CN103336855B - A kind of two-dimentional irregular nesting method based on many subgroups particle cluster algorithm - Google Patents
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- 239000002245 particle Substances 0.000 title claims abstract description 59
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- 239000000463 material Substances 0.000 claims abstract description 32
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- 238000010586 diagram Methods 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
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- 238000002922 simulated annealing Methods 0.000 description 2
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Abstract
A kind of two-dimentional irregular nesting method based on improved Particle Swarm Algorithm, comprise the following steps: the first step, the geometric figure of print and material is converted to a series of two-dimensional coordinate interval, then use the left searching algorithm in the heuristic end to judge the two dimension interval of print and material whether the overlapping print that moves is relative to the position in material; Second step, modified PSO search procedure: cross the method dividing multiple subgroup, when not changing the parameter tending to current optimum solution, add the impact of subgroup optimum solution on particle in subgroup, during the maximum iteration time set when the iterations of population reaches initial, particle stops iteration, obtains current globally optimal solution as final layout project.The invention provides a kind of there is good search capability while, search speed is fast, last solution is better, stock layout the is respond well two-dimentional irregular nesting method based on improved Particle Swarm Algorithm.
Description
Technical field
The present invention relates to Computer Aided Nesting technology, especially a kind of Nesting.
Background technology
At present, both at home and abroad the Nesting of irregular part is concentrated in didactic modern optimization method substantially, mainly contain simulated annealing, genetic algorithm, particle cluster algorithm (PSO) etc.In practice, because simulated annealing is by the impact of annealing speed, speed is fast, is easily absorbed in local extremum, and speed is then difficult to the needs that can not meet people slowly; Genetic algorithm is then often than being easier to " precocity ", and local search ability is poor; PSO algorithm has stronger local search ability, but is also easily absorbed in extremal region and is difficult to jump out.
The range of application of Cutting Stock Problem widely, as panel beating stock layout, glass tailor, cloth-cutting etc., because above-mentioned industry turnout is large, particularly some material is costly, and therefore, the raising of Nesting Algorithms efficiency can produce very large social benefit.
Summary of the invention
In order to overcome the deficiency being easily absorbed in extremal region, have impact on stock layout effect of existing Nesting, the invention provides a kind of there is good search capability while, search speed is fast, last solution is better, stock layout the is respond well two-dimentional irregular nesting method based on many subgroups particle cluster algorithm.
The technical solution adopted for the present invention to solve the technical problems is:
Based on a two-dimentional irregular nesting method for many subgroups particle cluster algorithm, comprise the following steps:
The first step, is converted to a series of two-dimensional coordinate by the geometric figure of print and material interval, then use the left searching algorithm in the heuristic end to judge the two dimension interval of print and material whether the overlapping print that moves is relative to the position in material;
Second step, modified PSO search procedure is as follows:
1) inverse of the height after entering using print is as fitness value, and fitness value 1/H is larger, enters effect better;
2) state that enters of each print mainly contains three kinds: enter order, the anglec of rotation and mirror image, described in enter the span 1 ~ n of order order, n is print sum; The span of anglec of rotation angle 0 ° ~ 360 °, whether symmetrical about y-axis mirror image mirror represents, 0 ~ 1,0 expression is not in relation to y-axis symmetry, and 1 represents symmetrical about y-axis;
3) using 2) in three parameters proposing as three elements of the elementary particle in constituent particle group, elementary particle described in random initializtion;
4) calculate the European geometric position of each particle, according to the order from small to large from initial point distance, all particles are divided into M subgroup, M < n;
5) each optimum configurations is as follows:
x
ij=〈order
ij，angle
ij，mirror
ij〉
The position vector of a jth particle in i-th subgroup;
v
ij=〈v_ord
ij，v_ang
ij，v_mir
ij〉
The velocity vector of a jth particle in i-th subgroup;
p
ij=〈p_ord
ij，p_ang
ij，p_mir
ij〉
The history optimum position vector of a jth particle in i-th subgroup;
psg
i=〈psg_ord
i，psg_ang
i，psg_mir
i〉
History optimum position, i-th subgroup vector;
p
g=〈pg
ord，pg
ang，pg
miri〉
Global history optimum position vector;
6) speed of particle and location updating formula as follows:
v
ij(d＋1)=w×v
ij(d)＋c
1×rand
1ij×[p
ij(d)-x
ij(d)]
+c
2×rand
2ij×[psg
i(d)-x
ij(d)]
+c
3×rand
3ij×[p
g(d)-x
ij(d)]
x
ij(d+1)=x
ij(d)+v
ij(d+1)
Wherein d is iterations, c
l, c
2, c
3represent the history optimum solution of trend particle own, the optimum solution of subgroup, the speeds control factor of globally optimal solution respectively, wherein c
3> c
2> c
l> 0, rand
1ij, rand
2ij, rand
3ijbe the random factor between 0 ~ 1, w is the value w(d of inertial factor, w) linear decrease with the increase of iterations:
w(d)=u-v×d/D
D is maximum iteration time, and the value of u, v meets;
7) more new historical optimum solution
After each particle carries out speed renewal, enter in material by the left searching algorithm in the heuristic end, calculate the fitness value F of particle, thus the history optimal location of more new particle itself, the optimal location of subgroup and the overall situation;
8), during the maximum iteration time set when the iterations of population reaches initial, particle stops iteration, obtains current globally optimal solution as final layout project; If do not reach maximum iteration time, continue to perform from step 6).
