CN109583020A - Logic-based chaotic maps and adaptive step drosophila cantilever beam variable measuring method - Google Patents
Logic-based chaotic maps and adaptive step drosophila cantilever beam variable measuring method Download PDFInfo
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Abstract
The invention belongs to Structural Engineering design optimizing field, a kind of logic-based chaotic maps and adaptive step drosophila cantilever beam variable measuring method are disclosed, fitness function is determined according to the objective function of cantilever beam optimization problem and constraint condition；Using logic chaotic maps thought, initial position and optimizing variable to drosophila are mapped to the region of chaotic space by chaotic mapping system；The stability that optimizing improves solution is iterated to the variable in chaos system, compensates for the disadvantage of drosophila algorithm stability difference；Traditional fixed step size is replaced using adaptive step, fixed step size is avoided easily to fall into local optimal searching；When current iteration step number is equal to greatest iteration step number, iteration is terminated, exports the value of global optimum's feasible solution and corresponding optimal optimizing variable.The present invention makes the Optimum Design Results of Design of Cantilever Beam optimization problem more preferable by introducing logic chaotic maps thought and adaptive step, and searching process is more stable.
Description
Technical field
The invention belongs to Structural Engineering design optimizing field more particularly to a kind of logic-based chaotic maps and adaptive
Answer step-length drosophila cantilever beam variable measuring method.
Background technique
Currently, the prior art commonly used in the trade is such that in mechanical engineering Optimal Structure Designing, structure engineering design
Optimization problem is that a kind of acquisition objective function is maximum or the Parametric optimization problem of minimum value, it will usually is related to complicated linear
Or nonlinear constraint condition.Most of structure engineering design optimization problem constraint conditions are all nonlinearities, wherein about
Complicated discrete or continuous design variable is usually contained in beam condition, traditional calculation method and numerical method are to solution
Such issues that be relatively out of strength.And the proposition of intelligent optimization algorithm, it is provided to solve this kind of Solution of Nonlinear Optimal Problem
A kind of new thinking.Wherein, drosophila optimization algorithm is gradually ground both at home and abroad with its efficient optimizing ability, stable performance
The concern for the person of studying carefully.In order to solve constrained engineering optimization problem, some heuristic artificial intelligence global optimization approaches are suggested.
Currently, mainly having genetic algorithm, ant group algorithm, particle swarm algorithm etc. for the intelligent algorithm of constraint processing.Genetic algorithm is mould
Quasi- biology in the natural environment the survival of the fittest, the heredity of the survival of the fittest and evolutionary process and the one kind formed has adaptive ability
, probability search method of overall importance.Ant group algorithm is the simulation to ant communities food collection process, for solving complexity
Combinatorial optimization problem.Particle swarm algorithm be by simulate flock of birds foraging behavior grow up it is a kind of based on group collaboration with
Machine searching algorithm etc..Although these algorithms can be good at solving these problems, but for the constraint condition of nonlinearity
Processing still have some flaws.In intelligent algorithm field, drosophila optimization algorithm, which has, to be easy to adjust, and calculation amount is small, optimizing
The higher advantage of precision, applicability is wide in solving practical problems.Drosophila optimization algorithm is deduced out by the foraging behavior of drosophila
The evolutionary Swarm Intelligent Algorithm of one kind.A kind of global optimization approach obtained by the foraging behavior of drosophila, with biography
System intelligent optimization algorithm is compared, and drosophila optimization algorithm has many advantages, such as simple, fast convergence rate and convergence precision is high.But it is traditional
There are still some problems for drosophila optimization algorithm, and convergence precision can be because initial value and optimizing walk in the entire optimization process of algorithm
Unstable state is presented in long selection.
