CN101637960B - Plastic injecting and shaping sprue location determining method based on surface mesh - Google Patents

Abstract

The invention belongs to the field of plastic injection and shaping, in particular to a plastic injecting and shaping sprue location determining method based on a surface mesh. The method directly converts a surface mesh output by a mesh generating tool into an undigraph with weight, which ensures that complicated fusant flowing length solving problems are converted into a shortest path solving problems of the top in the undigraph; by combining the advantages of a genetic algorithm and a hill climbing algorithm, a Generic-Hill Climbing method is built to search optimum single or multiple gate locations. The invention has the advantages that the invention directly utilizes surface mesh calculation to break through data model limitation and adopts the Generic-Hill Climbing method to search, which provides efficient and accurate result; the method of the invention not only can calculate the single optimum gate position, but also can calculate multiple gate position combination.

Description

A kind of plastic injecting and shaping sprue location determining method based on surface mesh

Technical field

The invention belongs to the injection-moulding plastic field, relate to the best gate location of injection-moulding plastic and determine method, more specifically to determining based on the best gate location of injection-moulding plastic of surface mesh.

Background technology

It is to influence one of most important factor of injected articles quality that gate location is selected.Inappropriate position may cause the serious defective of goods, as overfill, warpage, viscous flow or the like.It is present main design means that the auxiliary designer of application injection moulding CAE software carries out the gate location selection.The analyst at first rule of thumb or test design method select several gate locations, analyze relatively analog result data then by calculating, choose one preferably.This method too relies on designer's experience, and efficient is not high.Therefore, the optimizing application algorithm preferably becomes the hot issue of research to the gate location of injection moulding scheme on existing CAE software and theoretical basis.

General gate location determines that method is existing C AE software to be combined with search technique to iterate calculate till satisfying goal condition, and visible surplus moral opens, safely, and Wang Xicheng " the evolution method for designing of injection mold gate location "; Shen Changyu, people such as Yu Xiaorong " plastic injecting and shaping sprue position optimization "; Zhai Ming, Gu Yuanxian " optimal design of injection mould cast gate number and position "; Li Jiquan, Li Dequn, Guo Zhiying " towards the injection mold gate location optimization research of buckling deformation ".Though these class methods can obtain optimum gate location in theory, CAE software itself calculates needs a large amount of time, consuming time more in the process of iterating, and has surpassed the tolerance interval of actual use.

The geological information of veil lattice was determined optimum gate location in conjunction with genetic algorithm during some scholar utilized in addition, saw Yu Xiaorong, people such as Shen Changyu " based on the gate Location Optimization of Plastic Injection Molding of flow equilibrium ".The geometry that the two dimensional surface that middle veil lattice utilization imagination is positioned at the 3D solid center comes presentation-entity, this grid often can not directly obtain, it is not high to need the operator to carry out the secondary modeling efficiency, lower for complex parts efficient, and this grid uses few in actual production.The length of flow of this method hypothetical boundary node is the straight line of cast gate to boundary node simultaneously, does not reflect the influence of the complexity of thickness and part to melt flows, and the precision of calculating is not high.

Also have some scholars directly in CAD system, to generate boundary point, adopting the length of flow of boundary node is the assumed condition of cast gate to the straight line of boundary node, utilize searching algorithm to determine gate location, see Xiang Huiyu, Sun Sheng, Zhong Yuexian " optimization of planning of border point set and injection mold gate location ".With identical based on the method for middle veil lattice, the method exists that efficient is low, the not high defective of computational accuracy, is unfavorable for the application in production reality.

Surface mesh is also referred to as two-sided grid, it is a kind of finite element analysis model based on the solid object surface technology, different with middle veil lattice model data, surface mesh directly uses the enclosure space curved surface to come the presentation-entity part, utilize the locus set up entity up and down the corresponding relation on two surfaces carry out finite element analysis.Surface mesh has promptly kept whole technical characterstics of middle veil lattice and has realized the seamless integrated of CAE system and CAD system again, has obtained to use widely in actual production.But because veil lattice complexity is many in the surface mesh ratio, calculate the gate location, also do not have correlative study at present based on the best gate location system of selection of injection moulding of surface mesh except utilizing existing C AE software to carry out simple iterative modeling.

Summary of the invention

Technical problem to be solved by this invention is the defective that overcomes on the prior art, and a kind of plastic injecting and shaping sprue location determining method based on surface mesh is provided, and reaches the purpose of fast automatic definite best gate location.

Plastic injecting and shaping sprue location determining method based on surface mesh provided by the invention, its step comprises:

The 1st step was generated the surface mesh of part by the grid Core Generator according to the geometric modeling of part;

The 2nd step supposition gate location is positioned on the grid node, and the direction of melt flows is defined on the line of grid node; Generate the non-directed graph of cum rights value according to surface mesh;

Corresponding to all summits on the surface that cast gate can be set on the part, constitute the cast gate vertex set in the 3rd step selection non-directed graph by these summits;

Surface of existence is parallel to the minimum cuboid of coordinate plane in the 4th step setting space coordinate system, and all summits all are positioned at this minimum cuboid in the described cast gate vertex set; Utilize the plane parallel with coordinate plane that described minimum cuboid is cut into the little cuboid in space, the cast gate summit in each little cuboid constitutes the subclass of corresponding cast gate vertex set;

The 5th step was utilized near optimal gate location summit combination in the genetic algorithm search non-directed graph;

The near optimal gate location set of vertices that the 6th step obtained with the 5th step is combined into initial position, utilizes hill-climbing algorithm to search for the combination of best gate location summit;

The 7th step found node corresponding in the surface mesh of the 1st step generation as best gate location according to the summit in the combination of best gate location summit.

The preferred implementation procedure in above-mentioned the 2nd step is:

The 2.1st step generated summit corresponding in the non-directed graph according to the node in the surface mesh;

The 2.2nd step generated the arc between the summit in the non-directed graph according to internodal neighbouring relations in the surface mesh;

The 2.3rd step was calculated corresponding arc between adjacent two summits according to the thickness and the neighbouring relations of node coordinate value, node in the surface mesh according to following formula (I) weights W;

$W=\frac{2^{\mathrm{\λ}}\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2+{(z_1-z_2)}^2}}{{(b_1+b_2)}^{\mathrm{\λ}}}---\left(I\right)$

In the formula: (x ₁, y ₁, z ₁), (x ₂, y ₂, z ₂The coordinate of)-two summit corresponding node; b ₁, b ₂The thickness of-two summit corresponding node; λ-thickness compensation coefficient;

In surface mesh, have that to set up weights between the pairing summit of node of pair relationhip be 0 arc the 2.4th step.

