CN103164752A - Heuristic one-dimensional blanking method based on stratified random search algorithm - Google Patents

Heuristic one-dimensional blanking method based on stratified random search algorithm Download PDF

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CN103164752A
CN103164752A CN2013101156366A CN201310115636A CN103164752A CN 103164752 A CN103164752 A CN 103164752A CN 2013101156366 A CN2013101156366 A CN 2013101156366A CN 201310115636 A CN201310115636 A CN 201310115636A CN 103164752 A CN103164752 A CN 103164752A
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blank
stock layout
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CN103164752B (en
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卢伟康
邹细勇
王国建
孟灿
金尚忠
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China Jiliang University
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Abstract

The invention discloses a heuristic one-dimensional blanking method based on a stratified random search algorithm. The method includes: A, using a parameterized model to signify one-dimensional blanking problems; B, preprocessing billets for combination; C, obtaining various stock layout modes through the stratified random search algorithm combined by random search and deep search; D, picking out an optimal stock layout mode according to a heuristic rule; E, adding the optimal stock layout mode and a time which does not exceed the current needed maximum time of reusing the billets into a current stock layout scheme, and updating a billet set to be laid; F, repeating processes of C, D and E until the total length of the billets to be laid less than the length of raw materials, and outputting the current stock layout scheme; and G, repeating processes of B, C, D, E and F for many times, and then performing compared screening on all stock layout schemes so as to obtain an optimal stock layout scheme. The heuristic one-dimensional blanking method based on the stratified random search algorithm can avoid blindness of a traditional random search algorithm and is high in computation speed, and the obtained stock layout scheme adapts to practical production needs.

Description

A kind of heuristic one-dimensional stock-cutting method based on the stratified random searching algorithm
Technical field
The invention belongs to the integral nonlinear planning field, be specifically related to a kind of heuristic one-dimensional stock-cutting method based on the stratified random searching algorithm.
Technical background
In modern industry is produced, comprise the industries such as iron and steel, building materials, paper roll, film, all exist and how to arrange single cutting stock problems, wherein One-dimensional Cutting Stock Problem is the most general problem that faces in producing.How so-called One-dimensional Cutting Stock Problem when referring to that starting material and material requested dimension all are one dimension, optimizes cutting stock under known order requirements and raw material data, make starting material be fully used as far as possible, and cost obtains the planning problem saved as far as possible.
The single problem of blanking row belongs to np problem, and it has been generally acknowledged that does not have a kind of method can necessarily find the optimum solution of np problem.In general find the solution this problem two kinds of methods are arranged: a kind of method of finding the solution integral nonlinear planning that is based on, another kind is heuritic approach.
In the method for existing solution One-dimensional Cutting Stock Problem, such as the linear programming method take column generation method as representative, there is following problem:
(1) solution that generates is not generally integer solution, must round optimization, but easily causes again the blank number that blanking produces to surpass former demand after rounding optimization;
(2) the contained stock layout mode of the solution number that generates is more, makes in actual production and need repeatedly adjust cutting machine;
(3) when the blank kind of demand in order is more, increase severely the computing time of algorithm, is difficult to adapt to actual needs.
And the intelligent algorithms such as heuritic approach such as order heuritic approach, genetic algorithm, ant group algorithm are by dynamically setting up respective rule or value assessment formula, these rules or value assessment formula mean purpose and the direction of final solution, can bootstrap algorithm close to these purposes and direction dynamically, thus nearly optimum solution for this problem found.
Searching keyword " baiting method ", find following patented claim: application number is 200810227039.1 Chinese patent application " the raw-material one-dimensional stock-cutting method of a kind of saving "; Application number is 201110139183.1 Chinese patent application " Intelligent steel bar screening blanking optimization method ".Above patented claim is all with the practical problems that solves one-dimensional cutting-stock problem.