Further, in described step 7), when more excellent solution is not all found in certain subgroup in continuous n iterative process, judge that this subgroup has been absorbed in locally optimal solution, to the random replacement of described subgroup.
Further, in the described first step, it is as follows that the left searching algorithm in the heuristic end obtains process: print first enters from the lower left corner of material, print is below turned right and is entered successively, when print exceeds the right side of material, print is moved relative on material, and again search for the remaining space of material from the left side, so move in circles, until stop when print all enters or print overflows material top.
Technical conceive of the present invention is: by dividing the method for multiple subgroup, when not changing the parameter tending to current optimum solution, add the impact of subgroup optimum solution on particle in subgroup, local search ability is strengthened with this, and when subgroup is absorbed in local extremum, carry out eliminating to subgroup and reset, make colony have an opportunity to jump out local extremum.
Beneficial effect of the present invention is mainly manifested in: while having good search capability, search speed is fast, last solution is better, stock layout is respond well.
Accompanying drawing explanation
Fig. 1 is the program flow diagram of two-dimentional irregular nesting underlying algorithm.
Fig. 2 is the program flow diagram of modified PSO algorithm.
Fig. 3 is for certain cover fashion plate is based on stock layout design sketch of the present invention.
Embodiment
Below in conjunction with accompanying drawing, the invention will be further described.
With reference to Fig. 1 ~ Fig. 3, a kind of two-dimentional irregular nesting method based on many subgroups particle cluster algorithm, comprises the following steps:
The first step, the selection of two-dimentional irregular nesting underlying algorithm
For the typesetting of the two-dimentional irregular print of process, first the profile determining print is needed, to enter in process at print and to judge whether each print can be overlapping, the present invention selects the geometric figure of print and material to be converted to a series of two-dimensional coordinate interval, thus the complicacy departing from irregular geometric figures carries out stock layout, then use the heuristic end left searching algorithm (HBLS) judge the two dimension interval of print and material whether the overlapping print that moves is relative to the position in material, complete the underlying algorithm of two-dimentional irregular nesting with this, its flow process can refer to Fig. 1.
The basic ideas of HBLS algorithm are: print first enters from the lower left corner of material, print is below turned right and is entered successively, when print exceeds the right side of material, print is moved relative on material, and from the left side, again search for the remaining space of material, so move in circles, until stop when print all enters or print overflows material top.
Second step, modified PSO searching algorithm
1) print of layer with the end enters algorithm, the state parameter just entered by print by searching algorithm passes to underlying algorithm and processes, thus the fitness value F(the present invention calculating each individuality enter using print after the inverse (1/H) of height as fitness value, fitness value is larger, enters effect better).
2) state that enters of each print mainly contains three kinds: enter order (order, 1 ~ n, n are print sum), the anglec of rotation (angle, 0 ° ~ 360 °), mirror image (mirror, symmetrical about y-axis, 0 ~ 1)
3) using 2) in three parameters proposing as three elements of the elementary particle in constituent particle group, the sum of particle is set as 30 here, and these 30 particles of random initializtion.