Above-mentioned the 4th step is cut minimum cuboid according to following optimal way, and constitutes the subclass of cast gate vertex set:

The 4.1st step was determined minimum cuboid at X according to following formula (II), Y, three directions of Z cut apart umber d _x, d _y, d _z:

$d_x=\left[\frac{(x_{\max }^{\′}-x_{\min }^{\′}+2{\mathrm{\μ}}_1)}{a\×\stackrel{\‾}{h}}\right]+1$

$d_y=\left[\frac{(y_{\max }^{\′}-y_{\min }^{\′}+2{\mathrm{\μ}}_2)}{b\×\stackrel{\‾}{h}}\right]+1---\left(\mathrm{II}\right)$

$d_z=\left[\frac{(z_{\max }^{\′}-z_{\min }^{\′}+2{\mathrm{\μ}}_3)}{c\×\stackrel{\‾}{h}}\right]+1$

In the formula: a, b, c-is respectively X, Y, the cutting apart apart from weights of three directions of Z; X ' _Max, x ' _Min, y ' _Max, y ' _MinAnd z ' _Max, z ' _Min-be respectively in the cast gate vertex set summit at X, Y, the maximum of Z direction coordinate, minimum of a value; H-is the average thickness of part; μ ₁, μ ₂, μ ₃-be minimum cuboid coordinate offset weights;

The 4.2nd step is according to formula d=d _x* d _y* d _zCalculate sub-cuboid number d, d also is the number of vertex subset, and with the journal of each subclass according to 1～d;

The 4.3rd step was calculated each summit (x, y, z) the subclass sequence number d ' at place, and each summit joined in the corresponding subclass according to formula (III);

$d^{\′}=\left[\frac{x-x_{\min }^{\′}+{\mathrm{\μ}}_1}{a\stackrel{\‾}{h}}\right]+\left[\frac{y-y_{\min }^{\′}+{\mathrm{\μ}}_2}{b\stackrel{\‾}{h}}\right]\·d_x+\left[\frac{z-z_{\min }^{\′}+{\mathrm{\μ}}_3}{c\stackrel{\‾}{h}}\right]\·d_x\·d_y---\left(\mathrm{III}\right).$

The preferred implementation procedure in above-mentioned the 5th step is:

The 5.1st step initialization population

As the individuality in the genetic algorithm, the coordinate on each summit is as the individual phenotype of heredity in the combination with the 3rd combination that goes on foot the summit in the cast gate vertex set in the non-directed graph that is generated, and the individual set of forming is as the population in the genetic algorithm; The initialization population specifically is meant picked at random summit from the cast gate vertex set, and selected summit made up according to the quantity of determining gate location, according to the requirement of genetic algorithm the coordinate on summit is encoded again, form the gene that genetic manipulation can be handled in the genetic algorithm;

The 5.2nd step was calculated each individual adaptive value in the population;

If in the following criterion of the 5.3rd step an establishment is arranged, then finish search procedure, turned to for the 5.9th step, otherwise turned to for the 5.4th step:

Criterion one: whether the iterations of genetic manipulation reaches the preset upper limit value;

Criterion two: the adaptive value of optimized individual does not have to change substantially in the population;

The 5.4th step was selected genetic manipulation according to individual fitness size in the population, and the defect individual in the parent population is copied to progeny population;

It is right that the 5.5th step mixed into the individuality in the population at random, presses the part coding between the crossover probability exchange individuality, generates new individuality;

The 5.6th step was adjusted the new individuality that interlace operation generated, the coordinate that is about to the summit in the new individuality be set to new individuality in the coordinate on the nearest cast gate summit of vertex position;

The 5.7th step was selected a certain position in the individual coding at random by the variation probability, and the value of revising this is 1 or 0, generates new individuality;

The 5.8th step was adjusted the new individuality that mutation operation produced according to the mode in the 5.6th step, turned to for the 5.3rd step after finishing;

Choose behind the genetic manipulation that the set of vertices cooperation of the individual representative of adaptive value maximum is the summit array output of near optimal gate location in the population the 5.9th step, the genetic search process finishes;

The further preferred implementation in the 5th step is:

In the 5.2nd step, be initial position at first, utilize critical path method (CPM) to calculate the shortest path length on each summit in the non-directed graph with the summit in the individuality; Utilize shortest path length to calculate individual adaptive value again.

The 5.6th step was adjusted the individuality of new generation in the following manner:

(A1) individuality of new generation is decoded, the heredity decoding is the inverse process of coding, promptly is that the gene that will be used for genetic manipulation are converted to individual phenotype;

(A2) to the summit in the individuality of new generation, go on foot the nearest with it summit of search in the cast gate vertex set that is generated the 3rd, concrete steps are:

1. by formula (III) determines the sequence number d ' of the cast gate vertex subset at the place, summit in the new individuality that produces according to coordinate, has the summit to exist then directly the individual subclass of d ' as current vertex set if the d ' height is concentrated, and changes step 3., otherwise changes step 2.;

2. there are all cast gate vertex subset on summit in traversal, and choosing the subclass center is current vertex set with newly producing the nearest subclass of individual vertex position;

3. search and the new nearest summit of vertex position that produces individuality in current vertex set;

(A3) coordinate that newly produces the summit in the individuality is set to apex coordinate nearest with its position in the cast gate vertex set, and recompile;

(A4) calculate the adaptive value of adjusting the back individuality according to the computational methods of described individual fitness of the 5.2nd step.

The preferred implementation procedure in above-mentioned the 6th step is:

The set of vertices of the 6.1st step with expression near optimal gate location is combined into initial vertax combination g _s

The adaptive value of the 6.2nd step with the summit combination of expression near optimal gate location is initial adaptive value F _s

The 6.3rd step was set the current summit combination of intermediate quantity g _cAnd current adaptive value F _c, and make g _c=g _s, F _c=F _s

The 6.4th step was obtained all adjacent vertex combinations of current summit combination, be combined as initial position with each adjacent vertex successively and utilize critical path method (CPM) to calculate the shortest path length on each summit in the non-directed graph, utilize shortest path length to calculate the adaptive value of adjacent vertex combination again;

Maximum adaptation value in the adjacent vertex combination of the 6.5th step hypothesis current summit combination is F _Max, corresponding set of vertices is combined into g _Max, get F _MaxMake comparisons with current adaptive value, if F _Max＞F _cChangeed for the 6.6th step, otherwise changeed for the 6.7th step;

The 6.6th step was revised the combination of current summit and current adaptive value, that is: g _c=g _Max, F _c=F _Max, changeed for the 6.4th step;

The 6.7th step was the summit array output of best gate location with current set of vertices cooperation, and the search by hill climbing process finishes.

The present invention is according to the definition of best gate location, directly utilize the surface grid model data, surface mesh is converted into the non-directed graph of cum rights value, length of flow is found the solution the shortest route problem that problem is converted to figure, and, set up the Generic-HillClimbing method and search for best gate location in conjunction with the advantage of genetic algorithm and hill-climbing algorithm.Compared with prior art the invention has the advantages that: directly utilize surface mesh calculating optimum gate location to break through the restriction of data model; Adopt the Generic-HillClimbing method to search for, it is efficiently and accurately as a result; Not only can calculate single best gate location, also can calculate many gate location combinations.

