JPH1015727A - Two-dimensional plane cutting method optimizing device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a device determining an optimum cutting method in a short time even in the case of large n value, relating to a two-dimensional plane cutting method optimizing device obtaining an optimum cutting method minimizing a waste area, in the case of cutting out a prescribed number of sheets of small planes from a number of n sheets of two-dimensional planes. SOLUTION: A two-dimensional plane cutting information acquisition part 2 acquires information of how to cut pattern or the like relating to cutting of a two-dimensional plane. In a fitness function setting part 3, a weight coefficient is set to a fitness function used in an optimization processing part 4. In the optimization processing part 4, based on information obtained from the plane cutting information acquisition part 2, a group of chromosome, represented by a row or the like of how to cut pattern number in accordance with each two-dimensional plane, is generated, by genetic algorithm, genetic operation of selection, crossing, sudden variation of the chromosome is repeated, optimum solution or that approximate to the optimum solution is obtained.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for cutting out a necessary number of small planes having different sizes from a plurality of two-dimensional planes by using a genetic algorithm. The present invention relates to a two-dimensional plane cutting method optimizing apparatus to be obtained.

[0002]

2. Description of the Related Art When a plurality of two-dimensional planes (for example, a large original plate) are provided and a required number or more of small planes (for example, a shelf) are cut out from them by various cutting patterns. In addition, there is a problem that the total sum of the useless areas is minimized.

[0003] The same can be applied to the method of cutting a glass plate, paper or cloth, and the optimization problem of such a two-dimensional plane cutting method is conventionally solved using a linear programming method or a constraint satisfaction method. I was

[0004] References to the conventional method include, for example, the following. [References] (1) Costa, Une etude pratique de decoupes de pan
neaux de bois, RAIRORecherche operationnelle
/ Operations Research, 1984. (2) Dincbas et al., Solving a Cutting-Stock Prob
lem in Constraint Logic Programming, 5th Int. Conf.
Logic Programming, 1988. (3) Maruyama et al., Discrete Constraint Satisfaction / Optimization Using Sufficient Conditions for Violation of Constraints, Artificial Intelligence, 1992. As the number of problems increases and the scale of the problem increases, the calculation time for finding a solution increases exponentially, and it cannot be used as a practical solution.

[0005] On the other hand, although it is not used for the optimization problem of the cutting method of the two-dimensional plane, it is one of the methods for approximately solving a general combination optimization problem in a practical calculation time. One is a genetic algorithm.

A genetic algorithm is a method for simulating the evolution of living organisms, which is devised by imitating mechanisms such as natural selection, gene crossover, and mutation in the evolutionary process of living organisms, and an optimal combination by engineering. A method for solving the problem.

For example, there are the following references. [References] (4) Goldberg, DE, Genetic Algorithms in Search,
Optimization, and Machine Learning, Addison-Wesle
y Publishing Company, Inc., 1989. In general, in genetic algorithms, candidates for the solution of an optimization problem are represented by chromosomes consisting of character strings. Initially, multiple chromosomes are generated randomly, and selection, crossover, and mutation operations are repeatedly performed on those chromosomes according to the value of the objective function, thereby improving the solution candidates and ultimately To get the best solution.

In the selection, chromosomes are selected according to the fitness value of the solution represented by each chromosome. In crossover, a new chromosome (child) is generated from two chromosomes (parent).

In the mutation, a mutation is randomly generated in a chromosome. Genetic algorithm is a method to obtain the optimal solution by repeating these operations a predetermined number of times.
There is a feature that can flexibly cope with the constraints of the optimization problem.

[0010]

SUMMARY OF THE INVENTION The present invention utilizes the genetic algorithm to minimize the useless area generated when cutting out a plurality of types of small planes from a predetermined two-dimensional plane. Is to solve the problem.

[0011]

FIG. 1 is a diagram for explaining the principle of the present invention shown in FIG. In FIG. 1, reference numeral 1 denotes a processing device including a CPU and a memory, 2 denotes a two-dimensional plane cutting information acquisition unit, 3 denotes a fitness function setting unit, 4 denotes an optimization processing unit, and 5 denotes an optimization result output unit.

