CN109086862A - A kind of artificial bee colony algorithm - Google Patents
A kind of artificial bee colony algorithm Download PDFInfo
- Publication number
- CN109086862A CN109086862A CN201810935643.3A CN201810935643A CN109086862A CN 109086862 A CN109086862 A CN 109086862A CN 201810935643 A CN201810935643 A CN 201810935643A CN 109086862 A CN109086862 A CN 109086862A
- Authority
- CN
- China
- Prior art keywords
- nectar source
- bee
- stage
- source
- nectar
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/004—Artificial life, i.e. computing arrangements simulating life
- G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
Landscapes
- Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- Physics & Mathematics (AREA)
- Data Mining & Analysis (AREA)
- General Health & Medical Sciences (AREA)
- Biomedical Technology (AREA)
- Biophysics (AREA)
- Computational Linguistics (AREA)
- Life Sciences & Earth Sciences (AREA)
- Evolutionary Computation (AREA)
- Artificial Intelligence (AREA)
- Molecular Biology (AREA)
- Computing Systems (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- Software Systems (AREA)
- Health & Medical Sciences (AREA)
- Medicines Containing Material From Animals Or Micro-Organisms (AREA)
Abstract
The present invention relates to artificial bee colony algorithm technical fields, and in particular to a kind of artificial bee colony algorithm, including initial phase, lead the bee stage, follow the bee stage and investigation the bee stage, it is described to lead the bee stage and/or follow the formula for generating new nectar source in the bee stage are as follows: vij=xij+θ×(xij‑xkj), wherein the θ is the nonlinear change factor, vijIndicate new nectar source, xijIndicate current nectar source, xkjIndicate adjacent nectar source, k ∈ { 1,2 ..., SN }, j ∈ { 1,2 ..., D } is both randomly choosed, and k ≠ i；J represents the dimension being updated.The present invention devises the nonlinear change factor in nectar source more new formula, and as bee colony moves closer to optimal nectar source, nectar source updates step-length and slowly reduces, is conducive to the more good nectar source of bee colony search careful near current nectar source, improves the low optimization accuracy of algorithm.
Description
Technical field
The present invention relates to artificial bee colony algorithm technical fields, and in particular to a kind of artificial bee colony algorithm.
Background technique
1, the basic model of artificial bee colony algorithm:
Artificial bee colony algorithm is a kind of newer colony intelligence optimization algorithm, and algorithm is using the gathering honey process of bee colony as simulation pair
As.The member that one honeybee populations includes has thousands of honey, and each individual in so huge group must have
The specific division of labor and cooperation, otherwise will sink into complete confusion.All honeybees in the population of honeybee in nature have clearly
Workload partition, Each performs its own functions, while also having simple information interchange between the honeybee of the different division of labor, in addition to this different division of labor
Honeybee can also convert function, bee colony finds optimal nectar source by cooperating.Artificial bee colony algorithm simulates honeybee populations
The processes such as the division of labor, information interchange, the transformation of functions, three most basic elements for including in algorithm are as follows: nectar source, employ bee, not by
Employ bee.
(1) nectar source: nectar source is corresponding with the feasible solution in actual optimization problem, the shadow of the quality in nectar source by many factors
Ring, such as with the distance of honeycomb, nectar content just, difficulty of exploitation etc..Equally, it is solved in actual optimization problem
Quality is also influenced by many factors, for example function to be optimized includes multiple unknown parameters.In order to evaluate the superiority and inferiority of nectar source quality
The complexity of algorithm it is not significantly increased again simultaneously, a parameter is generally all only arranged in when practical application, we are with " adapting to herein
Degree " (fitness) evaluates the quality of nectar source quality, and the higher nectar source quality of fitness value is better.
(2) it employs bee: bee being employed also referred to as to lead bee or worker bee, commonly referred to as lead bee in the course of the description, one leads
The corresponding nectar source of bee, therefore the quantity of the two is equal.Bee is led to carry the description information in corresponding nectar source when gathering honey, such as honey
The distance in source, locating orientation, the enrichment degree in nectar source etc., actually these description informations correspond to each ginseng in practical problem
Several values.The description information in the nectar source for leading bee to be exploited is taken back honeycomb and is shared with the honeybee that do not employed in honeycomb, not
The honeybee employed selects nectar source using the selection mode of roulette.
(3) it is not employed bee: being divided into search bee and follow bee.If some nectar source nectar source quality after limited times iteration
It does not improve yet, then leading bee to translate into search bee and finding new nectar source by way of random search for this nectar source is exploited,
It finds to be again transformed into behind new nectar source and leads bee.Following the role of bee is that comparison is fixed, carries honey after leading bee to complete gathering honey
The relevant information in source returns to honeycomb, follows bee to select nectar source according to the selection mode of roulette, then starts gathering honey.In algorithm
Initial time, all honeybees are all without carrying any information in relation to nectar source, therefore the honeybee all in algorithm initial period
It is all search bee, behind random search nectar source, part honeybee is changed into other roles.
