CN104406593A

CN104406593A - Method for determining optimal route of airway of unmanned aerial vehicle

Info

Publication number: CN104406593A
Application number: CN201410725347.2A
Authority: CN
Inventors: 罗淇方; 周永权; 陈信
Original assignee: Guangxi University for Nationalities
Current assignee: Guangxi University for Nationalities
Priority date: 2014-12-03
Filing date: 2014-12-03
Publication date: 2015-03-11

Abstract

The invention provides a method for determining the optimal route of the UAV, which can more fully consider the threat of the combat area, have a more efficient global search capability, and provide a more accurate flight path for the UAV. Using the quantum encoding method, the quantum revolving gate and the quantum NOT gate are used to change the state of the basic qubit, and then update the position of the individual bat. Due to the diversity of quantum states, the Quantum Bat Algorithm (QBA) has a strong global search ability, which can find a feasible or even optimal route for UAVs to avoid threats and constraints. The experimental results show that the quantum bat algorithm is an effective and stable method for solving UAV route planning problems, and its search performance is better than other swarm intelligence algorithms.

Description

A method for determining the optimal route of unmanned aerial vehicles

技术领域technical field

本发明涉及一种确定飞机航路的方法，具体是指一种确定无人机航路最优路径的方法。The invention relates to a method for determining an aircraft route, in particular to a method for determining an optimal route of an unmanned aerial vehicle.

背景技术Background technique

无人作战飞行器(UCAV)是一种现代航空武器装备，由于其可以执行远程和危险环境中危险、重复性的工作，因而是未来战争潜在的必然趋势之一。无人机航路规划问题的目标是满足特定的约束条件下，在初始位置和所需的目的地之间寻找一条具有最小威胁代价的最优或接近最优的飞行路径。近年来，在军用和民用领域，无人机航路规划问题都得到了广泛的研究。部分智能算法已经在该问题中得到了应用，如混沌人工蜂群算法(CABC)，遗传算法(GA)，粒子群优化算法(PSO)，差分进化(DE)，混沌捕食生物地理学算法(CPBBO)，蚁群算法(ACO),萤火虫算法(FA)以及人工神经网络(ANN)等。Unmanned Combat Aerial Vehicle (UCAV) is a kind of modern aviation weaponry, because it can perform dangerous and repetitive tasks in remote and dangerous environments, it is one of the potential inevitable trends in future warfare. The goal of the UAV route planning problem is to find an optimal or near-optimal flight path with the minimum threat cost between the initial position and the desired destination under certain constraints. In recent years, the UAV route planning problem has been extensively studied in both military and civilian fields. Some intelligent algorithms have been applied in this problem, such as Chaotic Artificial Bee Colony Algorithm (CABC), Genetic Algorithm (GA), Particle Swarm Optimization Algorithm (PSO), Differential Evolution (DE), Chaotic Predation Biogeography Algorithm (CPBBO ), Ant Colony Algorithm (ACO), Firefly Algorithm (FA) and Artificial Neural Network (ANN), etc.

蝙蝠算法(BatAlgorithm,BA)是由X.S.Yang于2010年提出的，它源于对大自然中蝙蝠利用回声定位的原理进行搜索、捕食食物过程的模拟。在搜寻食物时，蝙蝠会发出超声波脉冲，此时的脉冲音强最大，这样有助于超声波传播更远的距离。在飞向猎物的过程中，脉冲音强会逐渐减小，而脉冲频度则会逐渐增加，这样会使蝙蝠更精确地获取食物的位置。蝙蝠算法已经在诸多领域得到了广泛应用，如全局工程优化问题，约束优化问题，结构优化问题，离散钢结构尺寸优化问题。G.G.Wang应用基本蝙蝠算法(BA)和融合了变异策略的改进蝙蝠算法(MBA)来求解无人机航路规划问题。在改进蝙蝠算法(MBA)中，差分进化中的变异操作被加入蝙蝠算法以加快全局收敛速度。The Bat Algorithm (BA) was proposed by X.S. Yang in 2010. It originated from the simulation of the process of bats searching and preying on food using the principle of echolocation in nature. When searching for food, bats emit ultrasonic pulses, which are at their strongest, which helps the waves travel longer distances. In the process of flying to the prey, the intensity of the pulse sound will gradually decrease, while the frequency of the pulse will gradually increase, which will allow the bat to more accurately obtain the location of the food. The bat algorithm has been widely used in many fields, such as global engineering optimization problems, constrained optimization problems, structural optimization problems, and discrete steel structure size optimization problems. G.G.Wang applied the Basic Bat Algorithm (BA) and the Modified Bat Algorithm (MBA) incorporating mutation strategies to solve UAV route planning problems. In the Modified Bat Algorithm (MBA), the mutation operation in differential evolution is added to the bat algorithm to speed up the global convergence.

现有技术中的基本的蝙蝠算法采用的是实数编码方法，具体步骤如下：What the basic bat algorithm in the prior art adopted is the real number coding method, and concrete steps are as follows:

第一步：建立无人机航路规划问题(UCAV)的数学模型如下：Step 1: Establish the mathematical model of the UAV route planning problem (UCAV) as follows:

即UCAV的威胁源模型，在该模型中，定义航路的起点为S，目标点为T。在无人机的作战任务区内有许多的威胁区域(如：雷达、导弹、火炮等)。这些威胁区域均以圆形区域的方式来表示，越接近圆形区域的中心便越易受攻击，在区域之外则不受攻击；飞行任务就是在考虑所有威胁区域的前提下，在S与T之间寻找一条最优的路线。That is, the threat source model of UCAV. In this model, the starting point of the defined route is S, and the target point is T. There are many threat areas (such as: radar, missile, artillery, etc.) in the combat mission area of the UAV. These threat areas are expressed in the form of a circular area, the closer to the center of the circular area, the more vulnerable it is to attack, and the outside of the area is not attacked; Find an optimal route between T.