The two-dimensional plane cutting information acquisition unit 2 receives the size and number of two-dimensional planes, the size and required number of small planes to be cut out, the required number of cutting patterns, This is a means for acquiring information such as a waste area in each cutting pattern.

The fitness function setting unit 3 is a means for setting a fitness function to be used for the genetic algorithm. In particular, when finding an optimal solution, the fitness function setting unit 3 adapts a trade-off between the evaluation of a waste area and the evaluation of a shortage of a shelf board. It has a function to set weighting factors for the fitness function in order to flexibly reflect it on the fitness function.

Based on the two-dimensional plane cutting information obtained from the two-dimensional plane cutting information acquiring unit 2, the optimization processing unit 4 uses a genetic algorithm to convert a predetermined number of two-dimensional planes (original plates) into several types of small planes. This is means for optimizing the cutting method so as to minimize the wasted area when cutting out the required number of (shelf boards).

Therefore, a chromosome to be operated in the genetic algorithm is a sequence of cutting pattern numbers used for each two-dimensional plane or the number of two-dimensional planes to be cut using each cutting pattern. Expressed in columns, randomly generate multiple chromosomes (initial population generation), evaluate and select chromosomes using a predetermined fitness function (selection),
A new chromosome is generated from two chromosomes (crossover), the gene in the chromosome is randomly mutated (mutation), and these processes are repeated a predetermined number of times or until a satisfactory solution is obtained to some extent (generation determination).

As the fitness function, a fitness function or the like obtained from the sum of the useless areas and the number of small planes or the difference between the total number of useless areas and the required number of small planes and the number of cutouts is used.

Further, a genetic algorithm is performed on a plurality of initial populations using the fitness functions given different weighting factors set by the fitness function setting unit 3, and an optimal solution or a quasi- Obtain the optimal solution. Further, in a predetermined generation, the genetic algorithm may be repeated while exchanging chromosomes between different chromosome populations, and finally an optimal solution or a solution close to the optimal solution may be obtained from a plurality of chromosome populations.

An optimization result output unit 5 converts a two-dimensional plane (original plate) to a small plane (original plate) based on information of a cutting pattern represented by a chromosome of an optimal solution or a suboptimal solution obtained by the optimization processing unit 4. Determine the optimal cutting pattern for cutting out the shelf
Output.

[0019]

DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below. An optimal solution of a cutting method for cutting out six types of shelf boards (shelf boards B1 to B6) from n large boards (original boards) is to be obtained.

FIGS. 2 to 4 are diagrams showing examples of two-dimensional plane cutting information. FIG. 2 shows an example of the size of an original plate and a shelf to be cut out, FIG. 3 shows an example of the required number of shelves, FIG. 4 shows the relationship between the number of shelves cut out according to the cutting pattern and the waste area.

When the number of original plates is n, as shown in FIG. 3, the required number of shelves B1 to B6 is n, respectively.
There are 4n sheets, n sheets, 4n sheets, 8n sheets, and 3n sheets, but each shelf board may be cut out more than the required number. This is effective in reducing the wasted area.

It is assumed that the number of shelves and the useless area for each cutting pattern are determined in advance, for example, as shown in FIG. In this example, 92 patterns of how to cut the shelves B1 to B6 with respect to the original plate are considered. Various other cutting patterns are conceivable. However, since the useless area becomes large, other cutting patterns are not used.

According to the cutting method of cutting pattern # 1,
From a master plate of size 1220 × 2500, shelf plate B2 (4
20 × 300), 2 shelves B4 (300 × 600), 15 shelves B5 (300 × 205), 15 shelves B6
(205 × 800) are cut out into 6 pieces, and the waste area is 27
500. For the other cutting patterns, the number of shelves that can be collected and the dead area are similarly determined.