Honeybee in artificial bee colony algorithm can be divided into three kinds according to work post difference: it leads bee, search bee and follows bee,
The quantity (NP) of middle honeybee is 2 times of nectar source, leads the quantity in bee and nectar source equal, during the execution of the algorithm the role of honeybee
It can mutually convert.The search process of entire bee colony can be described simply are as follows: lead bee to pass through random search when algorithm starts
Mode find nectar source and carry out preliminary neighborhood search to nectar source, follow bee from leading bee there to obtain the letter in all nectar sources
Breath, and neighborhood search is carried out by the selection mode of roulette selection quality preferably nectar source.After leading bee to be changed into search bee
The new nectar source of search, is then again transformed into and leads bee in global scope.
As shown in Figure 1, always there is the process of information interchange and role transforming, honeybee is logical during honeybee producting honey
It crosses mutual cooperation and completes gathering honey process.In the initial stage of algorithm, all honeybees be all search bee and to honeycomb week
The nectar source information enclosed does not have any understanding.Inherence and transient cause due to honeybee, honeybee will be according to the division of labor or Partition of role
Two types: 1. part honeybee is changed by search bee leads bee, leads bee random search nectar source, such as the route S in figure；2. another
A part of honeybee is changed by search bee follows bee, is leading bee to select nectar source when recruiting honeybee, is then carrying out to selected nectar source
Search, such as the route R in figure.
Assuming that existing there are two nectar source A and B, investigation bee is changed into after finding nectar source leads bee, lead bee according to itself
Attribute has write down the position in nectar source and the quality in nectar source and has started gathering honey.After the completion of gathering honey, leads bee to return to and unload honeycomb and unload flower
Honey leads bee to be faced with three kinds of selections after completing above-mentioned work: 1. abandoning the nectar source for leading bee itself to find, returns to recruitment and dance
Area, which is changed into, follows bee, as shown in figure 1 route UF；2. leading bee that recruitment dancing area is not gone to recruit follows bee, it is returned directly to original
Nectar source at continue gathering honey, as shown in figure 1 route EF2；3. leading bee that recruitment dancing area is gone to recruit follows bee, recruitment is led to arrive
Bee is followed to return to continuation gathering honey at original nectar source, as shown in figure 1 route EF1.
2, the process of artificial bee colony algorithm
As shown in Fig. 2, the artificial bee colony algorithm of standard includes 4 stages: initial phase leads the bee stage, follows bee
Stage and search bee stage.
(1) initial phase
Initial phase includes parameter initialization and the initial nectar source of generation.Artificial bee colony algorithm has 3 important parameters: honey
The quantity SN in source, the maximum cycle MaxCycle of algorithm, nectar source maximum number of iterations limit.Artificial bee colony algorithm exists
SN initial nectar sources are randomly generated by formula (1.1) in the initial stage of algorithm, then calculate the fitness value in each nectar source.
Wherein i ∈ { 1,2 ..., SN } indicates the quantity in nectar source；J ∈ { 1,2 ..., D }, indicates the dimension in nectar source；xijIt indicates
Solve xiJth dimension value,Indicate the value range of jth dimension variable.
(2) the bee stage is led
It leads the quantity in bee and nectar source equal, bee is led to find quality higher nectar source on the basis of initial nectar source, lead to
Formula (1.2) is crossed to carry out neighborhood search near nectar source and generate new nectar source.
vij=xij+r×(xij-xkj) (1.2)
Wherein vijNew nectar source is indicated, as can be seen that new nectar source is in current nectar source x from formula (1.2)ijWith adjacent nectar source
xkjOn the basis of obtained by changing the value of current nectar source jth dimension.Random number between r expression [- 1,1], k ∈ 1,2 ...,
SN }, j ∈ { 1,2 ..., D } is both randomly choosed, and k ≠ i.J represents the dimension being updated, and artificial bee colony algorithm is being drawn
Neck the bee stage by randomly choose certain it is one-dimensional be updated, obtain nectar source.For new nectar source vijIfThen enableIfThen enableIf the fitness value in new nectar source is greater than the fitness value in old nectar source,
Old nectar source is replaced with new nectar source, bee is otherwise led still to save old nectar source.
(3) the bee stage is followed
Honeycomb is returned to after leading bee to search nectar source, calculates the fitness value in each nectar source in all honey according to formula (1.3)
Shared ratio in the sum of the fitness value in source.Bee is followed according to the random number that system generates to determine whether that some is selected to lead bee
Nectar source scan for, if certain nectar source fitness value proportion be greater than system generate random number if follow bee will select honey
Source, this selection strategy are referred to as roulette selection strategy.
Fit in formulaiIt indicates the corresponding fitness value in i-th of nectar source, bee is followed to select a nectar source to carry out neighbour in this stage
Domain search, it is similar to the bee stage is led, new nectar source is generated by formula (1.2), is retained if the fitness value in new nectar source is higher
Otherwise new nectar source still retains old nectar source.
