JPH06161990A - Arranging system - Google Patents

Abstract

PURPOSE:To efficiently perform arrangement processing concerning an arrangement problem such as jamming in some rectangular arranging areas with different plural areas, etc. CONSTITUTION:This system is provided with a means 1 which performs the position decision of a rectangle whose position to be located is undecided and the change of a decided position at need, a means 2 which houses each rectangle in the arranging area and sets an initial restriction violation condition from a condition of restriction to prevent overlapping with each other and sets a near violation condition as the AND of a condition in which the coordinate of a point where violation condition that becomes tautology is not satisfied is substituted in a variable representing the coordinate of the lower left apex of a processing object rectangle within a satisfied violation condition when at least one restriction violation condition can be satisfied even when the processing object rectangle is located anywhere in the processing of the means 1, and a means 3 which stores the restriction violation condition set by the means 2, and the arrangement processing is performed so as not to satisfy all the violation conditions in the means 3.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a layout problem such as packing and loading. For example, the problem of cutting out a small rectangular shelf from a large rectangular board, or the problem of loading luggage packed in a box shape on a truck bed (with a hood).

[0002]

2. Description of the Related Art In such a placement problem, the potential solution space is combinatorially large and a simple search method cannot be applied. However, there are cases in which it is possible to identify a portion in the apparent solution space where the desired solution does not exist, and it may be possible to efficiently obtain the solution by effectively utilizing such a structure.

Conventionally, a general solution method is not applied to the above-mentioned problem group, and a program is individually created by utilizing the peculiarity of each problem.

[0004]

DISCLOSURE OF THE INVENTION Problems to be Solved by the Invention The present invention generally involves packing a plurality of rectangles each having a different shape in a given rectangular area without overlapping each other, and generally packing a plurality of rectangular parallelepipeds each having a different shape into each other. Problem of packing in a given rectangular area without any
Alternatively, it is intended to improve the efficiency of processing by maximally utilizing the failure information obtained up to the midpoint of the processing in the subsequent processing, for the problem that these problems are expanded to n dimensions.

[0005]

FIG. 1 is a block diagram showing the principle of the present invention. FIG. 3A shows the principle of the first invention.
In the figure, the principle configuration of the layout method that does not violate the constraint conditions when arranging the rectangles and does not overlap a plurality of rectangular parallelepipeds having different shapes with each other in the given rectangular layout area. It is shown.

Position determining / changing means 1 in FIG.
Corresponds to, for example, the position determining unit and the position changing unit, determines the position of a rectangle whose placement position is undetermined, and changes the position of the rectangle whose placement position has already been determined as necessary. That is, even for a rectangle whose position is once determined, its position is changed as necessary in order to successfully pack all the rectangles in the arrangement area.

The constraint violation condition setting means 2 corresponds to, for example, an initial constraint violation condition setting unit and a constraint violation condition generation unit, and a constraint condition for each rectangle to be placed within a given placement area, and an arbitrary constraint condition. The initial constraint violation condition, which is a sufficient condition for constraint violation, is first set based on the constraint condition that the two rectangles do not overlap each other, and is targeted when the position determination / change of the rectangle by the position determination / change means 1 is performed. When at least one constraint violation condition is satisfied no matter where the rectangle is placed, the coordinates of the point that does not satisfy the constraint violation condition that is true are the coordinates of the lower left vertex of the target rectangle in the satisfied constraint violation condition. A new constraint condition is generated as the logical product of the conditions assigned to the variables corresponding to. The constraint violation storage unit 3 stores the constraint violation condition set by the constraint violation condition setting unit 2.

FIG. 1B is a block diagram of the principle of the second invention. The figure shows the principle block of the layout method that fills a given layout area from the constraint conditions when arranging rectangles so that all the constraint satisfaction conditions are satisfied and multiple rectangles with different shapes do not overlap each other. It is a figure. In the figure, the position determining / changing means 4 performs the determination / changing process of the position of the rectangle, similarly to the position determining / changing means 1 in the first invention.

