CN103279793B - A kind of unmanned vehicle formation method for allocating tasks determined under environment - Google Patents

A kind of unmanned vehicle formation method for allocating tasks determined under environment Download PDF

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CN103279793B
CN103279793B CN201310146801.4A CN201310146801A CN103279793B CN 103279793 B CN103279793 B CN 103279793B CN 201310146801 A CN201310146801 A CN 201310146801A CN 103279793 B CN103279793 B CN 103279793B
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CN103279793A (en
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吴森堂
孙健
胡楠希
杜阳
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Beihang University
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Abstract

The invention discloses a kind of unmanned vehicle formation method for allocating tasks determined under environment, belong to unmanned vehicle technical field.The present invention includes following steps: the coded sequence determining task allocation algorithms; Determine that unmanned plane is formed into columns the advantage function of executing the task; Determine speed more new formula and the location updating formula of discrete particle cluster algorithm; Determine the flow process of tabu search; Determine the flow process of hybrid optimization.The present invention, by continuous print particle cluster algorithm discretize, is made algorithm simple, easy to operate simultaneously, and is indicated the validity of this discrete particle cluster method by emulation under the prerequisite ensureing its optimizing performance.The present invention proposes the replenishment strategy of tabu search algorithm, in the particle cluster algorithm inertia weight ω more i.e. population embodiment stronger multifarious moment, add the local optimal searching ability of strong algorithms, make the mutual supplement with each other's advantages of original two kinds of algorithm realization, the search performance improved, and in several groups of l-G simulation tests, demonstrate above-mentioned judgement.

Description

Unmanned aerial vehicle formation task allocation method under determined environment
Technical Field
The invention belongs to the technical field of unmanned aerial vehicles, relates to a flight formation task allocation technology, and particularly relates to an unmanned aerial vehicle formation task allocation method under a certain environment.
Background
There are currently as many as thirty or more countries that invest in significant amounts of human and financial resources to engage in the research and production of unmanned aerial vehicles. Through the development of twenty years, the technology is mature and plays a role in various fields of military and civilian, however, a single unmanned aerial vehicle has some problems in performing tasks, for example, the single unmanned aerial vehicle is possibly limited by the number of sensors, cannot observe a target area from multiple angles in an all-around manner, and cannot effectively cover the whole search area when facing a large-area search task; if the rescue task is executed, the single unmanned aerial vehicle is limited in the aspect of load, the efficiency of the whole rescue is often influenced, and larger loss is brought.
In recent years, due to the complexity of the environment and the multiplicity of tasks, a single unmanned aerial vehicle cannot meet the requirements of ground attack and rescue, and in view of the defects of the single unmanned aerial vehicle, the concept of common task execution by multiple unmanned aerial vehicles is proposed abroad in recent years and certain research results are obtained. The problem of multi-unmanned aerial vehicle cooperative task allocation is a key problem of multi-unmanned aerial vehicle joint task execution.
The multi-unmanned aerial vehicle cooperative task allocation is a multi-constraint and strong-coupling complex multi-objective integer optimization problem essentially, and is obviously characterized in that the values of decision variables are discrete, if a multi-objective optimization problem has non-inferior solutions, a plurality of non-inferior solutions often exist to form a non-inferior set, and a decider generally selects one or more satisfactory non-inferior optimal solutions as a final solution, so that the multi-objective optimization problem generally does not have a single optimal solution but a Pareto optimal set, and trade-off must be carried out between the optimal solutions of the Pareto optimal set, so that the optimal solution which is satisfactory for the decider is obtained.
The concept of multi-unmanned aerial vehicle cooperative task allocation is as follows: before multiple unmanned aerial vehicles carry out tasks, one or a group of ordered tasks (target or spatial position points) are allocated to each unmanned aerial vehicle according to the number or load of the unmanned aerial vehicles based on certain environmental knowledge and task requirements, so that the overall efficiency of the aircraft is optimal while the largest possible number of tasks are completed. Because the decision variables of the multi-objective integer optimization problem are discrete, the optimization theory and the basic method in the classical continuous mathematics can not be directly used for solving the integer optimization problem generally, and the following three main solutions are formed through the development of decades:
the first method comprises the following steps: the solutions of the discrete cases are limited, so that all feasible solutions can be found and then compared, which is called as an exhaustion method or an enumeration method, and the method can be generally used for small-scale problems only;
and the second method comprises the following steps: namely, firstly, ignoring the integer requirement, solving according to the continuous condition, and then carrying out integer processing on the solution. Such methods include branch-and-bound methods and secant-plane methods. The calculation amount of solving integer programming by a branch-and-bound method and a secant plane method is less than that of an enumeration method, but the problem to be solved is linear, and the calculation complexity is exponentially increased along with the problem scale, so that the method is rarely used for large-scale problems;
and the third is that: bionic intelligent computing, abstracting the biological population characteristics or phenomena in nature into mathematical expressions, simulating biological systems in nature, completely depending on the instinct of organisms, and optimizing the survival state of individuals by unconscious optimization to adapt to the environment requirement (the environment adaptability is generally represented by a fitness function). The bionic intelligent computing method has the advantages that (1) probabilistic global optimization is realized; (2) does not depend on strict mathematical properties of an optimization problem; (3) intrinsic parallelism; (4) self-organization and progressiveness, etc.