(1)处理方法，结合附图1；(1) processing method, in conjunction with accompanying drawing 1;

1、连接S与T；1. Connect S and T;

2、将ST分为D+1段(即D个节点)，分别标记为L₁,L₂,...,L_k,...L_D；2. Divide ST into D+1 segments (that is, D nodes), which are respectively marked as L ₁ , L ₂ ,...,L _k ,...L _D ;

3、在每个节点处作ST的垂线，构成一个离散点的集合：3. Make a vertical line of ST at each node to form a set of discrete points:

C＝{S,L₁(x(1),y(1)),L₂(x(2),y(2)),...,L_k(x(k),y(k)),...L_D(x(D),y(D)),T}按顺序将这些点连接起来便形成了一条路径。C={S,L ₁ (x(1),y(1)),L ₂ (x(2),y(2)),...,L _k (x(k),y(k)) ,...L _D (x(D),y(D)),T} connect these points in order to form a path.

(2)坐标系变换(2) Coordinate system transformation

为了加快搜索速度，可以把ST当作x轴，对每个离散点(x_k,y_k)做坐标变换In order to speed up the search, you can use ST as the x-axis, and do coordinate transformation for each discrete point (x _k , y _k )

$[\begin{matrix} {x x}^{' '} ((k k)) \\ {y the y}^{' '} ((k k)) \end{matrix}] = = [\begin{matrix} cos cos θ θ & sin sin θ θ \\ - - sin sin θ θ & cos cos θ θ \end{matrix}] [\begin{matrix} x x ((k k)) - - {x x}_{s the s} \\ y the y ((k k)) - - {y the y}_{s the s} \end{matrix}] - - - - - - ((11))$

其中，θ是原始坐标系的x轴逆时针旋转到平行于ST时的角度，(x_s,y_s)代表原始坐标系下的坐标。这样，x坐标便可以表示为离散点的集合C便可以转换为：Among them, θ is the angle when the x-axis of the original coordinate system is rotated counterclockwise to parallel to ST, and (x _s , y _s ) represents the coordinates in the original coordinate system. Thus, the x-coordinate can be expressed as The set C of discrete points can be transformed into:

C'＝{0,L₁(y'(1)),L₂(y'(2)),...,L_k(y'(k)),...L_D(y'(D)),0}C'＝{0,L ₁ (y'(1)),L ₂ (y'(2)),...,L _k (y'(k)),...L _D (y'(D )),0}

第二步，建立性能评价函数如下：The second step is to establish the performance evaluation function as follows:

对飞行路径的评价主要包括威胁代价J_t和油料代价J_f The evaluation of the flight path mainly includes the threat cost J _t and the fuel cost J _f

${J J}_{t t} = = {&Integral; &Integral;}_{00}^{L L} {w w}_{t t} dl dl - - - - - - ((22))$

${J J}_{f f} = = {&Integral; &Integral;}_{00}^{L L} {w w}_{f f} dl dl - - - - - - ((33))$

其中，w_t和w_f是与当前路径点，分别代表每段路线的威胁代价和油料代价，L是航线的总长度。Among them, w _t and w _f are the current waypoints, which represent the threat cost and fuel cost of each route respectively, and L is the total length of the route.

采用一种比较精确的近似策略，每段路线(两个离散点之间)的威胁代价，近似为五个点的总和：Using a more accurate approximation strategy, the threat cost of each route (between two discrete points) is approximately the sum of five points:

${w w}_{{t t,, L L}_{i i}} = = \frac{{L L}_{i i}}{55} \cdot \cdot {Σ Σ}_{k k = = 11}^{{N N}_{t t}} {t t}_{k k} \cdot \cdot ((\frac{11}{{d d}_{0.1 0.1,, i i,, k k}^{44}} + + \frac{11}{{d d}_{0.3 0.3,, i i,, k k}^{44}} + + \frac{11}{{d d}_{0.5 0.5,, i i,, k k}^{44}} + + \frac{11}{{d d}_{0.7 0.7,, i i,, k k}^{44}} + + \frac{11}{{d d}_{0.9 0.9,, i i,, k k}^{44}})) - - - - - - ((44))$

其中，N_t是威胁区域的数量，L_i是第i子段的长度，d_0.1,i,k是i子段上1/10分点到第k个威胁的距离，t_k是第k个威胁的威胁程度。Among them, N _t is the number of threat areas, L _i is the length of the i-th subsection, d _0.1,i,k is the distance from the 1/10 point on the i subsection to the kth threat, and t _k is the kth threat The threat level of the threat.

假设UCAV的速度为一常量，油料代价可以等价为总长度L。Assuming that the speed of UCAV is constant, the fuel cost can be equivalent to the total length L.

最终的总代价为：The final total cost is:

J＝kJ_t+(1-k)J_f (5)J＝kJ _t +(1-k)J _f (5)

其中，k＝0.5(0到1变化)，体现设计者的灵活性，k趋近于1，则路径更短，k趋近于1，则路径更长。Among them, k=0.5 (varies from 0 to 1), which reflects the flexibility of the designer. When k approaches 1, the path will be shorter, and if k approaches 1, the path will be longer.

第三步：确定蝙蝠的速度更新和位置更新Step 3: Determine the speed update and position update of the bat

假设搜索空间为n维，蝙蝠i在t时刻的位置为速度为则在t+1时刻的位置和速度更新公式如下：Assuming that the search space is n-dimensional, the position of bat i at time t is speed is Then the position at time t+1 and speed The update formula is as follows:

${f f}_{i i}^{t t} = = {f f}_{min min} + + (({f f}_{max max} - - {f f}_{min min})) β β - - - - - - ((66))$

${v v}_{i i}^{t t + + 11} = = {v v}_{i i}^{t t} + + (({x x}_{i i}^{t t} - - best the best)) {f f}_{i i}^{t t} - - - - - - ((77))$

${x x}_{i i}^{t t + + 11} = = {x x}_{i i}^{t t} + + {v v}_{i i}^{t t + + 11} - - - - - - ((88))$

其中，f_i，f_max，f_min分别表示蝙蝠i在当前时刻发出的声波的频率、声波频率的最大值和最小值。β∈[0,1]是随机产生的数。best表示当前全局最优解。Among them, f _i , f _max , and f _min respectively represent the frequency of the sound wave emitted by bat i at the current moment, the maximum value and the minimum value of the sound wave frequency. β∈[0,1] is a randomly generated number. best represents the current global optimal solution.

