CN106845704A - A kind of facility layout method based on collision detection - Google Patents

A kind of facility layout method based on collision detection Download PDF

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CN106845704A
CN106845704A CN201710038238.7A CN201710038238A CN106845704A CN 106845704 A CN106845704 A CN 106845704A CN 201710038238 A CN201710038238 A CN 201710038238A CN 106845704 A CN106845704 A CN 106845704A
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facility
rectangle
border
collision
point
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丛明
刘冬
廖忠情
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Dalian University of Technology
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Abstract

The present invention discloses a kind of facility layout method based on collision detection.First, traditional work unit synthetic relationship is converted into relational matrix as input quantity, random point is initially generated on two dimensional surface and represents facility, each point is subject to act it power from other points, and active force is based on relational matrix and amended Euclidean distance is calculated；Act on and drive point movement making a concerted effort on impact point, until reaching end-state；Secondly, an extension is rectangular, and border represents the wall in facility layout；Power is acted between the rectangle for colliding or between matrix and border, power drives facility movement.Finally, with the interaction between facility and between facility and border, successive elimination collision obtains optimal facility layout result.The present invention simply and effectively can obtain optimal layout result according to work unit complex interdependency.

Description

A kind of facility layout method based on collision detection
Technical field
The invention belongs to engineering manufacture field, it is related to a kind of facility layout method based on collision detection.
Background technology
In Industrial Engineering field, facility layout (Facility Layout) refers to the manufacture system in limited factory floor space System designer determines the arrangement form of each facility and the process of position according to reasonable manner.Facility layout is related to manufacture Many aspects, to material handling, delivery cycle, stock area, production efficiency etc. has a major impact, therefore in Design of Production Line When, it is necessary to resolve this problem.
The core of facility layout is the position relationship of facility, QAP models (Quadratic Assignment Problems) It is to solve the conventional Mathematical Modeling of this problem with MIP models (Mixed Integer Programming).For example, XijRepresent Facility and the relations of distribution in place, FikRepresent the discharge relation between facility i and j, DjlRepresent the distance of place j and l, then Facility layout problem can just be expressed as：This Kind of Combinatorial Optimization Model has complexity very high, and it is complete to substitute by intelligent algorithm to ask for locally optimal solution in practical application Office's optimal solution, including ant group algorithm, genetic algorithm, annealing algorithm etc..The computational complexity and storage complexity of these methods are high, Requirement for designer is very high.
The content of the invention
For a kind of not enough present in existing utility layout process, heuristic side based on collision detection of present invention proposition Method.The method can solve the problems, such as the facility layout that area is not waited according to the optimization aim of facility layout.
To achieve the above object, the technical solution adopted by the present invention is as follows：
In a kind of facility layout method based on collision detection, the point of initial random generation represents facility, is received on each point To the power produced to it from other points, stress is calculated based on relational matrix；Each point is the plane area that facility is mapped The centre of form in domain；Facility overlapping region (collision) is detected and eliminated with the heuristic of non-grid；Parameter can influence to calculate speed The accuracy of degree and result.Comprise the following steps that：
The first step, determines input quantity, and the intermolecular forces according to point are moved, and are iterated
1.1) carry out facility layout and first have to determine the correlation between facility that conventional method is used as industry unit synthesis Correlation figure represents that A, E, I, O, U and X represent different grades of relation respectively, as shown in Figure of description 1.In this method In, using relational matrix R=(relationsI, j) represent facility between correlation, relational matrix is symmetrical matrix, close The value for being element in matrix is real number, with accuracy higher；Described facility is represented that the length and width of rectangle are represented by rectangle The size of facility, the position of form center of rectangle represents the position of facility.Set strength grade, the effect of the active force produced by collision Force threshold, boundary threshold.
1.2) n point is generated at random in the square that length is 1, each point is the centre of form of corresponding matrix；Every two The computing formula such as (1) and (2) that power is acted between individual point is shown：
