CN105631093A - M-BSWA multi-target optimization based mechanical structure design method - Google Patents

Abstract

The invention discloses an M-BSWA multi-target optimization based mechanical structure design method and belongs to the technical field of mechanical design. The method comprises the following steps of 1, establishing a mathematical model for multi-target optimization design of a mechanical structure; 2, performing sampling by adopting an orthogonal experimental design method; 3, constructing a radial basis function agent model; 4, determining the precision of an evaluation agent model; 5, designing a multi-target optimization algorithm M-BSWA for solving an optimization problem; and 6, verifying the validity of an optimization result. The method is suitable for the multi-target optimization design of the mechanical structure, and the distribution of obtained mechanical structure parameters is more reasonable, so that the designed mechanical structure is better in performance; and a numerical calculation method is adopted, so that the calculation speed is high, the design cycle can be greatly shortened, and the purpose of improving comprehensive performance of the mechanical structure is achieved on the premise of not increasing the overall weight of the mechanical structure.

Description

A kind of Design of Mechanical Structure method based on M-BSWA multiple-objection optimization

Technical field

The invention belongs to Optimal Design of Mechanical Structure technical field, be specifically related to a kind of Design of Mechanical Structure method based on M-BSWA multiple-objection optimization.

Background technology

Optimal Design of Mechanical Structure refers on existing design basis, by optimizing process, makes design parameter to more excellent direction adjustment, until finding the most rational design within constraints scope. Compared with traditional optimization design, modern optimization design, with numerical value rationale for instructing, carries out optimizing in whole design domain, it is possible to quickly obtains design, and judges that gained scheme is good and bad, finally optimum scheme comparison in numerous schemes. Because of the method adopting numerical computations, save the design time, reduce cost.

Producing optimization problem in reality is often multi-objective optimization question, it is generally conflicting between the multiple sub-goals in multi-objective optimization question, the improvement of one target likely causes another one or the reduction of multiple sub-goal performance, that is multiple optimization aim can not reach optimum simultaneously, how to balance the relation between each performance indications, obtain the most rational optimizing design scheme, be the main task of multiple-objection optimization. " optimization " is the eternal topic in engineering design, how to design multi-objective optimization algorithm fast and effectively, thus the optimization method building frame for movement is the basis solving Practical Project problem.

Summary of the invention

The present invention considers the multinomial performance index of frame for movement, for instance the weight of the structure in lightweight problem, volume; Maximum energy absorption in collision problem, maximum deformation quantity, peak value crushing force etc. The present invention proposes a kind of Design of Mechanical Structure method based on multiple-objection optimization can taken into account simultaneously consider multiple structural behaviour indexs.

A kind of Design of Mechanical Structure method based on M-BSWA multiple-objection optimization of the present invention comprises the following steps:

1. set up the mathematical model of frame for movement multi-objective optimization design of power, comprise the following steps:

1.1 set up the initial cad model of frame for movement;

1.2 selected design variables, optimization object function and constraints;

1.3 mathematical modeies setting up frame for movement, its mathematic(al) representation is:

$\left\{\begin{array}{c}\begin{array}{c}\min F\left(x\right)=\[f_1\left(x\right),f_2\left(x\right),...,f_n\left(x\right)\];\\ X=(x_{1,}{x}_{2,}...,x_l);\end{array}\\ \begin{array}{cc}& x_i\≤x_i\≤{\stackrel{\‾}{x}}_i,i=1,2,...,l;\\ s.t.& {\stackrel{\‾}{h}}_j\left(x\right)\≤0,j=1,2,...,m;\\ & h_j\left(x\right)=0,j=m+1,m+2,...,k;\end{array}\end{array}\right.$

In formula: f₁(x),f₂(x),...,f_nX () represents the object function relevant with frame for movement performance; N is object function number; (x_1,x_2,...,x_l) represent design variable;Represent Design of Mechanical Structure scope; L is Design of Mechanical Structure variable number; h_j(x)��0,h_jX ()=0 represents the inequality constraints condition and equality constraint that should meet in concrete frame for movement optimization respectively;

2. adopt the sampling of orthogonal (DOE) method, including choosing empirical factor, orthogonal table level;

3. structure RBF agent model;

4. determining evaluation agent model accuracy, the mathematic(al) representation of the test point evaluation index adopted is:

$R^2=\frac{\underset{i=1}{\overset{M}{\Σ}}{({\hat{y}}_i-{\stackrel{\‾}{y}}_i)}^2}{\underset{i=1}{\overset{M}{\Σ}}{(y_i-{\stackrel{\‾}{y}}_i)}^2}$

$R_{adj}^2=\frac{1-\underset{i=1}{\overset{M}{\Σ}}{(y_i-{\hat{y}}_i)}^2(M-1)}{\underset{i=1}{\overset{M}{\Σ}}{(y_i-{\stackrel{\‾}{y}}_i)}^2(M-k-1)};$

In formula: R is factor of determination; R_adjFor adjusting factor of determination; M is number of samples; K is the number of design variable;It is illustrated respectively in the measured value of test point place Simulation Calculation, meansigma methods and predictive value; When factor of determination and adjustment factor of determination are closer to 1, Response Face Function and the agent model precision of structure are more high. Work as R²>=99.8%, R_adjWhen >=99.5%, the agent model of structure meets design requirement;

5. design is for the multi-objective optimization algorithm M-BSWA of solving-optimizing problem, comprises the following steps:

Multi-objective optimization question is converted into single-object problem by quadratic sum weighting method by 5.1, and its mathematic(al) representation is:

$\min f\left(x\right)=\stackrel{n}{\mathrm{\Σ}}{w}_i{\[f_i\left(x\right)-f_i^{*}\]}^2$

In formula: f_iX () represents object function, n is the number of object function; f_i ^*Optimal solution for each object function; w_iFor weight coefficient, $\underset{i=1}{\overset{2}{\Σ}}{w}_i=1,w_i>0;$

5.2 with Lagrangian multiplier method [see: Yuan Yaxiang. nonlinear optimization computational methods. [M] Beijing Science Press, 2008] the constrained optimization problem in step 1.5.1 is converted into unconstrained optimization problem, build following Lagrangian function:

$L(\stackrel{\→}{x},\mathrm{\λ},\mathrm{\α},\mathrm{\β})=f\left(x\right)+\stackrel{m}{\mathrm{\Σ}}{\mathrm{\λ}}_j{h}_i\left(x\right)+\stackrel{l}{\mathrm{\Σ}}{\mathrm{\α}}_i(x_i-x_i)+\stackrel{l}{\mathrm{\Σ}}{\mathrm{\β}}_i(x_i-{\stackrel{\‾}{x}}_i);$

In formula: ��_j,��_i,��_iFor Lagrangian multiplier;

5.3, after step 5.2 and step 5.3 process, set up the mathematical model of unconstrained optimization problem, and its mathematic(al) representation is:

$\left\{\begin{array}{c}X={(x_1,x_2,...,x_l)}^T;\\ \min L(\stackrel{\→}{x},\mathrm{\λ},\mathrm{\α},\mathrm{\β})=f\left(x\right)+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\λ}}_j{h}_i\left(x\right)+\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\α}}_i(\underset{-}{x_i}-x_i)+\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\β}}_i(x_i-{\stackrel{\‾}{x}}_i);\\ f\left(x\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_i{\[f_i\left(x\right)-f_i^{*}\left(x\right)\]}^2;\\ \underset{i}{\overset{n}{\Σ}}{w}_i=1,w_i>0;\end{array}\right.$

In formula: X is the vector of design variable composition;For the Lagrangian function constructed by Lagrangian multiplier method;

5.4 with M-BFGS Quasi-Newton algorithm [see: the Huanghai Sea, Lin Suihua. the comparison of several modified Rodrigues parameters. [J] Mathematics Research, 2011] calculate the iterative estimate value of design variable, the Iteration of M-BFGS Quasi-Newton algorithm is:

x_k+1=x_k+��_kd_k

In formula: ��_kSearch is step-length, is determined by Armijo inexact linear searching;

d_kFor the direction of search, it may be assumed that

In formula:For Hessian matrix approximate of jth object function,For the derivative of jth object function,For weighter factor;

5.5 adopt matlab instruments to step 5.1,5.2 and 5.3 formed be encoded programming for the multi-objective optimization algorithm M-BSWA of solving-optimizing problem, calculate the iterative estimate value of design variable, realize Optimization Solution, determine prioritization scheme;

6. verify the effectiveness of optimum results.