对于大小为n的蝙蝠群体，可随机地从中选择一只蝙蝠，并据公式(4)更新该蝙蝠相应的位置，这个过程可被理解为一个局部搜索的过程，即在被选择的解中产生一个新解。For a bat group of size n, a bat can be randomly selected from it, and the corresponding position of the bat can be updated according to formula (4). This process can be understood as a local search process, that is, the selected solution generates a new solution.

x_new(i)＝x_old+εA^t (9)x _new (i)＝x _old +εA ^t (9)

其中，x_old表示从当前最优解集中随机选择的一个解，A^t表示在t时刻前i只蝙蝠响度的平均值，随机向量ε的元素是区间[-1,1]的随机数。Among them, x _old represents a solution randomly selected from the current optimal solution set, A ^t represents the average loudness of i bats before time t, and the elements of the random vector ε are random numbers in the interval [-1,1].

第四步：确定响度和脉冲速率Step Four: Determine Loudness and Impulse Rate

通常，蝙蝠在搜寻开始时，脉冲音强大而脉冲频度小，在飞向食物的过程中，脉冲音强会逐渐降低，脉冲频度则会逐渐提高。蝙蝠i脉冲音强A(i)和脉冲r(i)可根据下述公式(5)(6)更新：Usually, at the beginning of the bat's search, the pulse sound is strong and the pulse frequency is small. In the process of flying to the food, the pulse sound intensity will gradually decrease, and the pulse frequency will gradually increase. The pulse sound intensity A(i) and pulse r(i) of bat i can be updated according to the following formula (5)(6):

r^t+1(i)＝r⁰(i)×[1-exp(-γt)] (10)r ^t+1 (i)=r ⁰ (i)×[1-exp(-γt)] (10)

A^t+1(i)＝αA^t(i) (11)A ^t+1 (i)=αA ^t (i) (11)

其中，0＜α＜1,λ＞0均为常量。A(i)＝0时意味着蝙蝠i刚刚发现一只猎物，暂时停止发出任何声音，不难发现：当t→∞时，A^t(i)→0,r^t(i)＝r⁰(i)。Among them, 0<α<1, λ>0 are all constants. When A(i)=0, it means that bat i has just found a prey and temporarily stops making any sound. It is not difficult to find: when t→∞, A ^t (i)→0, r ^t (i)=r ⁰ ( i).

第五步，开始按下列步骤实施基本蝙蝠算法The fifth step is to start implementing the basic bat algorithm as follows

Step1:初始化基本参数：群体规模N、脉冲音强衰减系数α、脉冲频度增加系数γ、最大脉冲频度r⁰、最大脉冲音强A和最大迭代次数iterMax；Step1: Initialize basic parameters: group size N, pulse sound intensity attenuation coefficient α, pulse frequency increase coefficient γ, maximum pulse frequency r ⁰ , maximum pulse sound intensity A and maximum iteration number iterMax;

Step 2:定义脉冲频率Q_i∈[Q_min,Q_max]和速度v；Step 2: Define pulse frequency Q _i ∈ [Q _min , Q _max ] and speed v;

Step 3:初始化蝙蝠的位置x_i，并寻找当前的最优解f_min；Step 3: Initialize the position x _i of the bat, and find the current optimal solution f _min ;

Step 4:进入主循环，如果rand＜r_i，则按照公式(7)(8)分别更新蝙蝠的速度和当前位置，否则对蝙蝠的位置进行随机扰动，并进入步骤5；Step 4: Enter the main loop, if rand<r _i , update the speed and current position of the bat according to the formula (7) (8), otherwise randomly disturb the position of the bat, and enter step 5;

Step 5:如果rand＜A_i并且f(x_i)＜f(x)，则接受新的解，并飞至更新之后的位置；Step 5: If rand<A _i and f(x _i )<f(x), accept the new solution and fly to the updated position;

Step 6:如果f(x_i)＜f_min，则替换之前的最优蝙蝠，并根据公式(10)、(11)调整脉冲音强A_i和脉冲频度r_i；Step 6: If f(x _i )＜f _min , then replace the previous optimal bat, and adjust the pulse sound intensity A _i and pulse frequency r _i according to formulas (10) and (11);

Step 7:对蝙蝠群体进行评估，找出最佳的蝙蝠及其所处位置；Step 7: Evaluate the bat population to find out the best bat and its location;

Step 8:满足算法的终止条件(达到最大搜索次数或是满足搜索精度)则进入步骤9；否则进入步骤4，进行下一次搜索；Step 8: If the termination condition of the algorithm is met (reaching the maximum number of searches or satisfying the search accuracy), then enter step 9; otherwise, enter step 4 for the next search;

Step 9:输出最优个体值和全局最优解。Step 9: Output the optimal individual value and the global optimal solution.

其中，rand是[0,1]上均匀分布的随机数。Among them, rand is a random number uniformly distributed on [0,1].

本发明专利的申请人经过多次实践发现，上述的基本蝙蝠算法采用的是实数编码方法，其中种群的多样性受到限制，使算法容易陷入到局部最优。一旦进入了局部最优解，就很难跳出了，实际上往往是根本就跳不出。但是在无人机的实际航线确定过程中，我们所要追求的是可以更充分地考虑作战区域的威胁，更加高效的全局搜索能力，能为无人机提供更为准确的飞行路径而不能陷入到局部最优中去。The applicant of the patent of the present invention has found through many times of practice that the above-mentioned basic bat algorithm uses a real number encoding method, in which the diversity of the population is limited, which makes the algorithm easy to fall into a local optimum. Once entering the local optimal solution, it is difficult to jump out, in fact, it is often impossible to jump out at all. However, in the process of determining the actual route of the UAV, what we want to pursue is to more fully consider the threat of the combat area, a more efficient global search capability, and provide a more accurate flight path for the UAV without falling into the Go to the local optimum.