The constraint satisfaction condition setting means 5 corresponds to, for example, an initial constraint satisfaction condition setting unit and a constraint satisfaction condition generation unit, and a constraint condition for each rectangle to be arranged to fit within a given rectangular area and an arbitrary condition. First, an initial constraint satisfaction condition, which is a necessary condition for constraint satisfaction, is set based on a constraint condition for preventing the two rectangles from overlapping with each other, and the target rectangle is used in the position determination / change processing of the rectangle by the position determination / change means 4. Where at least one constraint satisfaction condition is not satisfied, the coordinates of the point where the constraint satisfaction condition that is constant is not satisfied are set to the variable corresponding to the coordinates of the lower left vertex of the target rectangle in the constraint satisfaction condition that is not satisfied. A new constraint satisfaction condition is set as the logical sum of the substituted conditions. The constraint satisfaction condition storage means 6 stores the set constraint conditions.

[0010]

According to the present invention, a plurality of rectangles each having a different shape are placed in a given rectangle arrangement area without overlapping each other. Figure 1
In the first invention whose principle is shown in (a), the position determination / change processing of each rectangle is repeated so as not to satisfy all the constraint violation conditions stored in the constraint violation condition storage means 3. Then, the placement process is completed when the placement positions of all the rectangles are determined.

For example, an appropriate initial layout is generated, it is determined whether or not the layout does not meet the initial constraint violation condition,
If there is even one match, the rectangle is repositioned appropriately.

In this position changing process, if at least one constraint violation condition is satisfied no matter where the rectangle is placed in the arrangement area, the constraint violation condition that establishes the coordinates of the point where the constraint violation condition that is true is not satisfied. , A new constraint violation condition is generated as a logical product of the conditions assigned to the variables corresponding to the lower left vertices of the target rectangle, the condition is newly stored in the constraint violation condition storage means 3, and then the appropriate rectangle is again stored. Position change or position determination is repeated,
When the positions of all the rectangles are determined without satisfying all of the constraint violation conditions stored in the constraint violation condition storage unit 3, the placement process ends as placement success.

In the second invention whose principle is shown in FIG. 1 (b), rectangular arrangement is performed using a constraint satisfaction condition which is a necessary condition for constraint satisfaction in place of the constraint violation condition in the first invention. Be seen. That is, the constraint satisfaction condition storage means 6
The placement process ends when the positions of all the rectangles are determined so as to satisfy all the constraint satisfaction conditions stored in.

In the present invention, for example, every time a plurality of rectangles are successfully placed in the placement area, the value of the variable indicating the x coordinate of the right side of the placement area or the value of the variable indicating the y coordinate of the top side becomes greater. In addition to a strict value, that is, a value that reduces the area of the placement area and the placement process is repeated, a variable indicating the x coordinate of the right side of the placement area or the variable indicating the y coordinate of the top side of the variable is finally added. The placement process for obtaining the optimal placement is repeated until a constraint violation condition that does not include a variable is generated and it is determined that placement is impossible. Further, the present invention is applied not only to the two-dimensional rectangular arrangement but also to the arrangement processing of the rectangular parallelepiped in the three-dimensional space and the arrangement processing in the space of four or more dimensions.

As described above, in the present invention, the range of the lower left apex of the rectangle is narrowed down by determining / changing the position of the rectangle so as not to violate the constraint violation condition. Narrowed.

[0016]

2 is a block diagram showing the configuration of an embodiment of an arrangement system using the arrangement system of the first invention. In the figure, the initial constraint violation condition setting unit 11 has a constraint condition that a plurality of rectangles to be placed in the placement region fit within a given placement region and a constraint condition that any two rectangles do not overlap. From condition 10, an initial constraint violation condition that is a sufficient condition for constraint violation is set, and the constraint violation condition storage unit 15 is set.
To be stored in.