In conclusion problem of the existing technology is:
(1) some flaws are still had for the processing of the constraint condition of nonlinearity for the intelligent algorithm of constraint processing
Defect, in order to solve the constraint condition of nonlinearity, existing intelligent algorithm uses a kind of evolution side of efficient real-time coding
Method and a kind of new free parameter heuristic handle constraint condition, although these methods can be good at handling it is non-linear
Constraint condition, but will increase the complexity of algorithm and slowed down convergence speed of the algorithm.In order to make up these defects, the present invention
Nonlinear Constraints are handled using penalty function method after carrying out chaotic maps to optimizing variable, to effectively improve algorithm
Convergence rate.
(2) convergence precision can be because of initial value and optimizing step-length in the entire optimization process of traditional drosophila optimization algorithm
It chooses and unstable state is presented.
Solve the difficulty and meaning of above-mentioned technical problem:
The randomness of the inappropriate initial position that will increase drosophila of selection of initial value, so as to cause in the iteration optimizing stage
Can take more time, thus introduce chaotic maps thought, to initial position variable carry out chaotic maps, thus weaken due to
Initial position unreasonable the problem of causing.If fixed optimizing step-length chose conference and jumps out globally optimal solution, too small to lead
The increase of optimal time is caused, therefore the present invention proposes adaptive step, dynamically changes step-length according to the result of each iteration, from
And it avoids fixed minister and chooses inappropriate the problem of bringing.
Summary of the invention
In view of the problems of the existing technology, the present invention provides a kind of logic-based chaotic maps and adaptive step fruits
Fly cantilever beam variable measuring method.
The invention is realized in this way a kind of logic-based chaotic maps and the measurement of adaptive step drosophila cantilever beam variable
Method, the logic-based chaotic maps and adaptive step drosophila cantilever beam variable measuring method are according to cantilever beam optimization problem
Objective function and constraint condition determine fitness function；Using logic chaotic maps thought, initial position to drosophila and
Optimizing variable is mapped to the region of chaotic space by chaotic mapping system；Optimizing is iterated to the variable in chaos system；
Traditional fixed step size is replaced using adaptive step；When current iteration step number is equal to greatest iteration step number, iteration is terminated,
Export the value of global optimum's feasible solution and corresponding optimal optimizing variable.
Further, the logic-based chaotic maps and adaptive step drosophila cantilever beam variable measuring method are specifically wrapped
It includes:
Step 1: according to the objective function and constraint condition of Design of Cantilever Beam problem, cantilever beam optimization design problem is determined
Fitness function, while initializing the initial parameter of drosophila group；
Wherein, Ω is solution space, is directed to four variables: throat depth h (x1), the length l of welding point
(x2), the width t (x of beam3), the width b (x of beam4), X=(h, l, t, b)=(x1,x2,x3,x4)；fcostIt is set for cantilever beam optimization
The objective function (the least cost) of meter problem；Degree is violated for constraint condition, is the fitness function of infeasible solutions,It is the constraint condition of j-th of Design of Cantilever Beam；
The parameter of initialization drosophila group mainly includes the position of random initializtion drosophila group, greatest iteration algebra
The dimension N and population scale sizepop of Maxgen drosophila population；
Step 2: each component of the position of drosophila is carried out by chaotic maps transformation by logic chaotic maps formula, is obtained
To the chaotic maps variable of initial position, it is then reconverted into traditional variables；
Step 3: the random direction and distance of drosophila individual search of food are generated；
Step 4: drosophila is based on smell search of food and first estimates since drosophila can not learn the specific location of food
Then drosophila calculates flavor concentration decision content by this distance at a distance from origin；
Step 5: flavor concentration decision content is brought into flavor concentration decision function, fitness function Fitness
In Function, drosophila individual flavor concentration value Smell is found outi；
Step 6: finding out flavor concentration maximum value in drosophila group, and writes down drosophila group where maximum flavor concentration individual
Position in body；
Step 7, retains the coordinate of the drosophila individual of best flavors concentration, and flies to the best seat using the vision of drosophila
Cursor position；
Step 8 into iteration optimizing, and repeats step 2 to step 6, judges whether flavor concentration value is better than upper one
In generation, enters step seven, wherein the step-length of iteration optimizing will fix on the basis of traditional drosophila algorithm if being better than previous generation
Step-size change is adaptive step, finally obtains optimal solution.