For the multi-objective optimization algorithm M-BSWA of solving-optimizing problem, multi-objective optimization question being converted in the process of single-object problem described in step 5, often in group weight coefficient, a part adopts tolerance limit method to determine, another part based onPrinciple determine, then according to concrete Design of Mechanical Structure problem, by adjust object function tolerance limit provide 50-150 group weight coefficient w_i, i=1,2 ..., n.

With in practical engineering application, the M-BSWA of present invention design has that calculating speed is fast, meet constringent numerical computation method in theory.

The present invention is by building the mathematical model between multiple performance indications of concrete frame for movement and design variable, in order to accelerate to calculate speed, the complexity of reduction problem, construct again agent model, take into full account the mutual relation between each performance indications of frame for movement, by multiple evaluation index simultaneously as object function, designing a kind of numerical algorithm solving multi-objective optimization question, this algorithm can rapid solving Constrained multi-objective optimization question. Finally propose the method for designing of a kind of frame for movement based on M-BSWA multiple-objection optimization.

The present invention is applicable to the multi-objective optimization design of power of frame for movement, the mechanical configuration parameter distribution obtained is more reasonable, so that the frame for movement performance of design is better, the present invention adopts numerical computation method, calculating speed is fast, it is substantially shorter the design cycle, and ensures under the premise not increasing frame for movement total quality, it is achieved improve the target of frame for movement combination property.

Accompanying drawing explanation

Fig. 1 is the flow chart of the Design of Mechanical Structure method based on M-BSWA multiple-objection optimization

Fig. 2 is the design flow diagram of the M-BSWA algorithm of the Design of Mechanical Structure based on M-BSWA multiple-objection optimization

Fig. 3 is the structural representation of coachbuilt body front portion structure energy absorbing component

Fig. 4 is the structural representation of front part of saloon car energy-absorption box

Detailed description of the invention

Below in conjunction with front part of saloon car energy-absorption box structural design, the present invention is described in detail.

As depicted in figs. 1 and 2, a kind of front part of saloon car energy-absorption box construction design method based on M-BSWA multiple-objection optimization of the present invention, comprise the steps:

1. set up the mathematical model of car energy-absorption box structure multi-objective optimization design of power, including setting up the initial cad model of energy-absorption box structure, selected design variable, optimization object function and constraints;

2. select the sampling of orthogonal (DOE) method, construct RBF agent model, it is determined that evaluation agent model accuracy;

3. design is for the multi-objective optimization algorithm M-BSWA of solving-optimizing problem, according to solving flow process, is encoded programming, it is achieved Optimization Solution;

4. verify the effectiveness of optimum results.

In step 1, set up the mathematical model of car energy-absorption box structure multi-objective optimization design of power, comprise the steps:

1.1 set up the initial cad model of energy-absorption box structure as shown in Figure 4;

1.2 choose the wide b of energy-absorption box, energy-absorption box height h, wall thickness t are that three design variables are expressed as: x₁,x₂,x₃, and determine its scope of design: $\underset{-}{x_i}\≤x_i\≤\stackrel{-}{x_i},i=1,2,3;$

1.3 to choose crushing force efficiency (CFE) energy-absorbing ratio (SEA) be two optimization aim, and builds associated object function f₁(x),f₂(x);

1.4 arrange constraints: E (x) > E_c,M(x)��M_c;

In step 2, design the sampling of (DOE) method at choice experiment, construct RBF agent model, it is determined that the process of evaluation agent model accuracy mainly comprises the steps that

2.1 experimental design method samplings, adopt orthogonal experiment design sampling to obtain sample point and test point, and calculate the target function value of sample point and test point;

The precision of 2.2 evaluation agent models, sets agent model precision evaluation index, calculates the agent model response value at test point place and precision thereof, if the accuracy criteria of being not reaching to, then more new sample point, rebuilds agent model, and the test point evaluation index adopted is as follows:

$R^2=\frac{\underset{i=1}{\overset{M}{\Σ}}{({\hat{y}}_i-{\stackrel{\‾}{y}}_i)}^2}{\underset{i=1}{\overset{M}{\Σ}}{(y_i-{\stackrel{\‾}{y}}_i)}^2};$

$R_{adj}^2=\frac{1-\underset{i=1}{\overset{2}{\Σ}}{(y_i-{\hat{y}}_i)}^2(M-1)}{\underset{i=1}{\overset{2}{\Σ}}{(y_i-{\stackrel{\‾}{y}}_i)}^2(M-k-1)};$