Disclosure of Invention
The invention aims to solve the problems in the prior art, provides a task allocation strategy for formation of unmanned aerial vehicles under a determined environment, designs a hybrid optimization strategy based on a modern optimization algorithm aiming at the problem of large-scale complex multi-target integer optimization related to task allocation, and accelerates the convergence speed and the local search capability of the modern optimization algorithm.
The unmanned aerial vehicle formation task allocation strategy under the determined environment comprises the following steps:
the method comprises the following steps: determining a coding sequence of a task allocation algorithm;
step two: determining an advantage function of the unmanned aerial vehicle formation execution task;
step three: determining a speed updating formula and a position updating formula of a discrete particle swarm algorithm;
step four: determining a taboo search flow;
step five: and determining the flow of the hybrid optimization.
The invention has the advantages that:
(1) discretizing a continuous particle swarm algorithm. Compared with other particle swarm algorithms, the traditional continuous particle swarm algorithm has the advantages of simplicity in operation, convenience in understanding, high convergence speed and the like, and has the defects that the algorithm mostly aims at continuous problems and aims at the defects of the particle swarm algorithm.
(2) A large number of research results show that compared with other algorithms, the information sharing mechanism of the discrete particle swarm algorithm is different, for example, in the genetic algorithm, the information of chromosomes is shared after the information is subjected to a roulette method, namely, the moving speed of the whole population to an optimal area is uniform, the optimal particles of the particle swarm algorithm influence all the particles in the population in each generation of evolution process, and therefore the algorithm is easy to get early into local optimization. Aiming at the defect, the invention provides a supplement strategy of a tabu search algorithm, and the local optimization capability of the algorithm is enhanced at the moment when the inertia weight omega of the particle swarm algorithm is larger, namely the particle swarm embodies stronger diversity, so that the original two algorithms realize advantage complementation and improved search performance, and the conclusion is verified in a plurality of sets of simulation tests.
Drawings
FIG. 1 is a task advantage table;
FIG. 2 is a schematic diagram of an encoding method of a task allocation algorithm;
FIG. 3 is Si(t) in a vectorAndelements are exchanged schematically;
FIG. 4 is Si′(t) in the vector [ a, b]Between element and Pi(t) interchanging corresponding elements in the vector;
FIG. 5 is Si″(t) in the vector [ a, b]Between element and Pg(t) interchanging corresponding elements in the vector;
FIG. 6 is a flow chart of a discrete particle swarm algorithm;
FIG. 7 is a diagram illustrating an encoding method for constructing a neighborhood solution by tabu search;
FIG. 8 is a tabu search flow diagram;
FIG. 9 is a flow chart of a hybrid optimization assignment method for tasks of formation of unmanned aerial vehicles according to the present invention;
FIG. 10 is a forming overall merit function variation curve of unmanned aerial vehicle forming task allocation;
FIG. 11 is a formation global merit function simulation curve for unmanned aerial vehicle formation task allocation;
fig. 12 is a table of merit functions for 10 unmanned aerial vehicles performing 10 tasks;
FIG. 13 is a formation overall merit function variation curve for task allocation of three strategy types of unmanned aerial vehicle formation in the embodiment;
fig. 14 is a graph obtained by performing monte carlo simulation on the three strategies in fig. 13.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples.
Firstly, the problem to be solved is described, a task advantage table is shown in fig. 1, normalized numbers in the table represent how much capability an unmanned aerial vehicle (also called an unmanned aerial vehicle) has to execute the task, wherein values in the ith row and jth column represent how much capability the unmanned aerial vehicle i has to execute a task j (namely, a target j in the task advantage table), and are defined as Di,j1,2, …, 20 in fig. 1; j is 1,2, …, 10. The purpose of task allocation of unmanned aerial vehicle formation is to determine the combination of unmanned aerial vehicle execution tasks, so that the execution efficiency of unmanned aerial vehicle formation execution tasks is maximized.
