CN106127295A - A kind of Optimal Design of Pressure Vessel method based on self adaptation cuckoo Yu fireworks hybrid algorithm - Google Patents

Abstract

The invention discloses a kind of Optimal Design of Pressure Vessel method based on self adaptation cuckoo Yu fireworks hybrid algorithm, belong to improvement and the application of intelligent optimization algorithm.On the one hand, the step-size in search of cuckoo can be adjusted according to the gap between current Bird's Nest and optimum Bird's Nest environment adaptive value, and the probability of detection of bird egg calculates according to the standard deviation of individual fitness, thus improves the search efficiency of population.On the other hand, burst radius in fireworks algorithm uses the method for " segmentation value ", the number of spark then determines according to fried point search scope, individual in search procedure can the current demolition point of perception and the gap of optimal value, enable fireworks operator jumping characteristic, trans-regional search.Two independent sub-populations evolved mutually are merged through fixing algebraically, strengthens the communication for information between Different Individual.The advantage that present invention incorporates two kinds of intelligent algorithms, in Optimal Design of Pressure Vessel, has good optimizing effect.

Description

A kind of Optimal Design of Pressure Vessel based on self adaptation cuckoo Yu fireworks hybrid algorithm Method

Technical field

The invention belongs to improvement and the application of intelligent optimization algorithm, relate to two kinds of novel adaptive optimization algorithms And cuckoo and the fireworks hybrid algorithm that multigroup parallel is evolved.

Background technology

Design of pressure vessels is always in optimized algorithm the difficulties of application, owing to the structure of container is complicated, affect because of The element more and feasible zone many factors such as irregularly, uses traditional optimized algorithm cannot obtain preferable structural parameters.Cause This, some intelligent algorithms are gradually applied in this problem, such as genetic algorithm, differential evolution algorithm；But it is as modern industry The development of technology, technical staff has a higher requirement for the precision of Vessel Design and error, and basic intelligent algorithm Cannot meet the demand of people, for solving problems, the more excellent novel intelligent algorithm of some performances is gradually carried Go out.

Hatching this natural phenomena of nestling by observing cuckoo parasitism, Cambridge University Xin-SheYang (Yang Xin society) teaches Award and proposed cuckoo algorithm with S.Deb in 2009；The inspiration aloft exploded by fireworks, Tan and Zhu of Peking University in Within 2010, propose fireworks algorithm.It is similar that cuckoo has largely theoretically with fireworks algorithm, and algorithm idea comes Come from phenomenon universal in nature, simulate individuality by computer programming language in feasible zone, find optimized value Process.But, basic cuckoo algorithm and fireworks algorithm are all a kind of greediness, random searching algorithm, can be preferably Solve function optimization problem higher-dimension, unimodal, but in basic intelligent algorithm evolutionary process, parameter is fixed, individual oneself Perception and learning capacity are relatively low, and for multimodal, multivariable object function, single algorithm cannot jump out local optimum Solve, and parameter fixing in algorithm arranges and also reduces the individual adaptability for different search environments, for some targets Function low optimization accuracy is the highest.For solve for multimodal, the optimization problem of multivariate object function, have scholar have employed both or Both above hybrid algorithms replace single intelligent algorithm, thus in succession propose heredity and Particle Swarm Mixed Algorithm, grain Subgroup and differential evolution hybrid algorithm etc., by achieving two kinds of individual ways of search, dexterously by two in same population The Dominant Facies of individual algorithm combines.

Cuckoo algorithm have employed the mode of Lay dimension flight and have updated individual information, makes cuckoo constantly explore optimum It is worth region that may be present, after successive ignition selects, the individual globally optimal solution that finally can determine function.Fireworks are calculated Method generates substantial amounts of Mars, the adaptive value of the most all Mars by fried point to space all directions, retains optimal fried point Position, constantly improves the optimal value of every generation population.By cuckoo is mixed mutually with fireworks algorithm, in same population Use two kinds of evolution environment, then entered the regular hour remix evolution select, both ensure that the independence of each algorithm, also Be conducive to the mutual supplement with each other's advantages between different population model of evolution.

Summary of the invention

The invention aims to the optimization design problem of pressure container, in two sub-populations, cuckoo is calculated Method and fireworks algorithm parallel running, retain respective evolution characteristic, prevent individuality to be absorbed in locally optimal solution, it is ensured that population is various Property.