In formula: R is factor of determination; R_adjFor adjusting factor of determination; M is number of samples; K is the number of design variable;It is illustrated respectively in the measured value of test point place Simulation Calculation, meansigma methods and predictive value;

Work as R²>=99.8%, R_adjWhen >=99.5%, the agent model of structure can meet design requirement;

In step 3, design, for the multi-objective optimization algorithm M-BSWA of solving-optimizing problem, is used for solving energy-absorption box Optimal Structure Designing problem and comprises the following steps:

3.1 adopt quadratic sum weighting methods multi-objective problem is converted into single-object problem, concrete grammar can retouch into:

$\min f\left(x\right)=\underset{i=1}{\overset{2}{\mathrm{\Σ}}}{w}_i{\[f_i\left(x\right)-f_i^{*}\left(x\right)\]}^2---\left(1\right)$

In formula: f_i ^*X () is the optimal solution of each object function, w_iFor weight coefficient.

Often group weight coefficient in one adopt tolerance limit method determine, another based onPrinciple determine.

Then according to concrete Design of Mechanical Structure problem, 100 groups of weight coefficient w are provided by adjusting the tolerance limit of object function_i, i=1,2. Tolerance limit method defines: if ��_i��f_i(x)�ܦ�_i, i=1,2 ..., L, then claimTolerance limit for this object function.

The weight coefficient mathematic(al) representation determined by tolerance limit method is:

$w_i=\frac{1}{{\[{\mathrm{\Δf}}_i\left(x\right)\]}^2},i=1,2,...$

In sum, the mathematical model based on the front part of saloon car energy-absorption box structure multiple-objection optimization of quadratic sum weighting method can be expressed as:

$\{\begin{array}{c}X={(x_1,x_2,x_3)}^T\\ \min f\left(x\right)=\underset{i=1}{\overset{2}{\mathrm{\Σ}}}{w}_i{\[f_i\left(x\right)-f_i^{*}\left(x\right)\]}^2\\ E\left(x\right)>E_c;\\ M\left(x\right)\≤M_c;\\ \underset{-}{x_i}\≤x_i\≤\stackrel{-}{x_i},i=1,2,3;\\ \underset{i=1}{\overset{2}{\mathrm{\Σ}}}{w}_i=1,w_i>0(i=1,2);\end{array}---\left(2\right)$

3.2 adopt Lagrangian multiplier method that constrained optimization problem is converted into unconstrained optimization problem, specifically can be described as:

$L(\stackrel{\→}{x},\mathrm{\λ},\mathrm{\α},\mathrm{\β})=f\left(x\right)+\underset{j=1}{\overset{2}{\mathrm{\Σ}}}{l}_j{h}_i\left(x\right)+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{\mathrm{\α}}_i(\underset{-}{x_i}-x_i)+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{\mathrm{\β}}_i(x_i-{\stackrel{\‾}{x}}_i)---\left(3\right)$

In formula: l_j(j=1,2), ��_i,��_i(i=1,2,3) for Lagrange multiplier.

In conjunction with (3) formula, (2) formula is rewritable is:

$\left\{\begin{array}{c}X={(x_1,x_2,x_3)}^T\\ \min L(x,l,a,b)=\underset{i=1}{\overset{2}{\mathrm{\Σ}}}{w}_i{\[f_i\left(x\right)-f_i^{*}\left(x\right)\]}^2+\underset{j=1}{\overset{2}{\mathrm{\Σ}}}{l}_j{h}_j\left(x\right)+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{a}_i(\underset{-}{x_i}-x_i)+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{b}_i(x_i-{\stackrel{\‾}{x}}_i)\\ \underset{i=1}{\overset{2}{\mathrm{\Σ}}}{w}_i=1,w_i>0(i=1,2)\end{array}\right.---\left(4\right)$

Quasi-Newton algorithm is the prefered method solving unconstrained optimization problem, and it calculates speed and convergence efficiently so as to show good performance in solving unconstrained optimization problem.

The present invention has selected a kind of M-BFGS algorithm to solve the unconstrained optimization problem that (4) formula describes.

3.3 adopt BFGS (M-BFGS) algorithm of a kind of improvement to solve above-mentioned unconstrained optimization problem.

