CN114662638A - Mobile robot path planning method based on improved artificial bee colony algorithm - Google Patents

Mobile robot path planning method based on improved artificial bee colony algorithm Download PDF

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CN114662638A
CN114662638A CN202210189705.7A CN202210189705A CN114662638A CN 114662638 A CN114662638 A CN 114662638A CN 202210189705 A CN202210189705 A CN 202210189705A CN 114662638 A CN114662638 A CN 114662638A
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李鹏
蔡成林
周彦
盘宏斌
陈洋卓
窦杰
孟步敏
蔡晓雯
张莹
黄鹏
李锡敏
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Abstract

The invention discloses a mobile robot path planning method based on an improved artificial bee colony algorithm, which substitutes an optimal solution generated by each iteration of the artificial bee colony algorithm into a hunting stage of a grey wolf optimization algorithm, and generates a new honey source position by using the grey wolf optimization algorithm; the honey source is introduced during neighborhood searching in the stage of hiring bees, so that the local searching capacity of the artificial bee colony is improved; substituting the global optimal solution into a scout bee stage, improving a honey source search equation, and enabling an algorithm to get rid of local optimization more easily; the improved algorithm GW-ABC is applied to mobile robot path planning, and experimental results show that the improved algorithm is stronger in searching capability and faster in convergence speed.

Description

Mobile robot path planning method based on improved artificial bee colony algorithm
Technical Field
The invention relates to a robot path planning method, in particular to a mobile robot path planning method based on an improved artificial bee colony algorithm.
Background
The artificial bee colony Algorithm (ABC) was proposed by Karaboga in 2005. Inspired by the foraging behavior of the bees, the artificial bee colony algorithm divides the bee colony into three types of bees, and simulates the mutual cooperation process of searching the bee sources and collecting the bee sources among the bees. ABC algorithms have few control parameters and are easy to implement, and have been successfully applied to various practical problems such as pattern recognition, magnetics, neural network control, and the like.
In recent years, a large number of researchers have studied improving the ABC algorithm to achieve better results. And M.S.Kiran et al propose a multi-search equation strategy, so that bees select an optimal search equation to perform adaptive updating under the condition of considering various reference characteristics. M.s.kiran and o.findik recorded the update direction of the individual, and if the individual was successfully updated, the recorded update direction was used in the next generation; wedney et al adds a neighborhood search mechanism in the search formula of the artificial bee colony, exploits a better neighbor honey source from the ring neighborhood topology of the current honey source, balances the exploration and exploitation capabilities of the algorithm, and saves the search experience of the exploratory bee in a way of generating a reverse solution of the abandoned honey source by a general reverse learning strategy, thereby improving the search efficiency; zhu and Kwong introduce global optimal information for ABC, improve the development capability of ABC, and obtain higher solving precision. Gao et al divided the entire population into several sub-populations and proposed two communication mechanisms among them to facilitate optimal performance. The Liyangqi et al changes the searching process by using the information entropy to improve the searching efficiency. Akay and Karaboga propose a new frequency perturbation strategy to avoid trapping in local minima. To better balance the coarse and fine search capabilities of ABC, Gao proposed a new update equation, using two randomly selected food sources, using an orthogonal learning strategy. Kuang et al introduced chaotic distribution into the scout bee phase to enhance its global search capabilities. Gao et al defined a new search mechanism to overcome the oscillation phenomenon in employment bees and proposed an intelligent learning mechanism to accelerate the convergence rate of worst employment bees. The above-mentioned ABC algorithm has strong global search capability, but researchers find that it often faces the problems of slow convergence speed and easy falling into local optimum.
Disclosure of Invention
In order to solve the technical problems, the invention provides a mobile robot path planning method based on an improved artificial bee colony algorithm, which is high in convergence rate and strong in local searching capability.