(4) the search bee stage
If some nectar source fitness value after limit neighborhood search is not still improved, it indicate that working as
Preceding nectar source has been local optimum nectar source, corresponding with this nectar source to lead bee that abandon this nectar source and be changed into search bee, is scouted
Bee finds new nectar source according to formula (1.1) by way of random search, and search bee starts to scan for simultaneously this new nectar source
It is again transformed into and leads bee.
Judge whether the cycle-index of algorithm has reached maximum cycle MaxCycle.If reaching, terminator；If
Not up to, then it returns to second stage and updates nectar source by leading bee to continue field search.
3, the characteristics of artificial bee colony algorithm
By the research and analysis and summary to artificial bee colony algorithm, artificial bee colony algorithm has following 4 features:
(1) systemic.From honeybee producting honey behavior of the artificial bee colony algorithm in nature is abstract, has the one of systematics
A little typical features.Single honeybee can be with operating alone, at the same time in bee colony as a minor individual in huge bee colony
It influences each other, cooperate with each other again between honeybee individual, this feature of bee colony has embodied the relevance in systematics；Single
Honeybee can scan for several nectar sources, but be if to search for best nectar source in entire space and depend merely on some individual
It is difficult to complete, but the individual of substantial amounts cooperates with each other and can be relatively easy to completions in bee colony, it is whole greater than part
With this has embodied the globality in systematics.
(2) distributed.Bee colony such as look for food when a certain work, and the individual in bee colony all works independently, individually
One honeybee, which goes wrong not working, will not influence the work of entire bee colony.Equally, artificial bee colony algorithm is optimal in solution
Each individual is independently operated when solution, and an independent individual, which solves, of low quality will not influence final result.
(3) self-organizing.At the initial stage of artificial bee colony algorithm, the individual in bee colony seem all be it is independent, unordered, can
It is the individual into the later period bee colony of algorithm and the optimal solution that all levels off to, the individual in bee colony is filled from the process of disorder to order
That divides embodies the self-organization of algorithm.
(4) it feeds back.Lead bee gathering honey that can follow bee in honeycomb dancing area's jive after the completion to recruit, nectar source quality is got over
Height is recruited to following the probability of bee bigger, and the chance that the quality in nectar source is improved has more chances with regard to more again in this way
It recruits and more follows bee, nectar source quality steps up and gradually approach optimal solution, this embodies the positive feedback process of algorithm；
The update in nectar source is more casual in artificial bee colony algorithm, and quality can be obtained in search process less as the nectar source in preceding nectar source, in addition,
When quality still cannot improve after repeatedly searching in nectar source, current nectar source will be abandoned and reselect new nectar source, these processes
It ensure that the sufficiently large diversity with population in search range, this embodies the negative feedback process of algorithm.
Summary of the invention
The purpose of the present invention is to provide a kind of artificial bee colony algorithms, devise nonlinear change in nectar source more new formula
The factor, as bee colony moves closer to optimal nectar source, nectar source updates step-length and slowly reduces, and it is young near current nectar source to be conducive to bee colony
The more good nectar source of thin search, improves the low optimization accuracy of algorithm.
In order to reach above-mentioned technical purpose, the technical solution adopted in the present invention is as follows:
A kind of artificial bee colony algorithm, including initial phase, lead the bee stage, follow the bee stage and investigation the bee stage,
It is characterized in that:
It is described to lead the bee stage and/or follow the formula for generating new nectar source in the bee stage are as follows:
vij=xij+θ×(xij-xkj)
Wherein, the θ is the nonlinear change factor, vijIndicate new nectar source, xijIndicate current nectar source, xkjIndicate adjacent honey
Source, k, i ∈ { 1,2 ..., SN } indicate the quantity in nectar source, and k ≠ i, j ∈ { 1,2 ..., D } indicate the dimension in nectar source.
Further, the nonlinear change factor θ are as follows:
Wherein m, n are coefficient, and Cycle indicates previous cycle the number of iterations, and MaxCycle indicates largest loop the number of iterations,Wherein rand is random function.
Further, the value range of the m, n are respectively as follows: m ∈ [1,1.5], n ∈ [0,0.2].
Further, it is described follow the bee stage the following steps are included:
It sorts from low to high according to the size for the nectar source fitness value for leading bee, and assigns weight for each nectar source；
According to the fitness value for assigning weight, bee is followed to select nectar source by the selection mode of roulette and carry out neighborhood to search
Rope generates new nectar source.
Further, the calculation formula of the weight in the nectar source are as follows:
Wherein, w (i) indicates the weight in nectar source, and value range is between [0,1]；SN indicates to lead the quantity of bee；
I ∈ { 1,2 ..., SN }, indicates the quantity in nectar source.
