow that the update of the particle position is to obtain the position of the next moment by adding the movement speed of the current moment on the basis of the original position. The operation of the displacement and the velocity under the condition of the same dimension is an important factor for causing the particles to oscillate back and forth in the vicinity of the optimal solution. Therefore, the flight time of the particles can be changed according to the iteration number, and the particle searching capacity is improved.
The specific steps of utilizing the particle swarm optimization algorithm to carry out global optimization search are as follows:
the first step is as follows: generating an initial population POP consisting of m particles in an n-dimensional search space omega allowed by a control variable x0:X0＝(x1,x2,…,xm). In the whole population X0In (2), any one particle xi(i 1., m) represents a set of feasible solutions to the optimization problem, and the position of the particle is denoted as xi＝ (xi1,xi2,…,xin) The velocity is denoted by vi＝(vi1,vi2,…,vin)。
According to the improvement point (a) of the particle swarm optimization algorithm, the POP in the initial population0All particle positions x ofiWill be initialized randomly and evenly distributed in the n-dimensional search space omega, ensuring the diversity of the initial population. In addition, the initial velocity v of the respective particleiAnd carrying out random initialization processing according to specific requirements.
The second step is that: constructing a fitness function according to the objective function to be optimized and the specific requirements of the optimization problem
Figure RE-GDA0002750785710000111
The fitness function is used for evaluating the adaptability of each particle in the population, and the larger the value of the fitness function is, the stronger the adaptability of the particle is, the closer the adaptability is to the optimal solution is, otherwise, the weaker the adaptability is, the farther the adaptability is from the optimal solution. At present, there is no unified method for constructing the fitness function, and the fitness function needs to be constructed according to the specific requirements of the optimization problem, and common methods mainly include a direct construction method, a weighting coefficient construction method, a penalty function construction method, and the like, and the specific references can be found in related documents. Because the construction method of the fitness function is notIs the content of the present invention, and is not described herein again.
The third step: according to the position x of each particleiCalculating a fitness value
Figure RE-GDA0002750785710000112
For the current population Xt(t ＝1,…,N1) Performing an evaluation in which N1Finding out the optimal individual position in the contemporary population for the maximum iteration times of the particle swarm optimization algorithm
Figure RE-GDA00027507857100001111
And recording the currently obtained global optimal individual position by combining the previous iteration process
Figure RE-GDA00027507857100001112
(a) Comparing the fitness value of each particle with its historical optimal fitness value pbest, if so
Figure RE-GDA0002750785710000113
Then:
Figure RE-GDA0002750785710000114
if it is
Figure RE-GDA0002750785710000115
Then:
Figure RE-GDA0002750785710000116
(b) comparing the fitness value of each particle with the fitness value gbest of the current global optimal individual, if so
Figure RE-GDA0002750785710000117
Then:
Figure RE-GDA0002750785710000118
if it is
Figure RE-GDA0002750785710000119
Then:
Figure RE-GDA00027507857100001110
the fourth step: according to the principle that a particle swarm optimization algorithm follows the motion of the optimal particles, the speed and the position of the ith particle are updated as follows according to the currently searched individual historical optimal fitness value:
Figure RE-GDA0002750785710000121
in the formula, viIs the flight velocity vector of the particle; x is the number ofiIs the position vector of the particle; t is an evolution algebra; learning factor c1、c2Is a non-negative real number; omega is the inertial weight; r is1、r2Is in the interval of [0,1 ]]Obeying two random numbers that are uniformly distributed.
According to the improvement point (b) of the particle swarm optimization algorithm, the inertia weight omega is continuously adjusted in a self-adaptive mode according to the iteration process, and the adjustment algorithm is as follows:
Figure RE-GDA0002750785710000122
in the formula, alpha (x) represents the population evolution speed, beta (x) represents the population polymerization degree;
Figure RE-GDA0002750785710000123
representing the fitness value of the t-th generation globally optimal particle,
Figure RE-GDA0002750785710000124
representing the average fitness value of all particles in the current population.
According to the particleImprovement point (c) of group optimization algorithm, learning factor c1And c2The change rule is as follows:
Figure RE-GDA0002750785710000125
in the formula, c1sAnd c2sAre respectively a learning factor c1And c2Initial value of c1eAnd c2eAre respectively a learning factor c1And c2The end value of (1).