The technical scheme for solving the technical problems is as follows: a mobile robot path planning method based on an improved artificial bee colony algorithm comprises the following steps:
the method comprises the following steps: initializing honey source related parameters;
step two: generating an initial solution, calculating the fitness of the honey source, and starting iteration;
step three: substituting the optimal solution generated by each iteration of the artificial bee colony algorithm ABC into the hunting stage of the Greenwolf optimization algorithm GWO, generating a new honey source position by using the Greenwolf optimization algorithm, and introducing the new honey source when neighborhood searching is performed in the hiring bee stage to perform neighborhood searching; the onlooker bees select a path corresponding to a better honey source according to a greedy algorithm;
step four: substituting the global optimal solution into a scout bee stage, improving a honey source search equation, if the solution path is not updated for continuous limit times, hiring a bee to become a scout bee, abandoning the old solution, randomly generating a new solution path, and restarting iteration;
step five: judging whether the number of iterations reaches the maximum number of iterationsNumber tmaxAnd if so, outputting the optimal path nodes, sequentially connecting the nodes to obtain the optimal path, and otherwise, returning to the step three to continue execution.
In the second step, the artificial bee colony algorithm is a colony life optimization algorithm, and is inspired by the behavior of the bee colony, and the algorithm is executed in three stages, namely a hiring bee stage, a bystander bee stage and a scout bee stage; the artificial bee colony algorithm simulates the honey collection behavior of bees, wherein the position of one honey source represents a candidate solution, the amount of nectar in each honey source is considered as fitness, the number of employed bees and bystander bees is equal and is half of the whole colony size, the employed bees update the current honey source according to the position in the memory and share information about a new honey source with the bystander bees, and the scout bees perform neighborhood search according to the information; the specific process is as follows:
(1) initialization
In the initialization phase, a set of possible solutions is randomly generated by the following equation:
Figure BDA0003524540410000031
wherein x isi,jRepresenting a set of solutions, i is 1, 2, …, N is the population number, j is 1, 2, …, Dim represents dimensions;
Figure BDA0003524540410000032
and
Figure BDA0003524540410000033
representing the upper and lower bounds of the jth variable; rand (0,1) is [0,1 ]]A random number in between;
(2) hiring bee stage
In this stage, a new honey source is generated using the old honey source in the employed bee memory, i.e. a new candidate solution is generated:
Figure BDA0003524540410000034
wherein v isijIs the position of the new honey source,
Figure BDA0003524540410000035
is [ -1,1 [ ]]K is a randomly generated integer, k is 1, 2, …, N, and k is not equal to i;
(3) bystander bee stage
In the onlooker stage, the onlooker selects a probability P in the form of a roulette in the employed bee colonyiLarger individuals, then randomly generate a random number between (0,1) and probability PiComparison if PiIf the value is larger than the generated random number, selecting a honey source according to the formula (3), and selecting a better honey source according to a greedy algorithm by using new solutions generated by the commissioners and the onlookers, namely selecting a better solution by comparing the fitness values of the honey sources:
Figure BDA0003524540410000041
in the formula, PiRepresenting the probability that the solution of the i-th group is selected, fiFor the fitness of the honey source of the ith solution,
Figure BDA0003524540410000042
wherein, fitnessiFor the i solutions, abs (fixness)i) Representation of a fixnessiAbsolute value of (d);
(4) scouting bee stage
In the scout stage, once a honey source fails to improve further within a predetermined period, it is replaced by a new honey source, and the bees employed in connection with it subsequently become scout bees;
and (4) randomly generating a new honey source according to the formula (1), and repeating the steps from 2 to 4 until a termination condition is met.
