Apply genetic algorithm to undertake inclined dish model cylinder body of pump of axial force plunger optimizes a design

Keywords:O1 〕 of 〔 of algorithm of heredity of foreword of Algorithms1 of 　 of Ptimization 　 Genetic (Genetic Algorithms:GA) searchs algorithm randomly as a kind, optimize methodological photograph to compare with the tradition, be immersed in not easily in searching a process local and best, although the function in place definition is discontinuous, be not regulation or below the case that has noise, it also can find whole with very big probability optimum solution, because this is optimized in combination,waited for a lot of domains to receive successful application. It is contemporary that machinery optimizes a design the main component in optimizing a design, but, genetic algorithm optimizes the application in the design to get however in machinery very big limitation. Because machinery optimizes the problem in the design to restrain problem of solid parameter optimization to have normally,this basically is, and the common encode means of genetic algorithm is binary encode means. In the binary system encode expresses in, the case with particular length is strung together to fall in its, larger variable change area can cause a binary system denotive precision is insufficient, and express precision to improve a binary system, use more, can make algorithmic rate falls however. Both contradiction caused applied difficulty. So, the research that has tie optimization problem to solid parameter is one of difficulty of genetic algorithm. The article made abecedarian exploration in the light of the problem above, the problem translate into that tries to use castigatory function to will have a tie does not have obligation issue, used float check the number to state method and its corresponding genetic functor are operated in genetic algorithm, avoided to adopt the to expressing precision restriction that the binary system codes place is brought about thereby. It is a foundation with this, in the light of inclined dish model structure of cylinder body of pump of axial force plunger optimized design problem to undertake study, achieved satisfactory result. The genetic and algorithmic 　 that 2 have tie optimization problem (the construction of 1) chromosome normally, when using genetic algorithm, the binary code that has should undertake the binary system is changed not only, and expressive precision also can be restricted, assume there is X of variable of a design only in optimizing a design. Its upper limit is A, floor level is B, with the binary system denotive precision is (a length) that A-B)/n(n strings together for the binary system. Be like A-B=1cm, criterion Q=1/ncm. When N=8, q=0.

125cm; When N=16, q=0.

0625cm, when N=32, q=0.

03125cm. This shows, use a binary system to string together state a design is variable, although its string together length to achieve 32, also cannot achieve mechanical design 0 common.

The precision of 01 asks, and this is designing the issue in variable more the meeting is more outstanding. To solve this one problem, the article uses float check the number to show plan directly. Express in float check the number in, each generation member is to use chromosome to express, chromosome is parameter vector =(x1, x2, ... , xm) ∈ Rm, among them wait for a gene Xi to all be real number. The precision of notation of float check the number relies on the computer, but express to be gotten high than the binary system generally speaking much. In addition, float check the number can represent very old district, and below the case with length is strung together particular in the binary system, of area dimensions add congress to cause a binary system denotive precision drops. (Of 2) evaluation function choose machinery to optimize what the design often has a tie to optimize a design. The design is optimized in what have a tie in, should find a feasible solution and finding a best solution is same difficulty almost. To necessary information never is obtained in feasible solution, introduce castigatory function to will obligation issue translate into does not have obligation issue. Consideration tie is the least turn an issue, its form is Min G(x) , and make Bj(x) ≥ 0, j=1, 2, ... , m. it translate into does not have tie form. In construct namely and seeking form: 　 of P(x)(2)(3) (4)(5) of · of F(x)=G(x) of MaxF(x)(1) 　 　 among them, k and β are invariable: When G ＞ 0 when, β =1; When G  0 when, β =-1. P(x) is the castigatory function that violates an obligation, g(x) is the quality that magnanimity sees. In the computational process that gets used to a value, introduced at the same time get used to mechanism of value scale commutation, if primary function is F, scale gets used to function to be U, exponential scale commutation satisfies relation: *F) of β of U(F) ＝ Exp(- , from the watch 1 with the watch the 2 effect that can see exponential scale alternates: There are 6 to string together in the group, among them those who string together get used to a value very big. Undertake β =0 now.