Further, in the step 1, according to following formula initial drosophila group position at random:
X_axis=Value × rand () Y_axis=Value × rand ()；
Wherein, Value is initial position parameters, and rand () is the random number between (0,1), the preliminary examination position of drosophila are as follows:
Z_axis=[X_axis Y_axis].
Further, in the step 2 drosophila position are as follows:
Z_axis=[X_axis Y_axis]；
Position Z_axis is mapped as Chaos Variable Cz (n) by following formulai:
Cxi=(xi-ai)/(bi-ai)；
Wherein (Cz (n) i ∈ [0,1]), xiIndicate i-th of Chaos Variable Cx after chaotic maps variationiIt is converted into routine
The value of variable；
The formula of Logistic chaos system: n indicates the number of iterations, and u indicates chaos controlling parameter, usually as u=4,
Logistic system is in chaos state:
X (n+1)=ux (x) (1-x (x)) x (n) ∈ [0,1]；
By Cz (n)iEach component by carrying out chaos transformation below formula:
Cx(n+1)i=4Cx (n)i(1-Cx(n)i) i=1,2 ... N；
Wherein, Cx (n)iIndicate i-th of Chaos Variable Cx of chaotic mapsiValue after Chaos Variable, works as Cxi∈[0,
1] andWhen, which is in chaos state；
Chaotic maps variable is converted into traditional variables Z ' by following formulai(Z′i∈[ai,bi]):
x′i=ai+Cxi(bi-ai)。
Further, in the step 3, the random direction and distance of drosophila individual search of food are determined by following formula:
Xi=X_axis '+StepValue；Yi=Y_axis '+StepValue；
Wherein X_axis ' is Z 'iIn belong to the part of X_axis, Y_axis ' is Z 'iIn belong to the part of Y_axis,
StepValue is initial iteration step.
Further, in the step 4, it is based on smell search of food, wherein flavor concentration decision content is Si:
Si=1/Disti。
Further, in the step 5, drosophila individual flavor concentration value SmelliAre as follows:
Smelli=fcost(Si)。
Further, in the step 6, flavor concentration maximum value in drosophila group is calculated by following formula:
[bestSmell bestIndex]=max (Smell)；
Wherein, bestSmell is maximum flavor concentration value, and bestIndex is the corresponding drosophila group of maximum flavor concentration
Position.
Further, in the step 7, drosophila group is determined by the corresponding drosophila group position of best flavors concentration value
The position flown to, obtains optimal solution:
Smellbest=bestSmell
X_axis=X (bestIndex)
Y_axis=Y (bestIndex)；
In the step 8, the adaptive iteration step-length of drosophila optimization algorithm shows when flavor concentration decision content is larger
Distance objective is closer, and iteration step length becomes smaller at this time, when flavor concentration decision content is smaller, shows that distance objective farther out, changes at this time
Larger, the adaptive iteration step-length of length of riding instead of walk are as follows:
Another object of the present invention is to provide a kind of application logic-based chaotic maps and adaptive step drosophilas
The cantilever beam of cantilever beam variable measuring method.
In conclusion advantages of the present invention and good effect are as follows: since the optimizing step-length of traditional drosophila optimization algorithm is consolidated
Determine with iterative parameter without ergodic, the solution for causing traditional drosophila optimization algorithm to obtain when solving Solution of Nonlinear Optimal Problem is missed
Poor larger and stability is poor, and the present invention proposes that the cantilever beam of logic-based chaotic maps and adaptive step drosophila algorithm is set
Optimization method is counted, for solving Design of Cantilever Beam optimization problem, to obtain than traditional drosophila optimization algorithm and existing
Intelligent algorithm more preferably result.