The invention provides a task allocation method for formation of unmanned aerial vehicles under a certain environment, which comprises the following steps:
the method comprises the following steps: determining a coding sequence of a task allocation algorithm according to the task advantage table;
the coding sequence of the task allocation algorithm is shown in fig. 2, the coding mode adopts an integer coding sequence, the length of the coding sequence S is equal to the total number N of the unmanned aerial vehiclesSElements thereof are represented by si,1≤i≤NsRepresents, each element siThe positive random number in (1) represents the task number executed by the unmanned aerial vehicle, and the assumed task number is NTThen 1 is not more than si≤NT. According to the data in the task advantage table of FIG. 1, the total number of the unmanned aerial vehicles NSNumber of tasks N20TFor example 10, the coding sequence array in fig. 2 has 20 elements, so the coding sequence in fig. 2 indicates that drone 1 performs task 2, drone 2 performs task 1, drone 3 performs task 10, drone 4 performs task 3 … …, and so on, and finally drone 20 performs task 7.
Step two: determining an advantage function of the unmanned aerial vehicle formation execution task;
the advantage function of the unmanned aerial vehicle formation execution task is determined by the task advantage table and the coding sequence together, and the ith element s in the coding sequence is setiThe positive integer stored in (A) is j, i.e. siJ, assuming that there is a target sequence T, the number of elements in T is equal to the number of tasks NTElements in the target sequence T are represented by Tj(j=1,2,...,NT) Expressed, the calculation formula of the merit function C is:
<math> <mrow> <mi>C</mi> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>T</mi> </msub> </munderover> <msub> <mi>t</mi> <mi>j</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </math>
wherein,
<math> <mrow> <msub> <mi>t</mi> <mi>j</mi> </msub> <mo>=</mo> <mfenced open = '{' close = ''> <mtable> <mtr> <mtd> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>S</mi> </msub> </munderover> <msub> <mi>D</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <mi>i</mi> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>=</mo> <mi>j</mi> <mo>,</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>S</mi> </msub> </munderover> <msub> <mi>D</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>&lt;</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <mi>i</mi> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>=</mo> <mi>j</mi> <mo>,</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>S</mi> </msub> </munderover> <msub> <mi>D</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>&GreaterEqual;</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>
tj1 indicates that the formation of drones has completely performed the task tjSo the merit function taken as 1 does not increase any more.
Step three: determining a speed updating formula and a position updating formula of a discrete particle swarm algorithm;
the standard particle swarm algorithm is described as follows: in an M-dimensional target search space, there is a population of n particles. Wherein the position of the particle i is represented asThat is, the position of the ith particle in the target search space in the M dimension is Si. Position S of each particleiIs a potential feasible solution, and the position S can be obtained by substituting the potential feasible solution into the calculation formula (1) of the advantage functioniC (S) ofi) And is used for judging the quality of the particle i. The flight velocity of the particle i response is expressed asThe best position experienced by particle i is recorded as the individual extremum of particle i, expressed asWhole colonyThe best position that all particles have experienced is noted as a global extremum, denoted Pg=(pg1,pg2,...,pgM). Each particle updates its own velocity and position according to the individual extremum and the global extremum, as shown in the following equation:
<math> <mrow> <mfenced open = '{' close = ''> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>v</mi> <mi>j</mi> <mi>i</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mi>&omega;</mi> <mo>&CenterDot;</mo> <msubsup> <mi>v</mi> <mi>j</mi> <mi>i</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo>&CenterDot;</mo> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mn>1</mn> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <msubsup> <mi>p</mi> <mi>j</mi> <mi>i</mi> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>-</mo> <msubsup> <mi>s</mi> <mi>j</mi> <mi>i</mi> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <mo>&CenterDot;</mo> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mn>2</mn> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mrow> <mi>g</mi> <mi>j</mi> </mrow> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>-</mo> <msubsup> <mi>s</mi> <mi>j</mi> <mi>i</mi> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>s</mi> <mi>j</mi> <mi>i</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>s</mi> <mi>j</mi> <mi>i</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>v</mi> <mi>j</mi> <mi>i</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>M</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </math>
in the formula, t is an evolution algebra, omega is an inertia weight, the size of the inertia weight determines the inheritance of the current speed of the particle, and the proper selection of the inertia weight can enable the particle to have balanced exploration capacity and development capacity; c. C1,c2A normal number, called a learning factor, which gives itself the ability to move closer to its historical optimum and to the population historical optimum, allowing the particles to self-summarize and learn from superior individuals in the population, c1,c2Generally two are uniformly distributed in [0,1 ]]A random number in between. Therefore, the problem oriented by the standard particle swarm algorithm is continuous and is not suitable for solving the discrete problem of integer optimization, so that the invention provides a discrete particle swarm algorithm, and the flow chart of the discrete particle swarm algorithm is shown in FIG. 6.