According to the improvement point (d) of the particle swarm optimization algorithm, a time flight factor T is introduced, and the position and speed updating formula (6) of the particles can be rewritten into the following form:
Figure RE-GDA0002750785710000126
wherein, T ═ d + ω is taken, and when T ═ 1, the original particle position and velocity update formula (6) is obtained; when T is not equal to 1, a larger time factor is provided at the initial stage of iteration, so that global search can be realized quickly, the time factor is smaller and smaller along with the progress of iteration, the smaller time factor is favorable for particle swarm local fine search, and a high-precision global optimal solution can be found more easily.
The fifth step: obtaining the updated particle speed and position through the fourth step to generate a new generation of population, and returning to the third step; repeating the above process until the maximum iteration number N1. At the moment, the optimization problem is subjected to N by utilizing a particle swarm optimization algorithm1The global search process of the secondary iteration is finished, and finally a global suboptimal solution and a feasible solution in a group of global optimal solution neighborhoods of the optimization problem are obtained.
(3) And (3) synthesizing the global suboptimal solution and global optimal solution neighborhood obtained by searching through the particle swarm optimization algorithm in the step (2), and performing rapid local optimization searching through a genetic algorithm on the basis of a new population. In order to improve the local search capability of the traditional genetic algorithm, two improvements are made to the traditional genetic algorithm:
(a) the cross probability among population individuals is improved, and the full and complete information exchange among the whole population is ensured;
(b) and (4) eliminating mutation operators in the genetic algorithm to ensure that the filial generation individuals generated after crossing cannot jump out of the local area represented by the current population.
The specific steps of utilizing the genetic algorithm to carry out the rapid local search are as follows:
the first step is as follows: after global search is finished by utilizing particle swarm optimization algorithm, a new population is generated
Figure RE-GDA0002750785710000132
Initial population as genetic algorithm for local search. Then each particle in the particle swarm optimization algorithm is in one-to-one correspondence to be chromosome x in the genetic algorithm populationi(i ═ 1.., m), and n-dimensional chromosome xiThis indicates that the staining has n genes. Through N1After the next iteration of particle swarm optimization, a new population is obtained
Figure RE-GDA0002750785710000133
Already close to the global optimal solution of the optimization problem.
The second step is that: calculating each chromosome x in the populationiCorresponding fitness function value
Figure RE-GDA0002750785710000131
For the current population Xt(t＝N1,N1+1,…,N1+N2) Performing an evaluation in which N2Is the maximum number of iterations of the genetic algorithm.
The third step: and (6) selecting operation. And calculating the probability of each chromosome being selected as a parent according to the calculation result of the individual fitness in the whole population, wherein the calculation method comprises the following steps:
Figure RE-GDA0002750785710000141
in the formula, PiIs chromosome xiThe probability of selection of (a) is,
Figure RE-GDA0002750785710000142
is the minimum fitness value in the population.
When the selection operation is performed on the entire population according to the roulette game rule, the probability that an individual having a high selection probability is selected as a parent is high. The roulette game rules are described as follows:
(a) generating a random number rand over the interval (0, 1);
(b) calculating the ith chromosome xiThe calculation method of (2) is as follows:
Figure RE-GDA0002750785710000143
(c) if sumP is greater than or equal to rand, then the chromosome xiAre selected as parent individuals. If mp<And (d) repeating the steps (a) and (b) until m/2 groups of parent combinations are selected.
The selection operation of the present invention employs roulette game rules. In this method, a certain number of individuals are randomly selected from a population, and then the best individual is selected as a parent. This process is repeated until the selection of the individual is completed.
The fourth step: and (4) performing hybridization operation. And carrying out pairwise crossing operation on the parent combination generated by the selection operation in the third step to generate an offspring individual. Specific hybridization methods are various, such as fixed-point hybridization, random-point hybridization, single-point hybridization, and multi-point hybridization, and the details can be found in the relevant literature. Since the hybridization operation is not the focus of the present invention, it will not be described in detail herein.
The hybridization operation can be specifically described as:
(a) generating a random number rand over the interval (0, 1);
(b) comparison of hybridization probability pcrossAnd the size of the random number rand, determining whether the parent combination is subjected to hybridization operation. If p iscrossIf the number of the offspring individuals is more than or equal to rand, performing hybridization operation on the parent combination to generate two new offspring individuals; otherwise, no hybridization operation is performed.
(c) Repeating the processes (a) and (b) until all the parents are combined to complete the hybridization operation.
