WO2023158047A1

WO2023158047A1 - Optimal placement design method for 3d irregular objects in containers

Info

Publication number: WO2023158047A1
Application number: PCT/KR2022/014932
Authority: WO
Inventors: 김형철; 한삼희
Original assignee: 주식회사엔에스이
Priority date: 2022-02-18
Filing date: 2022-10-05
Publication date: 2023-08-24
Also published as: KR20230124268A

Abstract

A design method for optimally placing three-dimensional objects in containers according to the present invention comprises the steps of: (s1) generating a three-dimensional object model; (s2) deriving a minimum bounding box and adjusting the posture of the three-dimensional object model; (s3) generating a population of chromosomes coded in sequence and rotation types of the object model; (s4) applying a heuristic procedure to the chromosomes to determine the number of necessary containers and the position in which the object model is to be placed in each container coordinate space; (s5) evaluating the value of a fitness function including the number of necessary containers and the volume utilization ratio of the final container with regard to each chromosome, and selecting surviving chromosomes according to the rank thereof; (s6) determining whether convergence occurs by means of the diversity index value of the population; and (s7) declaring that the number of necessary containers related to the converging chromosomes and the position in which the object model is to be placed in each container coordinate space constituting an optimal solution. The present invention is advantageous in that, in connection with design for placing objects in containers, the maximum unoccupied space volume of the final container is secured while reducing the number of necessary containers.

Description

Container Optimal Arrangement Design Method for Irregular 3D Objects

The present invention relates to a method for designing an optimal container arrangement of irregular 3D objects, and more particularly, to a design method for accommodating and arranging a plurality of 3D objects in a minimum number of containers.

For effective logistics management, the bin packing problem has been studied for a long time in the field of operations research (OR). With the recent activation of 3D printing technology, arranging the products to be manufactured to have the maximum volume utilization within the partitioned build volume is one of the important design goals in the 3D printing plan. At this time, the OR field packaging algorithm Various methods have been developed and applied using the concepts. In the traditional boxing problem, it is to efficiently place a cuboid product box into a cuboid container, and in 3D printing, an irregular object is placed in a manufacturing volume. Although there are differences in application, the core concept is the same. . The batch algorithm is, for example, a heuristic procedure proposed by Karabulut et al. and a genetic algorithm integration method (A hybrid genetic algorithm for packing in 3D with deepest bottom left with fill method, in: T. Yakhno (Eds. ), Advances in Information Systems. ADVIS 2004, Lecture Notes in Computer Science, vol 3261, Springer, Berlin, Heidelberg, 2004, pp. 441-450).

Due to the limitation of the manufacturing volume of the 3D printer, in particular, in the case of manufacturing a set of relatively large quantities of items, it cannot be completed in one-time manufacturing and must be manufactured multiple times, which is a problem of batch design for multiple containers. do. Packaging of disposal containers for permanent disposal storage of toxic solid waste or radioactive waste fragments may also be addressed as a multi-container layout design issue.

The present invention relates to an optimal container arrangement design method of irregular three-dimensional objects, and is intended to provide a design method of accommodating and disposing a plurality of three-dimensional objects in a minimum number of containers for 3D printing or disposal and storage of waste pieces.

A method for designing an optimal container arrangement of a 3D object according to the present invention includes the steps of (s1) generating and indexing a 3D object model for irregular objects; (s2) deriving a minimum constraining box while rotating the 3D object model and adjusting the posture of the 3D object model accordingly; (s3) generating a population of chromosomes encoded in the sequence and rotation type of the 3D object model; (s4) determining the required number of containers and the arrangement position of the 3D object model in each container coordinate space by applying a heuristic procedure to the minimum constraining box sequence and rotation type by chromosomes; (s5) evaluating the value of the fitness function including the number of containers required and the volume utilization rate of the final container for each chromosome in the population and selecting surviving chromosomes according to the ranking; (s6) evaluating the diversity index value of the population and determining whether to converge; (s7) declaring the number of containers required for the chromosome having the highest degree of fitness and the arrangement position of the 3D object model in each container coordinate space as an optimal solution when it is determined that convergence is reached, and terminating; and (s8) generating a population of new chromosome generations by performing cross-mutation and mutation calculations when it is not determined as convergence and entering step (s4).