The position changing unit 12 changes the position of the rectangle whose arrangement has been decided in the arrangement area as needed, and the position deciding unit 13 decides the position of the rectangle whose arrangement has not been decided yet. To do. Position change unit 1
2 and the position determination unit 13 perform position change or position determination so as not to satisfy any one of the constraint violation conditions already stored in the constraint violation condition storage unit 15. However, such position determination or position change is performed. If it is impossible, the constraint violation condition generation unit 14 is activated.

In the determination of whether or not the constraint violation condition is satisfied, the constraint violation condition including the variable corresponding to the coordinate of the lower left vertex of the rectangle whose position is not yet determined, that is, the variable whose value is currently undetermined, is It is impossible to determine whether or not the condition is satisfied, and such a constraint violation condition is regarded as not satisfied.

The constraint violation condition generating unit 14 includes a position changing unit 1
2 or when activated by the position determining unit 13, a constant constraint violation condition is satisfied for the variable corresponding to the lower left vertex of the rectangle whose position is to be determined or the position is to be changed within the constraint violation condition that is satisfied. Substituting the coordinates of the points not to be generated, a new constraint violation condition is generally generated as a logical product of a plurality of conditions as the substitution result, and the new constraint violation condition storage unit 15
To store. That is, the constraint violation condition storage unit 15 stores only the initial constraint violation condition set by the initial constraint violation condition setting unit 11 immediately after the placement process is started, and then the constraint violation condition generated by the constraint violation condition generation unit 14. Will be sequentially stored.

That is, in the first aspect, the constraint violation condition stored in the constraint violation condition storage unit 15 is a sufficient condition that violates the constraint condition 10. When at least one constraint violation condition is satisfied for one rectangle to be placed no matter where the lower left vertex is placed, a variable corresponding to the lower left vertex of the target rectangle is generated as a numerical constraint violation condition. Narrows the rectangle whose position is to be changed, and narrows the range of the lower left apex. Also, by taking the logical product of multiple inequalities,
Sufficient conditions are expressed for constraint violations caused by multiple rectangular entanglements.

FIG. 3 is a block diagram showing the configuration of an embodiment of an arrangement system using the arrangement system of the second invention. As described above, in the second invention, the constraint satisfaction condition is used instead of the constraint violation condition in the first invention, and a plurality of rectangles are arranged so as to satisfy all the constraint satisfaction conditions.

In FIG. 3, the initial constraint satisfaction condition setting unit 16
Sets an initial constraint satisfaction condition, which is a necessary condition for constraint satisfaction, from the constraint condition 10 described in FIG. 2, and stores it in the constraint satisfaction condition storage unit 20. The position changing unit 17 and the position determining unit 18 change the position of the rectangle or determine the position similarly to the position changing unit 12 and the position determining unit 13 in FIG.

In this case, when at least one constraint satisfaction condition already stored in the constraint satisfaction condition storage unit 20 is not satisfied, the constraint satisfaction condition generation unit 19 is activated and the constraint satisfaction condition generation unit 19 is satisfied. Substituting the coordinates of the point that does not satisfy the constraint satisfaction condition, which is a constant, into the variable corresponding to the coordinates of the lower left vertex of the rectangle that is the position change or decision correspondence within the constraint satisfaction condition, and In general, a new constraint satisfaction condition is generated as a logical sum of a plurality of conditions and stored in the constraint satisfaction condition storage unit 20. In determining whether the constraint satisfaction condition is satisfied, the constraint satisfaction condition that includes the variable corresponding to the coordinates of the lower left vertex of the rectangle whose position is not yet determined, that is, the variable whose value is currently undetermined, is satisfied. Since the determination is impossible, the processing is performed assuming that it is established.

In the second invention, the initial constraint satisfaction condition stored in the constraint satisfaction condition storage unit 20 at the start of processing,
The constraint satisfaction condition additionally stored by the constraint satisfaction condition generation unit 19 is a necessary condition that must be satisfied because there is an arrangement that satisfies the constraint condition. When at least one constraint satisfaction condition is not satisfied no matter where the lower left apex of the placement target rectangle is placed, by generating a constraint satisfaction condition in which the variable corresponding to the lower left apex of the target rectangle is digitized, The rectangular area to be repositioned is narrowed down, and the area of the lower left apex is narrowed down. Moreover, by taking the logical sum of a plurality of inequalities, the necessary condition for preventing the constraint violation due to the entanglement of a plurality of rectangles is expressed.

