WO1998009239A1

WO1998009239A1 - Process and device for determining and optimizing a cutting outline for a reel cutter

Info

Publication number: WO1998009239A1
Application number: PCT/DE1997/001741
Authority: WO
Inventors: Klaus Nagel; Katrin Helbing; Rolf Ehrhardt
Original assignee: Siemens Aktiengesellschaft
Priority date: 1996-08-28
Filing date: 1997-08-13
Publication date: 1998-03-05
Also published as: DE19634826A1; EP0922263A1

Abstract

For a reel cutter, particularly in the paper industry, optimized cutting outlines need to be determined. According to the invention, this is done by the application of evolutionary algorithms, a population of possible solutions being presupposed for solving at least partial problems. These solutions are combined and/or mutated into new solutions. An associated device comprises of a programmable, digital computer composed of the usual components, which is programmed corresponding to the stated process and thus defines suitable means for operation of the reel cutter (100).

Description

description

Process and device for creating and optimizing a cutting plan for a slitter rewinder

The invention relates to a method for creating and optimizing a cutting plan for a slitter of continuously produced material webs, in particular in the paper industry. In addition, the invention relates to a device programmed according to the specified method, containing at least one programmable digital computer with a central unit, work, program and data memories and an input / output interface for data exchange with the slitter rewinder.

In the paper industry in particular, there is an order situation that can fluctuate greatly in a very short time. Flexible production optimization is therefore essential. In this context, machine occupancy planning for the so-called reel cutter, with which a paper web is cut into the geometry required by the customer, the so-called customer reels, is of central importance. This is associated with a suitable cutting plan creation, which is usually followed by an optimization of the cutting plan in order to minimize the waste of paper in ongoing production. In addition to the paper industry, other continuously produced material webs, for example foils or the like, also play. , the cutting plan creation plays an important role.

A cutting plan for a slitter consists of the information in which pattern the predecessor "Tambour" should be cut in order to produce the successor products "Rolls". The so-called drum has a given width. The rolls have different widths, whereby the weight of all roles of a customer order can fluctuate between a minimum and a maximum value. The length of a single roll can also vary between a minimum and a maximum value. A change of a cutting pattern involves a physical adjustment of the cutting knife of the slitter rewinder, which involves considerable set-up costs. In particular, the set-up costs affect the revenues to be achieved in the paper industry.

It is therefore endeavored to design the cutting plan in such a way that the sum of the revenues from the rolls minus the costs due to cutting losses minus the set-up costs becomes a maximum.

As is known, paper machines deliver very large rolls of machine width, for example 12 m wide and 40 km long. These rolls are tailored to customer requirements on roll cutters, for example 0.50 to 2.00 m wide and 10 km long.

The waste should be kept low. The set-up times for format changes must also be kept short.

The number of rolls to be made in one cutting process must not exceed the number of knives and winding stations available. Due to the design of the slitter rewinder, there may be further restrictions, for example the individual winding stations may have different width or weight restrictions. The revenue per customer role can depend not only on the size and weight, but also on individual tariffs or discounts from customers. The violation of requirements is measured in monetary values.

Cutting plans are sometimes still created by hand, but there are exact solutions for partial problems. The treatment Problems of this kind with methods of linear optimization are very difficult because of the constraints: In particular, the demand for integer solutions increases the problem size and thus the computing times very strongly. An optimization of a total cost function is not yet known from the prior art.

The object of the invention is therefore to provide an improved method and to create an associated device.

The object is achieved according to the invention in that evolutionary algorithms are used in a method of the type mentioned at the outset, with which a population of possible solutions is required to solve an overall problem and these are combined and / or mutated into new solutions.

Advantageously, to optimize cutting plans for slitter rewinder, the use of evolutionary algorithms can be done individually or one after the other. In a sub-step, a width plan can be drawn up, with which it is determined which order roles are placed in which litter. In another sub-step, winding stations can be assigned to the individual customer roles.

Thus, the invention can, given customer requirements, create a plan for a given manufacturing period that maximizes total revenue. The optimization takes advantage of the fact that the sales orders contain tolerances and that additional rolls that are not requested can be produced in stock.