According to the improvement point (a) of the genetic algorithm, the hybridization probability p is increased compared with the standard genetic algorithmcrossThe value of (2) ensures that the inside of the population is fully communicated with information.
According to the improvement point (b) of the genetic algorithm, compared with the standard genetic algorithm, in the process of generating the filial generation individuals by carrying out hybridization operation on the parent combination, the mutation operators are removed, namely, the mutation operation is not carried out on the filial generation individuals, the fact that the local area of the global optimal solution is not jumped out due to the mutation in the whole evolution iteration process is ensured, and whether the mutation operators are added or not can be selectively determined according to practical problems.
The hybridization operation adopts an effective track section hybridization method, and the specific method comprises the following steps:
1) first, it is determined whether four track nodes satisfying a certain condition are included in the two reference tracks, as shown in fig. 4.
2) And if the track section CD and the track section HI are exchanged and meet the track constraint condition, performing hybridization operation to obtain two new tracks.
Because the track sections are not from one grid node to the next adjacent grid node, the number of the track points between the track sections is different, and the track sections have length constraints, so that in the track planning process, mutation operators do not need to be removed, and a mutation operation mode combining a reconstruction operator and a disturbance operator is adopted. When mutation operation is carried out, an operator is randomly selected to carry out operation.
1) And (5) reconstructing an operator. Firstly, a node is randomly selected from the flight path as a variation starting node, such as the node A of the reference flight path 'flight path 1' in fig. 4, and secondly, a flight path which is different from the original flight path and meets the flight path constraint condition from the node A to a target point is searched.
2) And (5) disturbing an operator. Firstly, randomly selecting a node on a variant track as a disturbance node, such as a node C in a reference track "track 1" in fig. 4, and moving to a node C' after disturbance, wherein the track still meets a track constraint condition, so that the variant operation is successful.
The fifth step: according to the thought of an elite preservation strategy, the fitness values of all parent individuals and all offspring individuals are compared, n individuals with the largest fitness values are selected to form a new population, and the step is switched to the second step; repeating the above process until the maximum iteration number N2. At this time, after local optimization through a genetic algorithm, an optimal solution closest to the global optimal solution is obtained.
In the invention, a plurality of terrain grid nodes are spanned between two adjacent track nodes, and the terrain is complex, so that the search of the next node meeting the constraint condition from the current track joint may fail, and a rollback strategy is adopted to rollback to the previous node (namely an elite storage strategy (rollback strategy)).
Third, concrete flight path planning method
The specific process is as follows:
the first step is as follows: a general optimization problem is described as a mathematical expression form through a mathematical modeling method, and the dimension and the value range of a control variable are determined. All constraints of the optimization problem are determined according to actual requirements.
The second step is that: as shown in fig. 2 and fig. 3, performing global optimization calculation on the optimization problem by using an improved particle swarm optimization algorithm; iterating the particle swarm optimization algorithm to a designated algebra N1Then, the global optimization process is ended, and at this time, a global suboptimal solution is obtained and iteration reaches the neighborhood of the global optimal solution.
The third step: and when the particle swarm optimization algorithm iterates to a neighborhood of the global optimal solution, integrating the global suboptimal solution and the neighborhood of the global optimal solution obtained at the moment to generate a new population.
The fourth step: on the basis of the new population, an improved genetic algorithm is utilized to carry out rapid local optimization search; iterative arrival of genetic algorithm to designated algebra N2And then, the local searching process is finished, and the global suboptimal solution is obtained at the moment.
The fifth step: and carrying out flight path planning simulation or verification.
More specifically, as shown in fig. 5, the operation process of the algorithm mainly includes selection operation, crossover operation, mutation operation, and rollback policy design;
the first step is as follows: select and interleave operations
The selection operation employs roulette rules. In this method, a certain number of individuals are randomly selected from a population, and then the best individual is selected as a parent. This process is repeated until the selection of the individual is completed.
The crossing operation adopts an effective track section crossing method, and the specific method is as follows:
1) first, it is determined whether four track nodes satisfying a certain condition are included in the two reference tracks, as shown in fig. 4.
2) And if the track section CD and the track section HI are exchanged and meet the track constraint condition, performing cross operation to obtain two new tracks.
3) If the constraint condition is met, the search is continued.
The second step is that: mutation operation
And (3) adopting a mutation operation mode combining a reconstruction operator and a disturbance operator. When mutation operation is carried out, an operator is randomly selected to carry out operation.