FIG. 4 is a flow chart of an embodiment of the placement process in the first invention. When the process is started in the figure, first, in step (S) 24, an appropriate layout is generated as an initial layout, and in step S25, whether or not the constraint condition is satisfied is determined by any constraint violation condition (NJ). It is determined whether or not it is established, and when not established, S26
It is determined whether or not there is a rectangle whose placement position is undetermined, and when there is no rectangle, it is determined again in S27 whether or not there is any established NJ, and when there is not, it is determined that the placement is successful and the process ends.

If at least one NJ is satisfied in S25, an attempt is made to change the position of an appropriate rectangle among the rectangles whose arrangement has been determined in the initial arrangement in S28. And S29
It is determined whether or not the position change is successful, that is, whether or not one or more NJs are satisfied for all the positions in the arrangement area and all the positions are prohibited as the disposition is impossible. The processing moves to S26 and thereafter.

When it is determined in S26 that there is a rectangle whose position is to be determined, the position of the rectangle is determined in S3.
0 is tried, and it is determined in S29 whether or not all positions are prohibited.

If it is determined in S29 that all positions are prohibited for position change or position determination, S29
At 31, a new constraint violation condition (NJ) is generated.
The generation of this new NJ will be described later in detail based on its specific example. When a new NJ is generated in S31, S3
It is determined whether or not there is a variable on the left side of the NJ generated in 2. When there is no variable, the constraint violation condition becomes true, and the rectangle cannot be arranged. Therefore, the arrangement ends in failure and the processing ends. When it is determined in S32 that there is a variable on the left side, the generated NJ is S33 in FIG.
Are stored in the constraint violation condition unit 15 and the process after the position change of S28 is repeated for different rectangles.

FIG. 5 shows an example of an arrangement area and an arrangement target rectangle for explaining the arrangement method of the first invention. The same figure (a)
Indicates the placement area, and the coordinates of the lower left vertex are (0,0)
Given in. The coordinates of the lower right vertex are (10,8).

FIG. 3B shows three rectangles to be arranged, and these three rectangles are required to be arranged without overlapping in the arrangement area shown in FIG. The sides of each rectangle are arranged parallel to the coordinate axes, and may be arranged horizontally or vertically. For these rectangles, the bottom left corner of rectangle 1

[0031]

[Outer 1]

X, y coordinates of the vertices of, that is, variables x _i ,
y _i and the horizontal side of the outer rectangle 2,

[0033]

[Outside 2]

Constraint violation conditions are expressed using variables w _i and h _i which indicate the lengths of vertical sides. First, as the initial constraint violation condition stored in the constraint violation condition storage unit 15 in FIG. 2, the following four expressions x _i <0 (1 ) Y _i <0 (2) x _i + w _i > 10 (3) y _i + h _i > 8 (4) (1 ≦ i ≦ 3) is stored, and two rectangles are stored. X _i + w _i > x _j ∧y _i + h _i > y _j ∧x _j + w _j > x _i ∧y _j + h _j > y _i (1 ≦ i <j ≦ 3) ... (5) is stored.

As the constraint violation condition (5), for example, for a rectangle, x ₁ +8> x ₂ ∧y ₁ +6> y ₂ ∧x ₂ +5> x ₁ ∧y
₂ +2> y ₁ , which is the logical product of four inequalities.
In order for the rectangles to overlap each other, it is necessary that all of these four constraint violation conditions are satisfied. For example, even if only the inequality x ₁ +8> x ₂ is satisfied, if the rectangle and the rectangle can be arranged so as to be displaced in the y direction, the rectangle and the rectangle do not overlap.