Present invention employs self adaptation cuckoo and fireworks algorithm, parameters index in self-adaptative adjustment algorithm.Solve Method certainly specifically includes following step:

A kind of Optimal Design of Pressure Vessel method based on self adaptation cuckoo Yu fireworks hybrid algorithm, it is characterised in that Specifically include following steps:

Step one: by the mathematical modeling for pressure vessel, determine each variable affecting construction of pressure vessel performance And excursion, set up the object function that construction of pressure vessel optimizes；

The optimization design of pressure vessel is through regulating each structural parameters, obtains optimal container with minimum cost Performance, by for the functional relationship between pressure vessel parameter and performance, sets up following function model:

$\begin{array}{c}\min f\left(x\right)=0.6224x_1{x}_3{x}_4+1.7781x_2{x}_3^2+3.1661x_1^2{x}_4+19.84x_1^2{x}_3\\ \left\{\begin{array}{c}{g}_1\left(x\right)=-x_1+0.0193x_3\≤0\\ g_2\left(x\right)=-x_2+0.00954x_3\≤0\\ g_3\left(x\right)=-{\mathrm{\πx}}_3^2-\frac{4}{3}{\mathrm{\πx}}_3^2+1296000\≤0\\ g_4\left(x\right)=x_4-240\≤0.\end{array}\right.\end{array}---\left(1\right)$

In formula, x₁Represent the thickness of container inner wall, x₂Represent container rounded nose thickness, x₃For the internal diameter of head circular, x₄ Length for container cylindrical portion；In above formula, f (x) is required object function, and g₁(x)、g₂(x)、g₃(x)、g₄X () is ginseng The constraints of number；

Step 2: cuckoo and the initiation parameter of fireworks algorithm and population are set；

Initiation parameter: in cuckoo algorithm, step-size in search α, the detection probability P of cuckoo bird egg_α；In fireworks algorithm, The radius R of demolition point_i, the spark number M of demolition point_i, demolition point number of plies W；According to the object function dimension obtained in commercial production D, scale Np of population, individual maximum iteration time G_MAX, current iteration number of times t=0 is set, population is individual for i-th at t Body is represented by:

$X_i^t=(x_{i,1}^t,x_{i,2}^t,...,x_{i,D}^t),i=1,2,...,Np---\left(2\right)$

The feasible zone of the search of population is [X_min,X_max], the scope that regulation must be limited to of each dimension in individuality In；Initialization of population is:

$X_i^0=X_{min}+rand(1,Np)\×(X_{max}-X_{min}),i=1,2,...,Np---\left(3\right)$

Rand (1, Np) creates Np the uniform random number between (0,1) when algorithm runs；

Step 3: the population one of algorithm is divided into two sub-population N₁=Np/2, N₂=Np/2；Respectively by N₁And N₂Place (E in two completely self-contained evolution environment₁, E₂)；

Step 4: at evolution environment E₁In, population is carried out according to the basic procedure of cuckoo algorithm, including step 4.1～ Step 4.3:

Step 4.1: the present age, the position of cuckoo Bird's Nest wasI=1,2 ..., N₁, cloth Paddy bird finds Bird's Nest of future generation individual by Lay dimension formulaIt is achieved thereby that the random search to space；

Step 4.2: calculate the adaptive value of alternative Bird's Nest, compareWithAdaptive value, select adaptive value in two populations The individuality that ranking is forward, defines the new Bird's Nest of cuckooI=1,2 ..., N₁；

Step 4.3:In each Bird's Nest(i=1,2 ..., N₁, j=1,2 ..., D) all produce and be uniformly distributed Random number p_α, the probability that found by former Bird's Nest owner as cuckoo bird egg, if p_α＜ P_α, then illustrate that former host has discovered that Cuckoo bird egg, therefore, cuckoo needs the Bird's Nest that random searching is newBy contrastWithThe size of both adaptive values, Eliminate the Bird's Nest position being in a disadvantageous position；If p_α≥P_α, then cuckoo Bird's Nest does not changes；Finally, the position of cuckoo Bird's Nest obtains Arrive renewal, generate a new generation Bird's Nest position

Step 5: at evolution environment E₂In, sub-population is according to N₂Operate according to the flow process of fireworks algorithm, concrete such as step Rapid 5.1～step 5.4:

Step 5.1: for the object function optimization problem of D dimension, fireworks demolition pointi =1,2 ..., N₂, all directions in space, sequentially generate fried new Mars, the initial radium of every generation demolition point is R_i；

Step 5.2: fireworks operator outwards generates the Mars of W layer centered by fried point and explodes a little, the demolition point radius of each layer For jR_i/ W (j=1,2 ..., W)；With a fireworks demolition point for breeding parent, generate M_iIndividual sub-MarsThen demolition point is comparedWithOptimal value, so that it is determined that alternative fireworks kind of future generation Group

