CN106875050A - A kind of Engineering constraint parameter optimization method based on improvement chaos ant colony algorithm - Google Patents

A kind of Engineering constraint parameter optimization method based on improvement chaos ant colony algorithm Download PDF

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CN106875050A
CN106875050A CN201710076168.4A CN201710076168A CN106875050A CN 106875050 A CN106875050 A CN 106875050A CN 201710076168 A CN201710076168 A CN 201710076168A CN 106875050 A CN106875050 A CN 106875050A
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honeybee
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张悦
王国臣
范世伟
徐定杰
李倩
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Harbin Institute of Technology
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Abstract

A kind of Engineering constraint parameter optimization method based on improved ant colony algorithm, is a kind of new bionics optimized algorithm, and thought is the methods for using the route in bee colony search nectar source judge selection.Traditional Engineering constraint parameter optimization method there is a problem of many unsatisfactory, it is difficult to meet the demand of Engineering constraint parameter optimization, engineering parameter is optimized with stronger adaptability, positive feedback and robustness using traditional ant colony algorithm, but there is also and be easily absorbed in locally optimal solution.Chaos ant colony algorithm is the fully intermeshing using chaos algorithm, using Chaos Variable have ergodic, randomness and it is regular the characteristics of, improve the easy Premature Convergence of ant colony algorithm, easily sink into local optimum, it is inaccurate to edge positioning the problems such as.Carry out the optimization of Engineering constraint parameter using chaos ant colony algorithm herein, the method can quickly, clear, accurate and validity is strong.

Description

A kind of Engineering constraint parameter optimization method based on improvement chaos ant colony algorithm
Technical field
The invention belongs to intelligent algorithm applied technical field, more particularly to a kind of engineering based on improved ant colony algorithm is about Beam parameter optimization method.
Background technology
During engineering parameter optimization problem is universally present in daily production and living, traditional Engineering constraint parameter optimization method There is a problem of many unsatisfactory, it is difficult to meet the demand of Engineering constraint parameter optimization.In general, engineering parameter optimization Problem is all on the premise of many linearly or nonlinearly constraints.But, due at present to Engineering constraint Parametric optimization problem Method for solving understanding is deep not enough, if between search space non-differentiability or parameter being non-linear property, often cannot the overall situation Optimal solution, that is, be absorbed in local optimum.Therefore, the balancing of global search and Local Search to optimized algorithm it is successful when it is very heavy It is wanting, it is necessary to a kind of constrained parameters optimization method for embodying mode for not relying on system model.
Ant colony algorithm is a kind of new bionics optimized algorithm, and thought is entered using the route in bee colony search nectar source Row judges the methods of selection.The algorithm has stronger adaptability, positive feedback and robustness, but there is also and be easily absorbed in office Portion's optimal solution.Chaos ant colony algorithm is the fully intermeshing using chaos algorithm, using Chaos Variable have ergodic, randomness and Regular the characteristics of, the problems such as improving the easy Premature Convergence of ant colony algorithm, easily sink into local optimum, position inaccurate to edge. Carry out the optimization of Engineering constraint parameter using chaos ant colony algorithm herein, the method can quickly, clear, accurate and validity By force.
The content of the invention
It is an object of the invention to provide one kind can make up traditional ant colony algorithm exist complex structure be difficult to determine, it is local Optimization, the low shortcoming of search efficiency, propose that a kind of quick, clear, accurate algorithm solves the optimization of common engineering constrained parameters Method.
The object of the present invention is achieved like this：
Based on the Engineering constraint parameter optimization method for improving artificial bee colony algorithm, comprise the following steps：
Step one：Parameter vector i.e. its span is determined by chaos algorithm, with object function and equation or inequality It is described；Deliver sufficient amount of honeybee at random in the range of Experimental Area, can be constantly updated during honeybee random search path Pheromone Matrix, using the positive feedback of ant colony algorithm, the final Pheromone Matrix for producing, so that it is determined that the position in honeybee source.Just The Pheromone Matrix of beginning can not be 0, and honeybee transfer can not start, so initial as Pheromone Matrix using random matrix Change.The position to be walked of honeybee next step, is determined by transition probability.