Further, it is described lead the bee stage and/or follow and generate new nectar source in the bee stage after, if new nectar source fitness value is big
Fitness value in old nectar source then replaces old nectar source with new nectar source, on the contrary then retain old nectar source.
Further, further include following steps after the investigation bee stage: whether judging the cycle-index of the algorithm
Reach largest loop the number of iterations MaxCycle；If reaching, terminator；If not up to, return leads the bee stage, continue
The search of carry out field updates nectar source.
The invention has the following beneficial effects:
1, the random number r in nectar source more new formula is improved to nonlinear change factor θ by the present invention, with the fortune of algorithm
Row, scale factor θ can nonlinear change.Bigger in the initial stage θ value of algorithm, nectar source update step-length is also bigger, and honeybee is searched
The range of rope is also just bigger, and the diversity of population is also just relatively good；In the later period of algorithm, since bee colony moves closer to optimal honey
Source needs to carry out at this time small range of search, and θ value slowly reduces, and nectar source updates step-length and slowly reduces, and is conducive in current honey
The more good nectar source of careful search near source, improves the low optimization accuracy of algorithm.
2, the present invention is that each nectar source assigns weight, random in order to avoid occurring when using the selection mode of roulette
Property bigger, low efficiency and nectar source higher for quality exist leakage choosing possibility drawback；Following bee stage selection honey
When source, weight is assigned according to leading the nectar source quality of bee to be ranked up from low to high, and for each nectar source；The higher nectar source of quality
I value is bigger, and the weight of distribution is higher, and the selected probability in nectar source is also higher.The algorithm later period has been arrived, although all nectar sources
Fitness value reaches unanimity, but the nectar source that the nectar source weight of the weight in high-quality nectar source or specific mass difference is high, high-quality
It still is able to show one's talent, obtains more optimizing chance.
Detailed description of the invention
Fig. 1 is honeybee producting honey process schematic in the prior art；
Fig. 2 is standard intraocular's ant colony algorithm flow chart in the prior art；
Fig. 3 is artificial bee colony algorithm flow chart of the present invention；
Fig. 4 is the 3-D image of Sphere function in test function；
Fig. 5 is Rosenbrock function 3-D image in test function；
Fig. 6 is Ackley function 3-D image in test function；
Fig. 7 is Griewank function 3-D image in test function；
Fig. 8 is Rastrigin function 3-D image in test function；
Fig. 9-a is pair that the artificial bee colony algorithm for improving front and back using nectar source more new formula optimizes Sphere test function
Than figure；
Fig. 9-b is that the artificial bee colony algorithm of front and back is improved using nectar source more new formula to the optimization of Rosenbrock test function
Comparison diagram；
Fig. 9-c is pair that the artificial bee colony algorithm for improving front and back using nectar source more new formula optimizes Ackley test function
Than figure；
Fig. 9-d is what the artificial bee colony algorithm for improving front and back using nectar source more new formula optimized Griewank test function
Comparison diagram；
Fig. 9-e is that the artificial bee colony algorithm of front and back is improved using nectar source more new formula to the optimization of Rastrigin test function
Comparison diagram；
Figure 10-a is comparison diagram of the artificial bee colony algorithm to Sphere function optimization that front and back is improved using selection mechanism；
Figure 10-b is that comparison of the artificial bee colony algorithm of front and back to Rosenbrock function optimization is improved using selection mechanism
Figure；Figure 10-c is comparison diagram of the artificial bee colony algorithm to Ackley function optimization that front and back is improved using selection mechanism；
Figure 10-d is comparison diagram of the artificial bee colony algorithm to Griewank function optimization that front and back is improved using selection mechanism；
Figure 10-e is that comparison of the artificial bee colony algorithm of front and back to Rastrigin function optimization is improved using selection mechanism
Figure；
Figure 11-a is while utilizing the artificial bee colony algorithm of nectar source more new formula and improved selection mechanism front and back right
The comparison diagram of Sphere function optimization；
Figure 11-b is while utilizing the artificial bee colony algorithm of nectar source more new formula and improved selection mechanism front and back right
The comparison diagram of Rosenbrock function optimization；
Figure 11-c is while utilizing the artificial bee colony algorithm of nectar source more new formula and improved selection mechanism front and back right
The comparison diagram of Ackley function optimization；
Figure 11-d is while utilizing the artificial bee colony algorithm of nectar source more new formula and improved selection mechanism front and back right
The comparison diagram of Griewank function optimization；
Figure 11-e is while utilizing the artificial bee colony algorithm of nectar source more new formula and improved selection mechanism front and back right
The comparison diagram of Rastrigin function optimization.
Specific embodiment
Below by specific embodiment combination attached drawing, the present invention will be described in detail, it should be noted that in the feelings not conflicted
Under condition, the feature in embodiment and embodiment in the present invention be can be combined with each other, and the scope of protection of the present invention is not limited thereto.