Wherein, (1,2 ..., n), n represents the sum of facility to i, j ∈；X, y are the coordinate of the point in two dimensional surface.
Fig. 2 represents the distance (Z axis are represented) of any point-to-point (1,1) calculated using formula (2) in two dimensional surface, namely It is the x in (2) formulai=1, yi=1, xj∈ { -1,3 }, yj∈ { -1,3 }.The distance between 2 points of facility is not traditional sense On distance (Euclidean distance).Euclidean distance meets four basic conditions：Nonnegativity, the homogeneity of undistinguishable, symmetry And subadditivity.The distance of formula (2) only meets symmetry and subadditivity.If formula (2) meets homogeneity, infinitely connect The power of infinity can be produced between near two, therefore constant 5 and 1 is added in molecule and denominator.The range formula for being put forward It is not required to use 5 and 1, however it is necessary that selecting suitable number, the location interval with initial random generation is matched, and ensures meter The degree of accuracy of calculation.
1.3) act on to order about making a concerted effort on impact point and a little move, described impact point is step 1.2) in square Arbitrfary point, bring into operation this iterative process, and described iterative process is specially：
Setting maximum iteration N, in step 1.2) in random generation n point in, each is calculated according to formula (1) Impact point and the active force of other points, move 0.001 unit by point along Impact direction respectively, are made using maximum iteration To terminate iterated conditional, the n distribution of point is obtained.Each impact point one target rectangle of correspondence.
This iterative process is run multiple times, even if the point position of initial random generation each time is different, but the n for finally giving The distribution of individual point is approximate.100 iterative process of operation, are checked, the conspicuousness for obtaining to the distance between each point using t Much larger than 0.05, it is not significantly different between the sample of surface, the distribution for demonstrating point produced by iteration has stability.
Second step, by step 1.2) at random generation n point be extended to face, carry out posteriority collision detection
Using the wall in boundary representation facility layout, the shape on border is also rectangle, because all of facility is all necessary It is distributed in factory, so facility rectangle is also respectively in border.
By step 1.2) at random n point of generation be extended to face, described face is the facility of expression rectangle；When two facilities When rectangle is overlapped, that is, collide, mutually exclusive active force is produced between the rectangle for producing collision；By all of rectangle two-by-two Between collision take into account, carry out posteriority collision detection, posteriority collision detection is by comparing the border of facility rectangle, it is determined that touching Hit type.Described collision includes three major types, as shown in Figure 3.Force direction between two facilities for colliding with touch The centre of form for hitting facility rectangle is relevant with the centre of form of target facility rectangle, and the size of active force is proportional to the area of overlapping region. Fig. 4 in Figure of description illustrates the interaction force formed after two facilities collide.Cross hatched regions domain representation is overlapped Region, that is, the region for colliding, the area of overlapping region also represent the size of active force simultaneously.The direction of active force also and Crash type is relevant, and wherein the active force produced by the first kind and the collision of the 3rd class as shown in a in Fig. 4, produced by collision of the second kind Raw active force is as shown in b in Fig. 4.
3rd step, eliminates the collision between collision facility
The force action of the active force that other any rectangles are produced to target rectangle promotes rectangle to conjunction on target rectangle The side of power moves up, and the collision area of target rectangle is gradually reduced, and the power acted on target rectangle also reduces；When target square When active force in shape is reduced to given force threshold, active force promotes rectangle movement, target square after being multiplied by reinforcement coefficient The collision area of shape continues to reduce, until eliminating the collision between collision facility.
Described rectangle is directly proportional to the displacement on the direction made a concerted effort to making a concerted effort on target rectangle is acted on, ratio Coefficient represents that collision acts the strength grade of power, is divided into 1,2,3,4 four grades, and corresponding proportionality coefficient is incremented by successively, Set up strength grade and be for the efficiency that adjustment impact force is produced at any time in an iterative process, described efficiency can to iteration when Between produce influence.Described reinforcement coefficient is 10, this is done because when overlapping region very hour, the displacement of rectangle It is very small, can improve the efficiency of elimination collision using coefficient is strengthened.
4th step, calculates the active force that border produces to rectangle