发明内容Contents of the invention

本发明要解决的技术问题是，提供一种可以更充分地考虑作战区域的威胁，更加高效的全局搜索能力，能为无人机提供更为准确的飞行路径的确定无人机航路最优路径的方法。The technical problem to be solved by the present invention is to provide a more efficient global search capability that can more fully consider the threat of the combat area, and can provide a more accurate flight path for the UAV to determine the optimal path of the UAV route. Methods.

为解决上述技术问题，本发明提供的技术方案为：一种确定无人机航路最优路径的方法，它包括如下步骤：In order to solve the above-mentioned technical problems, the technical solution provided by the present invention is: a method for determining the optimal path of the unmanned aerial vehicle route, which includes the following steps:

第一步，基于基本蝙蝠算法的基础上采用量子位的概率幅对蝙蝠个体进行编码，即用量子旋转门对量子位的概率幅进行更新，采用量子非门作为变异操作以避免算法的早熟收敛；对于每个量子位具有两个概率幅，因此，每只蝙蝠可以表示优化空间的两个位置；The first step is to use the probability amplitude of the qubit to encode the bat individual based on the basic bat algorithm, that is, to update the probability amplitude of the qubit with the quantum revolving door, and to use the quantum NOT gate as a mutation operation to avoid premature convergence of the algorithm ; for each qubit there are two probability amplitudes, so each bat can represent two positions in the optimization space;

第二步，在量子计算中，最小的信息单元存储在一个量子比特中，该量子比特的状态可能为“0”，也可能为“1”，或是“0”和“1”之间的任意状态；一个量子比特的状态可以表示如下：In the second step, in quantum computing, the smallest information unit is stored in a qubit, and the state of the qubit may be "0", or "1", or between "0" and "1". Arbitrary state; the state of a qubit can be represented as follows:

|Ψ>＝α|0>+β|1> (12)|Ψ>=α|0>+β|1> (12)

其中，α和β满足：Among them, α and β satisfy:

|α|²+|β|²＝1 (13)|α| ² +|β| ² ＝1 (13)

其中，|α|²和|β|²分别表示趋于状态|0>和|1>的概率；Among them, |α| ² and |β| ² represent the probability of tending to the state |0> and |1>respectively;

一个n元量子比特可以定义为：An n-ary qubit can be defined as:

$[\begin{matrix} \begin{matrix} {α α}_{11} \\ {β β}_{11} \end{matrix} & |\begin{matrix} {α α}_{22} \\ {β β}_{22} \end{matrix}| & \begin{matrix} . . . . . . \\ . . . . . . \end{matrix} & |\begin{matrix} {α α}_{k k} \\ {β β}_{k k} \end{matrix}| & \begin{matrix} . . . . . . \\ . . . . . . \end{matrix} & |\begin{matrix} {α α}_{n no} \\ {β β}_{n no} \end{matrix}| \end{matrix}] - - - - - - ((1414))$

量子旋转门定义如下：A quantum revolving door is defined as follows:

$[\begin{matrix} cos cos ((Δθ Δθ)) & - - sin sin ((Δθ Δθ)) \\ sin sin ((Δθ Δθ)) & cos cos ((Δθ Δθ)) \end{matrix}] - - - - - - ((1515))$

量子非门定义如下：A quantum NOT gate is defined as follows:

$[\begin{matrix} 00 & 11 \\ 11 & 00 \end{matrix}] [\begin{matrix} α α \\ β β \end{matrix}] = = [\begin{matrix} β β \\ α α \end{matrix}] - - - - - - ((1616))$

第三步，产生初始种群The third step is to generate the initial population

算法采用的编码方案如下：The encoding scheme adopted by the algorithm is as follows:

$P P = = [\begin{matrix} \begin{matrix} cos cos (({θ θ}_{i i 11})) \\ sin sin (({θ θ}_{i i 11})) \end{matrix} & |\begin{matrix} cos cos (({θ θ}_{i i 22})) \\ sin sin (({θ θ}_{i i 22})) \end{matrix}| & \begin{matrix} . . . . . . \\ . . . . . . \end{matrix} & |\begin{matrix} cos cos (({θ θ}_{ik ik})) \\ sin sin (({θ θ}_{ik ik})) \end{matrix}| & \begin{matrix} . . . . . . \\ . . . . . . \end{matrix} & |\begin{matrix} cos cos (({θ θ}_{in in})) \\ sin sin (({θ θ}_{in in})) \end{matrix}| \end{matrix}] - - - - - - ((1717))$

其中，θ_ij是幅角，由式(17)可以看出每只蝙蝠对应了问题空间的两个位置，分别对应了量子态|0>和|1>的概率幅：Among them, _θij is the argument angle. From formula (17), it can be seen that each bat corresponds to two positions in the problem space, corresponding to the probability amplitudes of the quantum states |0> and |1>:

P_ic＝(cos(θ_i1),cos(θ_i2),...,cos(θ_in)) (18)P _ic ＝(cos(θ _i1 ),cos(θ _i2 ),...,cos(θ _in )) (18)

P_is＝(sin(θ_i1),sin(θ_i2),...,sin(θ_in)) (19)P _is ＝(sin(θ _i1 ),sin(θ _i2 ),...,sin(θ _in )) (19)

第四步，解空间的转换The fourth step is to transform the solution space

为了计算个体的适应度并对个体的优劣进行评价，我们需要对种群的解空间进行转换；个体的量子位的每个概率幅对应了问题的解空间的一个解，即每只蝙蝠对应了优化问题的两个解；In order to calculate the fitness of the individual and evaluate the pros and cons of the individual, we need to convert the solution space of the population; each probability amplitude of the qubit of the individual corresponds to a solution of the solution space of the problem, that is, each bat corresponds to Two solutions to the optimization problem;

${X x}_{ic ic}^{j j} = = \frac{11}{22} [[{X x}_{max max} ((11 + + {α α}_{i i}^{j j})) + + {X x}_{min min} ((11 - - {α α}_{i i}^{j j}))]] - - - - - - ((2020))$

${X x}_{is is}^{j j} = = \frac{11}{22} [[{X x}_{max max} ((11 + + {β β}_{i i}^{j j})) + + {X x}_{min min} ((11 - - {β β}_{i i}^{j j}))]] - - - - - - ((21 twenty one))$