Step 2：According to the number and span of the parameter vector determined in step one, artificial bee colony is initialized, it is determined that Maximum limitation iterations Limit, maximum cycle c and search target component number N, order lead honeybee in initial position field Inside randomly search for nectar source；
The involved honeybee initial position expression formula that leads is：
In formula, RijIt is the random number between 0 to 1, N is the setting value between 0 to 1；I=1....N, j=1...N, V are The number in nectar source,It is j-th minimum value of parameter,It is j-th maximum occurrences of parameter, rand (0,1) represents 0 Random number in the range of to 1；
The L-expression for leading honeybee initial position field L is：
Wherein, wijTo lead honeybee initial position, lijTo lead honeybee field searching position, φijIt is parameter search step-length, takes Value scope is [- F, F], and F is the random number between 0 to 1；
The expression formula of F is：
Step 3：The parameter determined by chaos algorithm using in probability P selecting step one introduces probability P as regulating object During command deployment in matrix-vector parameter number, and appropriate change step parameter F, first by leading honeybee in current honey The new nectar source of random search in the neighborhood of source, obtains the cost function value q in a nectar sourcei, by qiCalculate fitness function value Qi, working as The position Q of preceding searchiMore than qiWhen, then other nectar sources for being are transferred to, lead honeybee to search for and remember near new nectar source Record QiLarger nectar source positional information；
Involved M expression formulas are：
M=e-a·b/c
Wherein, b is bee colony cycle-index, and c is maximum cycle, and a is control parameter；
Involved fitness function value fitiExpression formula is：
In formula, abs () is the function that takes absolute value；
Step 4：Treat it is all lead honeybee to search for terminate, according to the fitness function value Q for respectively leading nectar source where honeybeei, obtain Honeybee is followed to go to each honeybee source probability Pi, carry out location updating according to probability, and record suitable in each bee colony iterative search procedures The maximum nectar source position w of response functional valuebest；
Involved transition probability PiExpression formula is：
Wherein, QminIt is fitness function value minimum value after this circulation, a is Dynamic gene；
Step 5：Repeat step three, step 4, searches for by limited cycle, and obtain parameter most has estimate.
When iterations is more than maximum limitation iterations Limit, nectar source where abandoning, while being replaced by investigating honeybee Honeybee is led to produce a new position.
The Engineering constraint parameter optimization method based on improvement artificial bee colony algorithm according to claims, its feature It is, when parameter exceedes its span, to update boundary condition, the new parameter that will be obtained is set as the most value on border.
Advantage of the invention is that：
In traditional artificial bee colony algorithm, some parameter is only changed in bee colony search procedure, the present invention is constantly with certain Whether probabilistic determination parameter is updated, and hunting zone is improved to various dimensions, no longer simply as traditional ant colony algorithm is only one-dimensional Therefore space search, also increase substantially the search capability of bee colony.When step-size in search is certain, but actual work in invention As searching times increase in journey, scope can constantly be changed, therefore step-length can also occur adaptive change, and the present invention is examined Consider this factor, in the case where search not the declining of the degree of accuracy is ensured, search time is reduced as far as possible, improve efficiency. Apply different surgings for different phase, the present invention changes the transition probability for following honeybee selection to lead honeybee, both ensures bee colony Diversity, the convergence rate of parameter Estimation is accelerated again, the chaos ant colony algorithm of this paper carries out the optimization of Engineering constraint parameter, energy It is enough quick, clear, accurate and validity is strong.
Brief description of the drawings
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 is the change step length searching schematic diagram that the present invention is provided；
Fig. 3 is the stretching structure schematic diagram that the present invention is provided；
Fig. 4 is traditional ant colony algorithm that the present invention is provided and improves chaos ant colony algorithm to Engineering constraint parameter optimization effect Comparison diagram；
Specific embodiment
Search strategy with reference to accompanying drawing to invention for traditional ant colony algorithm is improved, and gives full play to artificial bee colony algorithm Search capability and development ability, and the artificial bee colony searching algorithm after improvement is applied to Engineering constraint parameter optimisation procedure, Local optimum situation is avoided to occur, while, it is ensured that certain convergence rate and convergence precision.