Next, using the specific example of FIG. 5, the flow of FIG.
-Explain the procedure of the placement process performed according to the chart
It FIG. 6 shows an example of the initial arrangement. In this initial placement
Is a rectangle and only rectangles are arranged. Rectangle
For x₁= Y₁= 0, w ₁= 8, h₁= 6
And for rectangles x₂= 0, y₂= 6, w₂
= 5, h₂= 2, and the initial constraint violation condition (1)-
None of (5) holds.

Then, in S26 of FIG. 4, it is judged whether or not there is a rectangle whose position is undecided. Here, since the position of the rectangle is undecided, the position determination is tried in S30. In addition, here as the position where the rectangle can be placed,
It is assumed that the coordinates of the lower left apex are all limited to integers.

The rectangles are arranged horizontally, that is, w ₃
= 9, h ₃ = 2, the condition (3) is true when the x coordinate is 2 or more, and the condition (4) is true when y is 7 or more. Therefore, the X coordinate is 0, or It is only necessary to consider the point 1 and the point where y is 0 or more and 6 or less, but the y coordinate is 0.
The overlap with the rectangle becomes a problem in the above 5 or less points, and i
The constraint violation condition (5) with = 1 and j = 3 is satisfied.

Therefore, the logical product of the coordinates of twelve points whose x-coordinate is 0 or 1 and whose y-coordinate is 0 or more and 5 or less is substituted into the condition (5), is actually Only the four vertices of the rectangular range defined by these coordinates, that is, the four points with the x coordinate of 0 or 1, and the y coordinate of 0 or 5, should be considered (the logic corresponding to 12 points in total). The product and the logical product corresponding to these four points are equal). As a result, the following logical product is generated as a part NJ as a part of the constraint violation condition.

X ₁ + w ₁ > 1∧y ₁ + h ₁ >5∧9> x ₁ ∧2> y ₁ Here, for example, if 0 and 1 are substituted for the x coordinate in the first inequality of the equation (5), x ₁ + w ₁ > 0 and x ₁ + w ₁
> 1 but the intersection of these inequalities x ₁ + w
₁ > 1 is used as part of the part NJ.

At the point where the y coordinate is 6, the overlap with the rectangle becomes a problem. That is, the constraint violation condition (5) is satisfied when i = 2 and j = 3. x coordinate is 0 or 1, y
The following logical product is generated by taking the logical product of the coordinates of the two points having the coordinates of 6 and substituting for this condition.

X ₂ + w ₂ > 1∧y ₂ + h ₂ >6∧9> x ₂ ∧8> y ₂ Therefore, the part NJ for the rectangular horizontal arrangement w ₃ = 9, h ₃ = 2 is the logical product of these products. Further, by taking the logical product, it is given by the following equation.

X₁+ W₁> 1 ∧y₁+ H₁> 5∧9> x₁∧2> y₁∧x₂+ W₂> 1 ∧y ₂ + H₂> 6∧9> x₂∧8> y₂ ... (6) Next, when arranging rectangles in a portrait orientation, that is, w₃=
2, h₃= 9, where should the rectangle be placed?
Even if the constraint violation condition (4) becomes true,
The rectangle cannot be placed without being established, and the final
As a result, the partial NJ becomes equation (6).

In FIG. 4, the expression (6) is calculated as NJ in S33.
After that, the position change is tried in S28. Here is the long side
The position of the shape shall be changed, but the horizontal arrangement,
Chi w ₂= 5, h₂= 2, a part of NJ is established
So that the portrait orientation, ie w₂= 2, h₂= 5
Position the rectangle x₂= 8, y₂= 0, w₂= 2, h
₂Change to the position of = 5.

The position of the rectangle after this change is shown in FIG.
It is shown in (a). In this position change process, it is considered that the constraint violation condition including the variable corresponding to the coordinate of the lower left vertex of the rectangle whose position is not determined is not satisfied.
Specifically, it is applied to a rectangle, and x ₃ and y ₃ are variables whose values are undecided. For example, the constraint violation condition (5) when i = 2 and j = 3 is regarded as not satisfied.