Concretely comprising the following steps of M-BFGS algorithm:

A. initial point x is chosen₀��Rⁿ, initial symmetric positive definite matrix B₀��R^n��n, parameter ��, �� �� (0,1), �� �� (0,0.5). make k:=1;

If b. | | g_k| |�ܦ�, stop iteration; Otherwise solve system of linear equations B_kd_k+g_k=0, obtain direction of search d_k;

$d_x=-{\[\underset{j=1}{\overset{m}{\Σ}}{\mathrm{\λ}}_j\left(x\right){\▿}^2{B_j}^{*}\left(x\right)\]}^{-1}\underset{j=1}{\overset{m}{\Σ}}{\mathrm{\λ}}_j\left(x\right)\▿f_j\left(x\right),$

In formula:It is object function f_jThe Hessian matrix of (x).

C. step factor �� is determined by Armijo non-linear search rule_k;

${\mathrm{\α}}_k=max\left\{{\mathrm{\ρ}}^j\right|f(x_k+{\mathrm{\ρ}}^j{d}_k)-f_k\≤{\mathrm{\δ\ρ}}^j{g}_k^T{d}_k,j=0,1,2...\}.$

D. Iteration x_k+1:=x_k+��_kd_k;

Revise BFGS updating formula and calculate B_k+1:

$B_{k+1}=B_k-\frac{B_k{s}_k{s}_k^T{B}_k}{s_k^T{B}_k{s}_k}+\frac{\widehat{y_k}{\widehat{y_k}}^T}{s_k^T\widehat{y_k}}---\left(5\right)$

In formula: $\widehat{y_k}={\mathrm{ty}}_k+(1-t)r_k{s}_k;$

r_k=2 (f_k+1-f_k-g_k ^Ts_k)/||s_k||²;

s_k=f_k+1-f_k;

t��[0,1]��

E. make k:=k+1, go to step b.

According to step 3.1,3.2 and 3.3 describe algorithm, to for energy-absorption box optimize particular problem set up mathematical model be programmed, it is achieved Optimization Solution.

According to the parameters optimization value obtained, front part of saloon car energy-absorption box structure is optimized design.

The effectiveness of optimum results is verified finally by simulation software.

Claims (2)

1. the Design of Mechanical Structure method based on M-BSWA multiple-objection optimization, it is characterised in that comprise the following steps:

1.1 mathematical modeies setting up frame for movement multi-objective optimization design of power, comprise the following steps:

1.1.1 the initial cad model of frame for movement is set up;

1.1.2 selected design variable, optimization object function and constraints;

1.1.3 setting up the mathematical model of frame for movement, its mathematic(al) representation is:

$\left\{\begin{array}{c}\begin{array}{c}\min F\left(x\right)=\[f_1\left(x\right),f_2\left(x\right),...,f_n\left(x\right)\];\\ X=\left(x_{1,}{x}_{2,}...,x_l\right);\end{array}\\ \begin{array}{cc}s.t.& \begin{array}{c}\underset{\‾}{x_i}\≤x_i\≤\stackrel{\‾}{x_i},i=1,2,...,l;\\ h_j\left(x\right)\≤0,j=1,2,...,m;\\ h_j\left(x\right)=0,j=m+1,m+2,...,k;\end{array}\end{array}\end{array}\right.$

In formula: f₁(x),f₂(x),...,f_nX () represents the object function relevant with frame for movement performance; N is object function number;

(x_1,x_2,...,x_l) represent design variable;Represent Design of Mechanical Structure scope; L is Design of Mechanical Structure variable number;

h_j(x)��0,h_jX ()=0 represents the inequality constraints condition and equality constraint that should meet in concrete frame for movement optimization problem respectively;

1.2 adopt the sampling of orthogonal (DOE) method, including choosing empirical factor, choose orthogonal table level;

1.3 structure RBF agent models;

1.4 determine evaluation agent model accuracy, and the mathematic(al) representation of the test point evaluation index adopted is:

$R^2=\frac{\underset{i=1}{\overset{M}{\Σ}}{\left({\hat{y}}_i-{\stackrel{\‾}{y}}_i\right)}^2}{\underset{i=1}{\overset{M}{\Σ}}{\left(y_i-{\stackrel{\‾}{y}}_i\right)}^2};$

${R_{adj}}^2=\frac{1-\underset{i=1}{\overset{M}{\Σ}}{\left(y_i-{\hat{y}}_i\right)}^2\left(M-1\right)}{\underset{i=1}{\overset{M}{\Σ}}{\left(y_i-{\stackrel{\‾}{y}}_i\right)}^2\left(M-k-1\right)};$

