CN111985834A - Paper roll slitting method based on depth-first search and application thereof - Google Patents

Paper roll slitting method based on depth-first search and application thereof Download PDF

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CN111985834A
CN111985834A CN202010889954.8A CN202010889954A CN111985834A CN 111985834 A CN111985834 A CN 111985834A CN 202010889954 A CN202010889954 A CN 202010889954A CN 111985834 A CN111985834 A CN 111985834A
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王昊
管在林
郭子腾
岳磊
丁林山
王创剑
张正敏
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Huazhong University of Science and Technology
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Abstract

The invention belongs to the field of paper roll cutting research, and particularly discloses a paper roll cutting method based on depth-first search. The method comprises the following steps: collecting cutting data of the paper roll to be cut, and calculating the maximum cutting number of each order on the cutting machine according to the cutting data; traversing all combination strategies of the order by adopting a depth-first search algorithm, and finding out all matching and cutting schemes meeting the yield requirement; performing non-dominant sorting on all feasible match-cut schemes; and outputting the cutting scheme corresponding to the front surface, and taking the cutting scheme as a candidate cutting scheme set for actual production. The invention obtains all feasible matching and cutting schemes meeting the requirement of the finished product rate by utilizing depth-first search, and can greatly shorten the search time; meanwhile, the selection of the feasible matching and cutting schemes is regarded as a multi-objective optimization problem, a non-dominated sorting algorithm is introduced to layer all the feasible matching and cutting schemes, and the scheme on the front edge surface is used as a feasible matching and cutting scheme set recommended finally, so that the practical application on site is facilitated.

Description

Paper roll slitting method based on depth-first search and application thereof
Technical Field
The invention belongs to the field of paper roll cutting research, and particularly relates to a paper roll cutting method based on depth-first search and application thereof.
Background
At present, in the papermaking and packaging industries, due to the fact that orders are various, the difference between the specifications and requirements of the orders is large, and the specifications of parent rolls are more, workers often need to repeatedly test by means of self experiences to obtain a feasible production scheduling scheme, and waste of time, raw materials and the like of enterprises is caused.
Furthermore, in actual production, a feasible solution for matching a given order with a master batch of a certain specification may not be obtained, so that some enterprises allow the matching number of some orders to be zero when solving the matching solution for some orders, and all feasible matching solutions are desired to select the best solution for actual production.
Although the traditional brute force enumeration method can obtain all feasible matching schemes for decision makers to select, the time performance is poor, and especially under the conditions of large order quantity and large ratio of parent volume to order width, the time consumed by the brute force enumeration method cannot support real production at all.
Disclosure of Invention
Aiming at the defects and/or the improvement requirements of the prior art, the invention provides a paper roll slitting method based on depth-first search and application thereof, wherein the method obtains all feasible matching and cutting schemes meeting the yield requirement by utilizing depth-first search, and can greatly shorten the search time; meanwhile, the selection of the feasible matching and cutting schemes is regarded as a multi-objective optimization problem, a non-dominated sorting algorithm is introduced to layer all the feasible matching and cutting schemes, and the scheme on the front edge surface is used as a feasible matching and cutting scheme set recommended finally, so that the practical application on site is facilitated.
In order to achieve the purpose, the invention provides a paper roll slitting method based on depth-first search, which comprises the following steps:
s1, collecting cutting data of the paper roll to be cut;
s2, calculating the maximum cutting number of each order on the splitting machine according to the splitting data collected in the step S1;
s3, traversing all combination strategies of the order by adopting a depth-first search algorithm, and finding out all matching and cutting schemes meeting the yield requirement;
s4 carrying out non-dominance sorting on all feasible match cutting schemes obtained in the step S3;
s5 outputs the cutting plan corresponding to the leading face as a candidate cutting plan set for actual production.
Further preferably, in step S1, the slitting data includes a parent roll width, a maximum lane number, an order number, and an order width.