In particular, slitter rewinder optimization using evolutionary algorithms essentially takes place in two separate steps. First of all, a width plan is drawn up, which specifies which job roles are placed in which litter. In the second step, winding stations are assigned to the individual customer roles. This determines the knife positions for the throw. In addition, the second step is a cheap one Order for the production of the throws. The latter is possible on site using a PC or laptop with a suitable user interface and can be done in practice immediately before the start of the shift in production. In conjunction with the slitter rewinder, a device is thus created in which suitable means are defined by programming the digital computer in accordance with the specified method.

Within the scope of the invention, the evolutionary algorithms can be used in all or only in individual sub-steps when realizing cutting plans. If necessary, it is also possible to combine the method according to the invention for a single substep with another, deterministic method.

Further details and advantages of the invention result from the following description of the figures of exemplary embodiments with reference to the drawing in conjunction with further subclaims. Show it

1 shows the basic sketch of a roll cutter, FIG. 2 shows the diagram of a cutting plan,

FIG. 3 shows the embedding of the optimization in production planning in the paper industry and FIG. 4 shows the implementation in terms of equipment.

The figures are partially described below together.

The production of paper takes place in several steps: First, the raw paper is produced in the actual paper machine and, if necessary, finished in so-called coating machines. In this state, the base paper is in rolls with a width of approx. 5 to 10 m, which are referred to as so-called Ta boure. The length of the paper web rolled up in a reel can be The weight (weight) of the paper fluctuates greatly and can be up to 100 km.

The tapes are then cut into narrower strips in roll cutters, which are wound into individual rolls, the so-called hanging rolls. When the rollers have reached a given diameter, i.e. The paper cutter is stopped and the paper is cut transversely to the direction of travel. The entirety of the notice rolls thus created in one operation is referred to in the paper industry as a so-called litter.

The latter is illustrated with the aid of FIG. 1: A drum 1 is shown, from which a paper web 2 is drawn off and is cut lengthwise by means of individual knives 3, which are adjustable in the lateral direction, into narrower paper webs, for example into the webs 11 to 15. 21 to 25 are the so-called hanging rolls on which the smaller paper webs 11 to 15 are wound. In the

Line of the knives 3 are laterally knives 3 'for edge straightening, with which a lateral waste is removed, whereby means for edge suction are available. Overall, a winder 100 is thus realized.

2 shows the paper web 10 in a shortened projection. The diagram of a cutting plan, with which the length of the paper web 10 of a single reel 1 can be used to produce individual rolls of different widths, becomes clear. By cutting in the transverse direction of the

Tambours the individual lengths of the reels can be determined. As mentioned, a complete cut across the width of a reel defines a so-called throw with a throw number. For example, the first drum contains three throws and has three throw numbers, while the second and third drum have only two throw numbers. In the drum 1, the areas of the waste are shown hatched on the side, with a minimum waste resulting from the edge straightening according to FIG. 1. In general - due to the cutting plan - the actual blend is higher, which is indicated by hatching in the opposite direction. A key role in the creation of the cutting plan is to combine the number of customer roles specified in the width of the respective order with storage roles that are possible in the standard width for any subsequent orders in order to minimize the current waste.

The following objectives, which can be summarized by a quality function, serve to optimize production on the slitter rewinder 100 according to FIG. 1:

- minimization of waste

- Minimize set-up costs

- Maximize proceeds

- optimal fulfillment of the order specifications using the tolerances, e.g. the length and / or weight tolerances.

For the rest, the roll cutter assignment must be embedded in the entire production planning, which is illustrated by FIG. 3. The unit 30 contains the measures for optimizing the cutting plan, which essentially consists of a block 31 for data processing and a block 32 for production optimization for the slitter 100. In practice, a PC or laptop with a suitable user interface can be used. The PC 300, symbolically indicated in FIG. 4, as a programmable digital computer usually comprises a central unit (not shown in detail) as well as working, program and data storage. Via a suitable input / output interface, the determined cutting plans can be sent directly to the automation device 150 for the slitter rewinder 100 as a data record. It is crucial in the operation of the automation device 200 for the slitter rewinder 100 that after a selection of the customer orders and the data preparation in accordance with block 32 of FIG. 3 for a production optimization of the reel cutter as well as the production costs can be determined. The aim of optimizing the cutting plan is to maximize the profit that the determined cutting plan realizes. The set-up costs by changing knives or the like must also be taken into account and the exact set-up costs can only be determined when the roll arrangement within the litter is known.