Description of drawings

Fig. 1 is the flow chart of the inventive method;

Fig. 2 is converted into the flow chart of the non-directed graph of cum rights value for surface mesh;

Fig. 3 is a surface mesh pair relationhip schematic diagram;

Fig. 4 is genetic algorithm and hill-climbing algorithm comparison diagram;

Fig. 5 is the genetic algorithm flow chart;

Fig. 6 is an initialization population flow chart;

Fig. 7 is the hill-climbing algorithm flow chart;

Fig. 8 determines figure as a result for flat part list cast gate optimum position.

The specific embodiment

The present invention adopts simplified condition successfully the surface grid model data to be converted to the non-directed graph of cum rights value, make stream length find the solution the shortest route problem that problem changes figure into, and utilize critical path method (CPM) to find the solution the length of flow of corresponding each node, set up the Generic-HillClimbing hybrid optimization algorithm of constrained domain on this basis, can in product space, search for best gate location.

As shown in Figure 1, the concrete implementation step of the inventive method is:

(1) generates surface mesh

Generate the surface mesh of part according to the geometric modeling of part by the grid Core Generator, and obtain surface mesh node coordinate value scope by the coordinate figure of comparison surface grid node, promptly the surface mesh node is at the maximum of directions X coordinate, minimum of a value x _Max, x _Min, at the maximum of Y direction coordinate, minimum of a value y _Max, y _Min, at the maximum of Z direction coordinate, minimum of a value z _Max, z _Min, obtain the average thickness h of part in addition.

(2) generate the non-directed graph of cum rights value according to surface mesh

According to the principle of Finite Element Method, the present invention supposes that gate location must be positioned on the grid node, and the direction of melt flows is defined on the line of grid node.

On the basis of above hypothesis, the concrete steps of the non-directed graph of surface mesh generation cum rights value are as follows:

1) generates summit corresponding in the non-directed graph according to the node in the surface mesh one by one.

2) generate the arc between the summit in the non-directed graph according to internodal neighbouring relations in the surface mesh one by one.

3) according to the thickness of node coordinate value, node in the surface mesh and the weights of the corresponding arc of neighborhood calculation.

Under injection-moulding plastic thin-walled assumed condition, ignore the influence of temperature to viscosity of plastic melts, can think that the length of flow of plastic melt in die cavity is only relevant with the die cavity wall thickness under identical process conditions.According to above analysis, the thickness and the weights formula of the corresponding arc of neighborhood calculation according to node coordinate, node in the surface mesh of the present invention is as follows:

$W=\frac{2^{\mathrm{\&lambda;}}\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2+{(z_1-z_2)}^2}}{{({\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="H2009100616953E00021.png"\; state="\{\{state\}\}">b</figure-callout>}}_1+b_2)}^{\mathrm{\&lambda;}}}---\left(1\right)$

In the formula: the weights of corresponding arc between adjacent two summits of W-; (x ₁, y ₁, z ₁), (x ₂, y ₂, z ₂The coordinate of)-two summit corresponding node; b ₁, b ₂The thickness of-two summit corresponding node; λ-thickness compensation coefficient, λ are real number, and span is [1,3].

4) have in surface mesh that to set up weights between the pairing summit of node of pair relationhip be 0 arc

According to the thin-walled assumption principle, plastic melt two lip-deep flowing about the correspondence of part are harmonious.Flow for this coordination that on surface mesh, realizes melt, between two corresponding node on the thickness direction on corresponding two surfaces of surface mesh, set up the corresponding relation of node, be referred to as the internodal pair relationhip of surface mesh.As shown in Figure 3, node 1 is corresponding with node 2, and node 3 is corresponding with node 4, if node 1 has the melt-flow mistake in the mold filling process of melt, then node 2 must have the melt-flow mistake.

To the node of pair relationhip is arranged in the surface mesh, between the summit of its pairing non-directed graph, set up weights and be 0 arc.

According to above-mentioned rule, the present invention is converted into surface mesh the non-directed graph of cum rights value.

(3) generate cast gate vertex set in the non-directed graph

Cast gate summit in the non-directed graph of the present invention is meant the pairing summit of node in the surface mesh that may have cast gate, and all of cast gate summit is the cast gate vertex set.Think that generally speaking the surface of whole part can design cast gate, the cast gate vertex set is all summits in the non-directed graph that generated of step (2).Can only be positioned at the situation submarine gate that specific (special) requirements is arranged on some surface of part or on some zone, the cast gate vertex set is for designing the set on the summit in the surface of cast gate or the pairing non-directed graph of surface mesh node in the zone.

By apex coordinate value in the cast gate vertex set that is relatively generated, obtain in the cast gate vertex set summit at the maximum of directions X coordinate, minimum of a value x ' _Max, x ' _Min, the maximum of Y direction coordinate, minimum of a value y ' _Max, y ' _Min, the maximum of Z direction coordinate, minimum of a value z ' _Max, z ' _Min

(4) subclass of generation cast gate vertex set

Exist a surface to be parallel to the minimum cuboid of coordinate plane in the hypothesis space coordinate system, the cast gate summit that makes step (3) be generated all is positioned at this cuboid.The mode that embodies of minimum cuboid has a lot, and the present invention is not limited to specific expression way, and the coordinate with the diagonal summit is that example defines minimum cuboid below, the coordinate on its diagonal summit can be expressed as (x ' _Min-μ ₁, y ' _Min-μ ₂, z ' _Min-μ ₃), (x ' _Max+ μ ₁, y ' _Max+ μ ₂, z ' _Max+ μ ₃).The minimum cuboid that utilizes the plane parallel with coordinate plane to set cuts into the little cuboid in some spaces, cast gate summit in each little cuboid constitutes the subclass of corresponding cast gate vertex set, and, be designated as (x with the mean value of all apex coordinates in the subclass coordinate as the subclass center _{D '}, y _{D '}, z _{D '}), wherein d ' is the subclass sequence number.

The concrete steps of generation cast gate vertex set subclass of the present invention are as follows:

1. determine minimum cuboid at X, Y, three directions of Z cut apart umber d _x, d _y, d _z, computing formula is suc as formula (2)～(4):

$d_x=\left[\frac{(x_{\max }^{\&prime;}-x_{\min }^{\&prime;}+2{\mathrm{\&mu;}}_1)}{a\stackrel{\&OverBar;}{h}}\right]+1---\left(2\right)$

$d_y=\left[\frac{(y_{\max }^{\&prime;}-y_{\min }^{\&prime;}+2{\mathrm{\&mu;}}_2)}{b\stackrel{\&OverBar;}{h}}\right]+1---\left(3\right)$

$d_z=\left[\frac{(z_{\max }^{\&prime;}-z_{\min }^{\&prime;}+2{\mathrm{\&mu;}}_3)}{c\stackrel{\&OverBar;}{h}}\right]+1---\left(4\right)$

In the formula: a, b, c-is respectively X, Y, cutting apart apart from weights of three directions of Z generally got 5 to 15 integer, μ ₁, μ ₂, μ ₃-minimum cuboid coordinate offset weights, span is [0.1,1.0].