In the second step, the grey wolf algorithm simulates democratic social behaviors of a group of grey wolfs in hunting and hunting, the social level system of the grey wolfs has four levels, the highest level is the best solution of the grey wolfs, the second best solution is the beta wolfs and the delta wolfs, and the other solutions are the omega wolfs;
the gray wolf group hunting behavior comprises three stages of approaching a prey, enclosing the prey and attacking the prey, wherein the mathematical expression of the enclosing prey is as follows:
X(t+1)＝Xp(t)-A·D (5)
D＝|C·Xp(t)-X(t)| (6)
wherein t is the current iteration number, X (t) represents the current position of the wolf, and XpRepresenting the current position of the prey, D representing the distance between the wolf individual and the prey, and A and C being coefficient vectors; wherein, the first and the second end of the pipe are connected with each other,
A＝2ar1-a (7)
C＝2r2 (8)
Figure BDA0003524540410000051
wherein a is a convergence factor, r1And r2Is in the interval of [0,1 ]]A random number in between;
the mathematical model of the gray wolf attack prey stage is:
Da＝|C1·Xα(t)-X(t)| (10)
Dβ＝|C2·Xβ(t)-X(t)| (11)
Dδ＝|C3·Xδ(t)-X(t)| (12)
Da、Dβand DδDenotes the distance between alpha, beta and delta, respectively, and the other individual, Xa(t)、Xβ(t) and Xδ(t) represents the positions of α, β and δ at time t, respectively, and the coefficient vector A1、A2And A3Generated by equation (7), C1、C2And C3Is a random vector, generated by equation (8);
X1＝Xα(t)-A1·Dα (13)
X2＝Xβ(t)-A2·Dβ (14)
X3＝Xδ(t)-A3·Dδ (15)
X(t+1)＝(X1+X2+X3)/3 (16)
X1、X2、X3respectively, indicate the positions of α, β and δ with other individuals.
In the second step, in order to increase the local search capability and accelerate the convergence speed, a honey source search formula in the stage of hiring bees is modified:
Figure BDA0003524540410000052
Figure BDA0003524540410000053
generated by the hunting phase of the GWO algorithm,
Figure BDA0003524540410000054
the position of the honey source at the time t is shown,
Figure BDA0003524540410000055
denotes the position of the honey source searched by the GWO algorithm at time t, r is [ -1,1 [)]A random number in between;
the artificial bee colony algorithm calculates the adaptability value of the solution every iteration, the artificial bee colony algorithm is applied to path planning, the adaptability value is equivalent to the path length, and the minimum adaptability value of each iteration corresponds to an optimal solution XgbestIn order to improve the searching precision of the algorithm, the current optimal solution X is usedgbestIntroduced to the GWO algorithm:
Da′＝|C1·Xα-Xgbest| (18)
Dβ′＝|C2·Xβ-Xgbest| (19)
Dδ′＝|C3·Xδ-Xgbest| (20)
in the formula, Da′、Dβ' and Dδ' denotes the distance between α, β and δ, respectively, and the optimal individual;
X1′＝Xα(t)-A1·Dα′ (21)
X2′＝Xβ(t)-A2·Dβ’ (22)
X3′＝Xδ(t)-A3·Dδ′ (23)
X′(t+1)＝(X1′+X2′+X3′)/3 (24)
X′1、X′2、X3'represents the positions where alpha, beta and delta advance toward the current optimal individual in the wolf group, respectively, and X' (t +1) is the position of the wolf at the time t +1 in the optimization process;
GWO the value of a in formula (9) is decreased linearly from 2 to 0, but actually the process of optimizing honey source is not linear, and in order to adapt to the diversity of the algorithm and increase the convergence speed, formula (9) is changed to
Figure BDA0003524540410000061
In the formula fbestIs the current optimal solution XgbestAnd (4) corresponding honey source fitness value, wherein L is the linear distance of the starting point.
In the fourth step, in order to improve the ability of getting rid of local optimum, the search equation is improved:
Figure BDA0003524540410000062
wherein Q is a self-adaptive adjustment coefficient,
Figure BDA0003524540410000063
wherein f isbestFitness value of current optimal honey source, fiAnd (3) for the fitness value of the honey source of the solution of the ith group, the limitNum represents the failure times of the experiment, the initial value of the fitness value is 0, if the honey source i is not updated in each iteration, the limitNum is added to 1, if the honey source i is not updated for continuous limit times, the honey source is abandoned, and a new honey source is generated by the formula (26).
The invention has the beneficial effects that: the optimal solution generated by each iteration of the artificial bee colony algorithm is substituted into the hunting stage of the grey wolf optimization algorithm, and a new honey source position is generated by the grey wolf optimization algorithm; the honey source is introduced during neighborhood searching in the stage of employing bees, so that the local searching capability of the artificial bee colony is improved; substituting the global optimal solution into a scout bee stage, improving a honey source search equation, and enabling an algorithm to get rid of local optimization more easily; the improved algorithm GW-ABC is applied to path planning of the mobile robot, and experimental results show that the improved algorithm is stronger in searching capability and faster in convergence speed.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a schematic diagram of a first test environment in a simulation experiment.