Step 5.3: due to the strategy using greediness to select, the gap between fireworks explode a little can be gradually lowered；For keeping planting The multiformity of group, randomly selects the individuality of 50% in fireworks population, adds differential variation operation, as follows:

${\stackrel{\‾}{U}}_i^{t+1}=\{\begin{array}{cc}{\stackrel{\‾}{S}}_i^{t+1}+p({\stackrel{\‾}{S}}_j^{t+1}-{\stackrel{\‾}{S}}_k^{t+1})& \begin{array}{cc}if& rand\≤0.5\end{array}\\ & i=1,2,...,N_2;\\ {\stackrel{\‾}{S}}_i^{t+1}& otherwise\end{array}t=1,2,...,G_{MAX}---\left(4\right)$

In above formula, p is equally distributed random number, and p ∈ (0,1), j, k be randomly choose from fireworks population Body, can not be identical between i, j, k；Created the random number being evenly distributed between (0,1) by rand, population has obtained part There is candidate's demolition point of new characterIf candidate's demolition point is beyond the scope of feasible zone simultaneously, should be again to original fried PointCarry out differential variation operation, until

Step 5.4: select operation, selectWithIn advantage individual, constitute novel population of future generationFireworks explode and a little utilize differential variation to achieve searching in the range of whole feasible zone Rope；

Step 6: the communication for information operation between sub-population；

During Evolution of Population, every 10 generations, by sub-population N₁And N₂Melting is a population N, arranges single evolution environment For E, individual to cuckooIndividual with fireworksAdaptive value be ranked up, record current optimized individual

Step 7: terminate inspection；Whether evaluation algorithm meets end condition, if t is < G_MAX, then step 2, and t=are returned t+1；Otherwise, algorithm terminates, and exports optimal value.

Advantages of the present invention and having the active effect that

1) have adjusted sub-population N₁The step-size in search of middle cuckoo Lay dimension flight, the individual and optimum according to the present age in population The adaptive value relative size of body, the amplitude that Automatic adjusument cuckoo jumps.When cuckoo is in population optimal location field, Individual cognition strengthens Local Search；When individual fitness differs greatly with optimal value, step-size in search will increase, filial generation and parent Between distance increase, population expands Search Range.

2) due to probability of detection antithetical phrase population N in cuckoo algorithm₁Multiformity and individual densely distributed degree have weight The impact wanted, therefore, the standard deviation of probability of detection Yu population is set up functional relationship by the present invention, and cuckoo individuality can be worked as in perception For the population distribution situation in space, it is automatically adjusted follow-on probability of detection, active balance population diversity and convergence speed Relation between degree.

3) method that in the present invention, the burst radius of fireworks algorithm uses segmentation value, contrasts previous improved procedure, just Beginning radius only uses a kind of adjustment modes, and this method take into account some multimodals, optimal value object function jumpy, respectively Time enough is had to carry out overall situation and partial situation's search in early stage and later stage, it is therefore prevented that algorithm evolution stagnation behavior.

4) be placed in two independent environment with fireworks individuality evolve individual for cuckoo respectively, remain simultaneously cuckoo and Fireworks explode optimizing mode a little.Simultaneously through 10 generations, two populations carry out communication for information rather than every generation all carries out population and melts Close, effectively reduce the complexity of algorithm, improve population diversity.

5) being inspired by other intelligent algorithm, in the present invention, in fireworks algorithm, individuality have employed differential variation mode, replaces Gaussian manner in basic fireworks algorithm, i.e. simplifies evolutionary process and too increases the purposiveness of individual selection, increase searching Probability to more excellent individuality.

6) optimization design problem that the present invention will utilize cuckoo and fireworks hybrid algorithm to preferably resolve pressure vessel, Hybrid algorithm maintains population diversity during evolution, and Search of Individual can be divided at feasible zone according to optimal value adaptively Cloth rule, adjusts the search emphasis of self；Being contrasted by basic cuckoo algorithm and fireworks algorithm, cuckoo mixes with fireworks Algorithm reduces Vessel Design cost, has obtained the higher container parameters of precision.

Accompanying drawing explanation

Fig. 1 is schematic flow sheet of the present invention.

Fig. 2 is radius change function model curve in fireworks algorithm.

Fig. 3 is self adaptation cuckoo and fireworks hybrid algorithm (SCSFWA), basic cuckoo algorithm (CS), basic cigarette The convergence curve figure of flower algorithm (FWA)；Wherein (a)～(j) respective function f respectively₁～f₁₀。

Fig. 4 is construction of pressure vessel figure.