FIG. 5 shows an example of the arrangement of shelves on the original plate based on the cutting pattern in the case of the cutting pattern # 1 in FIG. The numbers shown in the rectangles in FIG. 5 represent the numbers of the shelf boards, and the hatched portions represent wasteful areas (wasteful areas).

[First Embodiment] In order to determine a combination of cutting methods for minimizing a waste area when cutting out the shelves B1 to B6 from n original plates by using a genetic algorithm, a chromosome is used. Is defined as a one-dimensional sequence of cutting pattern numbers for each original plate. Therefore, the length of the chromosome is equal to the number of original plates.

FIG. 6 is a diagram for explaining chromosome expression.
P _1, P ₂ in FIG. 6, ..., P _n denotes the cut side pattern number for the original plate. The fitness functions used in the genetic algorithm, the cut how chromosomal pattern P _{i (i} = 1~n)
Is defined as a value obtained by subtracting a weighted sum of the waste area and the number of insufficient shelves obtained from the constant from a certain constant.

[Example of fitness function] Fitness function = C ₀ − ｛Σ _i Waste area (P _i ) + C × Σ _j
Insufficient number of shelves (j)｝ where Σ _i is the sum of i = 1 to n, Σ _j is j = 1
To 6 (type of shelf). C ₀ is a constant for setting the fitness function to a positive value. The useless area (P _i ) is the useless area on the i-th original plate. C is
The weighting coefficient of the fitness function is set in advance so that the evaluation of the wasted area and the evaluation of the shortage of the shelf board are reflected in the fitness function with balance. The number of insufficient shelves (j) is shown in FIG.
Is the value obtained by subtracting the total number of j-th shelves obtained from the first to n-th original plates from the predetermined required number of shelves. However, when the number of insufficient shelves (j) is a negative number, the calculation is performed as 0.

Similar results can be obtained by using the reciprocal of the weighted coefficient sum of the useless area and the number of insufficient shelves as the fitness function. As the initial group of chromosomes, chromosome values are generated using random numbers based on the chromosome expressions shown in FIG. The value is a numerical value between 1 and 92. A plurality of chromosomes are prepared as a group.

For the selection, ordinary roulette selection or rank selection is used. The next generation chromosome is selected using the value of the fitness function of each chromosome. As the crossover and mutation method, a normal crossover method such as one-point crossover, multipoint crossover, and uniform crossover can be used. Mutation can also be performed by generating random numbers.

FIG. 7 shows an example of a specific chromosome when there are four large original plates. In this example, first, 12 such chromosomes are randomly generated at first, and used as an initial population of chromosomes.

According to the chromosome shown in FIG. 7, the first original plate is to be cut by the cutting pattern # 2, and the number of shelves and the dead area by the cutting pattern shown in FIG. From the information on the relationship, cut pattern # 2
Then, six shelves B1, four shelves B3, and four shelves B6
You can see that you take one. The useless area in the case of this cutting pattern # 2 is 33,600. Cutting pattern # 76,
With respect to the cutting pattern # 5 and the cutting pattern # 14, the number of sheets on each shelf and the waste area are similarly obtained. From these values, the value of the fitness function is calculated, and selection is performed based on the value of the fitness function.

Next, the crossover will be described. As shown in FIG. 8 (a), a random number for determining an intersection is generated for two parent chromosomes A and B, and, for example, the second and third rows from the parent (chromosome A and chromosome B) are generated. Perform a one-point crossover at the eye boundary. FIG. 8B shows the chromosomes A ′ and B ′ of the child generated by the crossover. A technique of uniform crossover using a multipoint crossover or a mask may be used.

As the mutation, the cutting pattern number of the original plate selected by the generation of random numbers is changed by the generation of random numbers 1 to 92. The selection, crossover, and mutation operations are repeated in this manner.

