CN108629400A - A kind of chaos artificial bee colony algorithm based on Levy search - Google Patents
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Abstract
The present invention relates to a kind of chaos artificial bee colony algorithms based on Levy search.The algorithm introduces chaology and L é vy theory of flight, realizes a kind of new artificial bee colony algorithm；Solution is initialized by chaology, accelerates algorithm the convergence speed；It is employing the bee optimizing stage that globally optimal solution boot policy is added, is improving the algorithm overall situation and search plain ability；It is following the bee stage that L é vy countermeasures are added, is jumping out locally optimal solution, so that inventive algorithm balances global and local optimizing ability, improve the precision of optimizing solution.
Description
Technical Field
The invention relates to a Levy search-based chaotic artificial bee colony algorithm.
Background
The traditional concept of 'group intelligence' in 1989[1]Meridian/channelIn recent 30 years, the group intelligent optimization algorithm is applied to a plurality of complex practical problems, and a good effect is achieved.
Karaboga et al, inspired by Bee foraging and dancing behavior in 2005, proposed an Artificial Bee Colony (Artificial Bee Colony) algorithm[2-3]. Optimizing is carried out by simulating the honey collection and dance characteristics of the bee colony, and a local optimal solution is quickly obtained. The artificial bee colony algorithm has high efficiency and good solving effect, is widely concerned, and has been successfully applied to the fields of feature classification, artificial neural network training, minimum attribute reduction and the like. The traditional artificial bee colony algorithm has the defects of early algorithm, low convergence speed, strong local searching capability, poor global optimizing capability and the like, along with the fact that the problems faced by human beings are more and more complex, the optimizing requirement on the algorithm is more and more high, how to improve the algorithm and fall into local optimization, the algorithm convergence speed is improved, the algorithm efficiency is improved, particularly, the stability of the algorithm is maintained when high-dimensional complex problems are met, and the problem to be solved urgently in the optimization of the artificial bee colony algorithm is formed.
In recent years, many scholars propose improvement of the artificial bee colony algorithm, and the global optimization capability and the solving precision of the algorithm are improved to a certain extent. In 2015, Zhang H4 et al proposed to use an improved artificial bee colony algorithm in the field of integrated circuit wiring; toosendan [5] et al introduced the rough set theory into the swarm algorithm and applied to the minimum attribute reduction problem. In 2017, He Y6 proposes a binary artificial bee colony algorithm to solve the problem of alliance knapsack, Cui L7 introduces a population scale self-adaptive mode into the artificial bee colony algorithm for balancing the development and search capability of the algorithm. In conclusion, the optimization of the artificial bee colony algorithm has academic research value and practical significance from the perspective of theory and application.
In order to improve the global optimization capability of the algorithm and the precision of the optimization solution and introduce a chaos theory and a Levy flight theory, the invention provides a novel artificial bee colony algorithm (LABC).
Reference documents:
[1]Hinchey M G,Sterritt R,Rouff C.Swarms and swarm intelligence[J].Computer,2007,40(4):111-113.
[2]Karaboga D.An idea based on honey bee swarm for numericaloptimization[J].Technical Report-TR06.Kayseri，Turkey:Erciyes University，2005.
[3]Karaboga D,Basturk B.A powerful and efficient algorithm fornumerical function optimization:Artificial bee colony algorithm[J].Journal ofGlobal Optimization，2007，39(3):459－471.
[4]Zhang H,Ye D.Key-node-based local search discrete artificial beecolony algorithm for obstacle-avoiding rectilinear Steiner tree construction[J].Neural Computing and Applications.2015,26(4):875-898.
[5] oriental buergerian, bright-aged, an effective combined artificial bee colony algorithm for the minimum attribute reduction problem [ J ] in the electronics report 2015(05): 1014-.
[6]He Y,Xie H,Wong T L,et al.A novel binary artificial bee colonyalgorithm for the set-union knapsack problem[J].Future Generation ComputerSystems,2018,78:77-86.
[7]Cui L,Li G,Zhu Z,et al.A novel artificial bee colony algorithmwith an adaptive population size for numerical function optimization[J].Information Sciences.2017,414:53-67.。
Disclosure of Invention
The invention aims to provide a Levy search-based chaotic artificial bee colony algorithm, which improves the global optimization capability and the accuracy of optimization solution.