1) And (5) reconstructing an operator. Firstly, a node is randomly selected from the flight path as a variation starting node, such as the node A of the reference flight path 'flight path 1' in fig. 4, and secondly, a flight path which is different from the original flight path and meets the flight path constraint condition from the node A to a target point is searched.
2) And (5) disturbing an operator. Firstly, randomly selecting a node on a variant track as a disturbance node, such as a node C in a reference track "track 1" in fig. 4, and moving to a node C' after disturbance, wherein the track still meets a track constraint condition, so that the variant operation is successful.
The third step: fallback policy
A plurality of terrain grid nodes are spanned between two adjacent track nodes, the terrain is complex, so that the search of the next node meeting the constraint condition from the current track joint may fail, and at the moment, a rollback strategy is adopted to rollback to the previous node. A rollback strategy is adopted, and the rollback times are limited so as to improve the efficiency. In the calculation process, a backspacing strategy is applied to the restructuring operators in the initialization operation and the mutation operation of the population.
The method verifies the mixed particle swarm optimization algorithm part combined with the genetic algorithm to obtain the profit contrast data of the algorithm. And (3) performing performance test on the hybrid particle swarm optimization algorithm by taking three typical nonlinear reference functions as a test result function. The test functions are respectively:
(1) alpine function
Figure RE-GDA0002750785710000171
In the formula, x1,2∈[0,10]. The Alpine function has a large number of local extrema and is at x1,2Take the global minimum f at 7.9171 *＝-7.8856。
(2) Rastigrin function
Figure RE-GDA0002750785710000181
In the formula, xiE (-10,10), n is 2. The Rastrigrin function is a multi-extreme point function at xiTaking a global minimum value f at (i ═ 1, 2.. times.n)2 *＝0。
(3) Schafer function
Figure RE-GDA0002750785710000182
In the formula, xi∈[-10,10]. Schafer function at x1,2Taking the global minimum f at 03 *＝0。
The three test functions are subjected to optimization calculation by applying a traditional genetic algorithm, a particle swarm algorithm and an improved mixed particle swarm optimization algorithm, each algorithm is tested repeatedly for 2000 times, and the parameter setting and the test result of the algorithm are shown in table 1.
Table 1 parameter settings and test results
Figure RE-GDA0002750785710000183
Figure RE-GDA0002750785710000191
As can be seen from table 1, compared with the conventional genetic algorithm and particle swarm optimization, the improved optimization result of the hybrid particle swarm optimization has a mean value closer to an accurate value and a smaller statistical variance. Meanwhile, the probabilities (expressed as success rates) of finding the global optimum by the improved hybrid particle swarm optimization algorithm are respectively 89.40%, 90.20% and 75.20%, and the probabilities are the highest in the three function tests. Therefore, the test result shows that the hybrid particle swarm optimization algorithm provided in this chapter has better searching capability and robustness.
Therefore, the invention provides a hybrid Particle Swarm Optimization Algorithm combined with a Genetic Algorithm, which integrates the advantages of strong global search capability of a Particle Swarm Optimization (PSO) Algorithm and high local convergence speed of the Genetic Algorithm (GA). firstly, global search is carried out by virtue of the characteristic of strong global search capability of the Particle Swarm Optimization Algorithm, and when the iteration times are carried out to a specified generation and are close to the global optimal solution, the whole population enters the neighborhood of the global optimal solution; secondly, local quick search is carried out in the neighborhood of the global optimal solution by utilizing an improved genetic algorithm, and finally the global optimal solution is reached.
The optimization algorithm provided by the invention is suitable for solving various engineering and theoretical complex optimization problems.
The objects, advantages and features of the present invention will be explained by the following non-restrictive description of preferred embodiments thereof. The embodiments are merely exemplary for applying the technical solutions of the present invention, and any technical solution formed by replacing or converting the equivalent thereof falls within the scope of the present invention claimed.

Claims (10)

1. An unmanned aerial vehicle flight path planning method based on an improved hybrid particle swarm optimization algorithm is characterized by comprising the following steps:
(1) adopting a full real number coordinate array coding mode to construct a three-dimensional space track code for track planning:
x1y1h1d1α1L xiyihidiαiL xnynhndnαn (1)
in the formula: n is the number of track points on the track; x is the number ofi、yi、hiCoordinates and elevation values of the ith terrain grid node in the track grid map are obtained; diLength of flight path from the ith node to the (i + 1) th node, alphaiIs a direction angle;
(2) selecting one of an Alpine function, a Rastrigrin function and a Schafer function as a target function used for flight path planning, and determining a constraint condition of a flight path section;
(3) searching the constructed planning space by using a hybrid particle swarm optimization algorithm from the initial terrain grid node, and adding the searched terrain grid node into the reference track when the constraint condition of the track section is met; and circulating until the end point terrain grid node is added into the reference track.