其中，由量子态|0>的概率幅求得，而是由量子态|1>的概率幅得到；in, From the probability amplitude of the quantum state |0> get it, and is the probability amplitude of the quantum state |1> get;

第五步，更新策略The fifth step is to update the strategy

在量子蝙蝠算法(QBA)中，采用蝙蝠算法(BA)的更新策略对量子位的幅角增量进行更新，其更新过程如下：In the quantum bat algorithm (QBA), the update strategy of the bat algorithm (BA) is used to update the argument increment of the qubit, and the update process is as follows:

Δθ_ij(t+1)＝Δθ_ij(t)+Δθ_g*Q(i)*stepnow (22)Δθ _ij (t+1)=Δθ _ij (t)+Δθ _g *Q(i)*stepnow (22)

θ_ij(t+1)＝θ_ij(t)+Δθ_ij(t+1) (23)θ _ij (t+1)＝θ _ij (t)+Δθ _ij (t+1) (23)

其中，Δθ_ij和θ_ij分别为幅角增量和幅角；Among them, Δθ _ij and θ _ij are argument increment and argument angle respectively;

${Δθ Δθ}_{g g} = = \{\begin{matrix} 22 π π + + {θ θ}_{gj gj} - - {θ θ}_{ij ij} & (({θ θ}_{gj gj} - - {θ θ}_{ij ij} < < - - π π)) \\ {θ θ}_{gj gj} - - {θ θ}_{ij ij} & ((- - π π \leq \leq {θ θ}_{gj gj} - - {θ θ}_{ij ij} \leq \leq π π)) \\ {θ θ}_{gj gj} - - {θ θ}_{ij ij} - - 22 π π & (({θ θ}_{gj gj} - - {θ θ}_{ij ij} > > π π)) \end{matrix} - - - - - - ((24 twenty four))$

$stepnow step now = = \frac{{((Maxgen Maxgen - - gen the gene))}^{w w}}{{((Maxgen Maxgen))}^{w w}} (({σ σ}_{s the s} - - {σ σ}_{e e})) + + {σ σ}_{e e} - - - - - - ((2525))$

在本文中，式(25)中的参数值分别为：w＝2，σ_e＝0，σ_s＝2；In this paper, the parameter values in formula (25) are: w=2, σ _e =0, σ _s =2;

利用量子旋转门对概率幅进行更新：Update the probability amplitude using a quantum revolving door:

$[\begin{matrix} cos cos (({θ θ}_{ij ij} ((t t + + 11)))) \\ sin sin (({θ θ}_{ij ij} ((t t + + 11)))) \end{matrix}] = = [\begin{matrix} cos cos (({Δθ Δθ}_{ij ij} ((t t + + 11)))) & - - sin sin (({Δθ Δθ}_{ij ij} ((t t + + 11)))) \\ sin sin (({Δθ Δθ}_{ij ij} ((t t + + 11)))) & cos cos (({Δθ Δθ}_{ij ij} ((t t + + 11)))) \end{matrix}] [\begin{matrix} cos cos (({θ θ}_{ij ij} ((t t)))) \\ sin sin (({θ θ}_{ij ij} ((t t)))) \end{matrix}] = = [\begin{matrix} cos cos (({θ θ}_{ij ij} ((t t)) + + {Δθ Δθ}_{ij ij} ((t t + + 11)))) \\ sin sin (({θ θ}_{ij ij} ((t t)))) + + {Δθ Δθ}_{ij ij} ((t t + + 11)) \end{matrix}] - - - - - - ((2626))$

得到两个新位置：to get two new positions:

$\overset{~ ~}{{P P}_{ic ic}} = = ((cos cos (({θ θ}_{ij ij} ((t t)) + + {Δθ Δθ}_{ij ij} ((t t + + 11)))),, . . . . . .,, cos cos (({θ θ}_{ij ij} ((t t)) + + {Δθ Δθ}_{ij ij} ((t t + + 11)))))) - - - - - - ((2727))$

$\overset{~ ~}{{P P}_{is is}} = = ((sin sin (({θ θ}_{ij ij} ((t t)))) + + {Δθ Δθ}_{ij ij} ((t t + + 11)),, . . . . . .,, sin sin (({θ θ}_{ij ij} ((t t)))) + + {Δθ Δθ}_{ij ij} ((t t + + 11)))) - - - - - - ((2828))$

第六步，变异策略The sixth step, mutation strategy

在量子蝙蝠算法(QBA)中，为了防止算法过早地陷入局部最优，本文采用变异策略来增加种群的多样性，变异策略通过量子非门实现；如果rand()＜p_m，则执行量子非门操作，将两个概率值进行兑换；其中，p_m为变异概率；In the Quantum Bat Algorithm (QBA), in order to prevent the algorithm from falling into a local optimum prematurely, this paper adopts a mutation strategy to increase the diversity of the population, and the mutation strategy is realized by a quantum NOT gate; if rand()<p _m , execute the quantum The NOT gate operation converts two probability values; among them, p _m is the mutation probability;

$[\begin{matrix} 00 & 11 \\ 11 & 00 \end{matrix}] [\begin{matrix} cos cos (({θ θ}_{ij ij})) \\ sin sin (({θ θ}_{ij ij})) \end{matrix}] = = [\begin{matrix} sin sin (({θ θ}_{ij ij})) \\ cos cos (({θ θ}_{ij ij})) \end{matrix}] = = [\begin{matrix} cos cos (({θ θ}_{ij ij} + + \frac{π π}{22})) \\ sin sin (({θ θ}_{ij ij} + + \frac{π π}{22})) \end{matrix}] - - - - - - ((2929)) . .$

采用上述方法后，本发明具有如下有益效果：算法采用量子比特的概念作为一种编码方法。量子旋转门用于更改量子比特的状态，量子非门用来实现量子比特的变异以避免早熟收敛。由于量子态的多样性，有效提高了QBA的全局搜索能力，并避免了蝙蝠个体过早陷入局部最优。仿真结果表明所提出的算法的鲁棒性与有效性。QBA可以更充分地考虑作战区域的威胁，为无人机(UCAV)得到更为准确的飞行路径。After adopting the above method, the present invention has the following beneficial effects: the algorithm adopts the concept of qubit as a coding method. The quantum revolving door is used to change the state of the qubit, and the quantum NOT gate is used to realize the mutation of the qubit to avoid premature convergence. Due to the diversity of quantum states, the global search ability of QBA is effectively improved, and the individual bats are prevented from falling into local optimum prematurely. Simulation results show the robustness and effectiveness of the proposed algorithm. QBA can more fully consider the threats in the combat area and get more accurate flight paths for unmanned aerial vehicles (UCAV).