The present invention is by being changed to adaptive step for fixed step size, and when drosophila group is when distance objective is closer, taste is dense
Degree decision content is larger, and iteration step length should be become smaller, and avoid jumping out optimal solution；When drosophila group distance objective farther out when, taste
Road concentration decision content is smaller, and iteration step length should be become larger, to accelerate the speed of optimizing.Logistic chaotic maps are introduced to think
Think: optimizing variable is mapped to the region of chaotic space by chaotic mapping system, then the variable in chaos system is carried out
Iteration optimizing, the Numerical solution obtained from is higher, while improving the ability of searching optimum and stabilization of traditional drosophila optimization algorithm
Property, avoid influence of the initiation parameter to optimizing result.
By using method of the invention, progress benchmark test function first carries out emulation experiment, and experiment shows the present invention
Method result obtained in four test functions is respectively as follows: 2.222693e-8,2.917590e-6,0.002455,
3.420569e-4, the results showed that, the present invention can obtain more preferably as a result, simultaneously at runtime between and standard deviation comparison on,
The method of the present invention the number of iterations under the same conditions, consume the less time, stability is more preferable.
The method of the present invention is applied in Design of Cantilever Beam optimization problem, obtained optimal result is 1.697432, is better than
Existing algorithm, while 100 emulation experiments are carried out, and SS is poor, the standard deviation that the method for the present invention obtains is
0.00062457, it is smaller than existing other methods, thus surface the method for the present invention solve Design of Cantilever Beam optimization problem on more
Add stabilization.
Detailed description of the invention
Fig. 1 is logic-based chaotic maps provided in an embodiment of the present invention and the measurement of adaptive step drosophila cantilever beam variable
Method flow diagram.
Fig. 2 is cantilever beam structure design diagram provided in an embodiment of the present invention.
Fig. 3 is logic-based chaotic maps provided in an embodiment of the present invention and the measurement of adaptive step drosophila cantilever beam variable
Method implementation flow chart.
Fig. 4 is that algorithms of different provided in an embodiment of the present invention solves Design of Cantilever Beam problem comparative result figure.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to embodiments, to the present invention
It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to
Limit the present invention.
The existing intelligent algorithm for constraint processing still has the processing of the constraint condition of nonlinearity
Flaw.Convergence precision can be because the selection of initial value and optimizing step-length be in the entire optimization process of traditional drosophila optimization algorithm
Existing unstable state.The present invention is based on logic chaotic maps and the Design of Cantilever Beam optimization method of adaptive step drosophila algorithm,
Chaotic maps are carried out to initial optimizing variable by logic chaotic maps, so that drosophila optimization algorithm has the characteristics that ergodic；
Simultaneously when iteration optimizing, the fixed step size of traditional drosophila optimization algorithm is changed to adaptive step, avoids drosophila
Local optimum is fallen into searching process.Improved drosophila optimization algorithm is applied in Design of Cantilever Beam optimization problem, is obtained
More preferably objective result.
Application principle of the invention is explained in detail with reference to the accompanying drawing.
As shown in Figure 1, logic-based chaotic maps provided in an embodiment of the present invention and adaptive step drosophila cantilever beam become
Quantity measuring method the following steps are included:
S101: fitness function is determined；
S102: processing constraint condition obtains initialization penalty function；
S103: the group's initial position for initializing drosophila is mapped as Chaos Variable using chaotic maps transformation for mula, so
Traditional variables are converted to by reverse formula afterwards；
S104: obtaining drosophila group current location by optimizing step-length, calculates drosophila flying distance, root by current location
Flavor concentration decision content is calculated according to flying distance；
S105: flavor concentration decision content is brought into fitness function, and is obtained initialization plus penalty factor and penalized letter
Number；
S106: initialization extreme value is obtained by initializing penalty function, including the best flavors concentration value (pole of fitness function
Small value) and the corresponding drosophila group of best flavors concentration value position；
S107: entering iteration optimizing, changes the step-length of iteration optimizing by adaptive step；
S108: retain the coordinate of the drosophila individual of best flavors concentration, and fly to the best coordinates using the vision of drosophila
Position；
S109: repeat the above steps S102 to step S107, and until reaching maximum number of iterations, stopping iteration is final to obtain
To optimal solution.