The essence of the discrete particle swarm algorithm is that the particles fly to the optimal position by constantly adjusting their position and velocity based on their own and companion flight experience, the new position of the particle being the result of the interaction of the particle velocity, the individual extrema, and the global extrema. Therefore, the position and speed updating formula of the standard particle swarm algorithm is redefined to obtain the position S of the ith particle in the M-dimensional target search space in the discrete particle swarm algorithmi
<math> <mrow> <msup> <mi>S</mi> <mi>i</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>f</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>P</mi> <mi>g</mi> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> <mo>(</mo> <mrow> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo>,</mo> <msup> <mi>P</mi> <mi>i</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <mi>&omega;</mi> <mo>,</mo> <msup> <mi>S</mi> <mi>i</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> <mo>)</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> </math>
Si(t +1) is the position of the particle i after the evolution algebra is t +1, Si(t) is the position of the particle i with the evolutionary algebra of t in the M-dimensional target search space, Pg(t) is the global extremum of the particle swarm after the evolution algebra t, Pi(t) is the individual extremum of particle i after the evolution algebra t, f1、f2、f3Respectively representing an inertia weight updating operator, a discrete particle swarm algorithm self-cognition operator and a social cognition operator. c. C1,c2To learn the factor, ω is the inertial weight.
Initializing omega, c1,c2Calculating a weight reduction coefficient lambdaωc1c2Initializing n initial particles Si(t); calculating the merit function P of the particle swarm according to the formula (1) and the formula (2)i(t)=Si(t) obtaining Pg(t);
Definition of Si′,Si″Intermediate variables, then:
<math> <mrow> <msup> <mi>S</mi> <mrow> <msup> <mi>i</mi> <mo>&prime;</mo> </msup> </mrow> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>,</mo> <msup> <mi>S</mi> <mi>i</mi> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = '{' close = ''> <mtable> <mtr> <mtd> <mrow> <msub> <mi>g</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mo>,</mo> <msup> <mi>S</mi> <mi>i</mi> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>,</mo> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mrow> <mo>(</mo> <mo>)</mo> </mrow> <mo>&le;</mo> <mi>&omega;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>S</mi> <mi>i</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mrow> <mo>(</mo> <mo>)</mo> </mrow> <mo>&gt;</mo> <mi>&omega;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> </math>
the formula is an inertial part of a discrete particle swarm algorithm, and is specifically described as follows, and a [0,1 ] is generated by a rand () function]Uniformly distributed random number in between, denoted as r1If the random number is greater than ω, the position S of the particlei′(t)=Si(t) remaining unchanged, and if the random number is not more than ω, Si′(t)=g1(Si(t)), wherein g1(Si(t)) means that two [1, N ] are generatedS]A and b, then Si(t) elements in the vector corresponding to a and bAndinterchanging is performed, as shown in fig. 3, the random numbers are 7 and 14, respectively, the corresponding elements are 4 and 9, respectively, and 4 and 9 are interchanged.
For intermediate variable Si″After the evolution passage is t, there are:
<math> <mrow> <msup> <mi>S</mi> <mrow> <msup> <mi>i</mi> <mrow> <mo>&prime;</mo> <mo>&prime;</mo> </mrow> </msup> </mrow> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo>,</mo> <msup> <mi>P</mi> <mi>i</mi> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>,</mo> <msup> <mi>S</mi> <mrow> <msup> <mi>i</mi> <mo>&prime;</mo> </msup> </mrow> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = '{' close = ''> <mtable> <mtr> <mtd> <mrow> <msub> <mi>g</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msup> <mi>P</mi> <mi>i</mi> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>,</mo> <msup> <mi>S</mi> <mrow> <msup> <mi>i</mi> <mo>&prime;</mo> </msup> </mrow> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>,</mo> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mrow> <mo>(</mo> <mo>)</mo> </mrow> <mo>&le;</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>S</mi> <mrow> <msup> <mi>i</mi> <mo>&prime;</mo> </msup> </mrow> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mrow> <mo>(</mo> <mo>)</mo> </mrow> <mo>&gt;</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow> </math>
the formula (6) is a self-cognition part of the discrete particle swarm algorithm, and is specifically described as follows, a [0,1 ] is generated by a rand () function]Uniformly distributed random number in between, denoted as r2If the random number is greater than c1Position S after t iterations of particle ii″(t)=Si′(t) remaining unchanged if the random number is c or less1Then S isi″(t)=g2(Pi(t),Si′(t)), wherein g2(Pi(t),Si′(t)) means that two [1, N ] are generatedS]A random number c and d between, then Si′(t) in the vector [ c, d]Between element and Pi(t) corresponding elements in the vector are interchanged as shown in FIG. 4.