The present invention includes following steps：
Step one：Parameter vector i.e. its span is determined by chaos algorithm, with object function and equation or inequality It is described；Deliver sufficient amount of honeybee at random in the range of Experimental Area, can be constantly updated during honeybee random search path Pheromone Matrix, using the positive feedback of ant colony algorithm, the final Pheromone Matrix for producing, so that it is determined that the position in honeybee source.Just The Pheromone Matrix of beginning can not be 0, and honeybee transfer can not start, so initial as Pheromone Matrix using random matrix Change.The position to be walked of honeybee next step, is determined by transition probability.
Step 2：According to the number and span of the parameter vector determined in step one, artificial bee colony is initialized, it is determined that Maximum limitation iterations Limit, maximum cycle c and search target component number N, order lead honeybee in initial position field Inside randomly search for nectar source；
Step 3：The parameter determined by chaos algorithm using in probability P selecting step one introduces probability P as regulating object During command deployment in matrix-vector parameter number, and appropriate change step parameter F, first by leading honeybee in current honey The new nectar source of random search in the neighborhood of source, obtains the cost function value q in a nectar sourcei, by qiCalculate fitness function value Qi, working as The position Q of preceding searchiMore than qiWhen, then other nectar sources for being are transferred to, lead honeybee to search for and remember near new nectar source Record QiLarger nectar source positional information；
Step 4：Treat it is all lead honeybee to search for terminate, according to the fitness function value Q for respectively leading nectar source where honeybeei, obtain Honeybee is followed to go to each honeybee source probability Pi, carry out location updating according to probability, and record suitable in each bee colony iterative search procedures The maximum nectar source position w of response functional valuebest；
Step 5：If selection nectar source, it is converted into and leads honeybee to search for new nectar source, while searched near nectar source and recorded The larger nectar source position of fitness function value；
Step 6：If iterations is more than maximum limitation iterations Limit, the optimal solution for obtaining still without change, Nectar source where abandoning, while being replaced leading honeybee to produce a new position by search bee；
Step 7：If a certain parameter exceedes its maximum occurrences scope, should be by maximum that the parameter setting is the border Or minimum value；
Step 8：Record the nectar source position x of the fitness function value maximum in each bee colony iterative search proceduresbest, weight Multiple step 3, by limited number of time cyclic search, obtains the optimal estimation value of parameter to step 7.
Each step is specially：
It is a kind of based on improve artificial bee colony algorithm Engineering constraint parameter optimization method, real time parameter estimation method include with Lower step：
Step one：Parameter vector i.e. its span is determined by chaos algorithm, with object function and equation or inequality It is described；Deliver sufficient amount of honeybee at random in the range of Experimental Area, can be constantly updated during honeybee random search path Pheromone Matrix, using the positive feedback of ant colony algorithm, the final Pheromone Matrix for producing, so that it is determined that the position in honeybee source.Just The Pheromone Matrix of beginning can not be 0, and honeybee transfer can not start, so initial as Pheromone Matrix using random matrix Change.The position to be walked of honeybee next step, is determined by transition probability.