The exponential scale of 01 alternates, the value after primary value and commutation sees a table 1, can discover difference of the group after classics commutation is narrow. Express =0 of 1 　 β .

01 when get used to value and scale commutation value to get used to a value formerly (F)20087654 scale gets used to a value (U)2.

7181.

0411.

0361.

0301.

0251.

There are 6 to string together in 020 groups, their get used to a value to be close to relatively. Undertake β =0 now.

The exponential scale of 1 alternates, the value after primary value and commutation sees a table 2. Can discover difference of the group after the course alternates is narrow. Express =0 of 2 　 β .

1 when get used to value and scale commutation value to get used to a value formerly (F)987654 scale gets used to a value (U)90553320127 is visible, get used to those who be worth mechanism of exponential scale commutation to introduce, because the group is medium,can searching initial phase in order to prevent on one hand few individual and opposite at great majority individual and character adaptability is first-rate and the premature astringent of generation, can entangle in order to prevent in search on one hand later period because of the group what get used to a value on average to be close to Yu Qun body is best the competition that get used to a value and produces disappears. (3) genetic functor operates 　 ① selection rule. The action of selection rule is a current group medium individual by with get used to a value proportionate probability duplicates in new group. Connecting general reason condition to fall, use roulette to choose a mechanism, its are main move is as follows: A.

Calculate what all chromosome in the group get used to a value to mix: B of 　 of 　 of S= Σ Fi.

Computation is worth M=RAND(O randomly, s) . C.

From inside the group number begins for the chromosome of 1, suit its value and succeed chromosome to get used to value addition mediumly, until cumulative and be more than or be equal to M. The chromosome that adds finally wants the chromosome of the choice namely. ② cross is regular. Because used floating-point to count encode program, accordingly, its cross functor and the mutation functor below must have numeric characteristic. The definition of cross functor is the linear combination that seeks two vector, namely if the individual Sv of T generation is mixed Sw cross, the filial generation that produces is: Mutation of ③ of 　 of 　 of St+1w=aStv+(1-a)Stw(7) of St+1v=aStw+(1-a)Stv(6) 　 　 is regular. Mutation functor definition is: If T generation is individual,be Xi=(V1, ... , vn) , criterion every heft Vk is identical have variation with probability, the eventuate that mutates (V1, ... , vk ′ , ... , vn) , n of ≤ of 1 ≤ K, the value of Vk presses random means decides the face: (Δ of 　 of 8) 　 (T, 〕 of Y)=y 〔 1-r(1-t/T)*b (9) among them, LB and UB are K respectively the or so group that joins variable definition region, r is 〔 0, the random number on 1 〕 , t is the biggest algebra in genetic algorithm. (4) stops criterion heredity algorithm already iteration beforehand the algebra of buy, perhaps achieved satisfactory result. 3 inclined dish model the GA algorithmic 　 that cylinder body of pump of axial force plunger optimizes a design (1) is inclined dish model the mathematical model that cylinder body of pump of axial force plunger optimizes a design is inclined dish model one of main breed that pump of axial force plunger is pump, its function that optimizes a design to ask to satisfying pump (below intensity of the Q) that discharge an amount and the premise that stiffness asks, make the structure of pump compact as far as possible (namely volume is minor, quality is light, with material little) . Accordingly it is problem of optimization of variable of a many design, much tie, solid parameter. According to bibliographical reference 〔 the cylinder body of 3 〕 earning designs theoretical model, can build as follows optimize a model (its structure and parameter see graph) : Design variable is taken for (function of target of 10) 　 is 〔 of 　 F(X)=Vc= π (D2-d21)(l+ Δ L-zx21l) 〕 / 　 of 4-zs0 Δ L(11) begs those who take F(X) the least value Min F(X) . In type: D=2R+2 δ + δ of =min(of δ of X1 　 　 1, 1=2Rsin(π of δ of 　 of δ 2) 　 / β of R=4qth/(zx1tg of 　 of 　 of 2=R-x1/2-d1v/2 of δ of Z)-x1 　 　 ) condition of strength of cylinder body of condition of tie of sketch map of parameter of structure of cylinder body of H of △ of Max+ of β of 2Rtg of ＋ of 　 　 L=x2 is: (Condition of stiffness of cylinder body of 12) 　 is: (Aperture of 13) 　 crock and condition of strength of force plunger contact are: The biggest opposite sliding velocity restrains force plunger of 　 of 0(14) of ≤ of 〕 of G3(X)=2Frl/x1- 〔 P condition: 　 of 0(15) of ≤ of 〕 of Max of υ of 〔 of Max/30- of β of G4(X)=R π Ntg is than power condition: Maxsin75 ° of β of 75tg of ＝ of φ of G5(X)=R(π N/30)(2/x1)(Frl) - 　 of 0(16) of ≤ of 〕 of 〔 P υ is assure geometrical length D, ll, δ must restrain a condition for what be worth and arise: 　 of 0(19) of ≤ of δ of G8(X)=- of 　 of 　 of 0(18) of ≤ of G7(X)=-x2 of 　 of 　 of G6(X)=-x1 ≤ 0(17) is assure denominator be more than from beginning to end 0 and the tie condition of generation: 　 of 　 of 0(20) of ≤ of Max of β of G9(X)=f(3L0/x2-2+ll/x2)sin β Max-cos (the genetic algorithm that the genetic and algorithmic cylinder body that 2) cylinder body optimizes a design optimizes a design is as follows: Step 1 initialization inputs parameter: Force plunger counts Pc of Z 　 algorithmic parameter, pm, pop_size, generation of Step 2 of Max_gen 　 　 is initiative kind group. Step 3 is calculated 　 ① presses the 　 of evaluation value I=1 of each chromosome correspondence of 2 (the castigatory function law in 3) and get used to value scale to alternate the mechanism is calculated of a chromosome get used to value F1. ② I=I+1, be like I ＞ Pop_size, turn to Step4; The Step4 of ① 　 　 that turns to Step3 otherwise suspends standard: Satisfy one of following requirements, algorithmic stop: ① iteration counts ＞ Max_gen; 　 of ε of ② Ft+1-ft ＜ turns to Step5 otherwise. Step5 chooses to use of 2 (the roulette of 3) ① chooses a mechanism. Step6 cross is used of 2 (regulation of 3) ② cross undertakes cross. Step7 mutation is used of 2 (the mutation regulation of 3) ③ has variation. Turn to Step3 next. 4 computation reach his to analyse the move according to above as a result, obtained a list the computational result of 3: Watch 3 optimize 2(cm)Frl(kN)71 of δ of 1(cm) of result Zd(cm)l1(cm)Vc(cm)R(cm)l(cm)D(cm) δ .

