Center cube layout method based on intelligent heuristic algorithm
By optimizing 3D layout using intelligent heuristic algorithms, combined with whale optimization algorithm and frog leap expansion strategy, the problem of insufficient multi-objective optimization in 3D layout of traditional algorithms is solved, realizing efficient and stable object layout, improving space utilization and engineering practicality.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- QINGDAO UNIV OF SCI & TECH
- Filing Date
- 2026-01-07
- Publication Date
- 2026-05-26
AI Technical Summary
Existing 3D layout methods are insufficient in balancing space utilization and engineering practicality, making it difficult to meet the needs of multi-objective optimization. Furthermore, traditional algorithms are prone to getting trapped in local optima, failing to effectively balance theory and practice, and posing risks of center of gravity shift and safety hazards.
A central cube layout method based on intelligent heuristic algorithms is adopted. By constructing a mathematical model and combining the whale optimization algorithm and the frog leap expansion strategy, a strategy for calculating, filtering and arranging objects in the sortable space is designed to optimize the expansion order of seed points and ensure that the layout conforms to physical laws and engineering requirements.
It improves the engineering feasibility and optimization accuracy of the layout scheme, reduces safety risks, and enhances the envelope box filling rate and layout stability, making it suitable for complex multi-object scenarios.
Smart Images
Figure CN121456937B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of three-dimensional layout technology, and more specifically to a center cube layout method based on intelligent heuristic algorithms. Background Technology
[0002] The three-dimensional containment box packaging problem is a core optimization problem in industrial production, logistics storage, engineering installation and other fields. Its core requirement is to rationally arrange objects in a fixed three-dimensional space to achieve a comprehensive balance between space utilization, functional efficiency and safety and stability. It is widely used in equipment layout, material storage, ship or platform module layout and other scenarios.
[0003] Existing 3D layout methods mainly include traditional heuristic algorithms (such as bottom-left algorithms, genetic algorithms, and simulated annealing algorithms) and basic intelligent optimization algorithms (such as basic ant colony optimization and particle swarm optimization). While traditional heuristic algorithms are simple to implement, they suffer from low optimization accuracy and a tendency to get trapped in local optima, making it difficult to simultaneously meet multi-objective optimization needs (such as simultaneously satisfying space utilization and centroid stability). Basic intelligent optimization algorithms, while improving optimization capabilities, do not fully consider the practical engineering characteristics of layout problems: on the one hand, they ignore physical feasibility constraints (such as no interference between objects and boundary restrictions) and functional correlation constraints (such as adjacent placement of related objects), resulting in optimization results remaining only at the theoretical level and unable to be directly implemented; on the other hand, they lack precise calculation and screening mechanisms for available space, leading to blind expansion of seed points, low utilization of available space, and a lack of specific placement strategies designed for the centroid control requirements of central cube layouts, resulting in layout schemes with excessive centroid offset and significant safety hazards.
[0004] Furthermore, existing algorithms fail to effectively balance the conflict between "space utilization" and "engineering practicality." Some algorithms, in pursuit of high fill rates, compress operation and maintenance space and ignore functional interrelationships, leading to layout schemes that are unmaintainable or functionally ineffective in the later stages. Other algorithms, while considering constraints, suffer from low constraint integration and cumbersome algorithm processes, resulting in solution efficiency that cannot meet the layout requirements of complex scenarios (multiple objects, multiple constraints). Therefore, there is an urgent need for an intelligent heuristic layout method that balances engineering constraints, optimization accuracy, and solution efficiency to address the pain points of existing technologies, namely "theory and practice disconnect, imbalance in multi-objective optimization, and insufficient solution efficiency." Summary of the Invention
[0005] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a central cube layout method based on intelligent heuristic algorithms.
[0006] This invention is achieved through the following technical solution: a center cube layout method based on an intelligent heuristic algorithm, comprising the following steps:
[0007] S1. Determine the size parameters of the space to be laid out {L, W, H}, the number of objects to be laid out N, and the box of each object to be laid out. i Dimensional parameters (l) i w i h i Set layout constraints and preset goals;
[0008] S2. Construct a mathematical model for the layout problem of the central cube, and define the layout state, envelope box, central cube, space to be arranged, and envelope box fill rate. The space to be arranged is divided into complete space, space to be expanded and dead space according to different object arrangement situations. The envelope box fill rate includes the volume fill rate and the area fill rate of the envelope box.