Application principle of the invention is further described with reference to the accompanying drawing.
As shown in Fig. 2, the structural design drawing of the design of cantilever beam, the objective function of the problem is to minimize total expense
fcost, it is directed to four variables: throat depth (h (x1)), the length (l (x of welding point2)), the width (t (x of beam3)),
Thickness (b (the x of beam4)), i.e.,Meanwhile relating to seven nonlinear complementary problem items
Part: g1(x), g2(x), g3(x), g4(x), g5(x), g6(x), g7(x)。
Objective function fcostIs defined as:
Four parametric variables meet seven constraint conditions: g1It is shear stress constraint, g2It is beam deflection stress constraint, g3,
g4, g7For boundary constraint, g5The constraint of c beam end amount of deflection, g5It is that bending load constrains on bar, constraint condition defined formula is as follows:
s.t.g1=τ (X)-τmax≤0
g2=σ (X)-σmax≤0
g3=x1-x4≤0
g4=0.125-x1≤0
g5=δ (X) -0.25≤0
g6=P-Pc(X)≤0
It is wherein r shear stress, σ is direct stress, PcFor Buckling Loads, δ is beam-ends amount of deflection, and the shear stress of weld seam is most
Big value τmax(τmax=13600psi), σmaxFor the maximum value (σ of the direct stress of beammax=3000psi), load P=6000lb.Its
Middle shear stress r consists of two parts, principal stress r1With secondary stress r2:
M and J (x) respectively represent torque and polar moment of inertia:
The maximum stress δ (X) of cantilever beam, beam end amount of deflection σ (X), bent load is respectively P on barc(X):
G=12 × 106Psi, E=30 × 106Psi, P=6000lb, L=14in；
Wherein, G is the modulus of shearing of cantilever material, and E indicates the Young's modulus of cantilever material, and P indicates that application is outstanding
Arm load, L indicate the length of the cantilever lever exposed.
Corresponding solution space, i.e., the constraint of four variables are as follows:
0.1≤x1≤2
0.1≤x2≤10
0.1≤x3≤10
0.1≤x4≤2；
As shown in figure 3, the Design of Cantilever Beam of logic-based chaotic maps and adaptive step drosophila algorithm of the invention is excellent
Specific step is as follows for change method:
Step 1: fitness function is determined:
And the position of drosophila group: Z_axis=[X_axis Y_axis], initial iteration step StepValue is initialized,
Population scale, maximum number of iterations.
Step 2: processing constraint condition obtains initialization penalty function (obtaining by step 3 to step 5).Cantilever beam is set
Meter optimization problem belongs to Solution of Nonlinear Optimal Problem, and the key of solution is how to handle constraint condition, and penalty function method is usual
Such issues that be the key that processing.The main thought of penalty function method is to obtain weighting by equality constraint and inequality constraints to ask
With, then behind objective function add penalty factor, will there is restricted problem to be converted into unconstrained problem, to obtain optimal
Solution.The main mathematical models of penalty function method are as follows:
It is wherein to obtain the corresponding solution of optimal value, fwIt is worst feasible solution,It is penalty factor.It is non-to above-mentioned seven
Linear Constraints are handled using penalty function, and constrained optimization problem is converted unconstrained problem.
Step 3: being mapped as Chaos Variable for the group's initial position for initializing drosophila using chaotic maps transformation for mula,
Then traditional variables are converted to by reverse formula:
Cxi=(xi-ai)/(bi-ai)；
x′i=ai+Cxi(bi-ai)；
Wherein, CxiIt is drosophila group position chaotic maps variable, x 'iIt is that the conventional of the drosophila position after reverse Mapping becomes
Amount.