4) calculate the European geometric position of each particle, according to the order from small to large from initial point distance, 30 particles are divided into 5 parts, every part of 6 particles, namely divide into 5 subgroups.Be to allow in original state each subgroup be distributed in zones of different as far as possible according to the object that European geometric distance divides, strengthen the ability of searching optimum of algorithm.
5) each optimum configurations is as follows:
x
ij=(order
ij,angle
ij,mirror
ij〉
The position vector of a jth particle in i-th subgroup
v
ij=〈v_ord
ij，v_ang
ij，v_mir
ij〉
The velocity vector of a jth particle in i-th subgroup
p
ij=〈p_ord
ij，p_ang
ij,p_mir
ij〉
The history optimum position vector of a jth particle in i-th subgroup
psg
i=〈psg_ord
i，psg_ang
i，psg_mir
i〉
History optimum position, i-th subgroup vector
p
g=<pg
ord，pg
ang，pg
miri>
Global history optimum position vector
6) speed of particle and location updating formula as follows:
v
ij(d+1)=w×v
ij(d)+c
1×rand
1ij,×[p
ij(d)-x
ij,(d)]
+c
2×rand
2ij×[psg
i(d)-x
ij(d)]
+c
3×rand
3ij×[p
g(d)-x
ij(d)]
x
ij(d+1)=x
ij(d)+v
ij(d+1)
Wherein d is iterations, it can thus be appreciated that the renewal of the every generation of particle is determined by the data of previous generation, c
l, c
2, c
3represent the history optimum solution of trend particle own, the optimum solution of subgroup, the speeds control factor of globally optimal solution respectively, wherein c
3> c
2> c
l> 0, rand
1ij, rand
2ij, rand
3ijbe the random factor between 0 ~ 1, w is inertial factor, and when w is larger, algorithm is to solution space extensive search; Otherwise algorithm is searched among a small circle, the value of w is linear decrease with the increase of iterations:
w(d)=u-v×d/D
D is maximum iteration time, and the value of u, v meets O < v < u < 1.
In classical PSO algorithm, the speed of particle more new formula is:
v
ij(d+1)=w×v
ij(d)+c′
1×rand
1ij×[p
ij(d)-x
ij(d)]
+c′
3×rand
3ij×[p
g(d)-x
ij(d)]
Contrast with the PSO algorithm parameter improved, have following relation:
c′
l=c
l+c
2
c′
3=c
3
Modified PSO algorithm adds the concept of subgroup, and in speed more new formula, add the impact of subgroup optimum solution, strengthens Local Search, but c
3do not change, thus ensure that algorithm convergence is not weakened in the trend of more excellent solution.
7) more new historical optimum solution
After each particle carries out speed renewal, enter in material by bottom Nesting Algorithms, calculate the fitness value F of particle, thus the history optimal location of more new particle itself, the optimal location of subgroup and the overall situation.
8) the superseded and reset mechanism of subgroup
The problem of locally optimal solution is easily absorbed in for PSO algorithm, eliminating and reset mechanism of the subgroup of subgroup is added in the present invention, when more excellent solution is not all found in certain subgroup in continuous n iterative process, so, think that this subgroup has been absorbed in locally optimal solution, now by the random replacement to subgroup, this subgroup can be made to have an opportunity to jump out locally optimal solution, thus enhance the ability of searching optimum of algorithm.
9), during the maximum iteration time set when the iterations of population reaches initial, particle stops iteration, obtains current globally optimal solution as final layout project.If do not reach maximum iteration time, continue to perform from step 6).
With reference to Fig. 3, stock layout design sketch of the present invention, (material width: 1200mmm, print number: 18, iterations: 600, stock layout height H: 901mm, stock utilization: 78.1%).