As the final step of the placement process for the example of FIG. 5, position determination for the rectangle is attempted in S30 of FIG. x ₃ = 0, y ₃ = 6, w ₃ = 9, h ₃ =
By setting the value to 2, the substantial placement process is completed. FIG. 7B shows the final result.

FIG. 8 is a processing flowchart of the optimum arrangement method. The optimum placement method here means, for example, in the first invention, a process of reducing the area of the placement region and performing the placement again when the rectangular placement is successful for a placement region according to the flowchart of FIG. Repeatedly, placing multiple rectangles to be placed in the placement area as compact as possible.

That is, every time the placement in the placement area is successful, the value of the variable indicating the x coordinate of the right side of the placement area or the variable indicating the y coordinate of the top side is updated to a stricter value, that is, a smaller value, and optimum placement is performed. The process will be repeated until.

In this process, for example, when the NJ generated in S31 of FIG. 4 does not include a variable other than the variable indicating the x coordinate of the right side of the placement area or the variable indicating the y coordinate of the upper side, the NJ is finally placed. It is determined to be impossible. That is, the generated NJ must be unsatisfied in order to be able to be arranged. However, if the NJ contains only variables related to the arrangement area, it is generated unless the size of the arrangement area changes. NJ will be established, and it is determined that the placement in the placement area is impossible.

When the processing is started in the flowchart for obtaining the optimum arrangement, that is, in FIG. 8, the constraint value is input in S40. Here, the constraint value is a value of a variable indicating the x coordinate of the right side of the placement area or a variable indicating the y coordinate of the upper side. At the start of the process, the constraint value input in S40 is not changed in S41, but the placement process was executed by the system of FIG. 2 or 3 in S42 using the constraint value, and was it possible to place in S43? It is determined whether or not. If it can be arranged, the process returns to S41, the constraint value is changed to a stricter (smaller) value, and the processes from S42 onward are repeated. When it is finally determined that the placement is impossible in S43, the process ends, and the placement at that time becomes the optimal placement.

As described above, as the two-dimensional arrangement problem, the arrangement method of arranging a plurality of rectangles in the rectangular area as the arrangement area has been described in detail, but the present invention can also be applied to the three-dimensional or more arrangement problem. Is. For example, as an initial constraint violation condition for the problem of arranging m rectangular parallelepipeds (width w _i , depth d _i , height h _i ) in the arrangement area of width a, depth b, and height c in the three-dimensional space, , The following six inequalities regarding not to extend from the arrangement region: x _i <0 y _i <0 z _i <0 x _i + w _i > a y _i + d _i > b z _i + h _i > c (1 ≦ i ≦ m) is a condition for preventing two arbitrary rectangular parallelepipeds from interfering with each other: x _i + w _i > x _j ∧y _i + d _i > y _j ∧z _i + h _i > z _j ∧x _j + w _j > x _i ∧y _j + d _j > y _j ∧z _j + h _j > z _j (1 ≦ i ≦ j ≦ m) is set by the initial constraint violation condition setting unit 11 in FIG. A solution to the placement problem can be found.

[0052]

As described in detail above, according to the present invention, for example, by generating a constraint violation condition in which a variable corresponding to the lower left vertex of a rectangle is digitized, the narrowing of the rectangle whose position is to be changed. And, it becomes possible to narrow down the range of the lower left apex. In addition, by taking the logical product of multiple inequalities, it is possible to express sufficient conditions for constraint violations caused by the entanglement of multiple rectangles, save unnecessary search for finding solutions, and efficiently solve placement problems. Can find a solution.

[Brief description of drawings]

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

FIG. 2 is a block diagram showing a configuration of an embodiment of an arrangement system using the first invention.

FIG. 3 is a configuration block diagram of an embodiment of an arrangement system using the second invention.

FIG. 4 is a flowchart of arrangement processing in the first invention.