As a further preferable, in step S2, the maximum cuttable number is calculated by the formula:
Figure BDA0002656601350000021
wherein, WMIs the width of the parent roll, WO(i) The width of an order i, i is an order number and takes the values of 1-N, NCIn order to maximize the number of channels,
Figure BDA0002656601350000022
indicating a rounded-down symbol.
As a further preference, step S3 includes the following sub-steps:
s31 orders the orders according to the order width, and records the ordered orders as O1,O2,…,OnSimultaneously, the maximum cuttable number N of each ordermaxRearranging according to the ordering result of the orders;
s32 using variable x respectively1,x2,…,xnIndicates order O1,O2,…,OnOf the order, wherein for any one order OiThe number of matched cuts xiHas a value range of 0,1,2, …, Nmax(i)，Nmax(i) The maximum cuttable number for the ith order; let xi0, with this pair [ x [ ]1,x2,…,xn]Initializing the formed combined matching and cutting scheme;
s33 calculating the total cutting width W of the order according to the current combined cutting schemesAnd the total number of channels occupied by the ordersJudging whether the backtracking condition is met, if yes, turning to step S34 for backtracking, and if not, directly entering step S35;
s34 judgment xnIf equal to 0, if yes, go back to find xjAn order other than 0 is substituted into step S36; if not, let j equal n-1, xnWhen it is 0, the process proceeds to step S36;
s35 judgment Ws/WMIf the ratio is less than the lowest requirement R of the finished product ratio, if so, abandoning the current combined matching and cutting scheme [ x ]1,x2,…,xn]And let j equal n; if not, the current combination matching and cutting scheme [ x ] is saved1,x2,…,xn]And let j equal n;
s36 judgment xjWhether or not less than Nmax(j) If yes, go to step S37; if not, go to step S38;
s37 judging whether j is less than or equal to 0, if yes, going to step S39; if not, let xj＝xj+1, and go to step S33, iterate according to the updated combined cutting scheme;
s38 order xjJ is 0, j is j-1, and then the process goes to step S36 to perform the re-judgment;
and S39, outputting the saved current combined matching and cutting scheme as a feasible scheme, so as to find all matching and cutting schemes meeting the yield requirement.
Further preferably, the backtracking condition in step S34 is two, one being the total cutting width W of the ordersGreater than the width W of the parent rollMThe other is the total number N of channels occupied by the ordersGreater than the maximum number of channels NCIf one of the conditions is met, the step S34 is carried out to backtrack; if neither of the two is satisfied, the process proceeds directly to step S35.
Further preferably, in step S4, maximizing yield and maximizing actual matched order number are adopted as the two targets for sorting.
According to another aspect of the invention, there is provided the use of the above-described paper roll slitting method based on depth-first search in paper roll slitting.
Generally, compared with the prior art, the above technical solution conceived by the present invention mainly has the following technical advantages:
1. the invention provides a paper roll slitting method based on depth-first search, which utilizes depth-first search to obtain all matching and cutting schemes meeting the requirement of the finished product rate, can greatly shorten the search time, is obviously superior to the existing violence enumeration method, and has stronger practical application value; meanwhile, in order to effectively reduce the decision pressure of field workers, the selection of the feasible matching and cutting schemes is regarded as a multi-objective optimization problem, a non-dominated sorting algorithm is introduced to layer all the feasible matching and cutting schemes, and the scheme on the front edge is used as a finally recommended feasible matching and cutting scheme set, so that the practical application on the field is facilitated;
2. particularly, the depth-first search process is optimized according to the practical problems in the paper roll cutting process, so that invalid calculation of the infeasible matching and cutting schemes can be effectively reduced, the solving speed is greatly increased on the premise of ensuring that all feasible matching and cutting schemes are enumerated, and the practical production requirements are met.