When the side of rectangle at least one is outside border, it is necessary to detect the collision between border and rectangle, border is produced to rectangle Raw active force is attraction, and active force promotes rectangle to be moved to the center of bounding rectangles.The rectangular area fallen outside border regards Make the overlapping region of rectangle and border, border is directly proportional to the active force that rectangle is produced to the area of overlapping region.
5th step, according to the active force that border produces to rectangle, boundary contraction or expansion
All of facility all must be distributed across in border, and the presence on border constrains the movement of facility.When initial, relative to institute There is the area sum of rectangle, the area of bounding rectangles is sufficiently large；While carrying out the collision elimination described in the 3rd step each time, side Boundary is gradually reduced since original state, and after carrying out multiple impacts elimination, border is contracted to the boundary threshold of setting, now enters again When row collision is eliminated, border proceeds by expansion；When border is more than boundary threshold, border contracting while collision is eliminated is carried out It is small.
Described border reduce or expansion degree and the active force that rectangle is produced to border with joint efforts numerically into anti- Than, that is, act on it is borderline smaller with joint efforts, border reduce or expand more.The diminution or expansion on described border Variable quantity be shrinkage/expand=α/(F+ β), wherein, α and β be constant, F is that rectangle acts on borderline conjunction Power.Rectangle is numerically equal to the area sum of the rectangular area outside border to the active force that border produces.
6th step, as iteration is carried out, border is excessive to the active force that facility rectangle is produced, and can suppress the movement of facility, Therefore the active force that border produces to wall needs to be standardized.The content of the 3rd step to the 5th step is repeated, the first round is carried out Iteration, boundary contraction, to border in free space be less than threshold value, terminate first round iteration, obtain the layout knot of facility Really.Described threshold value accounts for the 80% of boundary space for 0.8, i.e. free space；Described free space is given in the form of ratio,Wherein, areabRepresent boundary areas, areaiRepresent square Shape area.
7th step, if in the layout result that obtains of the 6th step, collision or facility between facility are deposited with the collision on border , proceed the second wheel iteration, the 3rd step to the 5th step is repeated, now facility expands border the active force that border produces .The condition of the second wheel iteration ends is that collision is completely eliminated, and iteration obtains the layout result of facility after terminating.
Beneficial effects of the present invention are：The layout method that area does not wait facility, phase can be efficiently solved there is provided a kind of Method than asking for being laid out optimal solution by complicated intelligent algorithm in practical application, the present invention is to can be effectively simply Optimal layout result is obtained according to work unit complex interdependency.
Brief description of the drawings
Fig. 1 is work unit complex interdependency figure
What Fig. 2 was represented is to use proposed range formula to calculate any point-to-point (1,1) to distance；
Fig. 3 is the crash type of facility；In figure, the rectangle with horizontal shading line represents target facility, with vertical hacures Rectangle represent collision facility, one is divided into 3 classes, is classified as a class per a line；A () is to be formed to touch in the upper right side of target facility Hit；B () is to form collision on the upper left side of target facility；C () is to form collision in the lower left of target facility；D () is in mesh The lower right for marking facility forms collision；E () is to form collision in the right of target facility；F () is in the upper square of target facility Into collision；G () is to form collision in the left of target facility；H () is the collision formed below in target facility；I () is in mesh That marks facility is internally formed collision, and the side of target facility four surrounds another facility；J () is to be touched in being internally formed for target facility Hit, the upper and lower both sides of target facility surround another facility；K () is the collision that is internally formed in target facility, target facility or so Both sides surround another facility；
Fig. 4 is the force diagram produced when facility collides；A () is target facility when upper left side forms and collides The impact force of generation；B () up forms the impact force produced during collision for target facility；
Specific embodiment
A kind of facility layout method based on collision detection, comprises the following steps：
(1) input quantity:Relational matrix R=(relationsI, j)；Facility size；Force strength produced by collision etc. Level；Force threshold；Boundary threshold.
(2) n point is generated at random in the square that length is 1, each point is the centre of form of corresponding matrix, wherein n Represent the sum of facility.Power is acted between each two point, the computing formula of power is such as shown in (1) and (2).
(3) act on to order about making a concerted effort on impact point and a little move, bring into operation this iterative process, described iteration mistake Journey is specially：