In order to achieve the purpose, the technical scheme of the invention is as follows: a chaos artificial bee colony algorithm based on Levy search comprises the following steps:
step S1, initializing the population quantity 2SN, each SN of the hiring bee and the following bee, the maximum iteration times itermax and the maximum search times limit of the following bee, and initializing the solution of the artificial bee colony algorithm by using a chaos theory;
step S2, generating a chaotic sequence by using a Logistic mapping formula (1), and initializing a candidate solution by using a formula (2):
wherein, mu belongs to [0, 4]]The sequence is a random number and is in a complete chaotic state when mu is 4, i is 1, …, SN is the number of honey sources; j is 1, 2, …, D is the individual dimension; k represents the number of iterations;the lower bound of the j-th dimension,is the jth dimension upper bound;
step S3, the hiring bee searching stage uses the global optimal guided strategy to find the candidate solution, and the formula is shown in (3):
wherein,for the jth dimension of the ith candidate solution in the t iteration,the jth dimension (k ≠ i φ) φ for the kth candidate solution is [ -1,1]The random number of (a) is set,for the j-th dimension of the current optimal solution,α is [0,1 ]]β is 0.5, iter is the current iteration number, itermax is the maximum iteration number;
step S4, performing neighborhood search by combining the bee following stage and a Levy flight strategy in a rhododendron algorithm, wherein the formula is shown as (4); the L vy flight is a Markov random process, the moving step length follows L vy distribution, and the formula is shown as (5):
wherein,for the jth dimension of the ith candidate solution in the t iteration,in the j dimension of the current optimal solution, r is a random number of (0,1), and s is the step length of the Levy flight strategy;
L(s)～|s|-1-β,0＜β≤2 (5)
wherein s is a random step length, as shown in formula (6):
s＝u/|v|1/β(6)
u and v satisfy a normal distribution, u to N (0, σ u)2)，v～N(0,σv2)：
Gamma is a standard Gamma function, wherein
Step S5, calculating the fitness value of the candidate solution according to the objective function value and a fitness calculation formula, wherein the formula is shown as (8), the follower bee selects an algorithm according to a greedy, and the formula is shown as (9), and if the fitness value of the updated candidate solution is higher than the original candidate solution, the updated candidate solution is replaced by the original candidate solution; otherwise, the original candidate solution is kept;
wherein p isiProbability of selection for honey source, fit (x)i) Is a honey source xiA fitness value of;
step S6, if the searched candidate solution is not updated when the maximum search times limit is reached, the hiring bee in the corresponding position is changed into a scout bee, a new candidate solution is generated by using a formula (2), and the formula (3) is used for continuing searching near the candidate solution neighborhood;
and step S7, outputting the found optimal solution when the algorithm termination condition is reached, and ending the algorithm.
Compared with the prior art, the invention has the following beneficial effects:
1) chaotic initialization: the invention adopts the chaos sequence to initialize the solution; the chaotic sequence has ergodicity and randomness, and the diversity and the randomness of the solution can be increased by initializing the chaotic sequence, so that the convergence speed is increased;
2) the global optimal solution guide search of the Levy flight strategy comprises the following steps: the method is inspired by a particle swarm algorithm, a global optimal solution guide strategy of the particle swarm algorithm is introduced in a search stage of hiring bees, parameters are improved, and the global search capability of the algorithm is improved; in the follower bee stage, the step length improvement parameters of the Levy flight strategy are adopted, the candidate solution neighborhood is searched, the capability of the algorithm for jumping out of local optimum can be increased, and the solving precision is improved;
3) the algorithm can be used for multi-objective optimization problems.
Drawings
FIG. 1 is a flow chart of the algorithm of the present invention.
Detailed Description
The technical scheme of the invention is specifically explained below with reference to the accompanying drawings.
As shown in fig. 1, the chaotic artificial bee colony algorithm based on Levy search of the present invention includes the following steps:
step S1, initializing the population quantity 2SN, each SN of the hiring bee and the following bee, the maximum iteration times itermax and the maximum search times limit of the following bee, and initializing the solution of the artificial bee colony algorithm by using a chaos theory;
step S2, generating a chaotic sequence by using a Logistic mapping formula (1), and initializing a candidate solution by using a formula (2):
wherein, mu belongs to [0, 4]]The sequence is a random number and is in a complete chaotic state when mu is 4, i is 1, …, SN is the number of honey sources; j is 1, 2, …, D is the individual dimension; k represents the number of iterations;the lower bound of the j-th dimension,is the jth dimension upper bound;
step S3, the hiring bee searching stage uses the global optimal guided strategy to find the candidate solution, and the formula is shown in (3):
wherein,for the jth dimension of the ith candidate solution in the t iteration,the jth dimension (k ≠ i φ) φ for the kth candidate solution is [ -1,1]The random number of (a) is set,for the j-th dimension of the current optimal solution,α is [0,1 ]]β is 0.5, iter is the current iteration number, itermax is the maximum iteration number;
step S4, performing neighborhood search by combining the bee following stage and a Levy flight strategy in a rhododendron algorithm, wherein the formula is shown as (4); the L vy flight is a Markov random process, the moving step length follows L vy distribution, and the formula is shown as (5):
wherein,for the jth dimension of the ith candidate solution in the t iteration,in the j dimension of the current optimal solution, r is a random number of (0,1), and s is the step length of the Levy flight strategy;
L(s)～|s|-1-β,0＜β≤2 (5)
wherein s is a random step length, as shown in formula (6):
s＝u/|v|1/β(6)
u and v satisfy a normal distribution, u to N (0, σ u)2)，v～N(0,σv2)：
Gamma is a standard Gamma function, wherein
Step S5, calculating the fitness value of the candidate solution according to the objective function value and a fitness calculation formula, wherein the formula is shown as (8), the follower bee selects an algorithm according to a greedy, and the formula is shown as (9), and if the fitness value of the updated candidate solution is higher than the original candidate solution, the updated candidate solution is replaced by the original candidate solution; otherwise, the original candidate solution is kept;
wherein p isiProbability of selection for honey source, fit (x)i) Is a honey source xiA fitness value of;
step S6, if the searched candidate solution is not updated when the maximum search times limit is reached, the hiring bee in the corresponding position is changed into a scout bee, a new candidate solution is generated by using a formula (2), and the formula (3) is used for continuing searching near the candidate solution neighborhood;
and step S7, outputting the found optimal solution when the algorithm termination condition is reached, and ending the algorithm.