Step 4: drosophila group current location Z ' is obtained by optimizing step-lengthi, by current location calculate drosophila flight away from
From Dist, flavor concentration decision content S is calculated according to flying distancei:
Xi=X_axis '+StepValue；Yi=Y_axis '+StepValue；
Si=1/Disti；
Step 5: by flavor concentration decision content SiIt is brought into fitness function, and is initialized plus penalty factor
Penalty function.
Smelli=fcost(Si)；
Step 6: by initialize penalty function obtain initialization extreme value, including best flavors concentration value (fitness function
Minimum) and the corresponding drosophila group of best flavors concentration value position:
[bestSmell bestIndex]=max (Smell)；
Step 7: entering iteration optimizing, changes the step-length of iteration optimizing by adaptive step:
The iteration step length of above-mentioned drosophila optimizing is updated with the formula is crossed.
Step 8: retain the coordinate of the drosophila individual of best flavors concentration, and fly to the best seat using the vision of drosophila
Cursor position.
Smellbest=bestSmell
X_axis=X (bestIndex)
Y_axis=Y (bestIndex)；
Step 9: two are repeated the above steps to step 7, until reaching maximum number of iterations Maxgen, stops iteration, most
Optimal solution is obtained eventually.
Application effect of the invention is explained in detail below with reference to emulation.
Embodiment 1:
In order to verify the validity of logic-based chaotic maps provided by the invention and adaptive step drosophila algorithm, to four
A typical reference function is tested, and is compared with traditional intelligent algorithm and original drosophila optimization algorithm,
It is independently emulated in the environment of MATLAB 100 times:
Table 1: benchmark test function
The global minimizer of aforementioned four reference function is equal are as follows: f (x)=0, xi=0, i=1,2,3 ..., n.
The optimum results of 2: four reference functions of table compare
As can be seen from the table, the method for the present invention can obtain target knot more better than other algorithms in optimal result
Fruit, while standard deviation is smaller, shows that the method for the present invention is more stable, after independently emulation 100 times, when the operation of the method for the present invention
Between be better than other methods.To demonstrate the cantilever beam the present invention is based on logic chaotic maps and adaptive step drosophila algorithm
The validity of design optimization method, while being obtained more preferably in Design of Cantilever Beam optimization problem compared to existing method is more enough
As a result, more stable, convergence rate is faster.
Embodiment 2:
In order to prove that the method for the present invention is solving the validity in cantilever beam optimization design problem, by optimization knot of the invention
Fruit compares with the more existing method for having solved Design of Cantilever Beam optimization problem, independently emulates in MATLAB
100 times, table 3 lists the optimal result that distinct methods obtain, and table 4 lists the corresponding statistic of distinct methods, and comparing result is such as
Shown in following table:
Table 3: Design of Cantilever Beam optimization problem Comparative result
Table 4: the statistic comparison of algorithms of different
| Method | It is optimal | Mean value | It is worst | Standard deviation |
| Hedaretal.(2006) | 1.7250022 | 1.7564428 | 1.8843960 | 0.0424175 |
| Q.Heetal.(2007) | 1.728024 | 1.748831 | 1.782143 | 0.012926 |
| Dimopoulos(2007) | 1.731186 | NA | NA | NA |
| Montesetal.(2007) | 1.724852 | 1.725 | NA | 1E-15 |
| Montesetal.(2008) | 1.737300 | 1.813290 | 1.994651 | 0.070500 |
| Cagninaetal.(2008) | 1.724852 | 2.0574 | NA | 0.2154 |
| Kavehetal.(2009) | 1.724849 | 1.727564 | 1.759522 | 0.008254 |
| Kavehetal.(2010) | 1.724918 | 1.729752 | 1.775961 | 0.009200 |
| Gandomietal(2011) | 1.7312065 | 1.8786560 | 2.3455793 | 0.2677989 |
| Mehtaetal.(2012) | 1.724855 | 1.724865 | 1.72489 | NA |
| Akayetal.(2012) | 1.724852 | 1.741913 | NA | 0.031 |
| Genetic algorithm | 1.729441 | 1.72532473 | 1.74534573 | 0.00165238 |
| Particle swarm algorithm | 1.732540 | 1.76832748 | 1.77687365 | 0.00076543 |
| Drosophila algorithm | 1.699149 | 1.70365492 | 1.71653453 | 0.00125643 |
| DSLC-FOA(2017) | 1.697640 | 1.69806175 | 1.70562196 | 0.00067427 |
| The method of the present invention | 1.697432 | 1.69765364 | 1.70547654 | 0.00062457 |
As can be seen that the optimal value of optimal four design variables and objective function that the present invention obtains from above-mentioned table 3
Are as follows:
Its result is better than existing other methods, while the statistic that table 4 is obtained by 100 independent emulation experiments
The result shows that the standard deviation of method of the invention is minimum, it is also optimal for being compared with other methods.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention
Made any modifications, equivalent replacements, and improvements etc., should all be included in the protection scope of the present invention within mind and principle.