In the optimal arrangement design method according to the present invention, the rotation type may be characterized in that the dimension of the applied minimum constraint box in one direction does not exceed the dimension of the container in the corresponding direction.

In the optimal arrangement design method according to the present invention, if there is no rotation type that does not allow the dimension of any one direction of the minimum constraining box to exceed the dimension of the corresponding direction of the container, it is characterized in that the arrangement is declared failure and terminated. can be done with

The present invention has an effect of deriving an optimal design solution for accommodating and arranging a plurality of 3D objects in a minimum number of containers.

The present invention has an effect of maximizing the volume of non-occupied space of a final container while reducing the number of containers required in a container arrangement design of a plurality of 3D objects. In addition, there is an effect of achieving maximum workload economic efficiency for the entire layout design project including the unit layout design.

In particular, the present invention excludes chromosomes that cannot accommodate a three-dimensional object in a container at the time of generating the initial population in the container arrangement design of large objects to enable the procedure of the present invention to be started and to secure statistically homogeneous initial conditions have an effect

The present invention has an effect of preventing unnecessary time consumption in calculation procedures.

1 is a flowchart of an optimal layout design method according to the present invention.

2 is a conceptual diagram for explaining a minimum constraining box.

3 is an exemplary view illustrating rotation types of the minimum constraining box.

Fig. 4 is an explanatory diagram of a heuristic procedure for arranging boxes in a container;

5 is an example of a matrix format of container placement solutions for chromosomes.

Fig. 6 is an example of a container arrangement solution obtained by applying the present invention.

Hereinafter, specific embodiments according to the present invention are described. However, the present invention can be implemented by modifying in various forms and is not limited to the embodiments described herein. The drawings accompanying the present invention have been simplified for convenience of explanation, and some exaggerated parts or parts irrelevant to the description have been omitted in order to clearly describe the present invention.

Hereinafter, a container optimal arrangement design method of a 3D object for arranging a plurality of atypical items in a standardized container to have a minimum consumed volume will be described. Here, the required volume means a value obtained by multiplying the build volume by the number of runs in the case of a 3D printer. Therefore, it is desirable to arrange the articles in such a way that the unoccupied volume space within the manufacturing volume is minimized, so that the article of interest is manufactured the minimum number of times. In addition, even in the case of packaging for permanent disposal of pieces of toxic solid waste or radioactive waste, since the goal is to package the pieces of target waste in the minimum number of disposal containers, the same concept of optimal container arrangement design method for 3D objects can be applied.

Referring to FIG. 1, a method for designing an optimal container arrangement of a 3D object according to the present invention includes the steps of (s1) generating and indexing a 3D object model for irregular objects; (s2) deriving a Minimum Bounding Box (MBB) while rotating the 3D object model and adjusting the posture of the 3D object model accordingly; (s3) generating a population of chromosomes encoded in the sequence and rotation type of the 3D object model; (s4) determining the required number of containers and the arrangement position of the 3D object model in each container coordinate space by applying a heuristic procedure to the MBB sequence and rotation type by chromosome; (s5) evaluating the value of the fitness function including the number of containers required and the volume utilization rate of the final container for each chromosome in the population and selecting surviving chromosomes according to the ranking; (s6) evaluating the diversity index value of the population and determining whether to converge; (s7) declaring the number of containers required for the chromosome having the highest degree of fitness and the arrangement position of the object model in each container coordinate space as an optimal solution when it is determined that convergence is reached, and terminating; and (s8) generating a new chromosome generation by performing cross-mutation and mutation calculations when it is not determined to be convergence and entering step (s4). Hereinafter, each step will be described in more detail.

In step s1, a 3D object model is created for an irregular object having an arbitrary irregular shape, and an index is given with a series of unique numbers. A three-dimensional model is usually created in the format of a stereolithography (STL) file.