Application number is 201110139183.1 Chinese patent application " Intelligent steel bar screening blanking optimization method ", taked traversal when obtaining the Steel Reinforcing Bar Material combination, in the situation that sample blank kind fewer can also being fit to also, but when sample blank kind increases, its blanking number of combinations is the exponential function attitude and rises, and obviously the method is not suitable for solving extensive cutting stock problems.And for traditional heuristic random searching algorithm, with reference to " based on the one dimension Optimization Cutting of gene colony " Shanghai Communications University's journal the 6th phase in 2006, when random fashion produces the blanking initial solution, general whole parts or the charge length sum that all can occur on same raw material surpasses its length restriction, namely is easy to occur the rough sledding of infeasible solution; When the blanking dividers mould increases, much more much bigger than Feasible Solution Region due to the random search territory, the blindness of traditional random search algorithm will make the initialization set of feasible solution will spend a large amount of computing times, be unfavorable for being applied in actual production and go.
During one-dimensional stock-cutting method also should be considered to use to the requirement of stock layout mode number, when in commercial production reality, starting material being carried out the blanking cutting, due to extra manpower and materials of need cost such as adjustment cutting machines, so enterprise can tend to the few layout project of stock layout mode number.
Summary of the invention
For the deficiency on prior art, fundamental purpose of the present invention is to provide a kind of one-dimensional stock-cutting method that solves extensive multi-blank kind, can automatically calculate in the short period of time according to length, the quantity required of raw-material length and demand blank excellent layout project.In order to overcome the blindness of traditional random search algorithm, the present invention has adopted the hierarchical search strategy, guarantees the validity of ground floor random search by the deep search of the second layer, and making the stock layout mode of at every turn obtaining is all a feasible solution.And in order to satisfy commercial Application to the requirement of stock layout mode number, the present invention has adopted preferential selection to be counted reusable stock layout mode by more times in heuristic rule.
For achieving the above object, the technical solution used in the present invention is as follows:
A kind of heuristic one-dimensional stock-cutting method based on the stratified random searching algorithm said method comprising the steps of:
A, One-dimensional Cutting Stock Problem is represented with parameterized model:
Raw-material length is L, the blank of total m kind different length specification in the blanking task, and length is respectively l 1, l 2L m, corresponding demand number is respectively d 1, d 2D mThe layout project of the solution of cutting stock problems for can repeatedly being combined into by multiple stock layout mode, wherein the stock layout mode is for to be combined into total length less than a kind of cutting mode of starting material length L with all size blank, and the clout length of every kind of stock layout mode is that the starting material length L deducts the difference after the blank pattern length in this stock layout mode; If total n kind stock layout mode in layout project, the number of times of reusing of each stock layout mode is respectively x 1, x 2X n, in i kind stock layout mode, the quantity of each blank is respectively a il, a i2A im, wherein i represents i kind stock layout mode; If the total radical of starting material that Z is blanking will be used is minimum as objective function take the total radical of consumption of raw material, the target of One-dimensional Cutting Stock Problem and constraint relation are not:
MinZ = Σ i = 1 n x i
St Σ i = 1 n a ij · x i = d j , j＝1，2......m
Σ j = 1 m a ij · l j ≤ L , i＝1，2......n
Wherein, x iAnd a ijBe integer and x i＞0, a ij〉=0;
B, blank combination pre-service, initialization blanking task be for being remained stock layout blank collection, and make that current layout project is sky;
C, obtain multiple stock layout mode by the stratified random searching algorithm, form stock layout mode sample;
D, every kind of stock layout mode to obtaining are no more than according to it number of times and corresponding clout length that multipotency of current demand of blank is reused, and optimize the highest stock layout mode of evaluation of estimate by heuristic rule;
E, stock layout mode that evaluation of estimate is the highest join in current layout project after being no more than with it number of times repeated combination that multipotency of current demand of blank is reused; Treat the stock layout blank by described stock layout mode and number of times deduction again from the blanking task, upgrade the stock layout demand of the treating number of all specification blanks, obtain new blanking task;
The process of F, repetition C, D, E, until treat that the total length of stock layout blank is less than the starting material length L in the blanking task after upgrading, treat that with residue the combination of stock layout blank joins in current layout project as last a kind of stock layout mode, obtains a complete current layout project and records this layout project this moment;
G, repeatedly repeat the process of B, C, D, E, F, then all layout project of record compared screening, with the optimum layout project that the filtered out solution as One-dimensional Cutting Stock Problem.