FIG. 5 is a diagram showing a specific example of an arrangement area and a rectangle.

FIG. 6 is a diagram showing an example of initial placement.

FIG. 7 is a diagram showing an arrangement after changing the position of a rectangle.

FIG. 8 is a flowchart of an optimal placement process.

[Explanation of symbols]

 1, 4 Position determination / change means 2 Constraint violation condition setting means 3 Constraint violation condition storage means 5 Constraint satisfaction condition setting means 6 Constraint satisfaction condition storage means 10 Constraint conditions 11 Initial constraint violation condition setting unit 12, 17 Position change unit 13, 18 Position determination unit 14 Constraint violation condition generation unit 15 Constraint violation condition storage unit 16 Initial constraint satisfaction condition setting unit 19 Constraint satisfaction condition generation unit 20 Constraint satisfaction condition storage unit

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Yuka Takizawa 1015 Kamiodanaka, Nakahara-ku, Kawasaki-shi, Kanagawa Fujitsu Limited

Claims (8)

[Claims] 1. In an arrangement method in which a plurality of rectangles each having a different shape are packed in a given arrangement area (rectangle) without overlapping each other, the position of a rectangle whose position is not determined in the arrangement area is determined. Then, the position determining / changing means (1) for changing the position of the rectangle whose position has already been decided as necessary.
Then, an initial constraint violation condition that is a sufficient condition for constraint violation is set from the constraint condition that each rectangle fits within the given arrangement area and the constraint condition that any two rectangles do not overlap each other. When at least one constraint violation condition is satisfied at any position in the arrangement area of the rectangle whose position is to be determined / changed in the process of the position determination / change means (1), the constraint violation condition that becomes true is A constraint violation condition setting means (2) for setting a new constraint violation condition as a logical product of the conditions obtained by substituting the coordinates of the points that do not hold into the variables corresponding to the coordinates of the lower left vertex of the target rectangle in the constraint violation condition that holds. A constraint violation condition storage means (3) for storing the constraint violation condition set by the constraint violation condition setting means (2), and the constraint violation condition storage means (3) stores the constraint violation condition storage means (3). Placement method which is characterized in that the determination / change processing locations of the rectangle by approximately the position-determining / changing means abuse conditions so as not to hold all (1). 2. A variable indicating the x-coordinate of the right side of the placement area or the y-coordinate of the top side of the placement area every time all placements of a plurality of rectangles to be placed in the placement area are determined in the placement method. Is updated to a value that reduces the area of the placement area, and the constraint violation condition does not include a variable other than the variable indicating the x coordinate of the right side of the placement area or the variable indicating the y coordinate of the top side. 2. The arrangement method according to claim 1, wherein when the is generated, the arrangement in the arrangement area is made impossible and the optimum arrangement of the plurality of rectangles is obtained. 3. In an arrangement method in which a plurality of rectangles each having a different shape are packed in a given arrangement area (rectangle) without overlapping each other, the position of the rectangle whose position is not determined in the arrangement area is determined. Then, the position determining / changing means (4) for changing the position of the rectangle whose position has already been decided as necessary.
And the constraint condition that each of the rectangles to be placed fits within the given placement area and the constraint condition that any two rectangles do not overlap, the initial constraint satisfaction condition that is a necessary condition for satisfying the constraint condition. Is set, and at least 1 is placed in the arrangement area where the rectangle whose position is to be determined / changed in the processing by the position determination / change means (4) is placed.
When the two constraint satisfaction conditions are not satisfied, the logical sum of the conditions in which the coordinates of the points that do not satisfy the constraint satisfaction condition that is false are substituted into the variables corresponding to the coordinates of the lower left vertex of the target rectangle in the constraint satisfaction condition that is not satisfied. A constraint satisfaction condition setting means (5) for generating a new constraint satisfaction condition, and a constraint satisfaction condition storage means (6) for storing the constraint satisfaction condition set by the constraint satisfaction condition setting means (5), The position determination / change means (4) so that all the constraint conditions stored in the constraint satisfaction condition storage means (6) are satisfied.