Step 2：According to the number and span of the parameter vector determined in step one, artificial bee colony is initialized, it is determined that Maximum limitation iterations Limit, maximum cycle c and search target component number N, order lead honeybee in initial position field Inside randomly search for nectar source；
Step 3：The parameter determined by chaos algorithm using in probability P selecting step one introduces probability P as regulating object During command deployment in matrix-vector parameter number, and appropriate change step parameter F, first by leading honeybee in current honey The new nectar source of random search in the neighborhood of source, obtains the cost function value q in a nectar sourcei, by qiCalculate fitness function value Qi, working as The position Q of preceding searchiMore than qiWhen, then other nectar sources for being are transferred to, lead honeybee to search for and remember near new nectar source Record QiLarger nectar source positional information；
Step 4：Treat it is all lead honeybee to search for terminate, according to the fitness function value fit for respectively leading nectar source where honeybeei, obtain Each nectar source probability P is transferred to honeybee is followedi, location updating is carried out according to probability；
Step 5：If selection nectar source, it is converted into and leads honeybee to search for new nectar source, while searched near nectar source and recorded The larger nectar source position of fitness function value；
Step 6：If iterations is more than maximum limitation iterations Limit, the optimal solution for obtaining still without change, Nectar source where abandoning, while being replaced leading honeybee to produce a new position by search bee；
Step 7：If a certain parameter exceedes its maximum occurrences scope, should be by maximum that the parameter setting is the border Or minimum value；
Step 8：Record the nectar source position x of the fitness function value maximum in each bee colony iterative search proceduresbest, weight Multiple step 3, by limited number of time cyclic search, obtains the optimal estimation value of parameter to step 7.
In step one, for concrete engineering restricted problem, parameter vector and its span, an Engineering constraint are determined Problem definable (can respectively represent area, volume, weight etc.) as follows：
Minf (x), x=(x1,x2,...,xn)∈Rn
s.t.g1(x)≤0, i=1,2 ..., n
hj(x)=0, j=1,2 ..., p
lk≤xk≤uk, k=1,2 ..., n
Wherein, x=(x1,x2,...,xn)∈RnIt is parameter vector, xi=(i=1 ..., n) it is a certain tool in parameter vector Body parameter, n is the number of parameter in parameter vector, and m and p represents the number of inequality constraints and equality constraint, f respectively X () is object function, gi(x)≤0 and hjX ()=0 represents boundary condition constraint of the parameter vector on n-dimensional space, lkAnd ukPoint X is not representedkLower bound and the upper bound.
In step 2, artificial bee colony is initialized, determine bee colony quantity, be divided into three groups and test respectively, first group leads honeybee Quantity more than following honeybee；To lead honeybee, second half is to follow honeybee to second group of half；Follow honeybee quantity to be more than in 3rd group to lead Honeybee.Second group of efficiency highest is found by emulation, therefore is set as that half leads honeybee, second half is to follow honeybee.
The maximum limitation iterations Limit of setting, largest loop time c and search target component number N.According to parameter vector Span, the random initial position for determining respectively to lead honeybee, i.e.,
Wherein, i=1...SN, j=1...D, SN for nectar source (leading honeybee) quantity, D be parameter vector in parameter Number,It is j-th minimum value of parameter,It is j-th maximum occurrences of parameter, rand (0,1) is represented in the range of 0 to 1 Random number.Order leads honeybee to randomly search for nectar source in initial position neighborhood after bee colony initialization.
In step 3, according to partial parameters in certain probability Selecting All Parameters vector as regulating object, in standard intraocular In ant colony algorithm, one-dimensional Parameters variation is only carried out, seriously constrain search performance, it is considered to be introduced into change in parameter M control process The number of parameter in parameter vector.When each leads honeybee to scan for, Parameters variation is carried out as the following formula
Wherein, wijTo lead honeybee initial position, lijTo lead honeybee field searching position, φijIt is parameter search step-length, takes Value scope is [- F, F], and F is the random number between 0 to 1；
When bee colony cycle-index is smaller, larger M is chosen, keep the diversity of bee colony, expand hunting zone, accelerate to search Rope process；When bee colony cycle-index is larger, less M is chosen, reduce hunting zone, improve search stability, it is ensured that search Precision.Therefore, consider speed and the precision influence of bee colony search, make M change by following rule；
M=e-a·b/c
Wherein, b is bee colony cycle-index, and c is maximum cycle, and a is control parameter.