Setting maximum iteration N, in the random n point for generating in step (2), each is calculated according to formula (1) Impact point and the active force of other points, move 0.001 unit by point along Impact direction respectively, are made using maximum iteration To terminate iterated conditional, the n distribution of point is obtained.The false code of iterative process is as follows：
(4) point by random generation in step (2) is extended to face, carries out posteriority collision detection.
By n point of generation is extended to face at random in step (2), described face is the facility for representing rectangle.Two facility squares When shape is overlapped, that is, collide, mutually exclusive active force is produced between the rectangle for producing collision.Collision detection algorithm will be all Rectangle two-by-two between overlap take into account, carry out posteriority collision detection.Active force between two facilities for colliding Direction is relevant with the centre of form of collision facility rectangle and the centre of form of target facility rectangle, the size of active force and the area of overlapping region It is proportional.Collision detection determines crash type by comparing the border of facility rectangle.The direction of active force also has with crash type Close, wherein the first kind and the 3rd class collide produced active force as shown in a in Figure of description 4, produced by collision of the second kind Active force as shown in b in Fig. 4.
(5) collision between collision facility is eliminated.
The force action of the active force that other any rectangles are produced to target rectangle promotes rectangle to conjunction on target rectangle The side of power moves up, and the collision area of target rectangle is gradually reduced, and the power acted on target rectangle also reduces；When target square When active force in shape is reduced to given force threshold, active force promotes rectangle movement, target square after being multiplied by reinforcement coefficient The collision area of shape continues to reduce, until eliminating the collision between collision facility.
The distance of described movement is directly proportional to making a concerted effort on target rectangle is acted on, and proportionality coefficient represents that collision produces work Strength grade firmly.Described reinforcement coefficient is 10, this is done because when overlapping region very hour, the movement of rectangle away from From also very small, the efficiency of elimination collision can be improved using coefficient is strengthened.(4) collision in collision detection and (5) in disappears The false code removed is as follows：
Define the threshold value of active force
It is overlap with border with the regional extent detection checkout facility on border according to facility
Regional extent according to facility and border determines the crash type of facility and border
Overlapping region and crash type according to detection calculate the active force that border produces to facility
Calculate force direction of the border to facility
Active force of the superposition border to target facility
(6) active force that border produces to rectangle is calculated.When the side of rectangle at least one is outside border, it is necessary to detect border Collision between rectangle, border is attraction to the active force that rectangle is produced, and active force promotes rectangle in bounding rectangles The heart is moved.The rectangular area outside border that falls is regarded as the overlapping region of rectangle and border, the active force that border produces to rectangle with The area of overlapping region is directly proportional.
(7) boundary contraction.When initial, relative to the area sum of all rectangles, the area of bounding rectangles is sufficiently large；It is each While the secondary collision carried out described in the 3rd step is eliminated, border is gradually reduced since original state, carries out multiple impacts elimination Afterwards, border is contracted to the boundary threshold of setting, and when now carrying out collision elimination again, border proceeds by expansion；When border is more than During boundary threshold, carry out border while collision is eliminated and reduce.
(8) repeat the content of the 3rd step to the 5th step, carry out first round iteration, boundary contraction, to border in free time it is empty Between be less than threshold value, terminate first round iteration, obtain the layout result of facility.Collision detection facility layout algorithm is persistently collided Detection and elimination, boundary contraction, until free space is less than threshold value, terminate first round iteration, obtain the layout result of facility.
(9) if in the layout result that obtains of the 6th step, collision or facility between facility exist with the collision on border, after Continuous to carry out the second wheel iteration, now facility makes boundary expansion to the active force that border produces.Second wheel iteration ends condition be Collision is completely eliminated, and iteration obtains the layout result of facility after terminating.The false code of first round iteration and the second wheel iteration is as follows：
The central point of initiation facility
Point is extended to face
Initialization border (compared with the area sum of all facilities, sufficiently large)