附图说明Description of drawings

图1是基本蝙蝠算法中无人机作战区域模型图。Figure 1 is a model diagram of the UAV combat area in the basic bat algorithm.

图2是基本蝙蝠算法中威胁代价计算方法流程图。Figure 2 is a flow chart of the threat cost calculation method in the basic bat algorithm.

图3是第一类实例D＝10时的结果图。Fig. 3 is a graph of the result when D=10 of the first type of instance.

图4是第一类实例D＝15时的结果图。Fig. 4 is the result diagram when D=15 of the first type of instance.

图5是第一类实例D＝20时的结果图。Fig. 5 is a graph of the result when D=20 of the first type of instance.

图6是第一类实例D＝25时的结果图。Fig. 6 is the result graph when D=25 of the first type instance.

图7是第一类实例D＝30时的结果图。Fig. 7 is the result graph when D=30 of the first type instance.

图8是第一类实例D＝35时的结果图。Fig. 8 is the result graph when D=35 of the first type instance.

图9是第一类实例D＝10时的适应度图。Fig. 9 is a fitness graph when D=10 of the first class instance.

图10是第一类实例D＝15时的适应度图。Fig. 10 is a graph of the fitness of the first class instance when D=15.

图11是第一类实例D＝20时的适应度图。Fig. 11 is a fitness graph of the first class instance when D=20.

图12是第一类实例D＝25时的适应度图。Fig. 12 is a fitness diagram of the first class instance when D=25.

图13是第一类实例D＝30时的适应度图。Fig. 13 is a fitness diagram of the first class instance when D=30.

图14是第一类实例D＝35时的适应度图。Fig. 14 is a fitness diagram of the first class instance D=35.

图15是第二类实例D＝5时的结果图。Fig. 15 is a result diagram of the second type instance D=5.

图16是第二类实例D＝10时的结果图。Fig. 16 is a graph of the result when D=10 of the second type of instance.

图17是第二类实例D＝15时的结果图。Fig. 17 is the result diagram when D=15 of the second type of instance.

图18是第二类实例D＝20时的结果图。Fig. 18 is the result graph when D=20 of the second type of instance.

图19是第二类实例D＝25时的结果图。Fig. 19 is the result graph when D=25 of the second type of instance.

图20是第二类实例D＝30时的结果图。Fig. 20 is a graph of the result when D=30 of the second type of instance.

图21是第二类实例D＝35时的结果图。Fig. 21 is the result graph when D=35 of the second type instance.

图22是第二类实例D＝40时的结果图。Fig. 22 is a graph of the result when D=40 of the second type of instance.

具体实施方式Detailed ways

下面结合附图对本发明做进一步的详细说明。The present invention will be described in further detail below in conjunction with the accompanying drawings.

结合附图1到附图22，一种确定无人机航路最优路径的方法，它包括如下步骤：In conjunction with accompanying drawing 1 to accompanying drawing 22, a kind of method for determining the optimal route of unmanned aerial vehicle route, it comprises the following steps:

|Ψ>＝α|0>+β|1> (12)|Ψ>=α|0>+β|1> (12)

其中，α和β满足：Among them, α and β satisfy:

|α|²+|β|²＝1 (13)|α| ² +|β| ² ＝1 (13)

一个n元量子比特可以定义为：An n-ary qubit can be defined as:

量子旋转门定义如下：A quantum revolving door is defined as follows:

量子非门定义如下：A quantum NOT gate is defined as follows:

第五步，更新策略The fifth step is to update the strategy

得到两个新位置：to get two new positions:

第六步，变异策略The sixth step, mutation strategy

上述的量子蝙蝠算法(QBA)转换成计算机执行流程后如下：The above-mentioned Quantum Bat Algorithm (QBA) is converted into the computer execution process as follows:

关于本发明涉及的算法的仿真实验如下The simulation experiment about the algorithm involved in the present invention is as follows

1仿真平台1 simulation platform

为验证算法在求解实际问题时的正确性和有效性，本文对量子蝙蝠算法、基本蝙蝠算法和差分进化算法进行对比测试实验。仿真测试平台：Matlab R2012(a)；CPU：AMD Athlon(tm)Ⅱ X4 640 Processor,主频：3.00GHz；RAM：3GB；操作系统：Windows 7。In order to verify the correctness and effectiveness of the algorithm in solving practical problems, this paper conducts comparative tests on the quantum bat algorithm, basic bat algorithm and differential evolution algorithm. Simulation test platform: Matlab R2012(a); CPU: AMD Athlon(tm) Ⅱ X4 640 Processor, main frequency: 3.00GHz; RAM: 3GB; operating system: Windows 7.

2参数设置2 parameter setting

蝙蝠算法的参数设置如下：The parameters of the bat algorithm are set as follows:

本文经过20次独立实验比较，对算法中的各项参数进行如下设置：In this paper, after 20 independent experiments and comparisons, the parameters in the algorithm are set as follows:

基本蝙蝠算法中，根据经验，一般对参数进行如下设置：搜索脉冲频率范围为[0,2]，最大脉冲频率r⁰＝0.5，最大脉冲音强A＝0.5，脉冲音强衰减系数α＝0.95，脉冲频度增加系数γ＝0.05。In the basic bat algorithm, based on experience, the parameters are generally set as follows: the search pulse frequency range is [0,2], the maximum pulse frequency r ⁰ =0.5, the maximum pulse sound intensity A=0.5, and the pulse sound intensity attenuation coefficient α=0.95 , pulse frequency increase coefficient γ = 0.05.