Embodiment 1
As shown in figure 3, a kind of artificial bee colony algorithm, which includes four-stage: initial phase, lead the bee stage,
Follow bee stage and search bee stage.
First stage: initial phase
The initial phase includes parameter initialization and the initial nectar source of generation.SN initial honey are randomly generated by following formula
Source:
Wherein, i ∈ { 1,2 ..., SN }, indicates the quantity in initial nectar source, and j ∈ { 1,2 ..., D } indicates the dimension in initial nectar source
Degree；xijIndicate solution xiJth dimension value, wherein xiIndicate that the nectar source when initial nectar source quantity is i solves；It indicates just
Minimum activity range and maximum range of activities when beginning nectar source dimension is j.SN initial nectar sources are generated according to formula (1.1), so
The fitness value in each initial nectar source is calculated afterwards, and records the highest initial nectar source of fitness value；
Second stage: the bee stage is led
It leads the quantity in bee and nectar source equal, bee is led to find quality higher nectar source on the basis of initial nectar source, lead to
It crosses formula (2.3) and generates new nectar source as leading the bee stage.
vij=xij+θ×(xij-xkj) (2.3)
Wherein vijIndicate new nectar source, xijIndicate current nectar source, xkjIndicate adjacent nectar source, θ indicates the nonlinear change factor, k
∈ { 1,2 ..., SN }, j ∈ { 1,2 ..., D } is both randomly choosed, and k ≠ i.J represents the dimension being updated.
New nectar source vijIt is in current nectar source xijWith adjacent nectar source xkjOn the basis of by changing current nectar source xijJth dimension
What value obtained.J represents the dimension that is updated, artificial bee colony algorithm lead the bee stage by randomly choosing certain one-dimensional progress more
Newly, new nectar source is obtained.
For new nectar source vijIfThen enableIfThen enableAlso
It is to say, if new nectar source is greater than maximum value, using maximum value as updated new nectar source；It, will if new nectar source is less than minimum value
Minimum value is as updated new nectar source；If the fitness value in new nectar source is greater than the fitness value in old nectar source, with new nectar source generation
For old nectar source, bee is otherwise led still to save old nectar source.
Nonlinear change factor θ in formula 2.3 are as follows:
Wherein m, n are coefficient, dimensionless；Cycle is previous cycle the number of iterations, and MaxCycle is largest loop iteration time
Number,
The value codomain of parameter alpha are as follows:
Random function rand defining range is (0,1) in the formula of initial nectar source, when rand is less than 0.5, α value -1；When
When rand is more than or equal to 0.5, α value 1.
Artificial bee colony algorithm due to standard is following the bee stage to be updated according to formula (1.2) to nectar source, updates public
Formula uses a codomain to control nectar source update step-length, random too big, the nothing of this way of search for the random factor r of [- 1,1]
Method be effectively ensured nectar source search range with algorithm carry out make corresponding change.
Therefore the nonlinear change factor θ that the present invention is proposed according to the characteristics of artificial bee colony algorithm, can be with algorithm
It carries out updating step-length according to the nonlinear change nectar source of iterative process (Cycle).In improved artificial bee colony algorithm, bee is followed
Stage nectar source is updated according to formula (2.3), and with the operation of algorithm, nonlinear change factor θ can nonlinear change.?
The initial stage θ value of algorithm is bigger, and nectar source update step-length is also bigger, and the range of honeybee search is also with regard to bigger, the multiplicity of population
Property also just it is relatively good.In the later period of algorithm, since bee colony moves closer to optimal nectar source, need to carry out small range of search at this time
Rope, θ value slowly reduce, and nectar source updates step-length and slowly reduces, and it is more good to be conducive to careful search near current nectar source
New nectar source improves the low optimization accuracy of algorithm.
Preferably, m takes [1,1.5], and effect is relatively good when n takes the value between [0,0.2].
Phase III: the bee stage is followed
It follows bee to select nectar source according to the selection mode of roulette, then carries out neighborhood search production further according to formula (2.3)
Raw new nectar source.It follows bee to retain new nectar source if the fitness value in new nectar source is greater than the fitness value in old nectar source, otherwise gives up new
Nectar source follows bee still to retain old nectar source.
Fourth stage: search bee stage
After leading the bee stage and following the bee stage, nectar source fitness value after limit iteration is checked whether there is
Still it does not improve, the nectar source is then given up in such nectar source if it exists, and corresponding this leads bee to be converted into investigation bee, then
New initial nectar source is generated with formula (1.1).
Judge whether the cycle-index of algorithm has reached maximum cycle MaxCycle.If reaching, terminator；If
Not up to, then it returns to second stage and updates nectar source by leading bee to continue field search.