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Fig. 1 is a general flowchart of a paper roll slitting method based on depth-first search according to a preferred embodiment of the present invention;
FIG. 2 is a flow chart of a depth first search provided by the preferred embodiment of the present invention;
3(a) -3 (c) are examples of the processing of trace-back condition 1 in the preferred embodiment of the present invention;
fig. 4(a) to 4(c) are examples of processing of the trace-back condition 2 in the preferred embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, the invention provides a paper roll slitting method based on depth-first search, which comprises the following steps:
s1 collecting cutting data of paper roll to be cut, including the width W of mother rollMMaximum number of channels NCOrder number n and order width WO；
S2, calculating the maximum cutting quantity of each order on the splitting machine according to the splitting data collected in the step S1, and specifically adopting the following formula to calculate:
Figure BDA0002656601350000041
wherein, WO(i) The width of an order i, i is an order number and takes the value of 1-n,
Figure BDA0002656601350000042
represents a rounded-down symbol;
s3, traversing all combination strategies of the order by adopting a depth-first search algorithm, and finding out all matching and cutting schemes meeting the yield requirement;
s4, for all feasible match-cutting schemes obtained in step S3, performing non-dominated sorting on two targets of maximizing yield and maximizing actual match-cutting order quantity;
s5 outputs the cutting plan corresponding to the leading face as a candidate cutting plan set for actual production.
Further, as shown in fig. 2, step S3 specifically includes the following sub-steps:
s31 orders the orders according to the order width, and records the ordered orders as O1,O2,…,OnSimultaneously, the maximum cuttable number N of each ordermaxRearranging according to the ordering result of the orders;
s32 using variable x respectively1,x2,…,xnIndicates order O1,O2,…,OnOf the order, wherein for any one order OiThe number of matched cuts xiHas a value range of 0,1,2, …, Nmax(i)，Nmax(i) The maximum cuttable number for the ith order; let xi0, with this pair [ x [ ]1,x2,…,xn]Initializing the formed combined matching and cutting scheme;
s33 calculating the total cutting width W of the order according to the current combined cutting schemesAnd the total number of channels occupied by the ordersAnd judging whether it meets the backtracking condition, i.e. total cutting width W of the ordersGreater than the width W of the parent rollMOr total number of channels occupied by the order NsGreater than the maximum number of channels NC(ii) a If at least one item is satisfied, go to step S34 for backtracking, if none is satisfied, go to step S35 directly; fig. 3(a) to (c) and fig. 4(a) to (c) are processing examples of two trace-back conditions;
s34 judgment xnIf equal to 0, if yes, go back to find xjAn order other than 0 is substituted into step S36; if not, let j equal n-1, xnWhen it is 0, the process proceeds to step S36;
s35 judgment Ws/WMIf the ratio is less than the lowest requirement R of the finished product ratio, if so, abandoning the current combined matching and cutting scheme [ x ]1,x2,…,xn]And let j equal n; if not, the current combination matching and cutting scheme is stored[x1,x2,…,xn]And let j equal n;
s36 judgment xjWhether or not less than Nmax(j) If yes, go to step S37; if not, go to step S38;
s37 judging whether j is less than or equal to 0, if yes, going to step S39; if not, let xj＝xj+1, and go to step S33, iterate according to the updated combined cutting scheme;
s38 order xjJ is 0, j is j-1, and then the process goes to step S36 to perform the re-judgment;
and S39, outputting the saved current combined matching and cutting scheme as a feasible scheme, so as to find all matching and cutting schemes meeting the yield requirement.
According to another aspect of the invention, there is provided the use of the above-described paper roll slitting method based on depth-first search in paper roll slitting.
The paper roll cutting method based on depth-preferred search provided by the invention is specifically explained according to the specific embodiment.