Additionally, increasing with iterations, self-adaptative adjustment step-size in search regulation parameter F, if as shown in figure 1, this is pre- Think that mobile direction is basically identical with the direction of current iteration optimal solution, increases step-length, otherwise reduce step-length, see Fig. 1, wherein φ is the angle of bee colony moving direction and optimal nectar source direction, wbestIt is that current bee colony searches the maximum position of fitness value. In order to ensure stability, step-length is limited maximum no more than Fmax.F is made to change by following rule
Honeybee is followed according to the corresponding cost function value f in each nectar sourcei, by fiObtain fitness function value fiti,
In formula, abs () is the function that takes absolute value.
The q in nectar source will be searchediWith the fitness function value Q of current nectar source positioniIt is compared, such as current search qiMeter Calculate fitness function value Qi, in the position Q of current searchiMore than qiWhen, then other nectar sources for being are transferred to, lead honeybee to incite somebody to action Q is searched for and recorded near new nectar sourceiLarger nectar source positional information；
In step 4, according to fitness function value Q obtained abovei, obtain and be transferred to a nectar source probability Pi, in standard In artificial bee colony intelligent algorithm, transition probability P is obtained by following formulai
Wherein, N represents the number in nectar source.
During optimal solution is searched for, the selection pressure of different phase is different, when bee colony cycle-index is smaller, it is desirable to suitable The relatively small honeybee that leads of response also has an opportunity to recruit to honeybee is followed, and bee colony is kept population diversity higher；When bee colony follows When ring number of times is larger, it is desirable to reduce hunting zone, accelerate search progress.
Transition probability P is calculated according to the fitness function value of honeybee is ledi, it is calculated as follows：
Wherein, N is the number in nectar source, QiIt is the corresponding fitness function value in the i-th each nectar source, bee colony cycle-index is c, QminFitness function value minimum value after this circulation, c is maximum cycle, and a is Dynamic gene.
Honeybee is followed to lead honeybee probability P according to above being transferred toi, selection wherein certain lead honeybee to be followed so that Carry out location updating.
In step 6, if by after certain number of iterations, the optimal solution for obtaining is not improved, honey where abandoning Source, while being replaced leading honeybee to produce a new position by search bee.In standard intraocular's ant colony algorithm, determine as the following formula new Position
Wherein, j is some parameter sequence number in change parameter vector,WithRepresent that current bee colony indicates respectively the J the minimum value and maximum of parameter,
As leading honeybee and following honeybee, the artificial bee colony algorithm of standard can only carry out one-dimensional parameter search, in order to improve The diversity of ant colony, makes following improvement
In formula, RijIt is the random number between 0 to 1, M is the setting value between 0 to 1, and leads value in honeybee search procedure Unanimously, M is made to change according to following rule：
M=e-a·b/c
Wherein, b is bee colony cycle-index, and c is maximum cycle, and a is control parameter.
In step 7, if a certain parameter exceedes its maximum occurrences scope in parameter vector, should be by the parameter setting The maximum and minimum value on the border, i.e.,
Wherein, j is some parameter sequence number in change parameter vector,WithRepresent that current bee colony indicates respectively the J the minimum value and maximum of parameter,
A kind of Engineering constraint parameter optimization method for substantially improving artificial bee colony algorithm of the invention, flow chart such as Fig. 2 institutes Show, including following steps：
Step one：For concrete engineering constrained parameters optimization problem, determine that parameter vector and its span are used
Object function and equation (or inequality) are described.
Specifically, being directed to concrete engineering restricted problem, parameter vector and its span are determined, use object function
It is described with equation (or inequality), the constrained parameters in common engineering refer to the mechanical structure chi of part Very little, length, diameter, number of teeth etc., object function are generally area, volume, weight etc., and an Engineering constraint problem definable is such as Under：
Minf (x), x=(x1,x2,...,xn)∈Rn
s.t.g1(x)≤0, i=1,2 ..., n
hj(x)=0, j=1,2 ..., p
lk≤xk≤uk, k=1,2 ..., n
Wherein, x=(x1,x2,...,xn)∈RnIt is parameter vector, xi=(i=1 ..., n) it is a certain tool in parameter vector Body parameter, n is the number of parameter in parameter vector, and m and p represents the number of inequality constraints and equality constraint, f respectively X () is object function, gi(x)≤0 and hjX ()=0 represents boundary condition constraint of the parameter vector on n-dimensional space, lkAnd ukPoint X is not representedkLower bound and the upper bound.