Based on the formula (5) and the formula (6), the position S of the particle i with the evolution algebra of t +1 is obtainedi(t +1) is:
<math> <mrow> <msup> <mi>S</mi> <mi>i</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>f</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>P</mi> <mi>g</mi> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>,</mo> <msup> <mi>S</mi> <mrow> <msup> <mi>i</mi> <mrow> <mo>&prime;</mo> <mo>&prime;</mo> </mrow> </msup> </mrow> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = '{' close = ''> <mtable> <mtr> <mtd> <mrow> <msub> <mi>g</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mi>g</mi> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>,</mo> <msup> <mi>S</mi> <mrow> <msup> <mi>i</mi> <mrow> <mo>&prime;</mo> <mo>&prime;</mo> </mrow> </msup> </mrow> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>,</mo> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mrow> <mo>(</mo> <mo>)</mo> </mrow> <mo>&le;</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>S</mi> <mrow> <msup> <mi>i</mi> <mrow> <mo>&prime;</mo> <mo>&prime;</mo> </mrow> </msup> </mrow> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mrow> <mo>(</mo> <mo>)</mo> </mrow> <mo>&gt;</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow> </math>
the formula is a social cognition part of a discrete particle swarm algorithm, and is specifically described as follows, a [0,1 ] is generated by a rand () function]Uniformly distributed random number in between, denoted as r3If the random number is greater than c2Then the particle position Si(t+1)=Si″(t) remaining unchanged if the random number is c or less2Then S isi(t+1)=g3(Pg(t),Si″(t)), wherein g3(Pg(t),Si″(t)) means that two [1, N ] are generatedS]Random numbers A and B, then Si″(t) in the vector [ A, B]Between element and Pg(t) corresponding elements in the vector are interchanged as shown in FIG. 5.
Updating the individual extremum and the global extremum if SiThe merit function of (t +1) is greater than Pi(t) a merit function, then Pi(t+1)=Si(t +1), otherwise Pi(t+1)=Pi(t); if SiThe merit function of (t +1) is greater than Pg(t) a merit function, then Pg(t+1)=Si(t +1), otherwise Pg(t+1)=Pg(t)。
Initial value omega of inertial weight omega in the inventionstartIs taken as 0.9, and increases with evolution algebra to obtain the final value omegaendDown to omegaend0.4, for example, if the evolution algebra n is 100, the tth generation inertia weight ω takes the value ωtIs omegat=ωend+(ωstartend) T/n, weight reduction factor λω=(ωstartend) (t/n), analogously to c1,c2Initial value c1start,c2startAll are 0.6, increase with evolution algebra, and the final value c1end,c2endAre all 0.2, the t generation c1Value c1tIs c1t=c1end+(c1start-c1end) T/n, weight reduction factorT th generation c2Value c2tIs c2t=c2end+(c2start-c2end) T/n, weight reduction factor <math> <mrow> <msub> <mi>&lambda;</mi> <msub> <mi>c</mi> <mn>2</mn> </msub> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>c</mi> <mrow> <mn>2</mn> <mi>start</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>c</mi> <mrow> <mn>2</mn> <mi>end</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mi>t</mi> <mo>/</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </math>
Step four: determining a taboo search flow;
the tabu search algorithm has the advantages of high convergence speed, strong local search capability and the like, but the final convergence result of the tabu search algorithm is greatly influenced by the initial solution, and the tabu search algorithm is easy to fall into local optimization due to poor selection of the initial solution. The tabu search algorithm is a manifestation of artificial intelligence and is an extension of the local neighborhood search algorithm. The basic ideas of the tabu search algorithm are: given a current solution and a neighborhood, several candidate solutions are then determined in the neighborhood of the current solution. If the dominant function corresponding to the optimal candidate solution is superior to the 'bestsofar' state, neglecting the taboo characteristic, replacing the current solution and the 'bestsofar' state with the dominant function, adding the corresponding object into a taboo table, and modifying the tenure of each object in the taboo table; if the candidate solution does not exist, selecting the non-taboo optimal state as a new current solution in the candidate solution regardless of the advantages and disadvantages of the current solution, adding the response object into the taboo table, and modifying the tenure of each object in the taboo table. The above process is repeated until the stop condition is satisfied.
The taboo search flow adopted by the invention is shown in fig. 8, and comprises the following specific steps:
and (4.1) setting parameters of a tabu search algorithm and initializing a tabu table.