Detailed description of the invention

Below in conjunction with the accompanying drawings the present invention is made further description.The present invention have employed self adaptation cuckoo and cigarette Flower hybrid algorithm, main purpose is the optimization design problem for pressure container.Basic intelligent algorithm for multimodal, Multivariate, higher-dimension object function low optimization accuracy low, individuality is easily absorbed in locally optimal solution, and the success rate of algorithm is low.The present invention ties Close two kinds of optimized algorithm-cuckoo algorithms the most novel, excellent effect and fireworks algorithm, improve the evolution of rudimentary algorithm Parameter and strategy, it is achieved that the mutual supplement with each other's advantages between two algorithms, improve convergence of algorithm performance.

Similar with the optimization design problem of pressure vessel, technical staff sums up substantial amounts of multimodal, many in various industries Variable, higher-dimension object function as follows:

Table 1 CEC2014 benchmark test function

In table 1, function has multiple local extremum in feasible zone, and between functional value, jumping characteristic is strong, but only one of which Globally optimal solution, according to basic optimized algorithm, such as climbing hill algorithm, genetic algorithm etc., optimal value precision is low even cannot Convergence.Optimization to this type of complicated function, needs algorithm to have high from heuristic power, whenever individuality is absorbed in locally optimal solution Time, population can adjust the parameter of self, promotes individuality to jump out locally optimal solution, keeps the multiformity of population.Therefore, employing is mixed Hop algorithm optimizes problems, can be blended by different search attributes, for single algorithm, cuckoo individual or Fireworks individuality all cannot avoid easily being absorbed in the deficiency of locally optimal solution, but both is combined, it is achieved that in two kinds of algorithms Individuality carries out random search in space parallel, increases the successful probability of algorithm.In the present invention, self adaptation cuckoo mixes with fireworks Hop algorithm is as it is shown in figure 1, concrete step is respectively as follows:

Step one: by the mathematical modeling for pressure vessel, determine each variable affecting construction of pressure vessel performance And excursion, set up the object function that construction of pressure vessel optimizes.

The optimization design of pressure vessel is through regulating each structural parameters, obtains optimal container with minimum cost Performance, the with reference to the accompanying drawings figure of pressure vessel in 4, set up following functional relationship between pressure vessel parameter and performance:

$\begin{array}{c}\min f\left(x\right)=0.6224x_1{x}_3{x}_4+1.7781x_2{x}_3^2+3.1661x_1^2{x}_4+19.84x_1^2{x}_3\\ \left\{\begin{array}{c}{g}_1\left(x\right)=-x_1+0.0193x_3\&le;0\\ g_2\left(x\right)=-x_2+0.00954x_3\&le;0\\ g_3\left(x\right)=-{\mathrm{\&pi;x}}_3^2-\frac{4}{3}{\mathrm{\&pi;x}}_3^2+1296000\&le;0\\ g_4\left(x\right)=x_4-240\&le;0.\end{array}\right.\end{array}---\left(1\right)$

In formula, x₁Represent the thickness of container inner wall, x₂Represent container rounded nose thickness, x₂For the internal diameter of head circular, x₄ Length for container cylindrical portion；In above formula, f (x) is required object function, and g₁(x)、g₂(x)、g₃(x)、g₄X () is ginseng The constraints of number.

Step 2: cuckoo and the initiation parameter of fireworks algorithm and population are set；

Initiation parameter: the step-size in search α of cuckoo, the detection probability P of bird egg_α, fireworks explode radius R a little_i, every generation In the Mars number M that generates of fried point_i, number of plies W of fried point.Required object function and dimension D, scale N of population_p, maximum enters Change algebraically G_MAX, order just initial algebra t=0, wherein in t generation, i-th individuality is represented by:

$X_i^t=(x_{i,1}^t,x_{i,2}^t,...,x_{i,D}^t),i=1,2,...,N_p---\left(2\right)$

Meanwhile, the hunting zone of population is [X_min,X_max], all individualities in the middle of population all should be limited to this feasible zone it In.Working as t=0, initialization of population is:

$X_i^0=X_{min}+rand(1,D)\&times;(X_{max}-X_{min}),i=1,2,...,Np---\left(3\right)$

Wherein, rand (1, D) be generation 1 × D dimension, between [0,1] equally distributed random number.In conjunction with in the present invention Accompanying drawing, in experiment, the initiation parameter fixed value of algorithm is: for all of object function G_MAX=1000；According in the present invention In table 1, test function and pressure vessel mathematical model, work as D=30, Np=45；Work as D=100, Np=100.