Embodiment 2
First stage, second stage and fourth stage are same as Example 1 in the present embodiment, the difference is that third
The selection mechanism for following the bee stage in stage is improved.Standard intraocular's ant colony algorithm is in the choosing for following the bee stage to use roulette
The mode of selecting selects nectar source, and randomness is bigger, and efficiency is not also high, and nectar source higher for quality has the possibility of leakage choosing.Institute
Using the selection mode of roulette, in order to the chance for optimizing the higher nectar source of quality more, standard intraocular
Ant colony algorithm is determined by the fitness value for calculating each nectar source ratio shared in the sum of the fitness value in all nectar sources
The selected probability optimized in nectar source.In fact, the quantity of population is more, the selected probability in each nectar source is just lower,
Convergence rate is slower.In addition, if there are the quality in some nectar source to be significantly larger than other nectar sources, then the probability that it is optimized
Will be very big, the optimised probability in other nectar sources can be very low, affects the diversity of population.The later period nectar source of algorithm is arrived
Fitness value reaches unanimity, and the high nectar source of quality does not protrude, the chance optimized the nectar source slightly worse with respect to other quality
Seldom, algorithm the convergence speed is slack-off.Therefore, the present embodiment has to following the selection mechanism in bee stage to do further improvement
Body is as follows:
Phase III: the bee stage is followed
Honeycomb is returned to after leading bee to search nectar source, and nectar source is arranged from low to high first, in accordance with the height of nectar source fitness value
Then sequence is that each nectar source assigns weight according to formula (2.4), follows bee to select nectar source, then update honey according to formula (2.3)
Source.
The weight computing formula in new nectar source is as follows:
Wherein, SN indicates to lead the quantity of bee, and i indicates i-th of new nectar source.W (i) indicates the weight in i-th of new nectar source.
As can be seen from the above equation, the value range of w (i) is between [0,1].The higher nectar source i value of quality is bigger, distribution
Weight is higher, and the selected probability in nectar source is also higher.The algorithm later period is arrived, although the fitness value in all nectar sources tends to one
It causes, but the ropy nectar source weight of the weight ratio in high-quality nectar source is high, high-quality nectar source still is able to show one's talent, obtain
To more optimization chances.
According to the fitness value for assigning weight, bee is followed to select nectar source by the selection mode of roulette, then according to public affairs
Formula (2.3) carries out neighborhood search and generates new nectar source.Bee is followed if the fitness value in new nectar source is greater than the fitness value in old nectar source
Retain new nectar source, otherwise give up new nectar source, bee is followed still to retain old nectar source.
Experimental result
Test function and parameter setting
(1) Sphere function
Function expression is such as shown in (3.1):
Sphere functional minimum value are as follows:
min(f1)=f1(0 ..., 0)=0 (3.2)
Sphere function is in xiReach minimum 0 when=0, as shown in Figure 4.
(2) Rosenbrock function
Shown in function expression such as formula (3.3):
Rosenbrock functional minimum value are as follows:
min(f2)=f2(1 ..., 1)=0 (3.4)
Rosenbrock function is in xiReach minimum 0 when=1, as shown in Figure 5.
Rosenbrock function is the unimodal function proposed by K.A.De Jone, is belonged in unimodal function more complicated
Function.From can be seen that its globe optimum is located on the straight line of the lowest point in image, it is difficult to distinguish during search
Direction is difficult to find its globe optimum.
(3) Ackley function
Shown in function expression such as formula (3.5):
Ackley functional minimum value are as follows:
min(f3)=f3(0 ..., 0)=0 (3.6)
Ackley function is in xiReach minimum when=0, as shown in Figure 6.
The global minimum of Ackley function is hidden in a narrow cone space bottom, and there are numerous for periphery
Local minizing point.
(4) Griewank function
Shown in function expression such as formula (3.7):
Griewank functional minimum value are as follows:
min(f4)=f4(0 ..., 0)=0 (3.8)
Griewank function is in xiReach minimum 0 when=0, as shown in Figure 7.
Griewank function is typical non-linear multi-modal function, and there are a large amount of Local Extremum, the numbers of extreme point
Amount is related with the dimension of problem, and with the increase of function dimension, exponentially multiple increases the number of extreme point.
(5) Rastrigin function
Shown in function expression such as formula (3.9):
Rastrigin functional minimum value are as follows:
min(f5)=f5(0 ..., 0)=0 (3.10)
Rastrigin function is in xiReach minimum 0 when=0, as shown in Figure 8.
Rastrigin function is multimodal and representative non-linear multi-modal function, is existed within the scope of domain
A local minimum of the about 10n dimension of problem (n be), it can be seen that wave crest is in the appearance of jumping characteristic from 3-D image, one
As optimization algorithm be difficult to search global optimum.
Minimum value of 5 functions described above in the range of restriction is all that 0, wherein Sphere and Rosenbrock are
Unimodal function will not fall into local optimum in optimization process；Ackley, Griewank and Rastrigin are Solving Multimodal Functions, are limited
There are a large amount of local best points in range, local optimum is easily trapped into optimization process.1 lists 5 test functions in table
Expression formula, optimal value and common search range, wherein search range then correspond to nectar source dimension j indicate range.