[0009] S3. Design an intelligent heuristic algorithm. The intelligent heuristic algorithm is designed based on the strategy of calculating the available space, the strategy of filtering the available space cubes, and the strategy of arranging the objects to be laid out.
[0010] S4, based on the intelligent heuristic algorithm designed in S3, combines the parameters of S1 and the mathematical model of S2 to solve the layout of the central cube and output a layout scheme that meets the layout constraints and preset objectives.
[0011] In S2, the object to be laid out is a box i The state at a certain moment when the items are arranged in the space as required is recorded as a layout state.
[0012] Lay, a certain intermediate layout state n The smallest cube containing all laid-out objects is called the envelope box.
[0013] The cube located in the center position is called the center cube;
[0014] In a certain intermediate layout state, the difference between the already placed objects and the 3D layout space is denoted as the space that can be arranged.
[0015] In S2, the space that can be arranged completely encompasses the object to be laid out is called the complete space;
[0016] If the size of an object to be laid out exceeds the available space, it is considered as space to be expanded.
[0017] The space where the size of the objects to be laid out all exceeds the available space is called the dead zone space.
[0018] In S2, the volume fill rate of the envelope box is the ratio of the volume of the laid-out objects to the volume of the envelope box in a certain layout state.
[0019] The area fill rate of the envelope box is the ratio of the bottom area of the laid-out objects to the bottom area of the envelope box in a certain layout state.
[0020] The specific strategy for calculating the space that can be arranged in S3 is as follows: set virtual seed points and establish a virtual space coordinate system, determine the filling step size, expand the seed points in multiple directions, and generate multiple space cubes that can be arranged.
[0021] The specific strategy for selecting sortable space cubes is as follows: the sum of the minimum Manhattan distances between the eight vertices of the sortable space cube and the corresponding vertices of the envelope box is recorded as the anchor distance, and the sortable space cube corresponding to the minimum anchor distance is selected as the priority sorting space.
[0022] The specific strategy for arranging objects to be laid out is as follows: determine the centerline matching degree, construct the spatial attitude matrix, calculate the envelope box expansion rate and the envelope box added volume filling rate, and then perform the object placement operation.
[0023] In the aforementioned space calculation strategy, the specific process of establishing a virtual space coordinate system is as follows:
[0024] Place a virtual seed point on any vertex of the already placed object. With the seed point O as the center, establish a virtual spatial coordinate system O-xyz for the seed point. The x, y, and z axes of the coordinate system are parallel to the length, width, and height directions of the space to be laid out, respectively.
[0025] When the seed point expands in multiple directions in the permissible space calculation strategy, the optimal expansion order is determined based on the whale optimization algorithm. The specific process is as follows:
[0026] Initialize the position of the whale population, which records the expansion order of all seed points, and initialize the convergence factor, coefficient vector, spiral parameter and probability;
[0027] Calculate the fitness value at different whale locations, using the envelope box filling rate as the evaluation index, and determine the current optimal location;
[0028] Iteratively update the convergence factor, coefficient vector, spiral parameters, and probability, and select the whale position update method based on the probability.
[0029] Check if the updated position exceeds the layout space. If it does, correct it, recalculate the fitness value and update the optimal position until the maximum number of iterations is reached, and output the optimal expansion order of the seed point.
[0030] The centerline matching degree in the object placement strategy is: in a certain layout state, for a selected space cube that can be placed, the geometric center distance between the object to be placed and the already placed center block in a certain placement mode.
[0031] The spatial attitude matrix uses Boolean variables. If any spatial attitude of the object to be laid out satisfies the constraint conditions, it is marked as 1, otherwise it is marked as 0.
[0032] Under unconstrained conditions, the spatial pose matrix of the object to be laid out is represented as Sposei=[1, 1, 1, 1, 1,1].
[0033] In a certain intermediate layout state, after the objects to be laid out are placed, the selected space cube that can be placed changes from a complete space to a space to be expanded. The expansion rate of the envelope box is the ratio of the volume of the envelope box before and after expansion.