Step 3: the population one of algorithm is divided into two sub-population N₁=Np/2, N₂=Np/2；Respectively by N₁And N₂Place (E in two completely self-contained evolution environment₁, E₂)。

Step 4: at evolution environment E₁In, population is carried out according to the basic procedure of cuckoo algorithm, including step 4.1～ Step 4.3:

Step 4.1: the present age, the position of cuckoo Bird's Nest wasI=1,2 ..., N₁, cuckoo Bird finds Bird's Nest of future generation individual by Lay dimension formulaAs follows:

Wherein L é vy (λ) creates random walk, and its migration step-length is obeyed Lay dimension and is distributed:

L é vy (λ)～u=t^-λ, (1 ＜ λ≤3) (5)

Understand step-size in search α by above formula and control the amplitude of cuckoo individuality search, for the optimizing of Solving Multimodal Function, search Step-length then to adjust according to the change of cuckoo search condition at any time at any time, and therefore the adjustable strategies of step-length cannot be with a certain Plant function variation model to match, but need to change for the search procedure of different object functions is made at any time according to population Becoming, to this, the step-size in search regulation strategy of cuckoo algorithm is herein:

$step=\left|\frac{f_i-f_{best}}{f_{best}-f_{worst}}\right|---\left(6\right)$

$\mathrm{\&alpha;}=\stackrel{\&OverBar;}{\mathrm{\&alpha;}}\&CenterDot;step---\left(7\right)$

In formula, f_bestAnd f_wrostIt is respectively optimum individual and the adaptive value of worst individuality in population.WhereinFor certain value, In conjunction with accompanying drawing 1,Using the relative distance between current individual and optimum individual as feedback quantity, according to individuality in search Different conditions residing for during regulates step-size in search in real time, adds the efficiency of algorithm.When the individuality in population and optimum When body adaptive value difference is bigger, the Bird's Nest of future generation selected by cuckoo will increase individual for entirely away from parent Bird's Nest The dynamics of office's search.If the present age, individuality differed less with optimum individual adaptive value, cuckoo can lay particular emphasis on Local Search.In the past Cuckoo step-size in search adjust mode only with some fixing function models, such as linear function, exponential function etc., herein Step-size in search be adjusted not based on the algebraically evolved, but be adjusted according to individual being actually needed, improve Convergence of algorithm performance, is also that algorithm more has universality.

Step 4.2: calculate the adaptive value of alternative Bird's Nest, compareWithAdaptive value, select adaptive value in two populations The individuality that ranking is forward, defines the new Bird's Nest of cuckooI=1,2 ..., N₁。

Step 4.3: at the new Bird's Nest of cuckooIn, each is individualAll randomly generate a corresponding probability of detection p_α, If p_α＜ P_α, then the former host of Bird's Nest is found that cuckoo bird egg, cuckoo individuality then need to find a new Bird's Nest at random RelativelyWithThe size of adaptive value, finds optimum Bird's Nest composition cuckoo next generation population.If p_α≥P_α, then former place is described Main discovery cuckoo bird egg, Bird's Nest invariant position.

Therefore, cuckoo Bird's Nest arranges the main purpose of probability of detection and is introduced into external Bird's Nest, prevents population to be absorbed in local Optimal solution, increases population diversity.Basic cuckoo algorithm probability of detection is definite value, and conventional improvement cuckoo algorithm uses The function model successively decreased, enables population global search in the early stage, and the later stage focuses on Local Search.The present invention is by cuckoo algorithm Individual fitness standard deviation be connected with probability of detection, specific strategy is as follows:

$std\left(S_i^t\right)=\sqrt{\frac{1}{N_1}\left({\mathrm{\&Sigma;}}_{j=1}^{N_1}{\left(fitness\left(s_j^t\right)-\mathrm{\&mu;}\right)}^2\right)}---\left(8\right)$

$P_{\mathrm{\&alpha;}}=1-\frac{std\left(s_j^t\right)}{max\left(std\right(s_i^t\left)\right)},,t=1,2,...,G_{MAX},i=1,2,...,N_1---\left(9\right)$

In above formula, μ is the t average environment adaptive value for individualities all in population,Represent algorithm The maximum standard deviation that recorded in evolutionary generation in the past.By calculating the standard deviation of every generation population, every generation population is owned by One optimum probability of detection, this regulative mode achieves and defines one between individual probability of detection and population diversity Closed loop control.When more disperseing between individuality, Population adaptation value standard deviation is relatively big, and cuckoo bird egg probability of detection is less, outward The probability that the random Bird's Nest come adds population of future generation is less, accelerates the speed of algorithmic statement；If concentration class is relatively between individuality Good, population norms difference is less, and the probability of detection of bird egg is relatively big, and cuckoo then can focus on the search for whole space, improves Population diversity.Therefore, using Population adaptation value standard deviation as feedback quantity, make Search of Individual more have motility, according to kind The search situation of the every generation of group, is automatically adjusted bird egg probability of detection, improves the precision of object function optimal value.