Step (s2) finds the minimum constraining box (MBB) while rotating the STL model in the azimuthal angle and zenithal angle directions in virtual space, and the posture of the 3D object model with the azimuthal and zenith angles corresponding to MBB Adjust the orientation. Referring to FIG. 2 as an example, in case (a), an axis aligned bounding box for a 3D model at the beginning of creation is displayed in a square shape. As it rotates, the volume of the axis aligned bounding box increases. The rectangle of the minimized case (b) corresponds to the MBB and becomes a 3D object model whose posture is adjusted at that time. Comparing the space occupied by an object and the unoccupied space in the axis alignment constraint box of FIG. 2, it can be conceptually understood that the volume of the unoccupied space of case (b), which is MBB, is minimized. However, although FIG. 2 is illustrated in two dimensions for convenience of description, this can be easily expanded to a three-dimensional space.

The reason for obtaining the MBB and adjusting the posture of the 3D object model in this way is that the heuristic procedure, which will be described later, was developed for an orthogonal box and an orthogonal container, and also an optimal solution by a genetic algorithm. Since the search is determined in the direction in which the volume utilization of the container is maximized, the MBB is used to minimize the unoccupied volume, thereby minimizing the inherent error. The volumetric utilization rate may be defined as a value obtained by dividing the sum of the volumes of boxes accommodated in a container by the volume of the container.

In step s3, the rotation type (rotation) of the MBB corresponding to the vector generated by the sequence of the 3D object model by random permutation of the index of the 3D object model and the random number type) to generate a population of chromosomes encoded by the vector. The index of a 3D object model is usually created with a series of natural numbers, and as shown in FIG. 3, 6 rotation types (r) are available for a cuboid box, and each rotation type is an integer from 0 to 5. It can be expressed as , and the length, width, and height dimensions change according to the rotation type.

In some cases, the size of the MBB may not be sufficiently small compared to the size of the container. In this case, depending on the rotation type, the MBB may not be accommodated within the container boundary. Therefore, when the rotation type is applied to the MBB, it is desirable to limit the value of the rotation type so that the dimension of one direction of the MBB does not exceed the dimension of the corresponding direction of the container. To this end, the length, width, and height of the container are entered in advance, and when the chromosome is created, a rotation type corresponding to each MBB is created. If the dimension in one direction exceeds the dimension in the corresponding direction of the container, A method of regenerating the rotation type can be used. This method fundamentally excludes chromosomes that cannot accommodate a 3D object in a container at the time of initial population generation, enabling the procedure of the placement design method according to the present invention to be started, and a potential solution area (potential solution) domain) has the effect of securing statistically homogeneous initial conditions. This effect is particularly noticeable in the container layout design for permanent disposal storage of bulky waste.

If there is no rotation type that does not allow the dimensions of the MBB in either direction to exceed the dimensions of the container in the corresponding direction, a placement failure may be declared and the placement design procedure may be terminated. This is a case where it is impossible to accommodate a container even if all rotation type values are sequentially applied to a certain MBB, and it is a case where container arrangement is impossible in the first place. This method may have an effect of preventing unnecessary calculation procedure attempts, which is particularly effective when a target object cannot be easily and intuitively grasped in advance in an arrangement problem in which the number of target 3D objects is large.

In step s4, a heuristic procedure is applied to the MBB sequence and rotation type of each chromosome included in the population to determine the required number of containers and the location of the object model in each container coordinate space.

The heuristic procedure is an a priori arrangement methodology, and the DBLF (Deepest Bottom Left with Fill) method proposed by Karabulut et al. mentioned above or various variant methods developed thereafter can be applied. For completeness of description of the present invention, an example of a heuristic procedure that can be used in step s4 will be described below.

4 shows a container space and a series of boxes stationary at the origin of a three-dimensional Cartesian coordinate system. The boxes are given the dimensions of length, width, and height by the previously derived MBB, are ordered according to the given sequence, and have length, width, and height dimensions according to the given rotation type. can Containers are also given a length, width and height.