2. The unmanned aerial vehicle flight path planning method of claim 1, wherein in the method,
the Alpine function used in step (2) is:
Figure FDA0002580210330000011
in the formula, x1,2∈[0,10]。
3. The unmanned aerial vehicle flight path planning method of claim 1, wherein in the method,
the Rastrigrin function used in the step (2) is as follows:
Figure FDA0002580210330000012
in the formula, xi∈(-10,10)，n＝2。
4. The unmanned aerial vehicle flight path planning method of claim 1, wherein in the method,
the schafer function used in step (2) was:
Figure FDA0002580210330000021
in the formula, xi∈[-10,10]。
5. The unmanned aerial vehicle flight path planning method of claim 1, wherein the searching the constructed planning space using the hybrid particle swarm optimization algorithm in the method step (3) comprises:
(31) firstly, performing global optimization search by using a particle swarm optimization algorithm to obtain a neighborhood of a global optimal solution;
(32) and secondly, performing local quick search in the neighborhood of the global optimal solution by using a genetic algorithm, and finally reaching the global optimal solution to obtain the terrain grid nodes to be added with the reference track.
6. An unmanned aerial vehicle flight path planning method according to claim 5, wherein in the method step (31), it is assumed that after modeling the problem by a mathematical modeling method, the problem to be optimized is:
Figure FDA0002580210330000022
formula (I) describes a problem to be optimized for multi-constraint, multi-control variables, where x ∈ RnFor controlling variables, the value space is Ω ═ { x | xi∈(mini,maxi) 1, 2.., n }; (x) represents the objective function to be optimized; n is a radical ofj≤gj(x)≤MjJ ═ 1,2,. m denotes m constraints; the optimization problem aims to find a group of n-dimensional control variables x meeting all constraint conditions by means of a specific optimization algorithm, so that the value of an objective function f (x) is maximum or minimum;
the method step (31) is specifically:
(311) generating an initial population POP consisting of m particles in an n-dimensional search space omega allowed by a control variable x0：x0＝(x1，x2，…，xm) (ii) a Wherein the population x0In (2), any one particle xiI 1, a, m; all represent a set of feasible solutions to the optimization problem and the position of the particle is represented as xi＝(xi1，xi2，…，xin) The velocity is denoted by vi＝(vi1，vi2，...，vin)；
(312) Constructing a fitness function according to the objective function to be optimized and the specific requirements of the optimization problem
Figure FDA0002580210330000031
The fitness function is used for evaluating the adaptability of each particle in the population, the larger the value of the fitness function is, the stronger the adaptability of the particle is, the closer the adaptability is to the optimal solution is, otherwise, the weaker the adaptability is, the farther the adaptability is from the optimal solution;
(313) according to the position x of each particleiCalculating a fitness value
Figure FDA0002580210330000032
For the current population xt，t＝1,…,N1(ii) a Performing an evaluation in which N1Finding out the optimal individual position in the contemporary population for the maximum iteration times of the particle swarm optimization algorithm
Figure FDA00025802103300000311
And recording the currently obtained global optimal individual position by combining the previous iteration process
Figure FDA00025802103300000312
(a) Comparing the fitness value of each particle with its historical optimal fitness value pbest, if so
Figure FDA0002580210330000033
Then:
Figure FDA0002580210330000034
if it is
Figure FDA0002580210330000035
Then:
Figure FDA0002580210330000036
(b) comparing the fitness value of each particle with the fitness value gbest of the current global optimal individual, if so
Figure FDA0002580210330000037
Then:
Figure FDA0002580210330000038
if it is
Figure FDA0002580210330000039
Then:
Figure FDA00025802103300000310
(314) updating the speed and the position of the ith particle according to the currently searched individual historical optimal fitness value:
Figure FDA0002580210330000041
in the formula (9), viIs the flight velocity vector of the particle; x is the number ofiIs the position vector of the particle; t is an evolution algebra; learning factor c1、c2Is a non-negative real number; omega is the inertial weight; r is1、r2Is in the interval of [0,1 ]]Two random numbers which are uniformly distributed; t is a time flight factor, and T is d + omega;
the inertia weight omega needs to be continuously adjusted in a self-adaptive manner according to an iteration process, and the adjustment algorithm is as follows:
Figure FDA0002580210330000042
in the formula (7), α (x) represents the population evolution rate, β (x) represents the population polymerization degree;
Figure FDA0002580210330000043
representing the fitness value of the t-th generation globally optimal particle,
Figure FDA0002580210330000044
representing the average fitness value of all particles in the current population;
learning factor c1And c2The change rule is as follows:
Figure FDA0002580210330000045
in the formula (9), c1sAnd c2sAre respectively a learning factor c1And c2Initial value of c1eAnd c2eAre respectively a learning factor c1And c2The end value of (d);
(315) obtaining the updated particle speed and position through (314), generating a new generation of population, and returning to (313); repeating the above process until the maximum iteration number N1At this time, a particle group is usedThe optimization algorithm performs N on the optimization problem1The global search process of the secondary iteration is finished, and finally a global suboptimal solution and a feasible solution in a group of global optimal solution neighborhoods of the optimization problem are obtained.