Claims (10)
1. a kind of logic-based chaotic maps and adaptive step drosophila cantilever beam variable measuring method, which is characterized in that described
Logic-based chaotic maps and adaptive step drosophila cantilever beam variable measuring method are according to the target letter of cantilever beam optimization problem
Several and constraint condition determines fitness function；Initial position and optimizing variable using logic chaotic maps thought, to drosophila
The region of chaotic space is mapped to by chaotic mapping system；Optimizing is iterated to the variable in chaos system；Using adaptive
Step-length is answered to replace traditional fixed step size；When current iteration step number is equal to greatest iteration step number, iteration is terminated, output is global
The value of optimal feasible solution and corresponding optimal optimizing variable.
2. logic-based chaotic maps as described in claim 1 and adaptive step drosophila cantilever beam variable measuring method,
It is characterized in that, the logic-based chaotic maps and adaptive step drosophila cantilever beam variable measuring method specifically include:
Step 1: according to the objective function and constraint condition of Design of Cantilever Beam problem, the suitable of cantilever beam optimization design problem is determined
Response function, while initializing the initial parameter of drosophila group；
Wherein, Ω is solution space, is directed to four variables: throat depth h (x1), the length l (x of welding point2),
Width t (the x of beam3), the width b (x of beam4), X=(h, l, t, b)=(x1,x2,x3,x4)；fcostIt is asked for cantilever beam optimization design
The objective function (the least cost) of topic；Degree is violated for constraint condition, is the fitness function of infeasible solutions,It is
The constraint condition of j-th of Design of Cantilever Beam；
The parameter of initialization drosophila group mainly includes the position of random initializtion drosophila group, greatest iteration algebra Maxgen fruit
The dimension N and population scale sizepop of fly population；
Step 2: each component of the position of drosophila is carried out by chaotic maps transformation by logic chaotic maps formula, is obtained just
The chaotic maps variable of beginning position, is then reconverted into traditional variables；
Step 3: the random direction and distance of drosophila individual search of food are generated；
Step 4: drosophila is based on smell search of food and first estimates drosophila since drosophila can not learn the specific location of food
At a distance from origin, flavor concentration decision content is then calculated by this distance；
Step 5: flavor concentration decision content is brought into flavor concentration decision function, fitness function Fitness Function
In, find out drosophila individual flavor concentration value Smelli；
Step 6: finding out flavor concentration maximum value in drosophila group, and writes down in the drosophila group of maximum flavor concentration individual place
Position；
Step 7, retains the coordinate of the drosophila individual of best flavors concentration, and flies to the best coordinates position using the vision of drosophila
It sets；
Step 8 into iteration optimizing, and repeats step 2 to step 6, judges whether flavor concentration value is better than previous generation, such as
Fruit is better than previous generation, then enters step seven, wherein the step-length of iteration optimizing is on the basis of traditional drosophila algorithm by fixed step size
Adaptive step is changed into, optimal solution is finally obtained.