S1 collecting the cutting data of the paper roll to be cut, the width W of the mother rollM1000mm, maximum number of channels N C13, the number of orders n is 7, the width of the order WORespectively 91mm, 63mm, 93mm, 75mm, 83mm, 64mm and 92mm, and the lowest requirement R of the finished product rate is 0.975;
s2 the maximum cuttable number N of each order can be calculated according to the following calculation formula max10, 13, 10, 13, 12, 13, 10;
Figure BDA0002656601350000061
s31 making each order according to order width WOSequencing from small to large, and recording the sequenced orders as O in sequence1,O2,…,OnSimultaneously, the maximum cuttable number N of each ordermaxRearranging according to the ordering results of the orders, wherein the ordering results are 13, 13, 13, 12, 10, 10 and 10;
s32 using variable x respectively1,x2,…,x7Indicates order O1,O2,…,O7Of the order, wherein for any one order OiThe number of matched cuts xiHas a value range of 0,1,2, …, Nmax(i)，Nmax(i) The maximum cuttable number for the ith order; let xi0, with this pair [ x [ ]1,x2,…,x7]Initializing the formed combined matching and cutting scheme;
s33 calculating the total cutting width W of the order according to the current combined cutting schemesAnd the total number of channels occupied by the ordersAnd judging whether it meets the backtracking condition, i.e. total cutting width W of the ordersGreater than the width W of the parent rollMOr total number of channels occupied by the order NsGreater than the maximum number of channels NC(ii) a If one of the two conditions is met, the step S34 is carried out for backtracking, and if the two conditions are not met, the step S35 is directly carried out;
s34 judgment x7If equal to 0, if yes, go back to find xjAn order other than 0 is substituted into step S36; if not, let j equal 6, x7When it is 0, the process proceeds to step S36;
s35 judgment Ws/WMIf the ratio is less than the lowest requirement R of the finished product ratio, if so, abandoning the current combined matching and cutting scheme [ x ]1,x2,…,x7]And let j equal to 7; if not, the current combination matching and cutting scheme [ x ] is saved1,x2,…,x7]And let j equal to 7;
s36 judgment xjWhether or not less than Nmax(j) If yes, go to step S37; if not, go to step S38;
s37 judging whether j is less than or equal to 0, if yes, going to step S39; if not, let xj＝xj+1, and go to step S33, iterate according to the updated combined cutting scheme;
s38 order xjJ is 0, j is j-1, and then the process goes to step S36 to perform the re-judgment;
s39, outputting the saved current combined matching and cutting scheme as a feasible scheme, and finding all matching and cutting schemes meeting the yield requirement;
s4, for all feasible match-cutting schemes obtained in step S3, performing non-dominated sorting on two targets of maximizing yield and maximizing actual match-cutting order quantity;
s5 outputs the cutting plan corresponding to the leading face as a candidate cutting plan set for actual production.
The depth-first search algorithm and the violent enumeration method designed by the invention are realized by C + + programming, and 10 calculation experiments are carried out on the embodiment by respectively adopting the two algorithms under the operating environment of 2.40GHz Intel (R) Core (TM) i7-5500U CPU, 8G RAM and win 10. The experimental result is that both algorithms solve all feasible matching schemes (6049 in total), but the running time of the depth-first search method is about 13 seconds, the running time of the brute-force enumeration method is about 17 seconds, and the optimization ratio is about 23.5%. In addition, as shown in the performance test experimental results of other larger-scale examples shown in table 1, the depth-first search algorithm designed by the present invention is obviously superior to a brute force enumeration method in solving the large-scale examples. In conclusion, the depth-first search algorithm designed by the invention can greatly shorten the search time for searching all feasible matching and cutting schemes, and has strong practical application value.
After 6049 feasible matching and cutting schemes are obtained, in order to effectively reduce the decision pressure of field workers, the selection of the feasible matching and cutting schemes is regarded as a multi-objective optimization problem, wherein the optimization objectives are to maximize the yield and maximize the number of actual matching and cutting orders, a non-dominated sorting algorithm is introduced to layer all the feasible matching and cutting schemes, and the scheme on the front edge surface is used as a finally recommended feasible matching and cutting scheme set. The set of feasible cut-to-match solutions finally recommended in this example is shown in table 2.