The above are preferred embodiments of the present invention, and all changes made according to the technical scheme of the present invention that produce functional effects do not exceed the scope of the technical scheme of the present invention belong to the protection scope of the present invention.
Claims (1)
1. A chaos artificial bee colony algorithm based on Levy search is characterized by comprising the following steps:
step S1, initializing the population quantity 2SN, each SN of the hiring bee and the following bee, the maximum iteration times itermax and the maximum search times limit of the following bee, and initializing the solution of the artificial bee colony algorithm by using a chaos theory;
step S2, generating a chaotic sequence by using a Logistic mapping formula (1), and initializing a candidate solution by using a formula (2):
wherein, mu belongs to [0, 4]]The sequence is a random number and is in a complete chaotic state when mu is 4, i is 1, …, SN is the number of honey sources; j is 1, 2, …, D is the individual dimension; k represents the number of iterations;the lower bound of the j-th dimension,is the jth dimension upper bound;
step S3, the hiring bee searching stage uses the global optimal guided strategy to find the candidate solution, and the formula is shown in (3):
wherein,for the jth dimension of the ith candidate solution in the t iteration,the jth dimension (k ≠ i φ) φ for the kth candidate solution is [ -1,1]The random number of (a) is set,for the j-th dimension of the current optimal solution,α is [0,1 ]]β -0.5,iter is the current iteration number, itermax is the maximum iteration number;
step S4, combining the bee-following stage with rhododendron algorithmThe flight strategy carries out neighborhood search, and the formula is shown as (4);flight is a Markov random process, with a moving step obeyedThe distribution is shown in the formula (5):
wherein,for the jth dimension of the ith candidate solution in the t iteration,in the j-th dimension of the current optimal solution, r is a random number of (0,1), and s isStep size of flight strategy;
L(s)～|s|-1-β,0＜β≤2 (5)
wherein s is a random step length, as shown in formula (6):
s＝u/|v|1/β(6)
u and v satisfy a normal distribution, u to N (0, σ)u 2)，v～N(0,σv 2)：
Gamma is a standard Gamma function, wherein
Step S5, calculating the fitness value of the candidate solution according to the objective function value and a fitness calculation formula, wherein the formula is shown as (8), the follower bee selects an algorithm according to a greedy, and the formula is shown as (9), and if the fitness value of the updated candidate solution is higher than the original candidate solution, the updated candidate solution is replaced by the original candidate solution; otherwise, the original candidate solution is kept;
wherein p isiProbability of selection for honey source, fit (x)i) Is a honey source xiA fitness value of;
step S6, if the searched candidate solution is not updated when the maximum search times limit is reached, the hiring bee in the corresponding position is changed into a scout bee, a new candidate solution is generated by using a formula (2), and the formula (3) is used for continuing searching near the candidate solution neighborhood;
and step S7, outputting the found optimal solution when the algorithm termination condition is reached, and ending the algorithm.
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| CN109558700A (en) * | 2019-02-12 | 2019-04-02 | 福州大学 | A kind of level Four design of gears method based on DSM-ABC algorithm |
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| CN111982118A (en) * | 2020-08-19 | 2020-11-24 | 合肥工业大学 | Method and device for determining walking track of robot, computer equipment and storage medium |
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| CN112995075A (en) * | 2021-02-15 | 2021-06-18 | 青岛科技大学 | Acoustic channel equalization method based on championship selection chaotic artificial bee colony algorithm |
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