Wherein, the combination of the blank described in step B pre-service is carried out in such a way:
First m kind blank is arranged from small to large by length, the corresponding length of each blank is respectively C 1, C 2C m
Then can repeatedly select and make up in m kind blank, be number that 1 to N blank set is a degree of depth combination, total M of described depth groups unification, and the value of M is:
M＝m 1+m 2+…+m N，
At last, M combination made up the length of interior blank and sequenced from small to large order by each.
Wherein, the stratified random searching algorithm described in step C comprises the search of two levels, and ground floor is the roulette random search, and the second layer is deep search; Transfer to when working as the accumulation charge length of random combine and enter in interval [inf, sup] in the ground floor search procedure and carry out second layer search; Second layer search is carried out in such a way:
From using binary search to search a degree of depth combination by length with in M the combination that sequence is good from small to large, when the random combine that makes described degree of depth combination and obtained in the ground floor search procedure formed a kind of stock layout mode together, the clout length Y of described stock layout mode was minimum.
Wherein, the end points value of described interval [inf, sup] is as follows:
inf＝L-N*C m，
sup＝L-C 1，
Wherein, due to when the random search, it is too small even less than 0 that N crosses the value that conference makes inf, actual conditions have been run counter in inf＜0, and the too small meeting of inf when causing obtaining a kind of stock layout mode the roulette random search procedure too short, with the hunting zone of limit algorithm, be unfavorable for obtaining stock layout mode preferably, therefore make the value of N satisfy inf＞1/3L, that is:
inf＝L-N*C m＞L/3；
Otherwise, will reduce the number of combinations M in deep search if N is too small, make the sample number of deep search process insufficient, be unfavorable for obtaining the stock layout mode that clout length Y tries one's best little.Comprehensive above the analysis, the value of setting N is:
N = min { 4 , [ 2 L 3 C m ] } .
Wherein, being no more than the number of times that the multipotency of the current demand of blank is reused described in step D calculates in the following manner:
Respectively with the current actual blank demand of each blank in current stock layout mode divided by the quantity that has arranged in current stock layout mode, and get smallest positive integral in above-mentioned set, the value that is no more than the number of times U that the multipotency of the current demand of blank is reused is:
U = min { [ d j a ij ] } , a ij＞0，j＝1，2…m，
The sequence number of wherein supposing current stock layout mode is i, d jCurrent actual blank demand after expression is upgraded, a ijThe quantity that represents the j kind specification blank that arranged in current stock layout mode.
Wherein, heuristic rule described in step D is for to carry out the calculating of evaluation of estimate according to following formula to every kind of stock layout mode:
V＝g 1*U-g 2*Y，
Wherein, g 1, g 2Be two positive integers, g 1Just represent that the weight of U value in the V value is larger greatlyr, on the contrary g 2Represent that the weight of Y value in the V value is larger greatlyr.
Wherein, relatively screen described in step G by following three priority target from high to low and undertaken:
Total radical of G1, raw materials consumption is minimum;
G2, stock layout mode are minimum;
Clout length in G3, last a kind of stock layout mode is maximum.