The tabu table is a first-in-first-out queue defined as LtabuThe queue length is 10, if the coding sequence continues to be algebraic n in the tabu tabletabu> 5, the coding sequence was deleted from the tabu table, indicating that the coding sequence was forgotten. Randomly generating an initial solution Si(t), t is 0, current solution
(4.2) at the initial solution Si(t) generating a plurality of neighborhood solutions which are not in the tabu table nearby, wherein the number of the neighborhood solutions is nSThe method of constructing a neighborhood solution is illustrated in fig. 7 as two, the first being the generation of two [1, N |)S]Different random numbers x and y between, then Si(t) elements of the vector corresponding to the random numbers x and yAndcarrying out interchange; the second is to generate a [1, N ]T]Random numbers z and [1, N ] in betweenS]Replacing the element of the u position with z to obtain the solution S with the maximum advantage function in the neighborhood solution setb i est(t);
(4.3) if Sb i est(t) merit functionGreater than Si(t) dominance function C (S)i(t)), then letWill be provided withAdding the tabu table, updating the duration of the tabu table, and continuing the generation number ntabuDeletion of coding sequence > 5; if it isOf the advantage functionLess than or equal to Si(t) dominance function C (S)i(t)), then holdWithout change, willAdding the tabu table, updating the duration of the tabu table, and continuing the generation number ntabuThe coding sequence > 5 is deleted.
(4.4) judging whether the tabu search algorithm is iterated to stipulate algebra or not, if so, ending the tabu search algorithm to output an optimization result, and otherwise, turning to the step (4.2);
the description of the tabu search flow shows that a neighborhood function, a tabu table and a continuous algebra are the keys of tabu search, wherein the neighborhood function follows the idea of local search; the tabu table embodies the defect that a tabu search algorithm avoids circuitous search; persistent algebra is a relaxation to the tabu strategy.
Step five: determining a mixing optimization process;
the discrete particle swarm algorithm has the advantages of simple operation, easy realization and strong global search capability, but the later convergence speed and the solving precision of the discrete particle swarm algorithm are not high. The discrete particle swarm algorithm guides optimization by depending on cooperation and competition among initial random groups, once a certain particle finds a current optimal position, the position is transmitted to other particles in a social cognitive part form of the discrete particle swarm algorithm, so that the other particles are quickly close to the optimal position, and if the optimal position is locally optimal, the other particles in the group cannot search other areas, so that the discrete particle swarm algorithm falls into the locally optimal position; secondly, due to the fact that the inertial weight exists, each particle in the group flies with certain inertia, and the optimal solution is likely to be missed in the flying process.
For the tabu search algorithm in step four, the following disadvantages also exist:
(1) the method has strong dependence on the initial solution, the good initial solution can enable the tabu search to search the good solution in the solution space, and the poor initial solution can reduce the convergence speed of the tabu search;
(2) the iterative search is serial, only a single state move, and not parallel.
In order to overcome the respective defects of the discrete particle swarm algorithm and the tabu search algorithm, the tabu search algorithm is introduced on the basis of the discrete particle swarm algorithm. The discrete particle swarm algorithm and the tabu search algorithm are combined, the global optimization capability of the discrete particle swarm algorithm and the local search capability of the tabu search algorithm are fully utilized, the advantages of the two algorithms are complemented, and the effect better than that of a single algorithm is achieved.
As shown in fig. 9, the overall framework of the unmanned aerial vehicle formation task hybrid optimization allocation strategy still uses the discrete particle swarm algorithm as the main framework, and the difference is that after one iteration of the discrete particle swarm algorithm, the next iteration process is not directly performed, but the global extreme value P of the particle swarm is setg(t) local tabu search is performed in a certain neighborhood of the vector, if Pg(t) finding a better global optimum position (global extremum) within a certain neighborhood of the vector, the position vector is usedReplacement of Pg(t) vector if at Pg(t) if no better global optimum position is found in a certain neighborhood of the vector, then P is not consideredg(t) updating the vector, i.e. adding a pair of global extrema P after each iteration of the discrete particle swarm optimizationg(t) tabu search operation of vector to increase local search capability of algorithm, the specific steps are as follows
And (5.1) setting parameters of a tabu search algorithm and initializing a tabu table.