TABLE 1 Performance test results of depth-first search algorithm and violence enumeration algorithm
Figure BDA0002656601350000081
Note: the algorithm 1 is a depth-first search algorithm designed by the invention, and the algorithm 2 is a violent enumeration method
TABLE 2 set of feasible cut-to-match scenarios for the Final recommendations
Figure BDA0002656601350000082
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (7)

1. A paper roll slitting method based on depth-first search is characterized by comprising the following steps:
s1, collecting cutting data of the paper roll to be cut;
s2, calculating the maximum cutting number of each order on the splitting machine according to the splitting data collected in the step S1;
s3, traversing all combination strategies of the order by adopting a depth-first search algorithm, and finding out all matching and cutting schemes meeting the yield requirement;
s4 carrying out non-dominance sorting on all feasible match cutting schemes obtained in the step S3;
s5 outputs the cutting plan corresponding to the leading face as a candidate cutting plan set for actual production.
2. The method for slitting paper rolls based on depth-first search of claim 1, wherein in step S1, the slitting data comprises a parent roll width, a maximum number of lanes, an order number, and an order width.
3. The paper roll slitting method based on depth-first search as claimed in claim 2, wherein in step S2, the maximum cuttable number is calculated by the formula:
Figure FDA0002656601340000011
wherein, WMIs the width of the parent roll, WO(i) The width of an order i, i is an order number and takes the values of 1-N, NCIn order to maximize the number of channels,
Figure FDA0002656601340000012
indicating a rounded-down symbol.
4. A paper roll slitting method based on depth-first search as claimed in claim 1, characterized in that step S3 comprises the following sub-steps:
s31 orders the orders according to the order width, and records the ordered orders as O1,O2,…,OnSimultaneously, the maximum cuttable number N of each ordermaxRearranging according to the ordering result of the orders;
s32 using variable x respectively1,x2,…,xnIndicates order O1,O2,…,OnOf the order, wherein for any one order OiThe number of matched cuts xiHas a value range of 0,1,2, …, Nmax(i)，Nmax(i) The maximum cuttable number for the ith order; let xi0, with this pair [ x [ ]1,x2,…,xn]Initializing the formed combined matching and cutting scheme;
s33 calculating the total cutting width W of the order according to the current combined cutting schemesAnd the total number of channels occupied by the ordersJudging whether the backtracking condition is met, if yes, turning to step S34 for backtracking, and if not, directly entering step S35;
s34 judgment xnIf equal to 0, if yes, go back to find xjAn order other than 0 is substituted into step S36; if not, let j equal n-1, xnWhen it is 0, the process proceeds to step S36;
s35 judgment Ws/WMIf the ratio is less than the lowest requirement R of the finished product ratio, if so, abandoning the current combined matching and cutting scheme [ x ]1,x2,…,xn]And let j equal n; if not, the current combination matching and cutting scheme [ x ] is saved1,x2,…,xn]And let j equal n;
s36 judgment xjWhether or not less than Nmax(j) If yes, go to step S37; if not, go to step S38;
s37 judging whether j is less than or equal to 0, if yes, going to step S39; if not, let xj＝xj+1, and go to step S33, iterate according to the updated combined cutting scheme;
s38 order xjJ is 0, j is j-1, and then the process goes to step S36 to perform the re-judgment;
and S39, outputting the saved current combined matching and cutting scheme as a feasible scheme, so as to find all matching and cutting schemes meeting the yield requirement.
5. The paper roll slitting method based on depth-first search as claimed in claim 4, wherein the backtracking condition in step S34 is two, one being a total cutting width W of the ordersGreater than the width W of the parent rollMThe other is the total number N of channels occupied by the ordersGreater than the maximum number of channels NCIf one of the conditions is met, the step S34 is carried out to backtrack; if neither of the two is satisfied, the process proceeds directly to step S35.
6. The paper roll slitting method based on depth-first search as claimed in claim 1, wherein in step S4, maximizing yield and maximizing actual matched order number are used as ranking dual targets.
7. Use of a paper roll slitting method based on depth-first search according to any one of claims 1 to 6 for paper roll slitting.
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