3. logic-based chaotic maps as claimed in claim 2 and adaptive step drosophila cantilever beam variable measuring method,
It is characterized in that, in the step 1, according to following formula initial drosophila group position at random:
X_axis=Value × rand () Y_axis=Value × rand ()；
Wherein, Value is initial position parameters, and rand () is the random number between (0,1), the preliminary examination position of drosophila are as follows:
Z_axis=[X_axis Y_axis].
4. logic-based chaotic maps as claimed in claim 2 and adaptive step drosophila cantilever beam variable measuring method,
It is characterized in that, the position of drosophila in the step 2 are as follows:
Z_axis=[X_axis Y_axis]；
Position Z_axis is mapped as Chaos Variable Cz (n) by following formulai:
Cxi=(xi-ai)/(bi-ai)；
Wherein (Cz (n) i ∈ [0,1]), xiIndicate i-th of Chaos Variable Cx after chaotic maps variationiIt is converted into traditional variables
Value；
The formula of Logistic chaos system: n indicates the number of iterations, and u indicates chaos controlling parameter, usually as u=4,
Logistic system is in chaos state:
X (n+1)=ux (x) (1-x (x)) x (n) ∈ [0,1]；
By Cz (n)iEach component by carrying out chaos transformation below formula:
Cx(n+1)i=4Cx (n)i(1-Cx(n)i) i=1,2 ... N；
Wherein, Cx (n)iIndicate i-th of Chaos Variable Cx of chaotic mapsiValue after Chaos Variable, works as Cxi∈ [0,1] andWhen, which is in chaos state；
Chaotic maps variable is converted into traditional variables Z by following formulai'(Zi'∈[ai,bi]):
xi'=ai+Cxi(bi-ai)。
5. logic-based chaotic maps as claimed in claim 2 and adaptive step drosophila cantilever beam variable measuring method,
It is characterized in that, in the step 3, the random direction and distance of drosophila individual search of food is determined by following formula:
Xi=X-axis'+StepValue；Yi=Y-axis'+StepValue；
Wherein X-axis' is Zi' in belong to the part of X-axis, Y-axis' Zi' in belong to the part of Y-axis,
StepValue is initial iteration step.
6. logic-based chaotic maps as claimed in claim 2 and adaptive step drosophila cantilever beam variable measuring method,
It is characterized in that, in the step 4, be based on smell search of food, wherein flavor concentration decision content is Si:
Si=1/Disti。
7. logic-based chaotic maps as claimed in claim 2 and adaptive step drosophila cantilever beam variable measuring method,
It is characterized in that, in the step 5, drosophila individual flavor concentration value SmelliAre as follows:
Smelli=fcost(Si)。
8. logic-based chaotic maps as claimed in claim 2 and adaptive step drosophila cantilever beam variable measuring method,
It is characterized in that, in the step 6, flavor concentration maximum value in drosophila group is calculated by following formula:
[bestSmell bestIndex]=max (Smell)；
Wherein, bestSmell is maximum flavor concentration value, and bestIndex is the position of the corresponding drosophila group of maximum flavor concentration
It sets.
9. logic-based chaotic maps as claimed in claim 2 and adaptive step drosophila cantilever beam variable measuring method,
It is characterized in that, in the step 7, determines what drosophila group flew to by the corresponding drosophila group position of best flavors concentration value
Position obtains optimal solution:
Smellbest=bestSmell
X-axis=X (bestIndex)
Y-axis=Y (bestIndex)；
In the step 8, the adaptive iteration step-length of drosophila optimization algorithm shows distance when flavor concentration decision content is larger
Target is closer, and iteration step length becomes smaller at this time, when flavor concentration decision content is smaller, shows distance objective farther out, at this time iteration step
Long larger, adaptive iteration step-length are as follows:
10. logic-based chaotic maps described in a kind of application claim 1~9 any one and adaptive step drosophila cantilever beam
The cantilever beam of variable measuring method.
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