1 test function of table
Experimental situation is 64 Windows7 systems of installation, is configured to the notes of Intel (R) Core (TM) i3, memory 4G
This, exploitation software is matlab R2012b.The maximum cycle MaxCycle that algorithm is arranged is 2000, and nectar source number SN is
20, the number of honeybee is 40, and the number of the honeybee refers to the total number for leading bee, following bee, search bee, the dimension of feasible solution
D=20, the maximum number of iterations limit=400 in nectar source, each function operation 20 times are averaged as final result.
It is compared in terms of convergence rate, low optimization accuracy, algorithm stability three, the more early table that tends towards stability of target function value
Show that convergence rate is faster, the smaller expression low optimization accuracy of target function value is higher, and standard deviation is smaller to show that test function is run multiple times
Target function value deviation it is smaller, i.e., algorithm stability is higher.
Nectar source updates formula contrast experiment:
In order to prove the validity of nectar source more new formula, will use the artificial bee colony algorithm of improved nectar source more new formula with
Standard intraocular's ant colony algorithm compares, and experimental result is as shown in Fig. 9-a~Fig. 9-e.
It can see from Fig. 9-a~Fig. 9-e, after the more new formula of improved nectar source, Sphere function, Griewank
Function, Rastrigin function convergence rate be significantly improved, while Sphere function, Rosenbrock function,
The low optimization accuracy of Griewank function is also higher, and the low optimization accuracy of Rastrigin function remains unchanged, the optimizing of Ackley function
Precision is basically unchanged.
Selection mechanism comparative experiments:
In order to prove the validity of improved selection mechanism, the artificial bee colony algorithm and mark of improved selection mechanism will be used
Quasi- artificial bee colony algorithm compares, and experimental result is as shown in Figure 10-a~Figure 10-e.
It can be seen that from Figure 10-a~Figure 10-e using after selection mechanism, the receipts of Sphere function and Griewank function
It holds back speed to be significantly increased, while the low optimization accuracy of Sphere function, Rosenbrock function and Griewank function is also
It improves, the convergence rate and low optimization accuracy of Ackley function and Rastrigin function are basically unchanged or slightly improve.
The comparative experiments of innovatory algorithm:
Front demonstrates the validity of improved nectar source more new formula and improved selection mechanism respectively, now by this
Two kinds of improved methods all introduce standard intraocular's ant colony algorithm, improved artificial bee colony algorithm and standard intraocular's ant colony algorithm
The comparing result of (Artificial Bee Colony, ABC) is as shown in Figure 11-a~Figure 11-e.
The operation result of 2 test function of table
From Figure 11-a~Figure 11-e as can be seen that improved artificial bee colony algorithm Sphere, Rosenbrock,
Convergence rate on tetra- functions of Griewank and Rastrigin is faster than the artificial bee colony algorithm of standard.As can be seen from Table 2
Improved artificial bee colony algorithm improved artificial bee colony algorithm on tri- functions of Sphere, Rosenbrock, Griewank
Low optimization accuracy is higher, the improved artificial bee colony algorithm on tetra- functions of Sphere, Rosenbrock, Ackley, Griewank
Stability it is higher.In general, artificial bee colony algorithm performance disclosed in the embodiment is better than standard intraocular's ant colony algorithm.
Finally, it should be noted that the above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although
Present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that: it still may be used
To modify the technical solutions described in the foregoing embodiments or equivalent replacement of some of the technical features；
And these are modified or replaceed, technical solution of various embodiments of the present invention that it does not separate the essence of the corresponding technical solution spirit and
Range.
Claims (7)
1. a kind of artificial bee colony algorithm, including initial phase, leads the bee stage, follows bee stage and investigation bee stage, it is special
Sign is:
It is described to lead the bee stage and/or follow the formula for generating new nectar source in the bee stage are as follows:
vij=xij+θ×(xij-xkj)
Wherein, the θ is the nonlinear change factor, vijIndicate new nectar source, xijIndicate current nectar source, xkjIndicate adjacent nectar source, k,
I ∈ { 1,2 ..., SN } indicates the quantity in nectar source, and k ≠ i, j ∈ { 1,2 ..., D } indicate the dimension in nectar source.
2. a kind of artificial bee colony algorithm according to claim 1, which is characterized in that the nonlinear change factor θ are as follows:
Wherein m, n are coefficient, and Cycle indicates previous cycle the number of iterations, and MaxCycle indicates largest loop the number of iterations,Wherein rand is random function.
3. a kind of artificial bee colony algorithm according to claim 2, which is characterized in that the value range of the m, n are respectively as follows:
M ∈ [1,1.5], n ∈ [0,0.2].