Step 5: at evolution environment E₂In, sub-population is according to N₂Operate according to the flow process of fireworks algorithm, concrete such as step Rapid 5.1～step 5.4:

Step 5.1: the fried point of fireworks is represented byI=1,2 ..., N₂, by N in space₂ Individual fried point generates Mars to D direction within respective territory, and the initial radium of every generation demolition point is R_i, wherein explode Point initial radium R_iIt is the key factor affecting fireworks algorithm search efficiency, for taking into account algorithm optimal value precision and convergence rate, Fried point should cover inside global scope in the algorithm starting stage as far as possible, and at later stage of evolution, the radius of fried point then to keep less Numerical value, strengthens for the search in locally optimal solution contiguous range, and therefore, the radius employing segmentation that in the present invention, fireworks explode a little takes Value:

$R_i=\left\{\begin{array}{cc}{R}_{\max },& t\&le;\frac{G_{MAX}}{3}\\ \hat{R}{(t-\frac{2G_{MAX}}{3})}^2+R_{\min }& \frac{G_{MAX}}{3}<t\&le;\frac{2G_{MAX}}{3}\\ R_{\min }& t>\frac{2G_{MAX}}{3}\end{array}\right.---\left(10\right)$

Wherein, R_max, R_minFor the maximum of fried some radius,It is a constant, in the present invention, R_max=10, R_min= 0.0001, andUnderstand in conjunction with function of radius change curve in accompanying drawing 2, fried point the algorithm initial stage with And the later stage is definite value, thus ensure that the time of individual overall situation and partial situation search, improve the precision of optimal value.In the algorithm Phase, the radius of demolition point is gradually lowered, it is achieved that individual gradually transition from global search to local optimal searching, enables individuality to exist The different phase of population adjusts the hunting zone of Mars.

Step 5.2: in fireworks algorithm, individual blast produces the Mars (W=D in experiment) of W layer, the blast of each layer of Mars Radius be jr/W (j=1,2 ..., W), centered by fried point, in territory generate M_iIndividual MarsCalculateWithIn the optimal value of each individuality being ranked up, select N₂Individual optimum Individual alternative fireworks population of future generation

During fried point generates Mars, the number of Mars should determine according to individual search capability, therefore, and M_iCalculate public affairs Formula is as follows:

Wherein, R_iFor currently exploding the initial radium of point,For the maximum radius value that recorded in algorithm running,For in definite value, this experimentMars number more determines according to the search radius of fried point, it is to avoid different The overlap of Mars between body, decreases the useless demolition point of algorithm, it is ensured that individuality is uniformly distributed for different search volumes, carries High algorithm search efficiency.

Step 5.3: choose the advantage individuality in Mars and replace the parent individuality that adaptive value is relatively low, the evolution plan of this greediness Slightly can reduce the multiformity of population.For increasing the distance between fireworks individuality, the present invention adds differential variation operation, specifically Method is as follows:

${\stackrel{\&OverBar;}{U}}_i^{t+1}=\{\begin{array}{cc}{\stackrel{\&OverBar;}{S}}_i^{t+1}+p({\stackrel{\&OverBar;}{S}}_j^{t+1}-{\stackrel{\&OverBar;}{S}}_k^{t+1})& \begin{array}{cc}if& rand\&le;0.5\end{array}\\ & i=1,2,...,N_2;\\ {\stackrel{\&OverBar;}{S}}_i^{t+1}& otherwise\end{array}t=1,2,...,G_{MAX}---\left(12\right)$

Wherein, p is the uniform random number between [0,1], and j, k are that the inequality randomly choosed in population is individual, i ≠ J, i ≠ k, the purpose adding differential variation operation is to introduce the individuality with brand-new character, prevents algorithm to be absorbed in Excellent solution

Step 5.4: select operation；By comparingWithAdaptive value size, choose optimum individual and constitute down A generation explodes position a little

Step 6: the communication for information between sub-population；

In two independent evolution environment, cuckoo algorithm and fireworks algorithm all maintain respective Evolution.For Strengthen the communication for information of whole population, every 10 generations, by sub-population N₁And N₂Merge and carry out selecting operation in an environment, will Currently available optimum individual adaptive value is as the history optimal solution of each population.