FIG. 3 is a diagram of a second test environment in a simulation experiment.
Fig. 4 is a graph of the shortest path result generated by the four algorithms under the first environment.
Fig. 5 is a convergence diagram of the four algorithms in the first environment.
Fig. 6 is a graph of the shortest path result generated by the four algorithms under the second environment.
Fig. 7 is a convergence diagram of the four algorithms in the second environment.
Detailed Description
The invention is further described below with reference to the figures and examples.
As shown in fig. 1, a mobile robot path planning method based on an improved artificial bee colony algorithm includes the following steps:
the method comprises the following steps: and initializing honey source related parameters.
Step two: and generating an initial solution, calculating the fitness of the honey source, and starting iteration.
The artificial bee colony algorithm is a colony life optimization algorithm, is inspired by the behavior of a bee colony, and is executed in three stages, namely a hiring bee stage, a bystander bee stage and a scout bee stage; the artificial bee colony algorithm simulates the honey collection behavior of bees, wherein the position of one honey source represents a candidate solution, the amount of nectar in each honey source is considered as fitness, the number of employed bees and bystander bees is equal and is half of the whole colony size, the employed bees update the current honey source according to the position in the memory and share information about a new honey source with the bystander bees, and the scout bees perform neighborhood search according to the information; the specific process is as follows:
(1) initialization
In the initialization phase, a set of possible solutions is randomly generated by the following equation:
Figure BDA0003524540410000081
wherein xi,jRepresenting a set of solutions, i ═ 1, 2, …, N is the population number, j ═ 1, 2, …, Dim represents the dimension;
Figure BDA0003524540410000082
and
Figure BDA0003524540410000083
representing the upper and lower bounds of the jth variable; rand (0,1) is [0,1 ]]A random number in between;
(2) hiring bee stage
In this stage, a new honey source is generated using the old honey source in the employed bee memory, i.e. a new candidate solution is generated:
Figure BDA0003524540410000084
wherein v isijIs the position of the new honey source,
Figure BDA0003524540410000085
is [ -1,1 [ ]]K is a randomly generated integer, k is 1, 2, …, N, and k is not equal to i;
(3) bystander bee stage
In the onlooker stage, the onlooker selects a probability P in the form of a roulette in the employed bee colonyiLarger individuals are then randomly generated a random number between (0,1) and probability PiBy comparison, if PiIf the value is larger than the generated random number, selecting a honey source according to the formula (3), and selecting a better honey source according to a greedy algorithm by using new solutions generated by the commissioners and the onlookers, namely selecting a better solution by comparing the fitness values of the honey sources:
Figure BDA0003524540410000091
in the formula, PiRepresenting the probability that the solution of the i-th group is selected, fiFor the fitness of the honey source of the ith solution,
Figure BDA0003524540410000092
wherein, fitnessiFor the i solutions, abs (fixness)i) Represents fitnessiAbsolute value of (d);
(4) scouting bee stage
In the scout stage, once a honey source fails to improve further within a predetermined period, it is replaced by a new honey source, and the bees employed in connection with it subsequently become scout bees;
and (4) randomly generating a new honey source according to the formula (1), and repeating the steps from the step 2 to the step 4 until a termination condition is met.