[0034] When dead zones occur during the placement of objects, the envelope box needs to be expanded. The fill rate of the increased volume of the envelope box is the ratio of the volume of the objects to be placed to the increased volume of the envelope box.
[0035] When placing objects into the layout, the objects should be placed in the order of the least centerline matching degree, and then placed in the order of full space, space to be expanded, and dead zone space.
[0036] Compared with the prior art, the beneficial effects of the present invention are:
[0037] This application improves the engineering feasibility of the layout scheme by deeply binding the abstract optimization problem with the actual application scenario through layout constraints and preset goals, thus avoiding the problem that the optimization result is theoretically feasible but practically unrealizable.
[0038] This application uses a space classification system of complete space, space to be expanded, and dead zone space, along with a selection mechanism that prioritizes the minimum anchor point distance, to ensure that the object layout conforms to physical laws and engineering installation requirements, allowing it to be directly deployed without additional adjustments.
[0039] This application combines the whale optimization algorithm to optimize the seed point expansion order with a centerline matching degree-oriented emission strategy. While improving the envelope box filling rate, it effectively controls the layout center height and offset, reduces safety risks, takes into account the adjacent layout requirements of functionally related objects, and reduces energy consumption and operating costs.
[0040] The intelligent heuristic algorithm proposed in this application is designed based on a space-based calculation strategy, a space-based cube selection strategy, and an object placement strategy. This application combines a seed point leapfrog expansion strategy with a whale optimization algorithm, solving the problems of blind seed point expansion and low optimization efficiency in traditional algorithms. By accurately matching the object placement shape through a spatial pose matrix and combining quantitative constraints on the envelope box expansion rate and the incremental volume filling rate, the optimization accuracy is improved, avoiding local optima traps. Compared to traditional algorithms, the algorithm of this invention has a faster convergence speed and more stable optimization results, and can efficiently handle complex layout scenarios with multiple objects and multiple constraints. Attached Figure Description
[0041] Figure 1 This is a flowchart of the method used in this application;
[0042] Figure 2This is a schematic diagram of an envelope box cube;
[0043] Figure 3 It is the remaining space that can be arranged in a single cube;
[0044] Figure 4 This is a schematic diagram of sortable space classification;
[0045] Figure 5 This is a schematic diagram of the expansion of the seed point;
[0046] Figure 6 This is a schematic diagram of the virtual space coordinate system of the seed point;
[0047] Figure 7 This is a diagram showing the distance between anchor points. Detailed Implementation
[0048] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.
[0049] Example 1
[0050] Reference Figures 1-7 The center cube layout method based on intelligent heuristic algorithm proposed in this application includes the following steps:
[0051] S1. Determine the size parameters of the space to be laid out {L, W, H}, the number of objects to be laid out N, and the box of each object to be laid out. i Dimensional parameters (l) i w i h i Set layout constraints and preset goals.
[0052] The layout constraints and preset objectives are mainly set based on the actual application scenario and demand response of the layout. The layout constraints can be, but are not limited to, boundary constraints (in actual scenarios, objects must not exceed the boundaries of the layout space), non-interference constraints between objects (no overlap or collision between objects), functional association constraints (adjacent layout of functionally related objects), etc. The preset objectives can be, but are not limited to, maximizing space utilization (aiming to reduce space waste and lower site occupancy costs), optimizing center of gravity stability (e.g., the center of gravity shift of equipment on offshore platforms will affect the stability of the ship, and excessively high center of gravity of stacked racks can easily lead to collapse, aiming for safe operation), etc.
[0053] S2. Construct a mathematical model for the layout problem of the central cube, and define the layout state, envelope box, central cube, space to be arranged, and envelope box fill rate. The space to be arranged is divided into complete space, space to be expanded, and dead zone space.