Claims (5)

1. a kind of facility layout method based on collision detection, it is characterised in that following steps：
The first step, determines input quantity, and the intermolecular forces according to point are moved, and are iterated
1.1) using relational matrix R=(relationsI, j) represent facility between correlation, and set collision produced by The strength grade of active force, force threshold, boundary threshold；Described relational matrix is symmetrical matrix, element in relational matrix Value be real number；Described facility is represented that the size of the length of rectangle and expression facility wide, the position of form center of rectangle is represented by rectangle The position of facility；
1.2) the random generation n points in the square that length is 1, each point is the centre of form of corresponding matrix；Each two point it Between act power computing formula such as (1) and (2) it is shown：
force(pointi, pointsj)=((xj-xi)×relationsI, j×distanceI, j, (yj-yi)relationsI, j ×distanceI, j), i ≠ j (1)
distance i , j = - ( ( x j - x i ) 2 + ( y j - y i ) 2 - 5 ) ( x j - x i ) 2 + ( y j - y i ) 2 + 1 - - - ( 2 )
Wherein, (1,2 ..., n), n represents the sum of facility to i, j ∈；X, y are the coordinate of the point in two dimensional surface；
1.3) act on to order about making a concerted effort on impact point and a little move, described impact point is step 1.2) appointing in square Meaning point, bring into operation iterative process, and described iterative process is specially：
Setting maximum iteration N, in step 1.2) in random generation n points in, each impact point is calculated according to formula (1) The active force put with other, moves 0.001 unit, using maximum iteration as termination by point along Impact direction respectively Iterated conditional, obtains the distribution of n points；Each impact point one target rectangle of correspondence；
This iterative process is run multiple times, even if the point position of initial random generation each time is different, but the n points for finally giving Distribution results are approximate, and the distribution of point produced by iteration has stability；
Second step, by step 1.2) in random generation n points be extended to face, carry out posteriority collision detection
Using the wall in boundary representation facility layout, the shape on border is also rectangle；All of facility is distributed in factory, Facility rectangle is also in border；
By step 1.2) in random generation n points be extended to face, described face is the facility for representing rectangle；When two facility rectangle weights When folded, that is, collide, mutually exclusive active force is produced between the rectangle for producing collision；By between all of rectangle two-by-two Collision is taken into account, carries out posteriority collision detection, and posteriority collision detection is by comparing the border of facility rectangle, it is determined that colliding class Type；
3rd step, eliminates the collision between collision facility
The force action of the active force that other any rectangles are produced to target rectangle on target rectangle, promote rectangle to make a concerted effort Side moves up, and the collision area of target rectangle is gradually reduced, and the power acted on target rectangle also reduces；When on target rectangle Active force when being reduced to given force threshold, active force promotes rectangle movement after being multiplied by reinforcement coefficient, target rectangle Collision area continues to reduce, until eliminating the collision between collision facility；Described rectangle is to the displacement on the direction made a concerted effort It is directly proportional to making a concerted effort on target rectangle is acted on；Adoption rate coefficient represents that collision acts the strength grade of power；
4th step, calculates the active force that border produces to rectangle
When the side of rectangle at least one is outside border, it is necessary to detect the collision between border and rectangle, border produces to rectangle Active force promotes rectangle to be moved to the center of bounding rectangles；The rectangular area outside border that falls is regarded as the overlay region of rectangle and border Domain, border is directly proportional to the active force that rectangle is produced to the area of overlapping region；
5th step, according to the active force that border produces to rectangle, boundary contraction or expansion
All of facility is distributed in border, the movement of boundary constraint facility；When initial, relative to all rectangles area it With the area of bounding rectangles is sufficiently large；While carrying out the collision elimination described in the 3rd step each time, border is opened from original state Beginning is gradually reduced, and after carrying out multiple impacts elimination, border is contracted to the boundary threshold of setting, when now carrying out collision elimination again, Border starts expansion；When border is more than boundary threshold, carries out border while collision is eliminated and reduce；
6th step, as iteration is carried out, border is excessive to the active force that facility rectangle is produced, and suppresses the movement of facility, border pair The active force that wall is produced needs to be standardized；The 3rd step is repeated to the 5th step, first round iteration, boundary contraction, to side is carried out Free space in boundary is less than threshold value, terminates first round iteration, obtains the layout result of facility；
7th step, if in the layout result that obtains of the 6th step, collision or facility between facility exist with the collision on border, after It is continuous to carry out the second wheel iteration, boundary expansion；The condition of the second wheel iteration ends is that collision is completely eliminated, and iteration is set after terminating The layout result applied.
2. facility layout method according to claim 1, it is characterised in that the reinforcement coefficient described in the 3rd is 10.
3. facility layout method according to claim 1 and 2, it is characterised in that the diminution on the border described in the 5th step Or the variable quantity of expansion is shrinkage/expand=α/(F+ β), wherein, α and β is constant, and F is that rectangle is acted on border Make a concerted effort；Described rectangle is numerically equal to the area sum of the rectangular area outside border to the active force that border produces.
4. facility layout method according to claim 1 and 2, it is characterised in that described in the 6th step Threshold value is 0.8, i.e., free space accounts for the 80% of boundary space；Described free space Wherein, areabRepresent boundary areas, areaiRepresent rectangular area.
5. facility layout method according to claim 3, it is characterised in that the threshold value described in the 6th step is 0.8, i.e. free space account for the 80% of boundary space；Described free space is given in the form of ratio,Wherein, areabRepresent boundary areas, areaiRepresent square Shape area.
CN201710038238.7A 2017-01-19 2017-01-19 A kind of facility layout method based on collision detection Pending CN106845704A (en)

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Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105989695A (en) * 2015-02-15 2016-10-05 中国移动通信集团公司 Guarding object movement risk evaluation method and device

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105989695A (en) * 2015-02-15 2016-10-05 中国移动通信集团公司 Guarding object movement risk evaluation method and device

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
AMIR MOHAMMAD ESMAIEELI SIKAROUDI等: "Facility layout by collision detection and force exertion heuristics", 《JOURNAL OF MANUFACTURING SYSTEMS》 *

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