2. according to formula d=d _x* d _y* d _zCalculate sub-cuboid number d, d also is the number of vertex subset, and with the journal of subclass according to 1～d.

3. calculate each summit (x, y, z) the subclass sequence number d ' at place, and each summit joined in the corresponding subclass according to formula (5);

$d^{\&prime;}=\left[\frac{x-x_{\min }^{\&prime;}+{\mathrm{\&mu;}}_1}{a\stackrel{\&OverBar;}{h}}\right]+\left[\frac{y-y_{\min }^{\&prime;}+{\mathrm{\&mu;}}_2}{b\stackrel{\&OverBar;}{h}}\right]\&CenterDot;d_x+\left[\frac{z-z_{\min }^{\&prime;}+{\mathrm{\&mu;}}_3}{c\stackrel{\&OverBar;}{h}}\right]\&CenterDot;d_x\&CenterDot;d_y---\left(5\right)$

(5) utilize near optimal gate location summit combination in the genetic algorithm search non-directed graph

Genetic algorithm is a kind of evolutionism thought of living nature natural selection, the survival of the fittest and optimization algorithm of random theory of utilizing, and be fit to the global optimization problem that the solution scale is big and model is complicated, but its local search ability is poor, accurately finds the solution inefficiency.As shown in Figure 4, the region of search can be divided into four parts, is labeled as 1,2,3 and 4 respectively, and wherein, 3 is optimal region.Utilize genetic algorithm to be easy to find inferior advantage B in the optimal region 3, then need to carry out a large amount of computings but searched for to optimum point A by inferior advantage B, efficient is not high.

According to this characteristic of genetic algorithm, the present invention utilizes the summit combination of genetic algorithm search near optimal gate location, its flow chart as shown in Figure 5, concrete steps are as follows:

(5-1) initialization population

The combination on the summit in the non-directed graph that the present invention is generated with step (3) in the cast gate vertex set is as the individuality in the genetic algorithm, and the coordinate on summit is as the individual phenotype (feature) of heredity, and the individual set of forming is as the population in the genetic algorithm.Initialization population of the present invention specifically is meant the summit of picked at random some from the cast gate vertex set, and selected summit made up according to the quantity of determining gate location, according to the requirement of genetic algorithm the coordinate on summit being encoded forms the accessible gene of genetic manipulation in the genetic algorithm again.Initialization population step specifically can be described as shown in Figure 6:

1) determines to select at random number of vertices N ₁

The number of vertices N that selects at random of the present invention ₁Be meant the number of selecting the summit from the cast gate vertex set that step (3) is generated, its span is [5,50].Determine N according to the number on summit in the cast gate vertex set and the quantity of definite gate location ₁Value, the number on summit is many more in the cast gate vertex set, determines that the quantity of gate location is few more, N ₁Value big more.

2) determine quantity M individual in the population

Individual quantity is meant that specifically hypothesis determines that the number of gate location represents (J is an integer, general J ∈ [1,4]) with J in definite population of the present invention, calculates quantity individual in the population according to formula (6) so:

M＝C(N ₁，J) (6)

3) select the summit at random

Of the present inventionly select the summit specifically to be meant from the cast gate vertex set that step (3) is generated at random to select N at random ₁Individual summit.

4) summit of selecting is made up

The of the present invention summit of selecting is made up specifically is meant the N that selects from random ₁Select J summit in the individual summit and do not consider putting in order of summit.The combination on a summit is as the body one by one of genetic algorithm, and anabolic process is till all possible combining form is selected.

5) coding

Coding of the present invention specifically be meant utilize binary character set 0, the code string that 1} constituted is represented the coordinate on the summit that heredity is individual, and its process specifically can be described as:

1. determine solving precision

K+1 position when solving precision of the present invention specifically refers to coding behind the reservation coordinate figure decimal point, the precision of then finding the solution is the k position, the span of k is [2,6].

2. the string of determining code character is long

The string of definite code character of the present invention is long specifically to be meant the cast gate apex coordinate that is calculated according to step (4) at X, Y, and the maximin of three directions of Z, the by formula long m of string of (7) calculation code character:

$\left\{\begin{array}{c}{2}^{m_x^{\&prime;}-1}<(x_{\max }^{\&prime;}-x_{\min }^{\&prime;})\&times;{10}^{k+1}\&le;2^{m_x^{\&prime;}}-1\\ 2^{m_y^{\&prime;}-1}<(y_{\max }^{\&prime;}-y_{\min }^{\&prime;})\&times;{10}^{k+1}\&le;2^{m_y^{\&prime;}}-1\\ z^{m_z^{\&prime;}-1}<(z_{\max }^{\&prime;}-z_{\min }^{\&prime;})\&times;{10}^{k+1}\&le;2^{m_z^{\&prime;}}-1\\ m^{\&prime;}=m_x^{\&prime;}+m_y^{\&prime;}+m_z^{\&prime;}\\ m=m^{\&prime;}\&times;J\end{array}\right.---\left(7\right)$

In the formula: the length of the individual coding of m-; The code length on m '-single summit; M ' _x, m ' _y, m ' _z-single summit is at X, Y, the code length of three direction coordinates of Z; The k-solving precision; X ' _Min, x ' _Max-cast gate summit is in the maximum of directions X coordinate, minimum of a value; Y ' _Min, y ' _Max-cast gate summit is in the maximum of Y direction coordinate, minimum of a value; Z ' _Min, z ' _Max-cast gate summit is in the maximum of Z direction coordinate, minimum of a value; J-determines the quantity of gate location.

3. the coordinate transforming value is an integer

Get apex coordinate value in the individuality, the k+1 position behind the reservation decimal point multiply by 10 ^K+1The integer that obtains coordinate is expressed.

4. calculate the binary representation of intermediate integer

Utilize to remove 2 binary expressions of getting surplus method coordinates computed integer.

5. form coding

With the binary expression of the coordinate integer asked according to x, y, the order on z and summit joins end to end, and forms individual coding.

(5-2) adaptive value of calculating population individuality

The adaptive value of calculating population individuality of the present invention is characterized by calculates adaptive value individual in the population one by one, and it is as follows that individual fitness calculates detailed process:

1) is initial position with the summit in the individuality, utilizes critical path method (CPM) to calculate the shortest path length on each summit in the non-directed graph;

2) melt flows of perfect condition refers to the edge that melt arrives part simultaneously, though this situation may occur hardly in actual production and numerical simulation process, best gate location can make the flow regime of melt near perfect condition.The expression melt flows state whether index of balance has a lot, as the length of flow difference minimum of boundary node, maximum fluidity length minimum or the like.The present invention utilizes shortest path strength length computation individual fitness to be not limited to specific method, is example with the minimum index of maximum fluidity length below, the computing formula that provides corresponding adaptive value F (X) as shown in Equation (8):

$F\left(X\right)=\frac{K^{\&prime;}}{\max \left(L_i^{\&prime;}\right)}---\left(8\right)$

In the formula: L ' _iThe shortest path length on each summit in the-non-directed graph; I-summit sequence number; K '-amplification coefficient, span is [10,1000].