[0054] The center cube layout problem is a special type of three-dimensional-container loading problem (3D-CLP). Specifically, it is described as follows: Assume there are N objects to be laid out in a three-dimensional space of fixed dimensions (length, width, and height denoted as {L, W, H}), denoted as {box1, box2, box3, box4, box5, box6, box7, box8, box9, box1 ...2, box3, box3, box4, box3, box4, box5, box6, box3, box4, box5, box6, box3, box4, box5, box6, box7, box8, box9, box1, box2, box3, box3, box3, box4, box3, box3, box4, box3, box3, box4, box3, box3, box4, box3, box3, box4, box3, box i , ..., box N}. Among them, box i The length, width, and height are represented as (l i w i h i If ), then its volume is l. i ×w i ×h i 3D-CLP means placing as many devices as possible in a three-dimensional space in an orthogonal manner.
[0055] Regarding the definition of layout state, the object to be laid out (box) i The state at a certain moment when the elements are arranged in the space as required is called a layout state, denoted as Lay; the initial layout state is denoted as Lay. t0 When all objects to be laid out have been placed, the layout is called terminated, denoted as Lay. Final ;Lay t0 To Lay Final Any intermediate state is called an intermediate layout, denoted as Lay. n .
[0056] The definition of an envelope box is to define a certain intermediate layout state as Lay. n The smallest cube containing all the laid-out objects is called the envelope box. Figure 2 As shown in the red border, denoted as Box n .
[0057] The volume of the envelope box is denoted as Volume. n The base area is denoted as Area. n The calculation formula is as follows:
[0058] Volume n = L n ×W n ×H n ;
[0059] Area n = L n×W n ;
[0060] Among them, L n W n H n Lay n Envelope Box in State n Length, width, and height.
[0061] The center cube is defined as the cube located at the center of a room. Figure 2 The blue portion is shown. The position of any central cube is characterized by six parameters, denoted as {l Center w Center h Center x Center y Center , z Center}, which are the length, width, height and coordinates of the central cube, respectively.
[0062] For the definition of sortable space, refer to... Figure 3 In a certain intermediate layout state, Lay n The difference between the existing objects and the 3D layout space is called the arrangeable space, denoted by π. To accurately describe the arrangeable space, the irregular arrangeable space is divided into multiple cubes, denoted as arrangeable space cubes. A vertex whose base surface contacts the middle layout (i.e.,...) Figure 3 The lower left vertex of the space can be arranged in the middle, and the opposite vertex of that vertex (i.e., Figure 3 The coordinates of the two vertices (x, y ... i1 y i1 , z i1 ), (x i2 y i2 , z i2 Then, the space that the space cube can hold is of length l. si =|x i1 - x i2 |、Width w si =|y i1 - y i2 |、High h si =|z i1 - z i2 |
[0063] Reference Figure 4 Based on the different arrangements of objects, the available space can be divided into complete space, space to be expanded, and dead zone space. Complete space refers to the available space that completely encompasses the objects to be arranged, such as... Figure 4 As shown in (a); the space to be expanded refers to the portion of the object to be laid out whose dimensions exceed the available space, such as... Figure 4As shown in (b), the dead zone space refers to the space where the size of all objects to be placed exceeds the available space, such as... Figure 4 As shown in (c).
[0064] The definition of the box fill rate is denoted as Boxfill. n This includes the volume fill rate and area fill rate of the envelope box. The volume fill rate of the envelope box is the fill rate of a given layout state. n The ratio of the volume of the laid-out object to the volume of the envelope box is denoted as Volfill. n Similarly, the ratio of the base areas is the area fill rate of the envelope box, denoted as Areafill. n The formula for calculating the envelope box fill rate is:
[0065] Boxfill n =[Volfill n Areafill n ].
[0066] Volfill n = ;
[0067] Areafill n = .
[0068] Among them, volume i area represents the volume of the i-th laid-out object. i This represents the base area of the i-th already laid-out object.
[0069] S3. Design an intelligent heuristic algorithm. The intelligent heuristic algorithm is designed based on the strategy of calculating the available space, the strategy of filtering the available space cubes, and the strategy of arranging the objects to be laid out.
[0070] The strategy for calculating the space that can be sorted is as follows:
[0071] To accurately calculate the sortable space, this application introduces the concept of a seed point, placing a virtual seed point at any vertex of the already arranged objects, specifically as follows: Figure 5 As shown. A virtual spatial coordinate system O-xyz is established with seed point O as the center, as follows: Figure 6 As shown, the x, y, and z axes of the coordinate system are parallel to the length, width, and height directions of the space to be laid out, respectively.