The grey wolf algorithm simulates the democratic social behavior of a group of grey wolfs in chasing and hunting, the social level system of the grey wolfs has four levels, the highest level, namely the optimal solution, is alpha wolf, the second best solution is beta wolf and delta wolf, and the other solutions are omega wolfs;
the gray wolf colony hunting behavior comprises three stages of approaching, enclosing and attacking prey, wherein the mathematical expression of enclosing prey is as follows:
X(t+1)＝Xp(t)-A·D (5)
D＝|C·Xp(t)-X(t)| (6)
wherein t is the current iteration number, X (t) represents the current position of the wolf, and XpRepresenting the current position of the prey, D representing the distance between the wolf individual and the prey, and A and C being coefficient vectors; wherein the content of the first and second substances,
A＝2ar1-a (7)
C＝2r2 (8)
Figure BDA0003524540410000093
wherein a is a convergence factor, r1And r2Is in the interval of [0,1 ]]A random number in between;
the mathematical model of the gray wolf attack prey stage is:
Da＝|C1·Xα(t)-X(t)| (10)
Dβ＝|C2·Xβ(t)-X(t)| (11)
Dδ＝|C3·Xδ(t)-X(t)| (12)
Da、Dβand DδDenotes the distance between alpha, beta and delta, respectively, and the other individual, Xα(t)、Xβ(t) and Xδ(t) represents the positions of α, β and δ at time t, respectively, and the coefficient vector A1、A2And A3Generated by equation (7), C1、C2And C3Is a random vector, generated by equation (8);
X1＝Xα(t)-A1·Dα (13)
X2＝Xβ(t)-A2·Dβ (14)
X3＝Xδ(t)-A3·Dδ (15)
X(t+1)＝(X1+X2+X3)/3 (16)
X1、X2、X3representing the positions between alpha, beta and delta, respectively, and other individuals.
In order to increase the local searching capability and accelerate the convergence speed, the formula of searching honey sources in the stage of hiring bees is modified:
Figure BDA0003524540410000101
Figure BDA0003524540410000102
generated by the hunting phase of the GWO algorithm,
Figure BDA0003524540410000103
the position of the honey source at the time t is shown,
Figure BDA0003524540410000104
denotes the position of the honey source searched by the GWO algorithm at time t, r is [ -1,1 [)]A random number in between.
The artificial bee colony algorithm calculates the adaptability value of the solution every iteration, the artificial bee colony algorithm is applied to path planning, the adaptability value is equivalent to the path length, and the minimum adaptability value of each iteration corresponds to an optimal solution XgbestIn order to improve the searching precision of the algorithm, the current optimal solution X is usedgbestIntroduced to the GWO algorithm:
Da′＝|C1·Xα-Xgbest| (18)
Dβ′＝|C2·Xβ-Xgbest| (19)
Dδ′＝|C3·Xδ-Xgbest| (20)
in the formula, Da′、Dβ' and Dδ' denotes the distance between α, β and δ, respectively, and the optimal individual;
X1′＝Xα(t)-A1·Dα′ (21)
X2′＝Xβ(t)-A2·Dβ’ (22)
X3′＝Xδ(t)-A3·Dδ′ (23)
X′(t+1)＝(X1′+X2′+X3′)/3 (24)
X′1、X′2、X3'denotes the positions where α, β and δ advance toward the current optimum individual in the wolf group, respectively, and X' (t +1) is the position of the wolf at time t +1 during the optimization.
GWO the value of a in formula (9) is decreased linearly from 2 to 0, but actually the process of optimizing honey source is not linear, and in order to adapt to the diversity of the algorithm and increase the convergence speed, formula (9) is changed to
Figure BDA0003524540410000111
In the formula fbestIs the current optimal solution XgbestAnd (4) corresponding honey source fitness value, wherein L is the linear distance of the starting point.
Step three: substituting the optimal solution generated by each iteration of the artificial bee colony algorithm ABC into the hunting stage of the Greenwolf optimization algorithm GWO, generating a new honey source position by using the Greenwolf optimization algorithm, and introducing the new honey source when neighborhood searching is performed in the hiring bee stage to perform neighborhood searching; and the onlooker bees select the path corresponding to the better honey source according to a greedy algorithm.
Step four: and substituting the global optimal solution into the scout bee stage, improving a honey source search equation, if the solution path is not updated for continuous limit times, changing the employed bee into the scout bee, abandoning the old solution, randomly generating a new solution path, and restarting iteration.
The reconnaissance bee stage of the ABC algorithm is designed for separating from local optimization, but the randomness of the search mode of the honey source equation updated in the reconnaissance bee stage is high, so that the reconnaissance bee stage is not beneficial to separating from the local optimization, and in order to improve the capability of separating from the local optimization, the search equation is improved:
Figure BDA0003524540410000121
wherein Q is a self-adaptive adjustment coefficient,
Figure BDA0003524540410000122
wherein f isbestFitness value of current optimal honey source, fiAnd (3) for the fitness value of the honey source of the solution of the ith group, the limitNum represents the failure times of the experiment, the initial value of the fitness value is 0, if the honey source i is not updated in each iteration, the limitNum is added to 1, if the honey source i is not updated for continuous limit times, the honey source is abandoned, and a new honey source is generated by the formula (26).