Step 2：According to the number and span of parameter vector, artificial bee colony is initialized, it is determined that maximum limitation iteration time Number Limit, maximum cycle c and search target component number N.It is random to determine respectively to draw according to the span of parameter vector The initial position of honeybee is led, i.e.,
Wherein, i=1...N, j=1...N, V are the quantity of nectar source (leading honeybee), and N is the number of parameter in parameter vector,It is j-th minimum value of parameter,It is j-th maximum occurrences of parameter, rand (0,1) is represented in the range of 0 to 1 Random number.
After bee colony initialization, order leads honeybee to randomly search for nectar source in initial position neighborhood.
Step 3：Using probability M Selecting All Parameters as regulating object, and Automatic adjusument step-size in search, order leads honeybee working as The new nectar source of random search in preceding nectar source neighborhood, obtains the cost function value q in each nectar sourcei, by qiCalculate fitness function value Qi, If the fitness function value of searching position is transferred to new nectar source more than the fitness function value in current nectar source.
Specifically, according to partial parameters in certain probability Selecting All Parameters vector as regulating object, in standard intraocular
In ant colony algorithm, one-dimensional Parameters variation is only carried out, seriously constrain search performance, it is considered to introduced parameter M controls and search Change the number of parameter in parameter vector during rope.When each leads honeybee to scan for, Parameters variation is carried out as the following formula
Wherein, wijTo lead honeybee initial position, lijTo lead honeybee field searching position, RijIt is the random number between 0 to 1, M is the setting value between 0 to 1, φijParameter search step-length, span is [- F, F], and F is the adjustable parameter between 0 to 1；
When bee colony cycle-index is smaller, larger M is chosen, keep the diversity of bee colony, expand hunting zone, accelerate to search Rope process；When bee colony cycle-index is larger, less M is chosen, reduce hunting zone, improve search stability, it is ensured that search Precision.Therefore, consider speed and the precision influence of bee colony search, make M change by following rule；
M=e-a·b/c
Wherein, b is bee colony cycle-index, and c is maximum cycle, and a is control parameter.
Additionally, increasing with iterations, self-adaptative adjustment step-size in search regulation parameter F, if as shown in figure 1, this is pre- Think that mobile direction is basically identical with the direction of current iteration optimal solution, increases step-length, otherwise reduce step-length, see Fig. 1, wherein φ is the angle of bee colony moving direction and optimal nectar source direction, wbestIt is that current bee colony searches the maximum position of fitness value. In order to ensure stability, step-length is limited maximum no more than Fmax.SF is made to change by following rule
Honeybee is followed according to the corresponding cost function value q in each nectar sourcei, by qiObtain fitness function value Qi,
In formula, abs () is the function that takes absolute value.
The fitness function value (honey amount) that nectar source will be searched is compared with the fitness function value of current nectar source position, If searching for the fitness function value of the fitness function value more than current nectar source in nectar source, new nectar source is transferred to, otherwise, after The new nectar source of continuous search.
Step 4, treat it is all lead honeybee to search for terminate, according to the fitness function value fit for respectively leading nectar source where honeybeei, obtain Each nectar source probability P is transferred to followingi
Wherein, N represents the number in nectar source.
During optimal solution is searched for, the selection pressure of different phase is different, when bee colony cycle-index is smaller, it is desirable to suitable The relatively small honeybee that leads of response also has an opportunity to recruit to honeybee is followed, and bee colony is kept population diversity higher；When bee colony follows When ring number of times is larger, it is desirable to reduce hunting zone, accelerate search progress.
Transition probability P is calculated according to the fitness function value of honeybee is ledi, it is calculated as follows：
Wherein, N is the number in nectar source, QiIt is the corresponding fitness function value in the i-th each nectar source, bee colony cycle-index is c, QminFitness function value minimum value after this circulation, c is maximum cycle, and a is Dynamic gene.