[0072] Starting from the seed point, expansion proceeds in different coordinate axis directions. Expansion stops when interference occurs along a coordinate axis with already placed objects or the surface of the envelope box. Once expansion in all directions is complete, a space that can be arranged is formed. If the octagonal directions (x, y) of a seed point... + y + z+ x - y - z - If none of the seed points can be expanded, then the seed point is marked as a dead point.
[0073] The seed point expands along the x, y, and z octagonal directions as one fill operation. The expansion distance is the fill step size, denoted as `fill`. The decomposition speed of the permissible space depends on the size of the fill step size. To avoid the cumbersome calculation process caused by an excessively small fill step size, this application adopts a long-distance jump strategy to expand the seed point. When the already placed object and the envelope box overlap, the expansion stops, and the fill step size is the difference between their coordinate values. That is, one fill step size is enough to achieve the overlap phenomenon.
[0074] When calculating the remaining permissible space, if a seed point can expand into multiple octants, different expansion orders will form different permissible spaces. To determine the optimal permissible space and maximize the fill rate, this application introduces a swarm intelligence optimization algorithm during the seed point expansion process. Since the Whale Optimization Algorithm (WOA) has good optimization accuracy and global optimization capabilities, it is widely used in solving problems with complex constraints. Therefore, this application chooses to use WOA for seed point expansion direction optimization. The implementation process of WOA includes a prey-hunting stage, a bubble-net capture stage, and a prey-searching stage.
[0075] The Whale Optimization Algorithm is inspired by the unique hunting methods of humpback whales. The algorithm treats each solution to the problem to be optimized as an individual whale and the entire solution space as the ocean. By simulating three behaviors of whales—encircling prey, hunting with bubble nets, and randomly searching for prey—it iteratively approaches the optimal solution.
[0076] During the prey-encirclement phase, after spotting prey, humpback whales sense its location and gradually reduce the distance between themselves and the prey, forming an encirclement. In the algorithm, this translates to each individual whale moving closer to the currently found optimal location, continuously narrowing the search area.
[0077] The bubble-net hunting phase is the humpback whale's most unique hunting method and a core highlight of the algorithm. The humpback whale swims around its prey, simultaneously expelling bubbles to form a circular or spiral bubble net, trapping the prey. The algorithm simulates this behavior using two modes: one is a shrinking encirclement, gradually reducing the bubble net's area for a focused, precise search of a local region; the other is spiral swimming, simulating the whale's spiral ascent around its prey to further approach the optimal solution. The two modes are randomly switched.
[0078] During the random prey search phase, when the whale fails to find a definite prey location or there is no better solution in the current area, it will abandon the current target and randomly choose other areas to explore. This behavior prevents the algorithm from getting stuck in local optima and enhances the flexibility of the global search.
[0079] If the seed point can be along x + y + z + x - y - z - directional expansion, x + y + z + Indicates the positive directions of the x, y, and z axes, x - y - z - Representing the negative x, y, and z axes, the specific process for determining the optimal expansion order of seed points based on the whale optimization algorithm is as follows:
[0080] Initialize the positions of the whale population (all whales), which record the expansion order of all seed points, and initialize the convergence factor a, coefficient vectors A and C, spiral parameter l, and probability p.
[0081] Calculate the fitness value at different whale locations, using the envelope box filling rate as an evaluation index, to determine the current optimal location;
[0082] Iteratively update parameters a, A, C, l, and p. Select the whale position update method based on probability p. If p < 0.5, determine whether to update to the current optimal position or a random whale position based on coefficient A. If p ≥ 0.5, update the position using the logarithmic spiral formula.
[0083] Check if the updated position is out of range. If it is, correct it, recalculate the fitness value and update the optimal position until the maximum number of iterations is reached, and output the optimal expansion order of the seed point.
[0084] The selection strategy for sortable space cubes is as follows:
[0085] A set of admissible space cubes π = {π1, π2, ..., π} is formed through an admissible space decomposition strategy. j , π n}, introduce anchor point distance positioning rules to filter out space cubes that can be sorted.