(5-3) judge whether to satisfy optimal conditions

The present invention judges whether that the criterion that satisfies optimal conditions has following two:

1) whether the iterations of genetic manipulation reaches higher limit R, R ∈ [10,50];

2) adaptive value of optimized individual does not interiorly change R ' ∈ [3,5] in R ' generation in the population;

If above-mentioned two conditions satisfy one, the present invention thinks that promptly genetic process has satisfied optimal conditions and turned to step (5-9), otherwise turns to step (5-4).

(5-4) select genetic manipulation

Selecting operation in the genetic algorithm is according to individual fitness size in the population, the defect individual in the parent population is copied to the operation of progeny population.

The present invention is not limited to specific method of operating, and selecting genetic manipulation with standard gambling dish below is example, illustrates that population carries out the detailed process that operation is selected in heredity:

1) to each individual v ^tCalculate adaptive value eval (v ^t), t is a sequence number individual in the population;

2) by formula (9) calculate all chromosomal adaptive values in the population and:

$F_{\mathrm{tal}}=\underset{t=1}{\overset{\mathrm{pop}\_\mathrm{size}}{\mathrm{\&Sigma;}}}\mathrm{eval}\left(v^t\right)---\left(9\right)$

In the formula: F _Tal-adaptive value and; The pop_size-population quantity; Eval (v ^t)-t individual adaptive value;

3) press formula (6) to each chromosome v ^t, calculate it and select Probability p _t

$p_t=\frac{\mathrm{eval}\left(v^t\right)}{F_{\mathrm{tal}}};$ t＝1，2，...，pop_size (10)

4) to each individual v ^t, calculate its cumulative probability q _t, promptly be before t chromosome all individual choice probability and;

$q_t=\underset{l=1}{\overset{t}{\mathrm{\&Sigma;}}}{p}_l$ t＝1，2，...，pop_size (11)

In the formula: l-represents the temporary variable of individual sequence number;

5) at [0,1] interval interior equally distributed pseudo random number r that produces, as if r≤q ₁Then select first chromosome v ₁, otherwise, select t chromosome v ^t(2≤t≤pop_size) makes q _T-1＜r≤q _t

6) repeat the 5th step operation pop_size time.

(5-5) interlace operation

The interlace operation of genetic algorithm is the individuality in the population to be mixed at random right, presses crossover probability p _cExchange the part coding between them, thereby generate new individuality, general p _c∈ [0.5,0.7].The present invention is not limited to specific interlace operation method, is operating as example with the crisscross inheritance of standard single-point below, and the concrete steps that population crisscross inheritance is operated describe:

1) intersecting number of individuals s is set to zero;

2) check the individuality of whether handling in the population, then change 3 if having), otherwise termination routine;

3) produce several r at random, if r＜p in interval [0,1] _cThen mark is current individual individual as intersecting, and s is added 1, otherwise changes 2);

4) value of inspection s is if s=2 changes 5); Otherwise change 2);

5) two current intersection individualities are carried out interlace operation.At first at random integer pos of generation between [1, m] (m presentation code length) exchanges the part of two chromosomal pos+1 to m positions then, changes 1).

(5-6) individuality of new generation is adjusted

After the interlace operation, the new summit that produces individuality might must be adjusted the individuality of new generation not in the cast gate vertex set, and the concrete steps of adjustment are as follows:

1) coding of individuality is decoded

The heredity decoding is the inverse process of coding, is that the gene that will be used for genetic manipulation are converted to individual phenotype.Decoding of the present invention is the coordinate that the string of binary characters that expression is individual is converted to summit in the individuality.If sequence number j when the pre-treatment summit ₁Expression and initial value are 0 to be j ₁=0, J is for determining the number (number of vertices) of gate location, and then Xie Ma concrete steps are as follows:

1. judge j ₁Whether＜J sets up, and changes 2. if set up then, otherwise finishes decode procedure;

2. take out j ₁The directions X coordinate character string on individual summit is promptly taken out j in the individual coded strings ₁* m ' position is to (j ₁* m '+m ' _x-1) binary string, forming one has m ' _xThe binary string of position, symbol m ' is single vertex encoding length, m ' _xCode length for summit directions X coordinate;

3. according to the m ' that takes out _xThe binary string of position by formula (12) calculates j ₁The coordinate of individual summit directions X:

$x=x_{\min }^{\&prime;}+(\underset{j=0}{\overset{m_x^{\&prime;}-1}{\mathrm{\&Sigma;}}}{b}_j\&CenterDot;2^j)\frac{x_{\max }^{\&prime;}-x_{\min }^{\&prime;}}{{10}^{k+1}}---\left(12\right)$

In the formula: the x-summit is at the coordinate of directions X; b _j-at the value of symbol of j position; The sequence number of j-position; X ' _Max, x ' _Min-cast gate apex coordinate is in the maximum of directions X, minimum of a value.

4. take out j ₁The Y direction coordinate character string on individual summit is promptly taken out j in the individual coded strings ₁* m '+m ' _xThe position is to (j ₁* m '+m ' _x+ m ' _y-1) binary string, forming one has m ' _yThe binary string of position, m ' _yCode length for summit Y direction coordinate;

5. according to the m ' that takes out _yThe binary string of position by formula (13) calculates j ₁The coordinate of individual summit Y direction:

$y=y_{\min }^{\&prime;}+(\underset{j=0}{\overset{m_y^{\&prime;}-1}{\mathrm{\&Sigma;}}}{b}_j\&CenterDot;2^j)\frac{y_{\max }^{\&prime;}-y_{\min }^{\&prime;}}{{10}^{k+1}}---\left(13\right)$

In the formula: the y-summit is at the coordinate of Y direction; b _j-at the value of symbol of j position; The sequence number of j-position; Y ' _Max, y ' _Min-cast gate apex coordinate is in the maximum of Y direction, minimum of a value.

6. take out j ₁The Z direction coordinate character string on individual summit is promptly taken out j in the individual coded strings ₁* m '+m ' _x+ m ' _yThe position is to (j ₁* m '+m '-1) binary string, forming one has m ' _zThe binary string of position, m ' _zCode length for summit Z direction coordinate;

7. according to the m ' that takes out _zThe binary string of position by formula (14) calculates j ₁The coordinate of individual summit Z direction:

$z=z_{\min }^{\&prime;}+(\underset{j=0}{\overset{m_z^{\&prime;}-1}{\mathrm{\&Sigma;}}}{b}_j\&CenterDot;2^j)\frac{z_{\max }^{\&prime;}-z_{\min }^{\&prime;}}{{10}^{k+1}}---\left(14\right)$

In the formula: the z-summit is at the coordinate of Z direction; b _j-at the value of symbol of j position; The sequence number of j-position; Z ' _Max, z ' _Min-cast gate apex coordinate is in the maximum of Z direction, minimum of a value.