差分进化算法中，缩放因子F＝0.5,交叉概率CR＝0.9。In the differential evolution algorithm, the scaling factor F=0.5, and the crossover probability CR=0.9.

量子蝙蝠算法中的基本参数与基本蝙蝠算法相同，量子幅角的范围设为θ_ij∈[-π,π]。其中，式(25)中的其他参数分别设置为：w＝2，σ_e＝0，σ_s＝2。The basic parameters in the quantum bat algorithm are the same as the basic bat algorithm, and the range of the quantum argument is set to θ _ij ∈[-π,π]. Wherein, other parameters in formula (25) are respectively set as: w=2, σ _e =0, σ _s =2.

3实验结果与分析3 Experimental results and analysis

本文采用了两种测试实例，对QBA算法在求解无人机航路规划问题时的性能进行验证。在本节的测试实验中，种群大小均设置为Popsize＝30，三种算法的最大迭代次数均取Maxgen＝200。In this paper, two test cases are used to verify the performance of the QBA algorithm in solving UAV route planning problems. In the test experiments in this section, the population size is set to Popsize=30, and the maximum iterations of the three algorithms are set to Maxgen=200.

表1 第一组测试实例威胁区域的相关信息Table 1. Information about the threat areas of the first group of test instances

无人机航路规划问题是寻找一条具有最小威胁代价的最优或是次优路线，当D取不同的值时，我们可以得到该问题不同的寻优结果。从表2的实验结果可以看出，开始时，随着分割维数D的不断增加，但是当分割维数D超过30时，飞行路径的精度开始降低。对于第一组测试实例，我们可以设置较为适当的分割维数D＝20。在表2中，量子蝙蝠算法(QBA)的最优值，平均值，最差值均优于蝙蝠算法(BA)和差分进化(DE)。因此，本文所提算法的优化性能明显优于蝙蝠算法(BA)和差分进化(DE)。标准方差的结果说明量子蝙蝠算法(QBA)具有最强的鲁棒性，能够稳定、有效地求解优化问题。The UAV route planning problem is to find an optimal or suboptimal route with the minimum threat cost. When D takes different values, we can get different optimization results of this problem. It can be seen from the experimental results in Table 2 that at the beginning, with the continuous increase of the segmentation dimension D, but when the segmentation dimension D exceeds 30, the accuracy of the flight path begins to decrease. For the first group of test cases, we can set a more appropriate segmentation dimension D=20. In Table 2, the optimal value, average value and worst value of Quantum Bat Algorithm (QBA) are better than Bat Algorithm (BA) and Differential Evolution (DE). Therefore, the optimization performance of the proposed algorithm is significantly better than that of Bat Algorithm (BA) and Differential Evolution (DE). The results of the standard deviation show that the quantum bat algorithm (QBA) has the strongest robustness and can solve optimization problems stably and efficiently.

表2 第一组测试实例的实验结果Table 2 Experimental results of the first set of test cases

从图3到图8，我们可以看到飞行路线被分成D个等分的单元。无人机尝试躲避威胁区域从而寻找一条威胁代价最小的路线。从图9到图14三种算法的收敛曲线图我们可以看出，量子蝙蝠算法(QBA)的收敛速度是最快的，不易陷入局部最优。对表2的实验结果进行分析，可以发现算法的优化性能(即飞行路径)的优劣与分割维数D之间并不是简单的正比例关系。并非分割维数D越大寻优的结果就越好。From Figure 3 to Figure 8, we can see that the flight path is divided into D equal units. The UAV tries to avoid the threat area in order to find a route with the least threat cost. From the convergence curves of the three algorithms in Figure 9 to Figure 14, we can see that the convergence speed of the quantum bat algorithm (QBA) is the fastest, and it is not easy to fall into local optimum. Analyzing the experimental results in Table 2, it can be found that the optimization performance of the algorithm (that is, the flight path) is not a simple proportional relationship with the segmentation dimension D. It is not that the larger the division dimension D is, the better the optimization result is.

在以下的测试实例中，为了更加充分地验证量子蝙蝠算法的有效性，将QBA与多个智能算法^[12]进行了对比实验，实验结果见表4、表5和表6。在该部分的测试实验中，种群大小均设置为Popsize＝30，各算法的最大迭代次数均取Maxgen＝200。In the following test examples, in order to more fully verify the effectiveness of the quantum bat algorithm, QBA was compared with multiple intelligent algorithms ^[12] . The experimental results are shown in Table 4, Table 5 and Table 6. In this part of the test experiment, the population size is set to Popsize=30, and the maximum number of iterations of each algorithm is set to Maxgen=200.

表3 第二组测试实例威胁区域的相关信息Table 3 Relevant information of the threat area of the second group of test instances

表4 第二组测试实例不同维数下的最优解Table 4 Optimal solutions under different dimensions of the second group of test cases

表5 第二组测试实例不同维数下的最差解Table 5 The worst solution under different dimensions of the second group of test cases

表6 第二组测试实例不同维数下的平均解Table 6 The average solution of the second group of test cases under different dimensions

图15到图22是量子蝙蝠算法(QBA)对第二类测试实例的寻优结果。从图中可以看出，针对不同的分割维数D，QBA均可以为无人机找到一条避开威胁区域的路径，使威胁代价尽可能小以保证飞行器的安全。Figures 15 to 22 are the optimization results of the quantum bat algorithm (QBA) for the second type of test cases. It can be seen from the figure that for different segmentation dimensions D, QBA can find a path for the UAV to avoid the threat area, making the threat cost as small as possible to ensure the safety of the aircraft.