[0086] Each sortable spatial cube has eight vertices corresponding to its envelope box, called anchor points, denoted as target corners. The sum of the minimum Manhattan distances between these vertices, calculated from the distances between them, is called the anchor point distance, denoted as the target corner distance. (See reference...) Figure 7Assuming anchor point coordinates A1(x1, y1, z1) and B1(x2, y2, z2), the Manhattan distance between A1 and B1 is calculated using the following formula:
[0087] Manhattan=|x1- x2|+|y1- y2|+|z1- z2|.
[0088] Similarly, the anchor distances of A2-B2, A3-B3, A4-B4, A5-B5, A6-B6, A7-B7, and A8-B8 can be obtained.
[0089] To maintain the continuity of the available space, the selection criteria for available space cubes prioritize placing those located in the center of the envelope box. The set of available space cubes corresponds to the set of anchor points, and the available space cube with the smallest anchor point distance is selected for priority placement.
[0090] The placement strategy for the objects to be laid out is as follows:
[0091] The strategy of selecting space cubes with the smallest anchor point distance is used to prioritize the placement of space cubes, and the centerline matching degree is introduced to determine the placement shape of the objects to be laid out.
[0092] In a certain layout state, Lay n In the context of a selected space cube, the object to be laid out is box. i The geometric center distance between a given placement configuration and an already positioned center block is called the centerline matching degree, denoted as CenterMat. i .
[0093] For a certain object to be laid out (l) i w i h i Under unconstrained conditions, an object can be arbitrarily rotated along the x, y, and z axes, resulting in six possible spatial orientations: (li, wi, hi), (li, hi, wi), (hi, li, wi), (li, hi, wi), (wi, hi, li), and (wi, li, hi). A Boolean variable is used to construct the spatial orientation matrix, denoted as Sposei. If any spatial orientation of the object satisfies the constraints, it is marked as "1"; otherwise, it is marked as "0". Under unconstrained conditions, the spatial orientation matrix of the object is Sposei = [1, 1, 1, 1, 1, 1].
[0094] When objects to be laid out are placed into the space that can be laid out, three scenarios occur: complete space, space to be expanded, and dead zone space. Based on the envelope box fill rate, the envelope box expansion rate and the envelope box added volume fill rate are introduced.
[0095] A certain intermediate layout state Layn In this context, after the objects to be arranged are placed, the selected cube of space changes from a complete space to a space to be expanded. The ratio of the volume of the envelope box before and after expansion is called the envelope box expansion rate, denoted as Volexp. n The calculation formula is as follows:
[0096] Volexp n = .
[0097] Among them, L n+1 W n+1 H n+1 Lay n+1 Envelope box in its expanded state n+1 Length, width, and height.
[0098] When dead zones occur during the placement of objects, the envelope box needs to be expanded. The ratio of the increased volume of the objects to the increased volume of the envelope box is called the envelope box volume fill rate, denoted as Voladdfill. n The calculation formula is as follows:
[0099] Voladdfill n = .
[0100] The rules for arranging objects to be laid out are as follows:
[0101] Rule 1, a certain intermediate layout state Lay n In the middle, the box of the object to be laid out i Prioritize the placement pattern with the lowest centerline matching degree.
[0102] Rule 2: The objects to be laid out should first be arranged in the envelope box configuration corresponding to the complete space; secondly, the arrangement configuration of the space to be expanded should be selected, satisfying Volexp. n ∈[Volexp n (min), Volexp n [(max)]; Finally, select the dead space arrangement to satisfy Voladdfill. n ∈[Voladdfill n (min), Voladdfill n (max)]. min and max correspond to the minimum and maximum values, respectively.
[0103] S4, based on the intelligent heuristic algorithm designed in S3, combines the parameters of S1 and the mathematical model of S2 to solve the layout of the central cube and output a layout scheme that meets the layout constraints and preset objectives.
[0104] Specifically, combining Figures 1-7The dimensions of the space to be laid out are {L, W, H}, the number of objects to be laid out is N, and the box of each object to be laid out is... i Dimensional parameters (l) i w i h i As the key input, initialize Sposei = [1, 1, 1, 1, 1, 1], and the range of the envelope expansion rate is [Volexp]. n (min), Volexp n (max)], the range of the envelope box volume fill rate is [Voladdfill] n (min), Voladdfill n (max)]. In addition, layout constraints and preset targets need to be determined.