Evolutionary algorithms can advantageously be used to solve the creation of the cutting plan. Such algorithms are based on the methods of the natural

Evolution and especially with binary functions are often referred to as genetic algorithms. They use a population of possible solutions and combine and mutate them into new solutions. All solutions are evaluated, better solutions are more likely to be used to combine new solutions. This leads to an improvement in the population.

In detail, it is suggested to first create a general plan: The general plan is intended to secure a high level of revenue by avoiding waste and preferentially profitable orders. On the other hand, it should enable short set-up times for the subsequent cutting plan calculation. To solve the problem, patterns have to be determined, ie groups of roles for a litter. The width B of the pattern is the sum of the roll widths Bi. Various sub-goals result from the requirements: - 1. The overall width of the sample is the same or only slightly narrower than the machine width. This ensures that there is little waste. - 2. The selected pattern can be repeated as often as possible.

Repeating the same pattern avoids set-up time.

- 3. Profitable roles are preferred. - 4. The maximum number of rolls to be cut in one operation is not exceeded.

- 5. Weight and width restrictions of the winding stations are observed.

For the sub-goals, proceeds or "penalties" are defined as monetary value. The sub-goals are given suitably determined weights and added, this weighted sum is maximized. The best pattern found is produced as often as possible, after which the same procedure is applied to the remaining ones Orders applied until all customer orders are satisfied.

By changing the weights, the strategy can be adapted to different conditions. For example, if the order situation is bad, the waste is punished more than if the situation is good, if one is willing to accept more waste for higher throughput.

An evolutionary algorithm is used to determine good patterns. An individual corresponds to a pattern, i.e. a selection of order roll widths. The same width can occur several times in a pattern. An initial population of initial patterns is generated randomly, each pattern is evaluated according to the criteria given above. Inadmissible patterns are rated so badly that they have no chance of asserting themselves.

For example, samples that exceed the machine width or that cannot be produced because there are more rolls of one size class than suitable winding stations are not permitted The widths Bi, BB _n occur under the orders. A pattern is described by an n-tuple

(Ki, K ₂ , ..., K _n ), where K ₄ indicates how often the width Bi occurs in the pattern.

In an evolutionary step, three patterns are selected from the population as individuals at random and evenly distributed. The worst rated pattern of these three individuals is replaced by a combination of the two better ones. The patterns for the father individual (Vi, V ₂ , ... V _n ) and that

Sample individual (Mi, M ₂ , ..., M _n ) are combined to form the child individual (Ki, K ₂ , ... K _n ) by including Ki equal to a random integer between Vj and Mi for all i, final values, is set. A mutation (Ki, K ₂ , ... K _n ) is applied to the child individual, which, if the pattern exceeds the machine width, decreases Ki randomly selected by one until the pattern is narrow enough. In any case, a predetermined number of times is then attempted to increase a randomly selected Ki by one if the pattern does not thereby exceed the machine width.

The population size remains constant with this method. The number of evolution steps is specified. The best pattern always remains in the population.

The entire process is repeated until the intended computing time has been used up. The best set of patterns from all runs includes the solution. The number of different patterns is also kept small, which means that it can be expected that the set-up times can be kept short.

The cutting plan is then completed: The cutting plan calculation is used to arrange the throws of the width plan so that the width and weight restrictions of the winding stations are observed and that the set-up times for the adjustment of the knives. The cutting plan calculation uses a simpler form of evolutionary algorithms: the population consists of only one individual. A mutation is formed from this individual and the better of both individuals (ie the original or the mutation) is selected. The evaluation criterion for the selection is the number of constant knives. In this case, the individual is the entire cutting plan, defined by the permutation of the litters and the permutations of the roles in the individual litters.

In this case, the initial plan as the initial population is generated as follows: For every two litters, it is determined how many common roll widths B _x occur in them. The order of the throws is determined so that the sum of the common roles between two successive throws is maximal. Various mutation operators are applied to the initial individual.

All operators use two basic operations A and B: In basic operation A, a throw is adapted to another unchanged throw so that as many knives as possible remain fixed. For this purpose, a sequence of the roles of the litter to be adjusted is determined in such a way that the cuts between the roles correspond to a maximum number of cuts of the fixed throw. In basic operation B two throws are adjusted to each other, the order of the roles is changed in both throws.