7. The unmanned aerial vehicle trajectory planning method of claim 5, wherein the method step (32) specifically comprises:
(321) after global search is finished by utilizing particle swarm optimization algorithm, a new population is generated
Figure FDA0002580210330000051
Serving as an initial population for local search of the genetic algorithm, and enabling each particle in the particle swarm optimization algorithm to correspond to a chromosome x in the genetic algorithm population one by onei(i ═ 1.., m), and n-dimensional chromosome xiIndicates that the staining has n genes;
(322) calculating each chromosome x in the populationiCorresponding fitness function value
Figure FDA0002580210330000052
For the current population Xt(t＝N1,N1+1,…,N1+N2) Performing an evaluation in which N2The maximum iteration number of the genetic algorithm;
(323) and calculating the probability of each chromosome being selected as a parent according to the calculation result of the individual fitness in the whole population, wherein the calculation method comprises the following steps:
Figure FDA0002580210330000053
in the formula, PiIs chromosome xiThe probability of selection of (a) is,
Figure FDA0002580210330000054
is the minimum fitness value in the population;
then, according to the roulette game rule, selecting the whole population;
(324) performing pairwise crossing operation on the parent combination generated by the selection operation in the step (323) to generate a child individual;
(325) comparing the fitness values of all the parent individuals and all the offspring individuals, selecting n individuals with the maximum fitness values from the fitness values to form a new population, and turning to the step (322); repeating the above process until the maximum iteration number N2(ii) a At this time, after local optimization through a genetic algorithm, an optimal solution closest to the global optimal solution is obtained.
8. A method for unmanned aerial vehicle trajectory planning according to claim 7, wherein the method step (323) comprises selecting an entire population according to roulette rules as follows:
(a) generating a random number rand over the interval (0, 1);
(b) calculating the ith chromosome xiThe calculation method of (2) is as follows:
Figure FDA0002580210330000061
(c) if sumP is greater than or equal to rand, then the chromosome xiAre selected as parent individuals. If sum < rand, repeating steps (a) and (b) until m/2 group of parent combination is selected.
9. The unmanned aerial vehicle flight path planning method of claim 7, wherein the method step (324) of the hybridization operation is as follows:
(a) generating a random number rand over the interval (0, 1);
(b) comparison of hybridization probability pcrossAnd the size of the random number rand, determining whether the parent combination is subjected to hybridization operation. If p iscrossIf the number of the offspring individuals is more than or equal to rand, performing hybridization operation on the parent combination to generate two new offspring individuals; otherwise, the hybridization operation is not carried out;
(c) repeating the processes (a) and (b) until all the parents are combined to complete the hybridization operation.
10. The unmanned aerial vehicle track planning method of claim 7, wherein when performing the hybridization operation in step (32), the preset reconstruction operator and the perturbation operator perform a constraint operation on the mutation, wherein the reconstruction operator operates to randomly select a node from the track as a starting node of the mutation, and then find a track which is different from the original track and satisfies the track constraint condition from the starting node to a target point;
and the disturbance operator operation is to randomly select a node on the variant track as a disturbance node, and when the disturbance operator moves to the disturbance node after disturbance, the track still meets the track constraint condition, and then the variant operation is successful.
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