Technique scheme has following beneficial effect:
1, the random search algorithm is improved, make algorithm can avoid blind search, improved significantly the search speed of feasible stock layout mode;
2, by setting up didactic value assessment formula, the bootstrap algorithm search can be by reusable stock layout mode as much as possible, thereby helps to reduce the number of stock layout mode in final layout project;
3, by three priority targets, all layout project are carried out automatic screening, the solution of the One-dimensional Cutting Stock Problem that obtains can save material resource, reduce cutting tool changing cost and make the remaining clout of last a kind of stock layout mode more;
4, one-dimensional stock-cutting method computing velocity of the present invention is fast, and layout project meets produces actual needs.
Description of drawings
Fig. 1 is the method flow schematic diagram that obtains a kind of stock layout mode and evaluation of estimate thereof in one-dimensional stock-cutting method of the present invention;
Fig. 2 produces the schematic flow sheet of a complete layout project in one-dimensional stock-cutting method of the present invention;
Fig. 3 is for to carry out with one-dimensional stock-cutting method of the present invention the result schematic diagram that an One-dimensional Cutting Stock Problem is found the solution.
Embodiment
The invention will be further described below in conjunction with embodiment and accompanying drawing.
As shown in Figure 1, for obtaining the method flow schematic diagram of a kind of stock layout mode and evaluation of estimate thereof in one-dimensional stock-cutting method of the present invention, the method comprises the following steps:
Step S11: initialization stock layout mode is about to represent that the chained list of stock layout mode is set to sky.
Step S12: with roulette algorithm random blank of choosing from the blank set for the treatment of stock layout, join in stock layout mode chained list, judge length and whether enter [inf, sup] interval.
The roulette algorithm refers to the identical random search algorithm of ratio that the selected probability of a certain length specification blank and its number account in treating the set of stock layout blank.As suppose that an order has Count=d 1+ d 2++ d mIndividual blank, with the random number in randomizer generation 1 to Count scope, it is interval which piece is random number fall, and just chooses this kind blank.
If T for the charge length of accumulation and, [inf, the sup] interval that judges whether the value of T enters; If turn step S13, continue cumulative otherwise turn step S12.
Step S13: but be to find a length and the most approaching combination less than clout length Y in degree of depth combination from the combination of M blank, the described degree of depth make up and existing by the roulette algorithm search to random combine form together a kind of stock layout mode.
Due to the execution along with algorithm, treat that the blank set meeting of stock layout diminishes, may cause in the combination of M degree of depth in the part combination certain blank number to surpass it and treat stock layout quantity, this combination can not be used when search depth makes up.Therefore under said circumstances, be K but suppose to have found the most approaching combination sequence number less than clout length Y, K can not be used due to this combination, so make K=K-1, namely searches forward.This search procedure last till find can adopted combination till.
Step S14: whether the length of judgement accumulation and T be greater than sup; If so, turn S15, otherwise turn S13.If search forward because the combination of certain degree of depth can not be used in step S13 adopt the shorter combination of length after, whole stock layout mode also may also need to add the short stock layout blank for the treatment of, this step has guaranteed the continuation combination of stock layout mode in this case.
Step S15: the multipotency that calculates this stock layout mode is reused number of times U and clout length Y, and calculates the value of this stock layout mode according to U and Y.
Wherein, the number of times U that multipotency is reused refers to that it is no more than the number of times that the current demand of blank treats that namely the multipotency of stock layout quantity is reused, and the stock layout mode is worth desirable g in the value formula of V 1/ g 2=10.
As shown in Figure 2, in one-dimensional stock-cutting method of the present invention, the flow process of a complete layout project of generation comprises the following steps:
S21: the initialization layout project is about to represent that the chained list of layout project is set to sky.
S22: judgement is treated the charge length of stock layout and whether less than the starting material length L, if turn step S25, otherwise is turned step S23.
S23: obtain multiple stock layout mode, therefrom find out the stock layout mode of evaluation of estimate maximum and this stock layout mode and multipotency thereof are reused number of times U and join in the layout project chained list.Wherein, adopt the step of S11 to S15 to obtain a sample loading mode and evaluation of estimate thereof at every turn, repeatedly, obtain multiple stock layout mode.