The mutations carried out with genetic algorithms in the above method are based on the following heuristics: 1. Litter 1 and 2, 3 and 4 etc. are matched to one another (operation B). , with an odd number of throws, the last throw is adapted to its predecessor (operation A) As an alternative, the throws 2 and 3, 4 and 5 etc. are adapted to each other (operation B), the first and at Even numbers of the last litter are adapted to their neighboring litter (Operation A).

2. A litter is selected at random and tentatively adapted to its two neighbors (Operation A). The better option is chosen.

3. A coherent sequence of throws is inserted in reverse order.

4. Two randomly selected neighboring litters are matched to each other (Operation B), then the other litters are adapted from the inside out to their predecessors.

5. A randomly chosen throw and a neighbor are matched to each other (operation B), the other neighbor is matched with operation A. The same is repeated with swapping the operations for the two neighbors. The better option is chosen.

The method described was tested in detail. In addition to the described complete execution of both partial steps with genetic algorithms, it may also be appropriate in individual cases to carry out only one of the partial steps with genetic algorithms. In particular, it makes sense to determine the master plan deterministically as the first sub-step and to carry out the roll or knife selection in accordance with the second sub-step using the described genetic algorithm. Suitable procedures for the deterministic determination of a master plan are described in a parallel application (GR 96 P 8579).

Claims

claims

1. Method for creating and optimizing a cutting plan for a slitter reel of continuously produced material webs, in particular in the paper industry, characterized by the use of evolutionary algorithms, whereby a population of possible solutions is required to solve at least partial problems and these are combined to new solutions and / or be mutated.

2. The method of claim 1, d a d u r c h g e k e n n z e i c h n e t that for the optimization of the cutting plan for the slitter rewinder, the application of the evolutionary algorithms takes place individually or in succession.

3. The method of claim 2, d a d u r c h g e k e n n z e i c h n e t that with the evolutionary algorithms in a substep a broad plan is drawn up, with which it is determined which job roles are placed in which litter

4. The method of claim 2, d a d u r c h g e k e n n z e i c h n e t that the evolutionary algorithms are assigned to the individual customer roles winding stations in another sub-step.

5. The method according to any one of claims 3 or 4, so that the solutions of the sub-steps are evaluated according to the type of genetic algorithms and better solutions are more likely to be used to combine new solutions.

6. The method according to claim 3, wherein in the intended sub-step, suitable patterns of width maps are generated in one throw of the material web, thereby indicates that a plurality of random initial patterns are generated first.

7. The method of claim 6, d a d u r c h g e k e n n - z e i c h n e t that from about 100 initial patterns as

Starting populatin an optimized pattern is determined by means of the genetic algorithms, whereby three individuals are selected from the population, the worst is eliminated and a new individual with better properties is combined and / or mutated from the two remaining individuals.

8. The method according to claim 4, wherein in a sub-step the knife position is determined in successive one throw by suitable operations, so that a favorable order for the production of the throws and for the order of the roles within a throw is determined.

9. The method of claim 8, d a d u r c h g e k e n n z e i c h n e t that in at least two throws a first optimized throw is fixed and the second and the other throws are adapted to it (operation A).

10. The method of claim 8, d a d u r c h g e k e n n z e i c h n e t that at least two throws two successive throws are adapted to each other by varying both throws (operation B).

11. The method according to claim 9 and 10, d a d u r c h g e k e n n z e i c h n e t that operations A and B are combined with one another in a plurality of throws.

12. The method according to claim 11, dadurchge - indicates that in a plurality of Throws two successive litters in groups are adjusted to each other.

13. The method according to claim 12, so that the last throw is adapted to its predecessor in the case of an odd number of throws and adaptation of successive throws.

14. The method according to claim 12, so that the first throw is adapted to its successor in the case of an even number of throws and adaptation of successive throws.

15. The method according to claim 11, so that a first throw is selected at random and the neighboring throws are adjusted.

16. Programmed according to the method of claim 1 or one of claims 2 to 15 device for creating and optimizing a cutting plan for a slitter winder, containing at least one programmable digital computer with a central unit, work, program and data memories and an input / output interface for data exchange with the slitter rewinder, characterized by a) means for generating patterns for cutting plans as the initial population of genetic algorithms, b) means for evaluating the patterns, c) means for performing evolutionary steps, d) means for aborting the process if a predetermined quality and / or computing time has been reached.

17. Apparatus according to claim 16, characterized in that for the definition of the cutting plan further means for determining the order of individual throws are available.