8. j ₁=j ₁+ 1, change 1.

2) according to the new coordinate that produces the summit in the individuality, the nearest with it summit of search in the cast gate vertex set that step (3) is generated, concrete steps are:

1. by formula (5) determine the new sequence number d ' that produces the cast gate vertex subset at individual place, summit according to coordinate, have the summit to exist then directly the individual subclass of d ' as current vertex set if the d ' height is concentrated, and change 3., otherwise change 2..

2. there are all cast gate vertex subset on summit in traversal, and choosing the subclass center is current vertex set with newly producing the nearest subclass of individual vertex position.

3. search and the new nearest summit of vertex position that produces individuality in current vertex set.

3) newly produce individual apex coordinate and be set in the cast gate vertex set coordinate with nearest summit, its position, and according to the described coding method recompile of step (5-1).

4) calculate the adaptive value of adjusting the back individuality according to the computational methods of the described individual fitness of step (5-2).

(5-7) mutation genetic operation

Mutation operation in the genetic algorithm promptly is to change the gene of chromosome on one or more according to certain probability.To binary coding, mutation operation becomes 1,1 with 0 exactly and becomes 0.This paper mutation operation algorithm can be sketched and be: if the variation probability is p _m, each gene (coding) is produced the several r in interval [0,1] at random, if r＜p _m, then change the value of current gene, p _mSpan be [0.01,0.1].

(5-8) the new individuality that produces of mutation operation is adjusted

The method that the new individuality that produces of mutation operation is adjusted of the present invention is identical with step (5-6), turns to step (5-3) after operation is finished.

(5-9) output near optimal gate location summit combination

The present invention chooses behind the genetic manipulation that the individual represented set of vertices of adaptive value maximum is combined into the summit array output of near optimal gate location in the population, and the genetic search process finishes.

(6) utilize hill-climbing algorithm calculating optimum gate location

Hill-climbing algorithm is a kind of heuristic algorithm of searching, and it is progressively searched in solution space, and each goes on foot all towards the current suboptimization target approaches that can reach, till reaching optimum point.The hill-climbing algorithm form simply is easy to realize, but only just can guarantee to obtain globally optimal solution when being protruding when the region of search.As shown in Figure 4, if the C point of initial point in zone 2 of hill-climbing algorithm search, Sou Suo result is the D point in the zone 2 so, is local optimum.If earlier find B point in the optimal region 3 with genetic algorithm, carry out part adjustment with hill-climbing algorithm again, then can be rapidly and find global optimum's point A accurately.

The near optimal gate location set of vertices that the present invention is calculated with genetic algorithm is combined into initial position, utilizes hill-climbing algorithm to search for the combination of best gate location summit, and concrete steps are as follows:

1) set of vertices of the expression near optimal gate location of being exported with step (5) is combined into initial vertax combination g _s

2) adaptive value of the summit of the expression near optimal gate location of being exported with step (5) combination is initial adaptive value F _s

3) set the current summit combination of intermediate quantity g _cAnd current adaptive value F _c, and make g _c=g _s, F _c=F _s

4) all adjacent vertexs of obtaining the combination of current summit make up, and are combined as initial position with adjacent vertex successively and utilize critical path method (CPM) to calculate the shortest path length L on each summit in the non-directed graph _i, and calculate the adaptive value F of each adjacent vertex combination according to formula (8) _i

5) the maximum adaptation value in the adjacent vertex combination of supposing to make up on current summit is F _Max, corresponding set of vertices is combined into g _Max, get F _MaxMake comparisons with current adaptive value, if F _Max＞F _cChange 6), otherwise change 7);

6) revise the combination of current summit and current adaptive value, that is: g _c=g _Max, F _c=F _Max, change 4);

7) be the summit array output of best gate location with current set of vertices cooperation, the search by hill climbing process finishes.

(7) summit of best summit combination finds node corresponding in the surface mesh of step (1) generation as best gate location in the non-directed graph according to hill-climbing algorithm output.

Below in conjunction with the accompanying drawing example the present invention is done and to describe in further detail.

As shown in Figure 8, a square flat part, thickness is even, 1 of default gate location, but the cast gate setting area is whole piece surfaces.

(1) exported the surface mesh of this part by the grid Core Generator, the surface mesh node has 1244, and part is at X, Y, and the maximum of three direction coordinates of Z, minimum of a value is:

x _min＝-50.0，x _max＝50.0；

Y _min＝-80.0，Y _min＝80.0；

z _min＝0，z _max＝3.0；

The average wall thickness of part is: h=3.0.

(2) generate the non-directed graph that 1244 summits are arranged according to surface mesh.

(3) since cast gate the position can be set is whole piece surfaces, then the cast gate vertex set is all of summit in the non-directed graph, totally 1244 summits, the apex coordinate scope is in the cast gate vertex set:

x′ _min＝-50.0，x′ _max＝50.0；

y′ _min＝-80.0，y′ _min＝80.0；

z′ _min＝0，z′ _max＝3.0。

(4) get and cut apart weights a=7, b=15, c=5; μ ₁=μ ₂=μ ₃=1 calculates at x according to formula (2) (3) (4), y, and the umber of cutting apart of three directions of z is: d _x=5, d _y=5, d _z=1, then the subclass number is d=5 * 5 * 1=25.According to formula (5) each node is joined in the corresponding subclass, and the subset of computations center position coordinates, its result such as table 1.

Table 1 vertex subset generates the result

The subclass sequence number	Number of vertices	The summit centre coordinate
			1	54	(-40.901655，-65.151730，1.500000)
2	49	(-20.403356，-64.017453，1.530612)
			3	50	(-0.197962，-64.230444，1.560000)
4	47	(18.982089，-65.184569，1.595745)
			5	60	(40.317826，-65.766170，1.500000)
6	52	(-40.333884，-32.261152，1.500000)
			7	44	(-20.236561，-33.625649，1.568182)
8	48	(0.189700，-31.519885，1.500000)
			9	46	(20.120800，-31.912563，1.565217)
10	48	(41.277176，-32.565882，1.500000)
			11	46	(-40.518483，-0.688685，1.500000)
12	53	(-19.888125，0.053553，1.584906)
			13	45	(0.170819，0.386909，1.533333)
14	48	(19.752756，-0.241632，1.500000)
			15	47	(41.458632，-0.596839，1.531915)
16	48	(-41.529150，30.533166，1.500000)
			17	46	(-20.890346，31.358225，1.500000)
18	42	(-20.890346，31.358225，1.500000)
			19	45	(20.922260，31.946751，1.533333)
20	56	(40.718846，32.431668，1.607143)

21	56	(-41.011139，64.737301，1.500000)
			22	54	(-19.373591，64.265978，1.611111)
23	51	(-0.253408，64.340081，1.529412)
			24	49	(19.328793，65.207233，1.530612)
25	60	(40.545714，64.670754，1.500000)

(5) utilize genetic algorithm to generate the combination of near optimal gate location summit

1) initialization population

The accurate figure place of getting coordinate is k=2, calculates according to formula (7) and can get m ' _x=14, m ' _y=14, m ' _z=9, m '=m=37.