4. a kind of artificial bee colony algorithm according to claim 1, which is characterized in that described to follow the bee stage include following step
It is rapid:
It sorts from low to high according to the size for the nectar source fitness value for leading bee, and assigns weight for each nectar source；
According to the fitness value for assigning weight, follows bee to select nectar source by the selection mode of roulette and carry out neighborhood search production
Raw new nectar source.
5. a kind of artificial bee colony algorithm according to claim 4, which is characterized in that the calculation formula of the weight in the nectar source
Are as follows:
Wherein, w (i) indicates the weight in nectar source, and value range is between [0,1]；SN indicates to lead the quantity of bee.
6. a kind of artificial bee colony algorithm according to claim 1, which is characterized in that described to lead the bee stage and/or follow
After generating new nectar source in the bee stage, old honey is replaced with new nectar source if the fitness value that new nectar source fitness value is greater than old nectar source
Source, it is on the contrary then retain old nectar source.
7. a kind of artificial bee colony algorithm according to claim 1, which is characterized in that also wrapped after the investigation bee stage
It includes following steps: judging whether the cycle-index of the algorithm has reached largest loop the number of iterations；If reaching, terminator；
If not up to, return leads the bee stage, continues field search and update nectar source.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810935643.3A CN109086862A (en) | 2018-08-16 | 2018-08-16 | A kind of artificial bee colony algorithm |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810935643.3A CN109086862A (en) | 2018-08-16 | 2018-08-16 | A kind of artificial bee colony algorithm |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN109086862A true CN109086862A (en) | 2018-12-25 |
Family
ID=64793525
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201810935643.3A Pending CN109086862A (en) | 2018-08-16 | 2018-08-16 | A kind of artificial bee colony algorithm |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109086862A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111709584A (en) * | 2020-06-18 | 2020-09-25 | 中国人民解放军空军研究院战略预警研究所 | Radar networking optimization deployment method based on artificial bee colony algorithm |
-
2018
- 2018-08-16 CN CN201810935643.3A patent/CN109086862A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111709584A (en) * | 2020-06-18 | 2020-09-25 | 中国人民解放军空军研究院战略预警研究所 | Radar networking optimization deployment method based on artificial bee colony algorithm |
| CN111709584B (en) * | 2020-06-18 | 2023-10-31 | 中国人民解放军空军研究院战略预警研究所 | Radar networking optimization deployment method based on artificial bee colony algorithm |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Xiao et al. | Artificial bee colony algorithm based on adaptive neighborhood search and Gaussian perturbation | |
| Zhu et al. | An efficient evolutionary grey wolf optimizer for multi-objective flexible job shop scheduling problem with hierarchical job precedence constraints | |
| US11886786B2 (en) | Two-step x-architecture steiner minimum tree construction method | |
| CN103279793B (en) | A kind of unmanned vehicle formation method for allocating tasks determined under environment | |
| CN103235743B (en) | A kind of based on decomposing and the multiple goal test assignment dispatching method of optimum solution follow-up strategy | |
| CN110533096A (en) | The DNA of multiverse algorithm based on K-means cluster stores Encoding Optimization | |
| CN110909787A (en) | Method and system for multi-objective batch scheduling optimization based on clustering evolutionary algorithm | |
| CN106997553A (en) | A kind of method for digging of the grouping of commodities pattern based on multiple-objection optimization | |
| CN109978050A (en) | Decision Rules Extraction and reduction method based on SVM-RF | |
| CN109326328A (en) | A kind of extinct plants and animal pedigree evolution analysis method based on pedigree cluster | |
| CN109101721A (en) | Based on the multiple no-manned plane method for allocating tasks of Interval Intuitionistic Fuzzy information under uncertain environment | |
| CN105976122A (en) | Multi-target resource allocation system | |
| CN113222165A (en) | Quantum line optimization method based on genetic algorithm | |
| CN106503092A (en) | A kind of method using multidimensional technique construction Spatial Multi-Dimensional degree search tree | |
| CN109086862A (en) | A kind of artificial bee colony algorithm | |
| CN106228235A (en) | A kind of land utilization space Optimal Configuration Method taking general layout and PROCESS COUPLING effect into account | |
| Verma et al. | A novel framework for neural architecture search in the hill climbing domain | |
| CN110866586A (en) | Improved genetic programming algorithm optimization method for resource-constrained multi-project scheduling | |
| CN106970840A (en) | A kind of Method for HW/SW partitioning of combination task scheduling | |
| CN110457490A (en) | A kind of semantic work stream index construction and search method based on domain body | |
| CN109829535A (en) | The method for solving No-wait flowshop problem based on quantum migratory bird optimization algorithm | |
| Banati et al. | Modeling evolutionary group search optimization approach for community detection in social networks | |
| CN114742593A (en) | Logistics storage center optimal site selection method and system | |
| CN106383863A (en) | Isomorphic sub-graph query optimization method | |
| CN114490799A (en) | Method and device for mining frequent subgraphs of single graph |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20181225 |
|
| RJ01 | Rejection of invention patent application after publication |