Honeybee is followed to lead honeybee probability P according to above being transferred toi, selection wherein certain lead honeybee to be followed so that Carry out location updating.
Step 5：If selection nectar source, it is converted into and leads honeybee to search for new nectar source, while searched near nectar source and recorded The larger nectar source position of fitness function value.
Step 6：If iterations is more than maximum limitation iterations Limit, the optimal solution for obtaining still without change, Nectar source where abandoning, while being replaced leading honeybee to produce a new position by search bee.
Specifically, if iterations is more than maximum limitation iterations Limit, the optimal solution for obtaining still without change, Nectar source where abandoning, while being replaced leading honeybee to produce a new position by search bee.In standard intraocular's ant colony algorithm, press Following formula determines new position
Wherein, j is some parameter sequence number in change parameter vector,WithRepresent that current bee colony indicates respectively the J the minimum value and maximum of parameter,
As leading honeybee and following honeybee, the artificial bee colony algorithm of standard can only carry out one-dimensional parameter search, in order to improve The diversity of ant colony, makes following improvement
In formula, RijIt is the random number between 0 to 1, M is the setting value between 0 to 1, and leads value in honeybee search procedure Unanimously, M is made to change according to following rule：
M=e-a·b/c
Wherein, b is bee colony cycle-index, and c is maximum cycle, and a is control parameter.
In step 7, if a certain parameter exceedes its maximum occurrences scope in parameter vector, should be by the parameter setting
The maximum and minimum value on the border, i.e.,
Wherein, j is some parameter sequence number in change parameter vector,WithRepresent that current bee colony indicates respectively the J the minimum value and maximum of parameter,
Step 8：Record the nectar source position w of the fitness function value maximum in each bee colony iterative search proceduresbest, weight Multiple step 3 is searched for step 7 by limited number of cycles, obtains the optimal estimation value of parameter.
Implementation process：Flexible rope structure is as shown in figure 3, the target of optimization is to seek to meet minimum deflection, shearing stress, surging A series of multiple angle car variables of constraintss such as frequency, and average coil diameter D (x1), linear diameter d (x2) and active volume quantity p(x3) so that the weight of flexible rope is minimum.
The Mathematical Modeling of flexible rope problem is described as follows：
Min f (x)=(x3+2)x2x1, x=(x1,x2,x3)∈R3
g4(x)=(x1+x2)/1.5-1≤0
0.05≤x1≤2,0.25≤x1≤ 1.3,3.2≤x1≤15
Primary condition：Artificial bee colony quantity N is 100, and maximum limited number of times Limit is 50, and maximum cycle is 1000, Target component number is 3, ant colony algorithm after being utilized respectively standard intraocular's ant colony algorithm and improving, and is contrasted under these conditions Emulation.
Simulation result is shown in Fig. 4, and simulation result shows：In Engineering constraint optimization problem, comparison with standard artificial bee colony The convergence time of the ant colony algorithm after algorithm improvement substantially shortens, that is, effectively improve search efficiency, and in convergence precision Improve a lot.
It is not difficult to find out from above example, there is complex structure for common engineering constraint ginseng place optimization method is difficult to really Fixed, local optimum, walk the low problem of left efficiency.The present invention on the basis of Traditional Man ant colony algorithm, improved search strategy and Selection strategy, gives full play to the search capability and development ability of artificial bee colony algorithm, and the artificial bee colony after improvement is searched for into calculation Method is applied to Engineering constraint parameter optimisation procedure, realizes that various dimensions are quick, clear, accurate and validity Engineering constraint parameter excellent Change.