S24: upgrade and treat stock layout blank collection and turn step S22.Renewal is treated stock layout blank collection namely from treating that the stock layout blank concentrate to remove the blank that has used this stock layout mode, and described removal process repeats U time, and the result after removal is completed is as the new stock layout blank collection for the treatment of.
S25: export complete layout project.
Before the various stock layout modes and the corresponding access times U that record in step S23, treat that with current a kind of single stock layout mode that stock layout blank collection forms is together as a kind of layout project.
In the inventive method, repeatedly repeated execution of steps S21 is to step S25, thereby obtain multiple layout project, at last relatively filter out optimized that layout project according to set three priority target from high to low, namely first choose the minimum final layout project of conduct of raw materials consumption radical in each layout project; If have a plurality of layout project raw materials consumption radicals identical, choose the final layout project of conduct that wherein stock layout mode number is few; If still there is the stock layout mode number of a plurality of layout project also identical, choose the final layout project of conduct of clout length Y maximum in last a kind of stock layout mode wherein.
For the validity of proved method, adopt the actual blanking task of a BOPP film to test.
In this blanking task, starting material are large volume film, and its physical length is 8280, treat that the stock layout blank is that rouleau film length and demand volume number thereof are as follows respectively: 390*4,450*4,480*4,520*3,540*4,590*4,630*4,640*4,680*4,720*4,780*4,860*4,890*4,1500*10,1700*10, above-mentioned long measure is mm.
Figure 3 shows that the result after using one-dimensional stock-cutting method of the present invention to above-mentioned blanking task solving, wherein, layout project comprises 4 kinds of stock layout modes, first three clout of planting the stock layout mode is 0, the 4th kind of stock layout mode clout is 2080, use altogether 8 starting material, the layout project of generation is the optimum solution of this blanking task.
The above is only embodiments of the present invention; should be pointed out that for those skilled in the art, under the prerequisite that does not break away from the technology of the present invention principle; can also make some improvement and modification, these improve and modification also should be considered as the protection domain of the inventive method.

Claims (7)

1. the heuristic one-dimensional stock-cutting method based on the stratified random searching algorithm, is characterized in that, said method comprising the steps of:
A, One-dimensional Cutting Stock Problem is represented with parameterized model:
Raw-material length is L, the blank of total m kind different length specification in the blanking task, and length is respectively l 1, l 2L m, corresponding demand number is respectively d 1, d 2D mThe layout project of the solution of cutting stock problems for can repeatedly being combined into by multiple stock layout mode, wherein the stock layout mode is for to be combined into total length less than a kind of cutting mode of starting material length L with all size blank, and the clout length of every kind of stock layout mode is that the starting material length L deducts the difference after the blank pattern length in this stock layout mode; If total n kind stock layout mode in layout project, the number of times of reusing of each stock layout mode is respectively x 1, x 2X n, in i kind stock layout mode, the quantity of each blank is respectively a i1, a i2A im, wherein i represents i kind stock layout mode; If the total radical of starting material that Z is blanking will be used is minimum as objective function take the total radical of consumption of raw material, the target of One-dimensional Cutting Stock Problem and constraint relation are not:
MinZ = Σ i = 1 n x i
St Σ i = 1 n a ij · x i = d j , j＝1，2......m
Σ j = 1 m a ij · l j ≤ L , i＝1，2......n
Wherein, x iAnd a ijBe integer and x i＞0, a ij〉=0;
B, blank combination pre-service, initialization blanking task be for being remained stock layout blank collection, and make that current layout project is sky;
C, obtain multiple stock layout mode by the stratified random searching algorithm, form stock layout mode sample;
D, every kind of stock layout mode to obtaining are no more than according to it number of times and corresponding clout length that multipotency of current demand of blank is reused, and optimize the highest stock layout mode of evaluation of estimate by heuristic rule;
E, stock layout mode that evaluation of estimate is the highest join in current layout project after being no more than with it number of times repeated combination that multipotency of current demand of blank is reused; Treat the stock layout blank by described stock layout mode and number of times deduction again from the blanking task, upgrade the stock layout demand of the treating number of all specification blanks, obtain new blanking task;
The process of F, repetition C, D, E, until treat that the total length of stock layout blank is less than the starting material length L in the blanking task after upgrading, treat that with residue the combination of stock layout blank joins in current layout project as last a kind of stock layout mode, obtains a complete current layout project and records this layout project this moment;
G, repeatedly repeat the process of B, C, D, E, F, then all layout project of record compared screening, with the optimum layout project that the filtered out solution as One-dimensional Cutting Stock Problem.