Step 7: terminate inspection；

Whether evaluation algorithm can terminate, if t is < G_MAX, then step 2, t=t+1 are returned；Otherwise, then algorithm terminates, output Optimal solution.

The above be self adaptation cuckoo and fireworks hybrid algorithm institute in steps with principle.For the test present invention calculates The effectiveness of method, tests FWA algorithm, CS algorithm and SCSFWA algorithm test function in Table 1, each survey respectively Trial function carries out 50 groups of experiments respectively, and statistics often organizes average optimal value and the standard deviation of experiment, as shown in table 2:

The average optimal value of 2 three kinds of algorithms of table and standard deviation

Accompanying drawing 3 have chosen algorithmic statement curve representative in often group experiment；The experiment knot of contrast CS, FWA algorithm Really, SCSFWA algorithm improves the order of magnitude of optimal value precision, it is therefore prevented that algorithm has been absorbed in locally optimal solution, for evolving not Dynamically regulating the individual direction of search with zone algorithm according to the search condition of population with the stage, the versatility of algorithm is stronger.

Being applied in the optimization design problem of pressure vessel by above-mentioned three kinds of algorithms, the structural parameters of container are as follows:

The pressure vessel parameters optimization that 3 three kinds of algorithms of table obtain

Algorithm	x1	x2	x3	x4	g(x1)	g(x2)	g(x3)	g(x4)	f(x)
										FWA	12.56	6.871	500.8	7.222	-2.909	-2.093	-5.42e+05	-232.7	4.66e+06
CS	9.058	5.469	461.8	9.507	-0.144	-1.063	-2.67e+05	-230.4	2.85e+06
										SCSFWA	8.657	5.760	420.5	7.218	-0.541	-1.748	-2.47e+02	-232.7	2.45e+06

In sum, SCSFWA algorithm, with minimum cost, has obtained optimal structural parameters, has improve pressure vessel Structural behaviour.

Claims (5)

1. an Optimal Design of Pressure Vessel method based on self adaptation cuckoo Yu fireworks hybrid algorithm, it is characterised in that tool Body comprises the steps:

Step one: by the mathematical modeling for pressure vessel, determine affect construction of pressure vessel performance each variable and Excursion, sets up the object function that construction of pressure vessel optimizes；

The optimization design of pressure vessel is through regulating each structural parameters, obtains optimal container with minimum cost Can, by for the functional relationship between pressure vessel parameter and performance, set up following function model:

In formula, x₁Represent the thickness of container inner wall, x₂Represent container rounded nose thickness, x₃For the internal diameter of head circular, x₄For holding The length of device cylindrical portion；In above formula,For required object function, andFor The constraints of parameter；

Step 2: cuckoo and the initiation parameter of fireworks algorithm and population are set；

Initiation parameter: in cuckoo algorithm, step-size in searchThe probability of detection of cuckoo bird eggIn fireworks algorithm, blast The radius R of point_i, the spark number M of demolition point_i, demolition point number of plies W；According to the object function dimension D obtained in commercial production, plant Scale Np of group, individual maximum iteration time G_MAX, current iteration number of times t=0 is set, population can table for i-th individuality at t It is shown as:

The feasible zone of the search of population is [X_min, X_max], in individuality, each dimension must limit within the limits prescribed； Initialization of population is:

Rand (1, Np) creates Np the uniform random number between (0,1) when algorithm runs；

Step 3: the population one of algorithm is divided into two sub-population N₁=Np/2, N₂=Np/2；Respectively by N₁And N₂It is placed on two (E in completely self-contained evolution environment₁,E₂);

Step 4: at evolution environment E₁In, population is carried out according to the basic procedure of cuckoo algorithm, including step 4.1 ~ step 4.3:

Step 4.1: the present age, the position of cuckoo Bird's Nest was Cuckoo Bird's Nest of future generation is found individual by Lay dimension formulaIt is achieved thereby that the random search to space；

Step 4.2: calculate the adaptive value of alternative Bird's Nest, compareAdaptive value, select adaptive value ranking in two populations Forward individuality, defines the new Bird's Nest of cuckoo

Step 4.3:In each Bird's NestAll produce and be uniformly distributed Random number, the probability that found by former Bird's Nest owner as cuckoo bird egg, ifThen illustrate that former host has been found that Cuckoo bird egg, therefore, cuckoo needs random to find new Bird's Nest, by contrastWithBoth adaptive values big Little, eliminate the Bird's Nest position being in a disadvantageous position；IfThen cuckoo Bird's Nest does not changes；Finally, cuckoo Bird's Nest Position is updated, and generates a new generation Bird's Nest position