Step five: judging whether the iteration number reaches the maximum iteration number tmaxAnd if so, outputting the optimal path nodes, sequentially connecting the nodes to obtain the optimal path, and otherwise, returning to the step three to continue execution.
Simulation (Emulation)
In order to verify the practicability of the algorithm, the improved algorithm GW-ABC is applied to the mobile robot path planning problem, and tests are carried out through matlabR2016a software under two environments shown in the figures 2 and 3. In the scene shown in fig. 2, the starting points are (0, 0), the end points are (25, 40), and the obstacles are randomly distributed, and in the scene shown in fig. 3, the starting points are (1, 11), the end points are (26, 14), and a U-shaped obstacle and a V-shaped obstacle are provided. Testing the shortest path planned by four algorithms of ABC algorithm, Particle Swarm Optimization (PSO), firefly swarm optimization (GSO) and GW-ABC under the test environment. Each algorithm runs 30 times under each environment respectively, the iteration times are 300, the dimension is 3, the shortest path obtained after each algorithm is iterated is recorded, and the average value is calculated.
Fig. 4 is a graph showing the shortest path results generated by four algorithms under the environment, fig. 5 is a convergence graph of the four algorithms, and table 1 is a comparison of experimental results of the four algorithms. Compared with the traditional ABC algorithm, the average path obtained by the improved GW-ABC algorithm is shortened by 12.70%, compared with the GSO algorithm and the PSO algorithm, the average path is respectively shortened by 14.25% and 7.17%, and the optimization performance of the algorithm is effectively improved. As can be seen from fig. 2, the classical ABC algorithm tends to be stable until 110 iterations, and the GW-ABC algorithm tends to be stable and reaches an optimal value after 35 iterations. Compared with the PSO algorithm and the GSO algorithm, the GW-ABC algorithm has obviously higher convergence rate.
TABLE 1
Algorithm Shortest path length/m Longest path length/m Average path length/m
ABC 56.38 69.91 63.30
GSO 58.69 74.45 64.44
PSO 55.97 66.18 59.53
GW-ABC 54.41 57.33 55.26
Fig. 6 shows a graph of the shortest path results generated by four algorithms under the second environment, fig. 7 shows a convergence graph of the four algorithms, and table 2 shows a comparison of experimental results of the four algorithms. Compared with the traditional ABC algorithm, the average path obtained by the improved GW-ABC algorithm is shortened by 16.72%, compared with the GSO algorithm and the PSO algorithm, the average path is shortened by 21.97% and 7.85%, and the optimization performance of the algorithm is effectively improved. As can be seen from FIG. 5, the GW-ABC algorithm tends to be stable after the number of iterations reaches 30, and the classical ABC algorithm tends to be stable after 50 iterations. Comparing the PSO algorithm and the GSO algorithm, it is clear that the GW-ABC algorithm approaches the optimum more easily and faster.
TABLE 2
Algorithm Shortest path length/m Longest path length/m Average path length/m
ABC 36.97 29.27 33.98
GSO 41.45 31.74 36.27
PSO 32.26 28.73 30.71
GW-ABC 30.62 27.86 28.30
The classical ABC algorithm is easy to fall into the situation of local optimization, and the improved GW-ABC algorithm can effectively avoid falling into the situation of local optimization, and is high in searching capability and high in convergence rate. Compared with the other three algorithms, the improved GW-ABC algorithm can find the shortest path more effectively and has faster convergence speed.