In formula: R is factor of determination; R_adjFor adjusting factor of determination; M is number of samples; K is the number of design variable; y_i,It is illustrated respectively in the measured value of test point place Simulation Calculation, meansigma methods and predictive value;

1.5 designs, for the multi-objective optimization algorithm M-BSWA of solving-optimizing problem, comprise the following steps:

1.5.1 by quadratic sum weighting method, multi-objective optimization question being converted into single-object problem, its mathematic(al) representation is:

$\min f\left(x\right)=\underset{i=1}{\overset{n}{\Σ}}{w}_i{\[f_i\left(x\right)-{f_i}^{*}\]}^2$

In formula: f_iX () represents object function; N is the number of object function; f_i ^*Optimal solution for each object function; w_iFor weight coefficient; $\underset{i=1}{\overset{n}{\Σ}}{w}_i=1,w_i>0;$

1.5.2 by Lagrangian multiplier method, the constrained optimization problem in step 1.5.1 is converted into unconstrained optimization problem, builds following Lagrangian function:

$\min L(\stackrel{\→}{x},\mathrm{\λ},\mathrm{\α},\mathrm{\β})=f\left(x\right)+\underset{j=1}{\overset{m}{\Σ}}{\mathrm{\λ}}_j{h}_j\left(x\right)+\underset{i=1}{\overset{l}{\Σ}}{\mathrm{\α}}_i(\underset{\‾}{x_i}-x_i)+\underset{i=1}{\overset{l}{\Σ}}{\mathrm{\β}}_i(x_i-{\stackrel{\‾}{x}}_i);$

In formula: ��_j,��_i,��_iFor Lagrangian multiplier;

1.5.3 after step 1.5.2 and step 1.5.3 processes, setting up the mathematical model of unconstrained optimization problem, its mathematic(al) representation is:

$\left\{\begin{array}{c}X={\left(x_1,x_2,...,x_l\right)}^T;\\ \min L\left(\stackrel{\→}{x},\mathrm{\λ},\mathrm{\α},\mathrm{\β}\right)=f\left(x\right)+\underset{j=1}{\overset{m}{\Σ}}{\mathrm{\λ}}_j{h}_j\left(x\right)+\underset{i=1}{\overset{l}{\Σ}}{\mathrm{\α}}_i\left(\underset{\‾}{x_i}-x_i\right)+\underset{i=1}{\overset{l}{\Σ}}{\mathrm{\β}}_i\left(x_i-{\stackrel{\‾}{x}}_i\right);\\ f\left(x\right)=\underset{i=1}{\overset{n}{\Σ}}{w}_i{\[f_i\left(x\right)-{f_i}^{*}\left(x\right)\]}^2;\\ \underset{i}{\overset{n}{\Σ}}{w}_i=1,w_i>0;\end{array}\right.$

In formula: X is the vector of design variable composition;For the Lagrangian function constructed by Lagrangian multiplier method;

1.5.4 calculate the iterative estimate value of design variable with M-BFGS Quasi-Newton algorithm, the Iteration of M-BFGS Quasi-Newton algorithm is:

x_k+1=x_k+��_kd_k

In formula: ��_kSearch is step-length, is determined by Armijo inexact linear searching; d_kFor the direction of search, it may be assumed that

In formula:For Hessian matrix approximate of jth object function,For the derivative of jth object function,For weighter factor,

1.5.5 the multi-objective optimization algorithm M-BSWA for solving-optimizing problem that step 1.5.1,1.5.2 and 1.5.3 are formed by employing matlab instrument is encoded programming, calculates the iterative estimate value of design variable, realizes Optimization Solution, determines prioritization scheme;

The effectiveness of 1.6 checking optimum results.

2. by the Design of Mechanical Structure method based on M-BSWA multiple-objection optimization described in claim 1, it is characterized in that for the multi-objective optimization algorithm M-BSWA of solving-optimizing problem, multi-objective optimization question being converted in the process of single-object problem described in step 1.5, often group weight coefficient in a part adopt tolerance limit method determine, another part based onPrinciple determine, then according to concrete Design of Mechanical Structure problem, by adjust object function tolerance limit provide 50-150 group weight coefficient w_i, i=1,2 ..., n.