由于粒子状态的多样性，量子蝙蝠算法具有较强的全局搜索能力。从表4、表5和表6中第二组测试实例的实验结果可以看出，在不同的分割维数D下，量子蝙蝠算法均可以取得更好的最优解，平均解只有在D＝25和D＝40两种情况下比混合蝙蝠算法(BAM)稍差，在D＝5情况下比差分进化(DE)差，最差解中只有在D＝5一种情况下比BAM要差。综合最优解、最差解和平均解进行评价，量子蝙蝠算法(QBA)的综合搜索性能要胜过其他10种算法。相比基本蝙蝠算法(BA)寻优性能成倍提高，而相比混合蝙蝠算法(BAM)寻优性能也有了明显提高。对于无人机(UCAV)航路规划问题，量子蝙蝠算法寻优精度更高，因此可以得到一条更优的飞行路线。Due to the diversity of particle states, the quantum bat algorithm has a strong global search ability. From the experimental results of the second group of test examples in Table 4, Table 5 and Table 6, it can be seen that under different division dimensions D, the quantum bat algorithm can obtain better optimal solutions, and the average solution is only when D= In the two cases of 25 and D=40, it is slightly worse than the mixed bat algorithm (BAM), and in the case of D=5, it is worse than the differential evolution (DE). In the worst solution, it is only worse than BAM in the case of D=5. . The comprehensive search performance of Quantum Bat Algorithm (QBA) is better than the other 10 algorithms by evaluating the best solution, worst solution and average solution. Compared with the basic bat algorithm (BA), the optimization performance has been doubled, and compared with the hybrid bat algorithm (BAM), the optimization performance has also been significantly improved. For the route planning problem of unmanned aerial vehicles (UCAV), the quantum bat algorithm has higher optimization accuracy, so a better flight route can be obtained.

本文提出一种新颖的量子蝙蝠算法(QBA)的无人作战飞机的路径规划问题。QBA具有极强的由于其多样性造成的概率表示的全局搜索能力。仿真实验表明，所提出的算法是可行和有效的方式在无人战斗机路径规划。QBA可以找到安全飞行路径，通过将空房的节点连接成本的最小威胁与最低的燃料成本。This paper proposes a novel Quantum Bat Algorithm (QBA) for the path planning problem of unmanned combat aircraft. QBA has an extremely strong global search ability of probabilistic representation due to its diversity. Simulation experiments show that the proposed algorithm is feasible and effective in path planning of UCAVs. QBA can find safe flight paths by connecting empty nodes with the least threat of cost and lowest fuel cost.

以上对本发明及其实施方式进行了描述，该描述没有限制性。总而言之如果本领域的普通技术人员受其启示，在不脱离本发明创造宗旨的情况下，不经创造性的设计出与该技术方案相似的方法及实施例，均应属于本发明的保护范围。The present invention and its embodiments are described above without limitation. All in all, if a person of ordinary skill in the art is inspired by it, without departing from the inventive concept of the present invention, without creatively designing methods and embodiments similar to the technical solution, it shall fall within the scope of protection of the present invention.

Claims

1. A method for determining an optimal path of an unmanned aerial vehicle airway is characterized in that: it comprises the following steps:

firstly, encoding the bat individuals by adopting the probability amplitude of the qubits on the basis of a basic bat algorithm, namely updating the probability amplitude of the qubits by using a quantum revolving gate, and adopting a quantum not gate as a variation operation to avoid premature convergence of the algorithm; there are two probability magnitudes for each qubit, and thus, each bat can represent two positions of the optimization space;

secondly, in quantum computation, the smallest information unit is stored in a qubit, and the state of the qubit can be '0', or '1', or any state between '0' and '1'; the state of a qubit can be represented as follows:

|Ψ>＝α|0>+β|1> (12)

wherein α and β satisfy:

|α|²+|β|²＝1 (13)

wherein | α |²And | β | |)²Respectively represent a trend state |0>And |1>The probability of (d);

an n-ary qubit can be defined as:

the quantum rotating gate is defined as follows:

the quantum not gate is defined as follows:

third, generating initial population

The algorithm uses the following coding scheme:

wherein, theta_ijIs the argument, and it can be seen from the formula (17) that each bat corresponds to two positions of the problem space, corresponding to the quantum state |0>And |1>The probability amplitude of (c):

P_ic＝(cos(θ_i1),cos(θ_i2),...,cos(θ_in)) (18)

P_is＝(sin(θ_i1),sin(θ_i2),...,sin(θ_in)) (19)

the fourth step, solving the spatial transformation

In order to calculate the fitness of an individual and evaluate the quality of the individual, the solution space of a population needs to be converted; each probability amplitude of an individual qubit corresponds to one solution of the solution space of the problem, i.e. each bat corresponds to two solutions of the optimization problem;

wherein,from quantum state |0>Amplitude of probability ofIs obtained byIs formed by quantum state |1>Amplitude of probability ofObtaining;

the fifth step, updating the strategy

In the Quantum Bat Algorithm (QBA), the amplitude and angle increment of the qubit is updated by adopting an updating strategy of the Bat Algorithm (BA), and the updating process is as follows:

Δθ_ij(t+1)＝Δθ_ij(t)+Δθ_g*Q(i)*stepnow (22)

θ_ij(t+1)＝θ_ij(t)+Δθ_ij(t+1) (23)

wherein, Delta theta_ijAnd theta_ijArgument increment and argument respectively;

<math> <mrow> <mi>stepnow</mi> <mo>=</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>Maxgen</mi> <mo>-</mo> <mi>gen</mi> <mo>)</mo> </mrow> <mi>w</mi> </msup> <msup> <mrow> <mo>(</mo> <mi>Maxgen</mi> <mo>)</mo> </mrow> <mi>w</mi> </msup> </mfrac> <mrow> <mo>(</mo> <msub> <mi>σ</mi> <mi>s</mi> </msub> <mo>-</mo> <msub> <mi>σ</mi> <mi>e</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>σ</mi> <mi>e</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>25</mn> <mo>)</mo> </mrow> </mrow> </math>

herein, the parameter values in equation (25) are: w is 2, σ_e＝0，σ_s＝2；

And (3) updating the probability amplitude by using a quantum revolving gate:

two new positions are obtained:

sixth, mutation strategy

In the Quantum Bat Algorithm (QBA), in order to prevent the algorithm from falling into local optima prematurely, a variation strategy is adopted herein to increase the diversity of the population, the variation strategy being implemented by a quantum not gate; if rand () < p_mIf so, executing quantum NOT gate operation and exchanging the two probability values; wherein p is_mIs the variation probability;