FIG. 9 is a diagram showing an example of the best chromosome in 12 generations. Here, the required number of shelves is n = 4 (the number of original plates) in FIG.
Sheets, 16 shelves B2, 4 shelves B3, 1 shelves B4
The number of shelves corresponding to this solution is 6, six shelves B1 and sixteen shelves B2 from the information in FIG. It can be seen that four shelves B3, sixteen shelves B4, thirty-four shelves B5 and sixteen shelves B6 have a waste area of 228,600. The percentage of the waste area with respect to the original plate is 1.87%. In this case, the optimal value was obtained. In the present embodiment, it has been demonstrated that when the number n of the original plates is 15 or more, the calculation time is shorter than in the conventional method.

[Second Embodiment] By the way, when the number n of the original plates is variously changed, depending on a given cutting problem, when the value of the weighting coefficient C of the fitness function is relatively small, As the fitness value, the value of the wasted area usually has a large effect, so that chromosomes satisfying the required number of shelves may not survive. Conversely, when the value of the weight coefficient C is relatively large, the chromosome that reduces the waste area may not survive.

As a method of avoiding such inconvenience,
A method is used in which a plurality of chromosome groups are prepared and a fitness function having a different value of weight coefficient C is assigned to each of them. For each chromosome group, the genetic operation is repeated a predetermined number of times using a fitness function having a different value of the weighting coefficient C, and then the chromosome groups having the best solution are compared. The best one is the final solution. As a result, it becomes possible to automatically select an appropriate weight coefficient.

Further, by performing chromosome exchange between different chromosome populations at appropriate generations,
More effective natural selection can be achieved. By occasionally exchanging chromosomes between chromosome groups using fitness functions having different weighting coefficients C, the best chromosomes can be obtained for various weighting coefficients C.

For example, it is assumed that five subpopulations are prepared, and each subpopulation contains 10 chromosomes. The weight coefficient of the fitness function of the k-th subgroup is 1/10 ^k−1 , k =
1, 2, ..., 5. Every 20 generations, the chromosomes with the lowest fitness value of the k-th subpopulation are replaced with chromosomes with the (k-1) -th highest fitness value, and the generations are changed.

The above is an example, and it goes without saying that the number of populations, how to assign weighting factors, and when to change generations of chromosomes are not limited to the methods described here. [Third Embodiment] Next, as another method of chromosome expression, a method of using the number of original plates using each cutting pattern as a gene will be described.

FIG. 10 is a diagram showing an example of chromosome expression. In FIG. 10, the value d _i of the number of original plates for each cutting pattern is defined as a column of chromosomes. In the example of the cutting pattern shown in FIG. 4, m = 92. Σd _i (i = 1 to m)
Is equal to the total number n of the original plates. The processing of the genetic manipulation is the same as that in the above-described example, and thus the detailed description is omitted. Further, the above-described method using a plurality of populations and the method of exchanging chromosomes between the populations can also be used.

[Fourth Embodiment] The fitness function used in the above-described example is a condition under the condition that an unnecessarily large number of shelves may be cut out. In the case where the number of sheets must not be cut out more than the required number, the fitness function is set as follows, for example.

[Example of Another Fitness Function] Fitness function = C ₀ − ｛Σ _i Wasted area (P _i ) + C × Σ _j
[Shelf number (j) - required number (j)] ^2} _{Here, Σ i, Σ j, P} i, C 0 and C are the same as the previous example. According to this fitness function, the smaller the waste area and the closer the total number of shelves cut out to the requested number as much as possible, the greater the fitness.

[0043]

As described above, according to the present invention,
By effectively using the genetic algorithm, an optimal solution or a solution close to the optimal solution can be obtained with less calculation time than the conventional method, especially when the number of large original plates is large.

Further, by using a plurality of chromosome groups having different weighting factor fitness functions, selection of a weighting factor for a weighted sum is facilitated.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating the principle of the present invention.

FIG. 2 is a diagram showing an example of sizes of an original plate and a shelf plate.

FIG. 3 is a diagram showing the required number of shelves in the present embodiment.

FIG. 4 is a diagram showing a relationship between the number of shelves and a waste area according to a cutting pattern.