As shown in FIG. 4, the left-bottom-back vertex of the first MBB is placed at the origin. Then, three adjacent vertexes are generated as candidate placement points (P1, P2, P3) in the order of decreasing x-z-y coordinate values. In the future, if there is an empty space below the two vertexes on the bottom side, the point projected downward onto the surface of another MBB encountered first or the bottom surface of the container becomes a candidate placement point. The second MBB checks the possibility of placement in the order of decreasing x-z-y coordinate values among the generated candidate placement points. If the current MBB for a candidate placement point satisfies the placement condition that the current MBB overlaps with another MBB previously placed or does not go beyond the boundary of the container, the MBB is placed at the candidate placement point, and the candidate is placed in the same way as before. Add points (P4, P5, P6). This procedure continues until there are no more candidate placement points in the container that satisfy the placement conditions or until the given number of MBBs is exhausted.

The initial required number of containers starts with a natural number greater than or equal to the sum of all given MBB volumes divided by the container volume. Therefore, although only one container is shown in FIG. 4 for convenience of description, there may be one or more N containers. If there are no candidate placement points satisfying the placement condition in the existing N containers for the current MBB, a new container is added and the required number of containers (N) is increased by 1. Containers to which the current MBB is allocated may be sequentially selected in the order of containers having the largest unoccupied space volume.

The heuristic procedure described above can be implemented by a computer program, and even if it is not the same, if the procedure can determine the number of containers required for a given box sequence and rotation type and the position of the box in each container coordinate space, , which corresponds to the heuristic procedure of step s4.

The batch solution determined by the heuristic procedure for chromosomes representing n MBBs can be expressed in a 6xn matrix format as shown in FIG. 5 . Here, the elements of the third row may have values from 1 to N. As described above, the placement point of the first MBB in the sequence is indicated as being located at the origin of the first container, and other elements of the matrix may be variously changed depending on the given chromosome.

In step (s5), for each chromosome included in the population, the value of the fitness function expressed including the number of consumed containers and the volume utilization of the final container is evaluated and the rank is ranked. Survival chromosomes are selected according to (ranking).

The fitness (f) function may be given as, for example, Equation 1 below.

Here, N is the number of containers required, and e represents the volume utilization rate of the container finally added in step s4. The volume utilization factor is a value obtained by dividing the sum of the volumes of the boxes accommodated in the container by the volume of the container, and has a value of 1.0 or less.

According to Equation 1, the fit value increases as the number of required containers decreases, and even when the required number of containers decreases, the fit value increases as the volume utilization rate of the final container decreases. Therefore, by adopting the fitness function according to Equation 1, if the number of containers required in the population is small and the number of containers required is the same, the chromosome with a small volume utilization rate of the final container ranks higher, and the fewer containers required in the final arrangement year. However, it has the effect of maximizing the volume of the non-occupied space of the final container.

Even if the required number of containers is the same, if the volume of the non-occupied space of the final container is secured to the maximum extent, the maximum capacity to accommodate extra objects that are not targeted in the current arrangement design problem is secured. Therefore, the maximum workload for the overall layout design project including the unit layout design concerned is first confirmed by the layout solution for N-1 containers, and the objects allocated to the Nth container are transferred to a separate additional layout design problem. There is an effect that can promote economic efficiency.

Since the fitness function is capable of various simple transformations that can bring about the same effect as above, the fitness function of the present invention is not necessarily limited to Equation 1.

In the case of surviving chromosome selection, all chromosomes included in the population can become surviving chromosomes in the case of the first generation population, but from the second generation, both the old generation chromosomes and the new generation chromosome population generated by step (s8) As a target, surviving chromosomes are selected according to the fitness ranking to form a population.

In step s6, a diversity index value of the population is evaluated and convergence is determined. The diversity index is an index that can evaluate how close the fitness value of each chromosome in the population is to the optimal value, and can be given as, for example, Equation 2 below.

where η is the diversity indicator, and f _best and f _worst represent the highest and lowest fitness within the population, respectively. Therefore, it is determined that the batch solution is converged when the diversity index value is reduced below a preset sufficiently small reference value or when the accumulated number of generations exceeds a set sufficiently large value. In the present invention, since the diversity index can perform various simple modifications that can perform the same role, the diversity index of the present invention is not necessarily limited to Equation 2.