Claims (5)

1. A mobile robot path planning method based on an improved artificial bee colony algorithm is characterized by comprising the following steps:
the method comprises the following steps: initializing honey source related parameters;
step two: generating an initial solution, calculating the fitness of the honey source, and starting iteration;
step three: substituting the optimal solution generated by each iteration of the artificial bee colony algorithm ABC into the hunting stage of the Greenwolf optimization algorithm GWO, generating a new honey source position by using the Greenwolf optimization algorithm, and introducing the new honey source when neighborhood searching is performed in the hiring bee stage to perform neighborhood searching; the bystander bees select paths corresponding to the better honey sources according to a greedy algorithm;
step four: substituting the global optimal solution into a scout bee stage, improving a honey source search equation, if the solution path is not updated for continuous limit times, hiring a bee to become a scout bee, abandoning an old solution, randomly generating a new solution path, and restarting iteration;
step five: judging whether the iteration number reaches the maximum iteration number tmaxIf yes, outputting optimal path nodes, connecting the nodes in sequence to obtain an optimal path, and otherwise, returning to the step three to continue execution.
2. The method for planning the path of a mobile robot based on an improved artificial bee colony algorithm of claim 1, wherein in the second step, the artificial bee colony algorithm is a colony life optimization algorithm, which is inspired by the behavior of the bee colony and is executed in three stages, namely, a hiring bee stage, a bystander bee stage and a scout bee stage; the artificial bee colony algorithm simulates the honey collection behavior of bees, wherein the position of one honey source represents a candidate solution, the amount of nectar in each honey source is considered as fitness, the number of employed bees and bystander bees is equal and is half of the whole colony size, the employed bees update the current honey source according to the position in the memory and share information about a new honey source with the bystander bees, and the scout bees perform neighborhood search according to the information; the specific process is as follows:
(1) initialization
In the initialization phase, a set of possible solutions is randomly generated by the following equation:
Figure FDA0003524540400000021
wherein xi,jRepresents the set of solutions, i is 1, 2, …, N is the population numberJ ═ 1, 2, …, Dim representing the dimension;
Figure FDA0003524540400000022
and
Figure FDA0003524540400000023
representing the upper and lower bounds of the jth variable; rand (0,1) is [0,1 ]]A random number in between;
(2) hiring bee stage
In this phase, a new honey source is generated, i.e. a new candidate solution, using the old honey source in the memory of the hiring bee:
Figure FDA0003524540400000024
wherein v isijIs the position of the new honey source,
Figure FDA0003524540400000025
is [ -1,1 [ ]]K is a randomly generated integer, k is 1, 2, …, N, and k is not equal to i;
(3) bystander bee stage
In the onlooker stage, the onlooker selects a probability P in the form of a roulette in the employed bee colonyiLarger individuals, then randomly generate a random number between (0,1) and probability PiBy comparison, if PiIf the value is larger than the generated random number, selecting a honey source according to the formula (3), and selecting a better honey source according to a greedy algorithm by using new solutions generated by the commissioners and the onlookers, namely selecting a better solution by comparing the fitness values of the honey sources:
Figure FDA0003524540400000026
in the formula, PiRepresenting the probability that the solution of the i-th group is selected, fiFor the fitness of the honey source of the ith solution,
Figure FDA0003524540400000027
wherein, fitnessiFor the i solutions, abs (fixness)i) Representation of a fixnessiThe absolute value of (a);
(4) scouting bee stage
In the scout stage, once a honey source fails to improve further within a predetermined period, it is replaced by a new honey source, and the bees employed in connection with it subsequently become scout bees;
and (4) randomly generating a new honey source according to the formula (1), and repeating the steps from 2 to 4 until a termination condition is met.