FIG. 5 is a diagram showing an example of an arrangement of shelves on an original plate based on a cutting pattern.

FIG. 6 is a diagram illustrating an example of chromosome expression.

FIG. 7 is a diagram showing an example of a chromosome.

FIG. 8 is a diagram illustrating an example of crossover.

FIG. 9 is a diagram showing an example of the best chromosome.

FIG. 10 is a diagram illustrating an example of chromosome expression.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Processing apparatus (CPU / memory) 2 Two-dimensional plane cutting information acquisition part 3 Fitness function setting part 4 Optimization processing part 5 Optimization result output part

Claims (5)

[Claims] 1. A two-dimensional plane cutting method optimizing apparatus which obtains an optimal cutting method by using a genetic algorithm when a predetermined number of different types of small planes are cut out from a plurality of two-dimensional planes. A two-dimensional plane cutting information acquisition unit for acquiring two-dimensional plane cutting information including information on the size of the small plane, the required number of pieces, a cutting pattern in a predetermined two-dimensional plane, and a waste area in each cutting pattern;
A sequence of cutting pattern numbers used for each of the two-dimensional planes is defined as a chromosome, and a genetic algorithm is executed by using a fitness function obtained from the sum of the dead areas and the number of deficient small planes. Alternatively, there is provided a two-dimensional plane cutting method optimizing apparatus, comprising: an optimizing processing unit for obtaining a solution close to the optimum solution. 2. A two-dimensional plane cutting method optimizing apparatus for obtaining an optimal cutting method by using a genetic algorithm when a predetermined number of different types of small planes are cut out from a plurality of two-dimensional planes. A two-dimensional plane cutting information acquisition unit for acquiring two-dimensional plane cutting information including information on the size of the small plane, the required number of pieces, a cutting pattern in a predetermined two-dimensional plane, and a waste area in each cutting pattern
A sequence of the number of two-dimensional planes using each of the cutting patterns is used as a chromosome, and a genetic algorithm is executed using a fitness function obtained from the sum of the dead area and the shortage of the small planes to obtain an optimal solution or An apparatus for optimizing a two-dimensional plane cutting method, comprising: an optimization processing unit that obtains a solution close to an optimal solution. 3. A two-dimensional plane cutting method optimizing apparatus for obtaining an optimum cutting method by using a genetic algorithm when a predetermined number of different small planes are cut out from a plurality of two-dimensional planes. A two-dimensional plane cutting information acquisition unit for acquiring two-dimensional plane cutting information including information on the size of the small plane, the required number of pieces, a cutting pattern in a predetermined two-dimensional plane, and a waste area in each cutting pattern;
The sequence of the pattern number to be used for each of the two-dimensional planes is defined as a chromosome, and the genetic algorithm is used by using the sum of the dead area and the fitness function obtained from the difference between the required number of the small planes and the number of the cut out planes. By executing
An optimization processing unit for obtaining an optimal solution or a solution close to the optimal solution. 4. The two-dimensional plane cutting method optimizing apparatus according to claim 1, further comprising: a fitness function setting unit configured to set a plurality of fitness functions having different weight coefficients. And generating a plurality of chromosome populations corresponding to the fitness functions having the different weighting factors, and using the fitness functions having different weighting factors for the plurality of chromosome populations. A two-dimensional plane cutting method optimizing apparatus, wherein the optimal solution or a solution close to the optimal solution is obtained from a plurality of chromosome populations. 5. The two-dimensional plane cutting method optimizing apparatus according to claim 1, further comprising a fitness function setting unit configured to set a plurality of fitness functions having different weighting coefficients. And generating a plurality of chromosome populations corresponding to the fitness functions having the different weighting factors, and using the fitness functions having different weighting factors for the plurality of chromosome populations. That the genetic algorithm is repeated while exchanging chromosomes between different chromosome populations in a given generation to finally obtain an optimal solution or a solution close to the optimal solution from a plurality of chromosome populations. Characteristic two-dimensional plane cutting method optimization device.