604.

28289.

32.

806.

608.

／ of 50 ／ ／ 51.

784.

10425.

83.

086.

409.

781.

840.

920.

3461.

683.

87316.

22.

886.

048.

971.

200.

765.

6571.

603.

69248.

12.

745.

778.

410.

780.

675.

1081.

493.

58231.

22.

765.

688.

260.

620.

744.

5091.

383.

50231.

12.

865.

668.

250.

580.

893.

97 analysises express 3 medium data, the conclusion that can reach as follows: (1) expresses the metabolic concern of 3 medium Vc and D, accord with the conclusion that reachs in 3 〕 of bibliographical reference 〔 : Inside the interval of 2cm of ＜ of 0 ＜ D, of D tiny increase can make Vc is reduced very quickly. (2) optimizes those who use the Vc that genetic algorithm gets the value that algorithm of useful and random search gets 3 〕 of value and bibliographical reference 〔 tries to compare, can discover former excel is latter, the watch understands genetic algorithm to have the characteristic that overall situation optimizes in searching a process, palpability of farther also watch uses genetic algorithm at solid parameter, having tie optimization problem is feasible. (The cross functor that the two vector linear that 3) counts encode program to use floating-point and uses combines has height to mode destroy effect. Put forward to use functor of two kinds of cross in 2 〕 of bibliographical reference 〔 , use the cross of linear combination with the probability of 50% namely, the probability of 50% uses solid region cross, to the effectiveness of this kind of method, still remain at further research. CNC Milling CNC Machining