An arrangement method characterized in that the position determination / change processing of the rectangle is performed by. 4. A variable indicating the x-coordinate of the right side of the placement area or the y-coordinate of the top side of the placement area each time all placements of a plurality of rectangles to be placed in the placement area are determined in the placement method. Is updated to a value that reduces the area of the placement area, and the constraint satisfaction condition does not include a variable other than the variable indicating the x coordinate of the right side of the placement area or the variable indicating the y coordinate of the upper side. 4. The arrangement method according to claim 3, wherein when the is generated, the arrangement in the arrangement area is disabled and the optimum arrangement of the plurality of rectangles is obtained. 5. In an arrangement method in which a plurality of rectangular parallelepipeds each having a different shape are packed in a given arrangement area (rectangular parallelepiped) without being congested with each other, the position to be set in the arrangement area is determined for a rectangular parallelepiped. , Position determining / changing means (1) for changing the position of a rectangular parallelepiped whose position has already been determined as necessary
And the constraint condition that each rectangular parallelepiped to be placed is within the given placement area, and the constraint condition that any two rectangular parallelepipeds do not easily congest each other, the initial constraint violation that is a sufficient constraint violation condition When a condition is set and at least one constraint violation condition is satisfied no matter where the target rectangular parallelepiped is placed at the time of position determination / change processing by the position determination / change means (1), a true constraint violation condition is satisfied. A constraint violation condition setting means (2) for setting a new constraint violation condition as a logical product of the conditions obtained by substituting the coordinates of the points not to the variables corresponding to the coordinates of the lower left front vertex of the target rectangular parallelepiped in the established constraint violation condition. A constraint violation condition storage means (3) for storing the constraint violation condition set by the constraint violation condition setting means (2), and all the constraints stored in the constraint violation condition storage means (3) Placement method which is characterized in that the determination / change processing locations of the rectangular parallelepiped by the position-determining / changing means so as not to establish a counter-condition (1). 6. The arrangement method for arranging the three-dimensional rectangular parallelepiped in a three-dimensional arrangement area (rectangular parallelepiped), wherein the arrangement area and the arrangement target are expanded into an n-dimensional space in which n is 4 or more. The arrangement method described in 5. 7. In an arrangement method in which a plurality of rectangular parallelepipeds each having a different shape are packed in a given arrangement area (rectangular parallelepiped) without mutually obstructing each other, the position of the rectangular parallelepiped whose position to be set in the arrangement area is not determined Then, the position determining / changing means (4) for changing the position of the rectangular parallelepiped whose position has already been decided as necessary.
And the constraint condition that each rectangular parallelepiped to be arranged is within a given arrangement area and the constraint condition that any two rectangular parallelepipeds do not easily congest each other, the initial constraint satisfaction that is a necessary condition for constraint satisfaction is satisfied. When a condition is set and at least one constraint satisfaction condition is not satisfied no matter where the target rectangular parallelepiped is placed during the position determination / change processing by the position determination / change means (4), a constraint satisfaction condition that is false is satisfied. A constraint satisfaction condition setting means (5) for setting a new constraint satisfaction condition as a logical sum of conditions obtained by substituting the coordinates of points not to be satisfied into the variables corresponding to the coordinates of the lower left front vertex of the target rectangular parallelepiped in the constraint satisfaction condition that does not hold. , Constraint satisfaction condition storage means (6) for storing the constraint satisfaction condition set by the constraint satisfaction condition setting means (5), and all the constraint satisfaction condition storage means (6) The position-determining / changing means so as to satisfy the about satisfying condition (4)
An arrangement method characterized by performing determination / change processing of the position of a rectangular parallelepiped by. 8. A method of arranging the three-dimensional rectangular parallelepiped in a three-dimensional arrangement area (a rectangular parallelepiped), wherein the arrangement area and the arrangement target are expanded to an n-dimensional space in which n is 4 or more. 7. The arrangement method described in 7.