3. The mobile robot path planning method based on the improved artificial bee colony algorithm as claimed in claim 2, wherein in the second step, the grey wolf algorithm simulates democratic social behaviors of a group of grey wolfs in chasing and hunting, and there are four levels in the social level system of the grey wolfs, the highest level is the best solution as α wolf, the second level is β wolf and δ wolf, and the other solutions are ω wolf;
the gray wolf colony hunting behavior comprises three stages of approaching, enclosing and attacking prey, wherein the mathematical expression of enclosing prey is as follows:
X(t+1)＝Xp(t)-A·D (5)
D＝|C·Xp(t)-X(t)| (6)
wherein t is the current iteration number, X (t) represents the current position of the wolf, and XpRepresenting the current position of a prey, D representing the distance between the wolf individual and the prey, and A and C being coefficient vectors; wherein the content of the first and second substances,
A＝2ar1-a (7)
C＝2r2 (8)
Figure FDA0003524540400000031
in which a isConvergence factor, r1And r2Is in the interval of [0,1 ]]A random number in between;
the mathematical model of the gray wolf attack prey stage is:
Da＝|C1·Xα(t)-X(t)| (10)
Dβ＝|C2·Xβ(t)-X(t)| (11)
Dδ＝|C3·Xδ(t)-X(t)| (12)
Da、Dβand DδDenotes the distance between alpha, beta and delta, respectively, and the other individual, Xα(t)、Xβ(t) and Xδ(t) represents the positions of α, β and δ at time t, respectively, and the coefficient vector A1、A2And A3Generated by equation (7), C1、C2And C3Is a random vector, generated by equation (8);
X1＝Xα(t)-A1·Dα (13)
X2＝Xβ(t)-A2·Dβ (14)
X3＝Xδ(t)-A3·Dδ (15)
X(t+1)＝(X1+X2+X3)/3 (16)
X1、X2、X3respectively, indicate the positions of α, β and δ with other individuals.
4. The method for planning the path of a mobile robot based on the improved artificial bee colony algorithm of claim 3, wherein in the second step, in order to increase the local searching capability and the convergence speed, the formula of the honey source for searching in the stage of employing bees is modified:
Figure FDA0003524540400000041
Figure FDA0003524540400000042
generated by the hunting phase of the GWO algorithm,
Figure FDA0003524540400000043
the position of the honey source at the time t is shown,
Figure FDA0003524540400000044
denotes the position of the honey source searched by the GWO algorithm at time t, r is [ -1,1 [)]A random number in between;
the artificial bee colony algorithm calculates the fitness value of the solution every iteration, the artificial bee colony algorithm is applied to path planning, the fitness value is equivalent to the path length, and the minimum fitness value of each iteration corresponds to an optimal solution XgbestIn order to improve the searching precision of the algorithm, the current optimal solution X is usedgbestIntroduced to the GWO algorithm:
Da′＝|C1·Xα-Xgbest| (18)
Dβ′＝|C2·Xβ-Xgbest| (19)
Dδ′＝|C3·Xδ-Xgbest| (20)
in the formula, Da′、Dβ' and Dδ' denotes the distance between α, β and δ, respectively, and the optimal individual;
X1′＝Xα(t)-A1·Dα′ (21)
X2′＝Xβ(t)-A2·Dβ’ (22)
X3′＝Xδ(t)-A3·Dδ′ (23)
X′(t+1)＝(X1′+X2′+X3′)/3 (24)
X1′、X2′、X3'denotes the positions where α, β and δ advance toward the currently optimum individual in the wolf pack, X' (t +1)The position of the wolf at the moment t +1 in the optimizing process;
GWO the value of a in formula (9) is decreased linearly from 2 to 0, but actually the process of optimizing honey source is not linear, and in order to adapt to the diversity of the algorithm and increase the convergence speed, formula (9) is changed to
Figure FDA0003524540400000051
In the formula fbestIs the current optimal solution XgbestAnd (4) corresponding honey source fitness value, wherein L is the linear distance of the starting point.
5. The method for planning the path of the mobile robot based on the improved artificial bee colony algorithm according to claim 4, wherein in the fourth step, in order to improve the ability to get rid of the local optimum, the search equation is improved:
Figure FDA0003524540400000052
wherein Q is a self-adaptive adjustment coefficient,
Figure FDA0003524540400000053
wherein f isbestFitness value of the current optimal honey source, fiAnd (3) for the fitness value of the honey source of the solution of the ith group, the limitNum represents the failure times of the experiment, the initial value of the fitness value is 0, if the honey source i is not updated in each iteration, the limitNum is added to 1, if the honey source i is not updated for continuous limit times, the honey source is abandoned, and a new honey source is generated by the formula (26).
CN202210189705.7A 2022-02-28 2022-02-28 Mobile robot path planning method based on improved artificial bee colony algorithm Pending CN114662638A (en)

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CN117146833B (en) * 2023-10-31 2024-01-05 北京卓翼智能科技有限公司 Unmanned aerial vehicle path planning method and device based on improved bat algorithm

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