Claims (2)
1., based on a two-dimentional irregular nesting method for many subgroups particle cluster algorithm, it is characterized in that: comprise the following steps:
The first step, is converted to a series of two-dimensional coordinate by the geometric figure of print and material interval, and whether the overlapping print that moves is relative to the position in material for the two-dimensional coordinate interval of print and material then to use the left searching algorithm in the heuristic end to judge;
Second step, modified PSO search procedure is as follows:
1) inverse of the height after entering using print is as fitness value, and fitness value 1/H is larger, enters effect better;
2) state that enters of each print mainly contains three kinds: enter order, the anglec of rotation and mirror image, described in enter the span 1 ~ n of order order, n is print sum; The span of anglec of rotation angle 0 ° ~ 360 °, whether symmetrical about y-axis mirror image mirror represents, 0 ~ 1,0 expression is not in relation to y-axis symmetry, and 1 represents symmetrical about y-axis;
3) using 2) in three parameters proposing as three elements of the elementary particle in constituent particle group, elementary particle described in random initializtion;
4) calculate the European geometric position of each particle, according to the order from small to large from initial point distance, all particles are divided into M subgroup, M < n;
5) each optimum configurations is as follows:
x
ij＝<order
ij，angle
ij，mirror
ij>
The position vector of a jth particle in i-th subgroup;
v
ij＝<v_ord
ij，v_ang
ij，v_mir
ij>
The velocity vector of a jth particle in i-th subgroup;
p
ij＝<p_ord
ij，p_ang
ij，p_mir
ij>
The history optimum position vector of a jth particle in i-th subgroup;
psg
i＝<psg_ord
i，psg_ang
i，psg_mir
i>
History optimum position, i-th subgroup vector;
p
g＝<pg
ord，pg
ang，pg
miri>
Global history optimum position vector;
6) speed of particle and location updating formula as follows:
v
ij(d+1)＝w×v
ij(d)+c
1×rand
1ij×[p
ij(d)-x
ij(d)]
+c
2×rand
2ij×[psg
i(d)-x
ij(d)]
+c
3×rand
3ij×[p
g(d)-x
ij(d)]
x
ij(d+1)＝x
ij(d)+v
ij(d+1)
Wherein d is iterations, c
1, c
2, c
3represent the history optimum solution of trend particle own, the optimum solution of subgroup, the speeds control factor of globally optimal solution respectively, wherein c
3> c
2> c
1> 0, rand
1ij, rand
2ij, rand
3ijbe the random factor between 0 ~ 1, w is inertial factor, and the value w (d) of w is linear decrease with the increase of iterations:
w(d)＝u-v×d/D
D is maximum iteration time, and the value of u, v meets 0 < v < u < 1;
7) more new historical optimum solution
After each particle carries out speed renewal, enter in material by the left searching algorithm in the heuristic end, calculate the fitness value F of particle, thus the history optimal location of more new particle itself, the optimal location of subgroup and the overall situation;
When more excellent solution is not all found in certain subgroup in continuous n iterative process, judge that this subgroup has been absorbed in locally optimal solution, described subgroup is reset at random;
8), during the maximum iteration time set when the iterations of population reaches initial, particle stops iteration, obtains current globally optimal solution as final layout project; If do not reach maximum iteration time, continue from step 6) perform.
2. a kind of two-dimentional irregular nesting method based on many subgroups particle cluster algorithm as claimed in claim 1, it is characterized in that: in the described first step, it is as follows that the left searching algorithm in the heuristic end obtains process: print first enters from the lower left corner of material, print is below turned right and is entered successively, when print exceeds the right side of material, print is moved relative on material, and from the left side, again search for the remaining space of material, so move in circles, until stop when print all enters or print overflows material top.
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| CN109214557A (en) * | 2018-08-15 | 2019-01-15 | 浙江优尼家装饰科技有限公司 | A kind of irregular plate Nesting of two dimension |
| CN111275243B (en) * | 2020-01-08 | 2020-09-29 | 广东工业大学 | Two-dimensional irregular layout method for single-specification plate |
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| CN113189553A (en) * | 2021-01-28 | 2021-07-30 | 北京理工大学 | Multi-modal optimization-based micro-maneuvering multi-target rapid detection method |
| CN113032921B (en) * | 2021-03-16 | 2022-12-13 | 山东科技大学 | Layout algorithm based on parallel adaptive parameter cuckoo search and lowest horizontal line |
| CN113762607B (en) * | 2021-08-26 | 2023-05-30 | 甘肃同兴智能科技发展有限责任公司 | Prediction method for carbon emission of power grid enterprise |
| CN115629537A (en) * | 2022-12-22 | 2023-01-20 | 南京净环热冶金工程有限公司 | Heating furnace combustion control method and system based on subgroup improved particle swarm optimization PID |
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