In step (s7), when it is determined that convergence is determined in step (s6), the number of containers required for the chromosome having the highest degree of fitness and the location of the object model in each container coordinate space are declared as the optimal solution, and the solution is terminated. The optimal solution can be expressed in the form of FIG. 5, and each column can be collected and expressed separately for each container.

In step s8, if convergence is not determined in step s6, crossover and mutation operations are performed to generate a population composed of new chromosome generations, and step s4 is entered. do.

The cross-mutation operation selects parent chromosome pairs from the current population with fitness-based probabilities, randomly selects some strings of chromosome codes, and reproduces children chromosome pairs by exchanging them with each other. Additionally, a flip mutation operation that changes the rotation type of some randomly selected child chromosomes is performed with a set probability. Through this operation, a population of a new generation is formed by generating chromosomes equal to the size of the population.

It is preferable to limit the rotation type according to the flip mutation operation so that the dimension of one direction of the applied MBB does not exceed the dimension of the corresponding direction of the container. To this end, when a mutation operation is performed on a certain MBB, if the dimension in one direction exceeds the dimension in the corresponding direction of the container, a method of regenerating the rotation type can be used. By doing this, it is possible to prevent generation of child chromosomes that cannot be accommodated in the container for mutation calculation, and to prevent unnecessary time consumption in subsequent calculation procedures.

FIG. 6 is an example of a part of a layout design obtained by using the layout design method of the present invention through 3D visualization in a problem of arranging 166 3D objects in a container of a specific size. The number of required containers was calculated to be 24, and 3D object arrangement states for the first 3 and last 3 containers among them were shown as an example. As described in detail in the description of the fitness function in step (s5), it can be visually confirmed that the least number of 3D objects are placed in the final 24th container, so that a wide non-occupied space is secured.

The present invention can be used to create a design plan that can perform the work with the minimum number of times in the 3D printing task of manufacturing a large number of atypical items, and also the number of disposal containers for permanent disposal storage of pieces of toxic solid waste or radioactive waste Since it can be applied to minimization, etc., there is a possibility of use in related industries.

Claims

(s1) generating and indexing a 3D object model for irregular objects;

(s2) deriving a minimum constraining box while rotating the 3D object model and adjusting the posture of the 3D object model accordingly;

(s3) generating a population of chromosomes encoded in the sequence and rotation type of the 3D object model;

(s4) determining the required number of containers and the arrangement position of the 3D object model in each container coordinate space by applying a heuristic procedure to the minimum constraining box sequence and rotation type by chromosomes;

(s5) evaluating the value of the fitness function including the number of containers required and the volume utilization rate of the final container for each chromosome in the population and selecting surviving chromosomes according to the ranking;

(s6) evaluating the diversity index value of the population and determining whether to converge;

(s7) declaring the number of containers required for the chromosome having the highest degree of fitness and the arrangement position of the 3D object model in each container coordinate space as an optimal solution when it is determined that convergence is reached, and terminating; and

(s8) generating a population of a new chromosome generation by performing cross-mutation and mutation operations when it is not determined to be convergence, and entering step (s4); a container optimal arrangement design method for a 3-dimensional object including.
According to claim 1,

In step (s3)

The rotation type is a container optimal arrangement design method of a three-dimensional object, characterized in that the dimension of any one direction of the applied minimum constraint box does not exceed the dimension of the corresponding direction of the container.
According to claim 2,

A container optimal arrangement design method of a 3D object, characterized in that when there is no rotation type that prevents the dimension of either direction of the minimum constraint box from exceeding the dimension of the corresponding direction of the container, an arrangement failure is declared and terminated.
According to claim 1,

The rotation type according to the mutation operation in step (s8) is limited so that the dimension of any one direction of the applied minimum constraint box does not exceed the dimension of the container in the corresponding direction.