Claims (2)

1. it is a kind of based on improve artificial bee colony algorithm Engineering constraint parameter optimization method, it is characterised in that the method include with Lower step：
Step one：Parameter vector i.e. its span is determined by chaos algorithm, is carried out with object function and equation or inequality Description；Deliver sufficient amount of honeybee at random in the range of Experimental Area, information can be constantly updated during honeybee random search path Prime matrix, using the positive feedback of ant colony algorithm, the final Pheromone Matrix for producing, so that it is determined that the position in honeybee source.Initial Pheromone Matrix can not be 0, and honeybee transfer can not start, so to be initialized as Pheromone Matrix using random matrix. The position to be walked of honeybee next step, is determined by transition probability.
p ( l , m ) ( i , j ) n = [ τ i , j n - 1 ] α · [ η i , j ] β Σ ( i , j ) ∈ Ω ( l , m ) [ τ i , j n - 1 ] α · [ η i , j ] β
Step 2：According to the number and span of the parameter vector determined in step one, artificial bee colony is initialized, it is determined that maximum Limitation iterations Limit, maximum cycle c and search target component number N, order lead honeybee in initial position field with Machine ground search nectar source；
The involved honeybee initial position expression formula that leads is：
In formula, RijIt is the random number between 0 to 1, N is the setting value between 0 to 1；I=1....N, j=1...N, V are nectar source Number,It is j-th minimum value of parameter,It is j-th maximum occurrences of parameter, rand (0,1) represents 0 to 1 model Enclose interior random number；
The L-expression for leading honeybee initial position field L is：
Wherein, wijTo lead honeybee initial position, lijTo lead honeybee field searching position, φijIt is parameter search step-length, value model It is [- F, F] to enclose, and F is the random number between 0 to 1；
The expression formula of F is：
F i ( t ) = F i - 1 ( t ) * ( 1 + c o s &phi; ) , i f c o s &phi; > 0 F i - 1 ( t ) / ( 2 - c o s &phi; ) , i f c o s &phi; < 0
Step 3：The parameter determined by chaos algorithm using in probability P selecting step one introduces probability P control as regulating object In search procedure in matrix-vector parameter number, and appropriate change step parameter F, first by leading honeybee adjacent in current nectar source The new nectar source of random search in domain, obtains the cost function value q in a nectar sourcei, by qiCalculate fitness function value Qi, searched currently The position Q of ropeiMore than qiWhen, then other nectar sources for being are transferred to, lead honeybee to be searched near new nectar source and record Qi Larger nectar source positional information；
Involved M expression formulas are：
M=e-a·b/c
Wherein, b is bee colony cycle-index, and c is maximum cycle, and a is control parameter；
Involved fitness function value fitiExpression formula is：
Q i = 1 / ( 1 + q i ) i f q i &GreaterEqual; 0 1 + a b s ( q i ) i f q i < 0
In formula, abs () is the function that takes absolute value；
Step 4：Treat it is all lead honeybee to search for terminate, according to the fitness function value Q for respectively leading nectar source where honeybeei, followed Honeybee goes to each honeybee source probability Pi, location updating is carried out according to probability, and record the fitness in each bee colony iterative search procedures The maximum nectar source position w of functional valuebest；
Involved transition probability PiExpression formula is：
P i = e - a &CenterDot; b / c &CenterDot; Q i &Sigma; i = 1 N Q i + ( 1 - e - a &CenterDot; b / c ) &CenterDot; Q i - Q min &Sigma; i = 1 N ( Q i - Q min )
Wherein, QminIt is fitness function value minimum value after this circulation, a is Dynamic gene；
Step 5：Repeat step three, step 4, searches for by limited cycle, and obtain parameter most has estimate.
When iterations is more than maximum limitation iterations Limit, nectar source where abandoning, while replacing leading by investigating honeybee Honeybee produces a new position.
2. according to claims based on the Engineering constraint parameter optimization method for improving artificial bee colony algorithm, its feature exists In, when iterations is more than maximum limitation iterations Limit, nectar source where abandoning, while being replaced leading by search bee Honeybee produces a new position.
The Engineering constraint parameter optimization method based on improvement artificial bee colony algorithm according to claims, its feature exists In when parameter exceeds its maximum occurrences scope, by maximum or minimum value that the parameter setting is the border.
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Application publication date: 20170620