The tabu table is a first-in-first-out queue defined as LtabuThe queue length is 10, if the coding sequence continues to be algebraic n in the tabu tabletabuIf > 5, the coding sequence is deleted from the tabu list, meaning that the coding sequence is forgotten, and the initial solution P is randomly generatedg(t), t is 0, the current solution Pgcur(0)=Pg(0);
(5.2) at the initial solution Pg(t) generating a plurality of neighborhood solutions which are not in the tabu table nearby, wherein the number of the neighborhood solutions is nSThe method of constructing the neighborhood solution is consistent with fig. 7, and the solution P with the maximum dominance function in the neighborhood solution set is solvedgbest(t);
(5.3) if Pgbest(t) dominance function C (P)gbest(t)) is greater than Pgcur(t) dominance function C (P)gcur(t)), then let Pgcur(t)=Pgbest(t) adding Pgcur(t) adding the tabu table, updating the duration of the tabu table, and continuing the algebra ntabuDeletion of coding sequence > 5; if Pgbest(t) dominance function C (P)gbest(t)) P is not more than Pgcur(t) dominance function C (P)gcur(t)), then P is maintainedgcur(t) without change, adding Pgbest(t) adding the tabu table, updating the duration of the tabu table, and continuing the algebra ntabuThe coding sequence > 5 is deleted.
(5.4) judging whether the tabu search algorithm is iterated to stipulate algebra or not, if so, ending the tabu search algorithm to output an optimization result Pgcur(t), otherwise, the step (5.2) is switched to.
Fig. 10 shows a formation overall dominance function variation curve of the unmanned aerial vehicle formation task allocation by using the discrete particle swarm algorithm alone, the unmanned aerial vehicle formation task allocation by using the tabu search algorithm alone, and the unmanned aerial vehicle formation task allocation by using the hybrid strategy of the discrete particle swarm algorithm and the tabu search algorithm, where the dominance function table of the task allocation is shown in fig. 1, and it can be seen that the hybrid strategy of the discrete particle swarm algorithm and the tabu search algorithm can converge on the optimal solution after evolution for 10 generations, and is superior to the former two methods in both the convergence rate and the quality of the obtained optimal solution. Fig. 11 performs monte carlo simulation on the above three strategies, the simulation times are 50, the evolution algebra of each method is 50, and it can be seen that the quality of the solution obtained by using the mixed strategy of the discrete particle swarm optimization and the tabu search algorithm is superior to the quality of the solution obtained by using the method alone. The optimal solution vector obtained is [7,6,2,6,4,8,7,5,10,1,3,9,5,2,9,1,6,3,4,8 ].
In order to verify the universality of the hybrid strategy, fig. 12 shows an advantage function table of 10 tasks performed by 10 unmanned aerial vehicles, fig. 13 shows a formation overall advantage function change curve of the unmanned aerial vehicle formation task allocation by using the discrete particle swarm algorithm alone, the unmanned aerial vehicle formation task allocation by using the tabu search algorithm alone, and the unmanned aerial vehicle formation task allocation by using the hybrid strategy of the discrete particle swarm algorithm and the tabu search algorithm, so that the hybrid strategy of the discrete particle swarm algorithm and the tabu search algorithm can be converged on the optimal solution after 5 generations of evolution, and is superior to the former two methods in both convergence speed and quality of the obtained optimal solution. Fig. 14 performs monte carlo simulation on the above three strategies, the simulation times are 50, the evolution algebra of each method is 50, and it can be seen that the quality of the solution obtained by using the mixed strategy of the discrete particle swarm optimization and the tabu search algorithm is superior to the quality of the solution obtained by using the method alone. The optimal solution vector obtained is [9,3,8,10,3,7,6,7,10,6 ].

Claims (2)

1. A task allocation method for formation of unmanned aerial vehicles under a certain environment is characterized by comprising the following steps:
the method comprises the following steps: determining a coding sequence of a task allocation method;
step two: determining an advantage function of the unmanned aerial vehicle formation execution task;
step three: determining a speed updating formula and a position updating formula of the discrete particle swarm algorithm to obtain the position S of the ith particle in the M-dimensional target search space in the discrete particle swarm algorithmi
Step four: determining a taboo search flow;
step five: determining a mixing optimization process;
the coding sequence adopts an integer coding sequence, and according to a task advantage table, the length of the coding sequence S is equal to the total number N of the unmanned aerial vehiclesSElements thereof are represented by si,1≤i≤NsRepresents, each element siThe positive random number in (1) represents the task number executed by the unmanned aerial vehicle, and the assumed task number is NTThen 1 is not more than si≤NT
The advantage function is determined by the task advantage table and the coding sequence, and the ith element s in the coding sequence is setiThe positive integer stored in (A) is j, i.e. siJ, assuming that there is a target sequence T, the number of elements in T is equal to the number of tasks NTElements in the target sequence T are represented by TjDenotes, j ═ 1,2, …, NTThen, the calculation formula of the dominance function C is:
<math> <mrow> <mi>C</mi> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>T</mi> </msub> </munderover> <msub> <mi>t</mi> <mi>j</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </math>
wherein,
<math> <mrow> <msub> <mi>t</mi> <mi>j</mi> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>S</mi> </msub> </munderover> <msub> <mi>D</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <mi>i</mi> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>=</mo> <mi>j</mi> <mo>,</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>S</mi> </msub> </munderover> <msub> <mi>D</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>&lt;</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <mi>i</mi> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>=</mo> <mi>j</mi> <mo>,</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>S</mi> </msub> </munderover> <msub> <mi>D</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>&GreaterEqual;</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>
tj1 indicates that the formation of drones has completely performed the task tjSo the merit function is taken to be 1 and no longer increases, j is 1,2, …, NT,Di,jA value representing the ith row and the jth column in the task dominance table;
the position S of the ith particle in the target search space of the dimension M in the discrete particle swarm optimizationi
Si(t+1)=f3(c2,Pg(t),f2(c1,Pi(t),f1(ω,Si(t))))(4)
Si(t +1) is the position of the particle i with the evolution algebra of t + 1; si(t) is the position of the particle i with the evolutionary algebra of t in the M-dimensional target search space; pg(t) is the global extremum of the particle swarm after the evolution algebra t; pi(t) is the individual extremum of the particle i after the evolution algebra t; f. of1、f2、f3Respectively representing an inertia weight updating operator, a discrete particle swarm algorithm self-cognition operator and a social cognition operator; c. C1,c2Is a learning factor, ω is an inertial weight;
the taboo search process comprises the following steps:
(4.1) setting a taboo search algorithm parameter and initializing a taboo table;
the tabu table is a first-in-first-out queue defined as LtabuIf the coding sequence continues to be algebraic n in the tabu tabletabuIf more than 5, the coding sequence is deleted from the tabu list, indicating that the coding sequence is forgotten, and randomly generating an initial solution Si(t), t is 0, current solution S c u r i ( 0 ) = S i ( 0 ) ;
(4.2) at the initial solution Si(t) generating a plurality of neighborhood solutions which are not in the tabu table nearby, wherein the number of the neighborhood solutions is nSThe method of constructing a neighborhood solution is divided into two, the first being to generate two [1, N ═ 10S]Different random numbers x and y between, then Si(t) elements of the vector corresponding to the random numbers x and yAndcarrying out interchange; the second is to generate a [1, N ]T]Random numbers z and [1, N ] in betweenS]Replacing the element of the u position with z to obtain the solution with the maximum advantage function in the neighborhood solution set
(4.3) ifOf the advantage functionGreater than Si(t) dominance function C (S)i(t)), then letWill be provided withAdding the tabu table, updating the duration of the tabu table, and continuing the generation number ntabuDeletion of coding sequence > 5; if it isOf the advantage functionLess than or equal to Si(t) dominance function C (S)i(t)), then holdWithout change, willAdding the tabu table, updating the duration of the tabu table, and continuing the generation number ntabuDeletion of coding sequence > 5;
(4.4) judging whether the tabu search algorithm is iterated to stipulate algebra or not, if so, ending the tabu search algorithm to output an optimization result, and otherwise, turning to the step (4.2).
2. The unmanned aerial vehicle formation task allocation method under the certain environment according to claim 1, wherein: the hybrid optimization process comprises the following specific steps:
(5.1) setting a taboo search algorithm parameter and initializing a taboo table;
the tabu table is a first-in-first-out queue defined as LtabuThe queue length is 10, if the coding sequence continues to be algebraic n in the tabu tabletabuIf > 5, the coding sequence is deleted from the tabu list, meaning that the coding sequence is forgotten, and the initial solution P is randomly generatedg(t), t is 0, the current solution Pgcur(0)=Pg(0);
(5.2) at the initial solution Pg(t) generating a plurality of neighborhood solutions which are not in the tabu table nearby, wherein the number of the neighborhood solutions is nSConstructing a neighborhood solution, and solving a solution P with the maximum dominance function in a neighborhood solution setgbest(t);
(5.3) if Pgbest(t) dominance function C (P)gbest(t)) is greater than Pgcur(t) dominance function C (P)gcur(t)), then let
Pgcur(t)=Pgbest(t) adding Pgcur(t) adding the tabu table, updating the duration of the tabu table, and continuing the algebra ntabuDeletion of coding sequence > 5; if Pgbest(t) dominance function C (P)gbest(t)) P is not more than Pgcur(t) dominance function C (P)gcur(t)), then P is maintainedgcur(t) without change, adding Pgbest(t) adding the tabu table, updating the duration of the tabu table, and continuing the algebra ntabuDeletion of coding sequence > 5;
(5.4) judging whether the tabu search algorithm is iterated to stipulate algebra or not, if so, ending the tabu search algorithm to output an optimization result Pgcur(t), otherwise, the step (5.2) is switched to.
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