Step 5: at evolution environment E₂In, sub-population is according to N₂Operate according to the flow process of fireworks algorithm, concrete such as step 5.1 ~ step 5.4:

Step 5.1: for the object function optimization problem of D dimension, fireworks demolition point All directions in space, have sequentially generated fried new Mars, and the initial radium of every generation demolition point is R_i；

Step 5.2: fireworks operator outwards generates the Mars of W layer centered by fried point and explodes a little, and the demolition point radius of each layer isWith a fireworks demolition point for breeding parent, generate M_iIndividual sub-MarsThen demolition point is comparedWithOptimal value, so that it is determined that alternative fireworks kind of future generation Group

Step 5.3: due to the strategy using greediness to select, the gap between fireworks explode a little can be gradually lowered；For keeping population Multiformity, randomly select the individuality of 50% in fireworks population, add differential variation operation, as follows:

In above formula, p is equally distributed random number, andIt is the individuality randomly choosed from fireworks population,i, j, kBetween can not be identical；Pass throughrandCreating the random number being evenly distributed between (0,1), population has obtained part to be had Candidate's demolition point of new characterIf candidate's demolition point is beyond the scope of feasible zone, should be again to original fried point simultaneously Carry out differential variation operation, until

Step 5.4: select operation, selectIn advantage individual, constitute novel population of future generationFireworks explode and a little utilize differential variation to achieve the search in the range of whole feasible zone；

Step 6: the communication for information operation between sub-population；

During Evolution of Population, every 10 generations, by sub-population N₁And N₂Melting is a population N, and arranging single evolution environment is E, Individual to cuckooIndividual with fireworksAdaptive value be ranked up, record current optimized individual

Step 7: terminate inspection；Whether evaluation algorithm meets end condition, ifThen return step 2, andt=t+1； Otherwise, algorithm terminates, and exports optimal value.

2. Optimal Design of Pressure Vessel method based on self adaptation cuckoo Yu fireworks hybrid algorithm as claimed in claim 1, It is characterized in that, in step 3.1, cuckoo finds Bird's Nest of future generation by Lay dimension flight, as follows:

WhereinFor step-size in search,For Lay dimension distribution；Cuckoo algorithm search step-length can adapt to according to current individual The change of value adjusts at any time, as follows:

WhereinFor the optimal value of adaptive value, worst-case value in contemporary populationFor certain value,stepIt is to weigh current bird The tolerance of gap between nest and optimum Bird's Nest.

3. Optimal Design of Pressure Vessel method based on self adaptation cuckoo Yu fireworks hybrid algorithm as claimed in claim 1, It is characterized in that, described step 3.3 sets a random number for each Bird's NestCuckoo bird is found as former host The probability of egg；Therefore, the probability of detection of algorithm initialization phase setsControl the external Bird's Nest influence degree for population, By suitable regulationThe dispersion degree between individuality can be changed；General in the standard deviation of contemporary population and the discovery of cuckoo Following functional relationship is established between rate:

WhereinFor adaptive value individual average in population,For in the previous evolutionary process of kind of group records, the maximum of appearance Standard deviation, this parameter is determined by the relative standard deviation between evolutionary generation, enables individuality to divide in space according to optimal value Cloth situation changes probability of detection at any time.

4. Optimal Design of Pressure Vessel method based on self adaptation cuckoo Yu fireworks hybrid algorithm as claimed in claim 1, It is characterized in that, the initial radium R of step 4.1 fireworks demolition point_iSegmentation value is used to be adjusted, fried some M_iThen with self Region of search size set rational numerical value；The demolition point radius of fireworks algorithm and number according to the different evolution time periods, Different changing patteries is set, as follows:

In above formula, R_max、R_minIt is respectively the maxima and minima of fried some radius,For constant, it is present to ensure that the company of function Coherence, for different algorithm parameters, value is the most different；For certain value,Represent fried some radius maximum in population.

5. Optimal Design of Pressure Vessel method based on self adaptation cuckoo Yu fireworks hybrid algorithm as claimed in claim 1, It is characterized in that, step 5 is by sub-population N₁And N₂It is mixed into a population N every 10 generations, promotes between two Different Individual Communication for information；For all of individualityCalculate corresponding adaptation Value, the optimal value of record population, and as N₁And N₂History optimal value when two sub-populations are independently evolved.