From the cast gate vertex set, select N at random ₁=50 summits, because default gate location J=1, individual number M=50 in the population then, each summit is that a summit constitutes individuality, all individually forms populations, again with its coding.

2) calculating of adaptive value

With the summit in the individuality is initial position, utilizes critical path method (CPM) to try to achieve the shortest path length on each summit in the non-directed graph, gets K '=10, calculates individual fitness according to formula (8).

Preceding 10 individualities and adaptive value thereof in the initialization population are as shown in table 2:

The coding and the adaptive value of preceding 10 individualities in the table 2 initialization population

Sequence number	Coded strings	Adaptive value
			1	0000000000000000000001011111000000000	0.169906
2	0000000000000000000000000000001101001	0.167198
			3	0000000000000000000000000000000000000	0.164076
4	0000000000000011011110010011000000000	0.176745
			5	0000000000000011001000000011001101001	0.182792
6	0000000000000011001000000011000000000	0.191997
			7	0000000000000011011010001101000000000	0.179866
8	0000000000000010011000010101000000000	0.216106
			9	0000000000000010111111100010000000000	0.202369
10	0000000000000000110110100101000000000	0.192311

3) judge whether to satisfy the genetic optimization condition

Set genetic algebra higher limit R=10,, otherwise change 4) then when genetic algebra end genetic evolution process greater than 10 time.

4) select operation

According to gambling calculate method to the individuality in the population select the operation.

5) interlace operation

The setting crossover probability is p _c=0.6, carry out interlace operation according to the single-point crossover algorithm.In the process of heredity for the first time, selected the 7th and the 8th individuality to carry out interlace operation at random, the crosspoint is the 16th gene position, the result of intersecting is as shown in table 3:

Table 3 interlace operation result

6) adjust

By calculating, be 297 with intersecting afterwards the nearest cast gate summit sequence number of the 7th individuality, the apex coordinate of then revising the 7th individuality is the coordinate on the 297th cast gate summit, encodes again.Adjust being encoded to of the 7th individuality in back: 1010110000100001101010010001000000000

By calculating, be 198 with intersecting afterwards the nearest cast gate summit sequence number of the 8th individuality, the apex coordinate of then revising the 7th individuality is the coordinate on the 198th cast gate summit, encodes again.Adjust being encoded to of the 8th individuality in back: 0001101100111001000101101101000000000

7) variation

The variation probability of setting is p _m=0.03, carry out mutation operation by this probability.

8) adjust

The individual adjustment process in variation back with intersects after the adjustment process of individuality identical.After finishing, adjustment turns to 3).

9) output near optimal cast gate summit

Through 10 genetic manipulations of taking turns, near optimal gate location summit block position is found out, and is No. 350 summit, and its adaptive value is 0.267.

(6) utilize hill-climbing algorithm calculating optimum cast gate summit

1) utilize No. 350 summit to be initial vertax, i.e. g _s=350;

2) utilize 0.267 to be initial adaptive value, i.e. F _s=0.267;

3) setting current summit and current adaptive value is: g _c=350, F _c=0.267;

4) adjacent vertex on the current summit of search, and be the adaptive value that initial point utilizes critical path method (CPM) and formula (8) calculating adjacent node with the adjacent node.Maximum adaptation value F in the adjacent vertex _Max=0.274152, g _Max=1100;

5) because F _Max＞F _c, g then _c=1100, F _c=0.274152, change 4);

6) repeat 4) 5) after 2 times, the maximum adaptation value in the adjacent vertex is not more than current adaptive value, and this moment, current summit was g _c=586, as the output of best cast gate summit, table 4 has shown the moving process on current summit in the hill-climbing algorithm with summit 586.

The moving process on current summit in table 4 hill-climbing algorithm

Mobile number of times	The summit sequence number	Adaptive value
			Initial position	350	0.267
1	1100	0.274152
			2	278	0.287187
3	586	0.297347

(7) determine best gate location

Finding node corresponding in the surface mesh according to best cast gate summit is No. 586 node, and coordinate is (2.766163,2.281798,0.000000), and this node is best gate location, as shown in Figure 8.

The present invention is not limited to the above-mentioned specific embodiment; persons skilled in the art are according to content disclosed by the invention; can adopt other multiple specific embodiment to implement the present invention; therefore; every employing project organization of the present invention and thinking; do some simple designs that change or change, all fall into the scope of protection of the invention.

Claims (1)

1. plastic injecting and shaping sprue location determining method based on surface mesh, its step comprises:

The 1st step was generated the surface mesh of part by the grid Core Generator according to the geometric modeling of part;

The 2nd step supposition gate location is positioned on the grid node, and the direction of melt flows is defined on the line of grid node; Generate the non-directed graph of cum rights value according to surface mesh; This step specifically comprises following process:

The 2.1st step generated summit corresponding in the non-directed graph according to the node in the surface mesh;

The 2.2nd step generated the arc between the summit in the non-directed graph according to internodal neighbouring relations in the surface mesh;

The 2.3rd step was calculated corresponding arc between adjacent two summits according to the thickness and the neighbouring relations of node coordinate value, node in the surface mesh according to following formula (I) weights W;

$W=\frac{2^{\mathrm{\&lambda;}}\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2+{(z_1-z_2)}^2}}{{(b_1+b_2)}^{\mathrm{\&lambda;}}}---\left(I\right)$

In the formula: (x ₁, y ₁, z ₁), (x ₂, y ₂, z ₂The coordinate of)-two summit corresponding node; b ₁, b ₂The thickness of-two summit corresponding node; λ-thickness compensation coefficient;

In surface mesh, have that to set up weights between the pairing summit of node of pair relationhip be 0 arc the 2.4th step;

Corresponding to all summits on the surface that cast gate can be set on the part, constitute the cast gate vertex set in the 3rd step selection non-directed graph by these summits;

Surface of existence is parallel to the minimum cuboid of coordinate plane in the 4th step setting space coordinate system, and all summits all are positioned at this minimum cuboid in the described cast gate vertex set; Utilize the plane parallel with coordinate plane that described minimum cuboid is cut into the little cuboid in space according to following the 4.1st step to the 4.3rd mode that goes on foot, the cast gate summit in each little cuboid constitutes the subclass of corresponding cast gate vertex set;

The 4.1st step was determined minimum cuboid at X according to following formula (II), Y, three directions of Z cut apart umber d _x, d _y, d _z:

$d_x=\left[\frac{(x_{\max }^{\&prime;}-x_{\min }^{\&prime;}+2{\mathrm{\&mu;}}_1)}{a\&times;\stackrel{\&OverBar;}{h}}\right]+1$

$d_y=\left[\frac{(y_{\max }^{\&prime;}-y_{\min }^{\&prime;}+2{\mathrm{\&mu;}}_2)}{b\&times;\stackrel{\&OverBar;}{h}}\right]+1---\left(\mathrm{II}\right)$

$d_z=\left[\frac{(z_{\max }^{\&prime;}-z_{\min }^{\&prime;}+2{\mathrm{\&mu;}}_3)}{c\&times;\stackrel{\&OverBar;}{h}}\right]+1$

In the formula: a, b, c-is respectively X, Y, the cutting apart apart from weights of three directions of Z; X ' _Max, x ' _Min, y ' _Max, y ' _MinAnd z ' _Max, z ' _Min-be respectively in the cast gate vertex set summit at X, Y, the maximum of Z direction coordinate, minimum of a value; -be the average thickness of part; μ ₁, μ ₂, μ ₃-be minimum cuboid coordinate offset weights;

The 4.2nd step is according to formula d=d _x* d _y* d _zCalculate sub-cuboid number d, d also is the number of vertex subset simultaneously, and with the journal of each subclass according to 1～d;

The 4.3rd step was calculated each summit (x, y, z) the subclass sequence number d ' at place, and each summit joined in the corresponding subclass according to formula (III);

$d^{\&prime;}=\left[\frac{x-x_{\min }^{\&prime;}+{\mathrm{\&mu;}}_1}{a\stackrel{\&OverBar;}{h}}\right]+\left[\frac{y-y_{\min }^{\&prime;}+{\mathrm{\&mu;}}_2}{b\stackrel{\&OverBar;}{h}}\right]\&CenterDot;d_x+\left[\frac{z-z_{\min }^{\&prime;}+{\mathrm{\&mu;}}_3}{c\stackrel{\&OverBar;}{h}}\right]\&CenterDot;d_x\&CenterDot;d_y---\left(\mathrm{III}\right);$

The 5th step was utilized near optimal gate location summit combination in the genetic algorithm search non-directed graph; The 5th step specifically comprised following process:

The 5.1st step initialization population

As the individuality in the genetic algorithm, the coordinate on each summit is as the individual phenotype of heredity in the combination with the 3rd combination that goes on foot the summit in the cast gate vertex set in the non-directed graph that is generated, and the individual set of forming is as the population in the genetic algorithm; The initialization population specifically is meant picked at random summit from the cast gate vertex set, and selected summit made up according to the quantity of determining gate location, according to the requirement of genetic algorithm the coordinate on summit is encoded again, form the gene that genetic manipulation can be handled in the genetic algorithm;

The 5.2nd step was an initial position with the summit in the individuality at first, utilized critical path method (CPM) to calculate the shortest path length on each summit in the non-directed graph; Utilize shortest path length to calculate each individual adaptive value in the population again;

If in the following criterion of the 5.3rd step an establishment is arranged, then finish search procedure, turned to for the 5.9th step, otherwise turned to for the 5.4th step:

Criterion one: whether the iterations of genetic manipulation reaches the preset upper limit value;

Criterion two: the adaptive value of optimized individual does not have to change substantially in the population;

The 5.4th step was selected genetic manipulation according to individual fitness size in the population, and the defect individual in the parent population is copied to progeny population;

It is right that the 5.5th step mixed into the individuality in the population at random, presses the part coding between the crossover probability exchange individuality, generates new individuality;

The 5.6th step was adjusted the new individuality that interlace operation generated, the coordinate that is about to the summit in the new individuality be set to new individuality in the coordinate on the nearest cast gate summit of vertex position; The 5.6th step was adjusted the individuality of new generation in the following manner:

(A1) individuality of new generation is decoded, the heredity decoding is the inverse process of coding, promptly is that the gene that will be used for genetic manipulation are converted to individual phenotype;

(A2) to the summit in the individuality of new generation, go on foot the nearest with it summit of search in the cast gate vertex set that is generated the 3rd, concrete steps are:

1. by formula (III) determines the new sequence number d ' that produces the cast gate vertex subset at the place, summit in the individuality according to coordinate, has the summit to exist then directly the individual subclass of d ' as current vertex set if the d ' height is concentrated, and changes step 3., otherwise changes step 2.;

2. there are all cast gate vertex subset on summit in traversal, and choosing the subclass center is current vertex set with newly producing the nearest subclass of individual vertex position;

3. search and the new nearest summit of vertex position that produces individuality in current vertex set;

(A3) coordinate that newly produces the summit in the individuality is set to apex coordinate nearest with its position in the cast gate vertex set, and recompile;

(A4) calculate the adaptive value of adjusting the back individuality according to the computational methods of described individual fitness of the 5.2nd step;

The 5.7th step was selected a certain position in the individual coding at random by the variation probability, and the value of revising this is 1 or 0, generates new individuality;

The 5.8th step was adjusted the new individuality that mutation operation produced according to the mode in the 5.6th step, turned to for the 5.3rd step after finishing;

Choose behind the genetic manipulation that the set of vertices cooperation of the individual representative of adaptive value maximum is the summit array output of near optimal gate location in the population the 5.9th step, the genetic search process finishes;

The near optimal gate location set of vertices that the 6th step obtained with the 5th step is combined into initial position, utilizes hill-climbing algorithm to search for the combination of best gate location summit; The 6th step specifically comprised following process:

The set of vertices of the 6.1st step with expression near optimal gate location is combined into initial vertax combination g _s

The adaptive value of the 6.2nd step with the summit combination of expression near optimal gate location is initial adaptive value F _s

The 6.3rd step was set the current summit combination of intermediate quantity g _cAnd current adaptive value F _c, and make g _c=g _s, F _c=F _s

The 6.4th step was obtained all adjacent vertex combinations of current summit combination, be combined as initial position with adjacent vertex successively and utilize critical path method (CPM) to calculate the shortest path length on each summit in the non-directed graph, utilize shortest path length to calculate the adaptive value of each adjacent vertex combination again;

Maximum adaptation value in the adjacent vertex combination of the 6.5th step hypothesis current summit combination is F _Max, corresponding set of vertices is combined into g _Max, get F _MaxMake comparisons with current adaptive value, if F _Max＞F _cChangeed for the 6.6th step, otherwise changeed for the 6.7th step;

The 6.6th step was revised the combination of current summit and current adaptive value, that is: g _c=g _Max, F _c=F _Max, changeed for the 6.4th step;

The 6.7th step was the summit array output of best gate location with current set of vertices cooperation, and the search by hill climbing process finishes;

The 7th step found node corresponding in the surface mesh of the 1st step generation as best gate location according to the summit in the combination of best gate location summit.

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