2. a kind of heuristic one-dimensional stock-cutting method based on the stratified random searching algorithm as claimed in claim 1, is characterized in that, the blank combination pre-service described in step B is carried out in such a way:
First m kind blank is arranged from small to large by length, the corresponding length of each blank is respectively C 1, C 2C m
Then can repeatedly select and make up in m kind blank, be number that 1 to N blank set is a degree of depth combination, total M of described depth groups unification, and the value of M is:
M＝m 1+m 2+…+m N，
At last, M combination made up the length of interior blank and sequenced from small to large order by each.
3. a kind of heuristic one-dimensional stock-cutting method based on the stratified random searching algorithm as claimed in claim 1, it is characterized in that, stratified random searching algorithm described in step C comprises the search of two levels, and ground floor is the roulette random search, and the second layer is deep search; Transfer to when working as the accumulation charge length of random combine and enter in interval [inf, sup] in the ground floor search procedure and carry out second layer search; Second layer search is carried out in such a way:
From using binary search to search a degree of depth combination by length with in M the combination that sequence is good from small to large, when the random combine that makes described degree of depth combination and obtained in the ground floor search procedure formed a kind of stock layout mode together, the clout length Y of described stock layout mode was minimum.
4. a kind of heuristic one-dimensional stock-cutting method based on the stratified random searching algorithm as described in claim 1 or 3, is characterized in that, the end points value of described interval [inf, sup] is as follows:
inf＝L-N*C m，
sup＝L-C 1，
Wherein, the value of described N is:
N = min { 4 , [ 2 L 3 C m ] } .
5. a kind of heuristic one-dimensional stock-cutting method based on the stratified random searching algorithm as claimed in claim 1, is characterized in that, is no more than the number of times that the multipotency of the current demand of blank is reused described in step D and calculates in the following manner:
Respectively with the current actual blank demand of each blank in current stock layout mode divided by the quantity that has arranged in current stock layout mode, and get smallest positive integral in above-mentioned set, the value that is no more than the number of times U that the multipotency of the current demand of blank is reused is:
U = min { [ d j a ij ] } , a ij＞0，j＝1，2…m，
The sequence number of wherein supposing current stock layout mode is i, d jCurrent actual blank demand after expression is upgraded, a ijThe quantity that represents the j kind specification blank that arranged in current stock layout mode.
6. a kind of heuristic one-dimensional stock-cutting method based on the stratified random searching algorithm as claimed in claim 1, is characterized in that, described in step D, heuristic rule is for to carry out the calculating of evaluation of estimate according to following formula to every kind of stock layout mode:
V＝g 1*U-g 2*Y，
Wherein, g 1, g 2Be two positive integers, g 1Just represent that the weight of U value in the V value is larger greatlyr, on the contrary g 2Represent that the weight of Y value in the V value is larger greatlyr.
7. a kind of heuristic one-dimensional stock-cutting method based on the stratified random searching algorithm as claimed in claim 1, is characterized in that, relatively screens described in step G by following three priority target from high to low and undertaken:
Total radical of G1, raw materials consumption is minimum;
G2, stock layout mode are minimum;
Clout length in G3, last a kind of stock layout mode is maximum.
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