[0105] Establish a three-dimensional spatial coordinate system and begin arranging the central cube. Further, you can first filter out the core objects (mainly those that play a crucial role and have a large volume and weight) and prioritize them. The remaining objects are then prioritized according to their functional association (the closer the functional association with the core object, the higher the priority). If priorities are the same, they are sorted in descending order of volume.
[0106] Based on the sortable space calculation strategy, seed points are set for the bottom vertices of the already laid-out objects. The filling step size is determined by the frog-jump strategy. The whale optimization algorithm is used to complete the multi-directional expansion of the seed points, generate multiple sortable space cubes, and divide the space into complete space, space to be expanded, and dead zone space.
[0107] Based on the sortable space cube screening strategy, the anchor point distance of each sortable space cube is calculated, and the sortable space cube with the smallest anchor point distance is selected as the current priority sorting space.
[0108] Based on the object placement strategy, the placement patterns of the objects that meet the constraints are selected, the centerline matching degree of each pattern is calculated, and the pattern with the smallest centerline matching degree is selected. According to the type of priority placement space, objects are placed in the order of complete space, space to be expanded, and dead zone space, ensuring that the envelope expansion rate ∈ [Volexp] during placement. n (min), Volexp n [(max)] (space to be expanded) or envelope box added volume fill rate ∈ [Voladdfill] n (min), Voladdfill n [(max)] (dead zone space).
[0109] Check whether the layout result after the current objects are placed meets the set layout constraints. If it does, update the layout status; otherwise, re-filter the available spaces or re-select the object placement shape until the constraints are met.
[0110] For layout state updates, the currently placed object is added to the set of already laid-out objects, and the envelope box model is updated (the length L of the envelope box is recalculated). n Width W n Height H n Update the set of available space cubes (remove occupied available space and fill in newly generated available space), and recalculate the envelope box fill rate of the current layout state;
[0111] If the set of laid-out objects contains all N objects to be laid out, or the number of iterations reaches the preset maximum number of iterations, then the current layout scheme is output as the final result; otherwise, the process of calculating the available space until the layout state is updated is repeated for the next object to be laid out.
[0112] Example 2
[0113] Based on Example 1, this application was coded in Matlab 2020a and simulation experiments were conducted on a computer configured with Intel® Core™ i5-2400, CPU@3.0GHz, 2GB RAM, and Windows 10.
[0114] Fifteen classic SCLP test cases were selected to verify the effectiveness and practicality of this application. Different types of objects were placed in a 20ft standard container (L=587cm, W=233cm, H=220cm). The length of the objects to be laid out was limited to [30, 120], the width to [25, 100], and the height to [20, 80]. Based on the differences in the types of objects to be laid out, the 15 test cases were divided into weak heterogeneity (BR1-BR7) and strong heterogeneity (BR8-BR15), as shown in Table 1.
[0115] Table 1 Classic SCLP Test Examples
[0116]
[0117] Each set of examples underwent 100 tests. The simulation results of the IHACCLP algorithm in this application were compared with those of existing algorithms such as H_BR, H_B_al, ABC, MIABC, MDCLP-H, MDCLP-S, and Hybrid-BA, as shown in Table 2.
[0118] Table 2 Comparison of Simulation Results for Test Examples
[0119]
[0120] As shown in Table 2, the algorithm of this application achieves satisfactory results. Example BR1 achieves the highest fill rate of 90.98%, while example BR13 achieves the lowest fill rate of 82.63%. Overall, the weakly heterogeneous cube layouts of BR1-BR7 perform well, with an average fill rate of 86.96%. For the strongly heterogeneous cubes of BR8-BR15, the average fill rate decreases slightly with the increase in layout types, reaching 83.99%. The average fill rate of the 15 sets of examples is 85.38%, which is within an acceptable range. Compared with H_BR, H_B_al, ABC, MIABC, MDCLP-B, MDCLP-S, and HybridBA, the algorithm of this application achieves better results in solving the 3D container problem, further validating the effectiveness and superiority of the proposed algorithm.
[0121] The above description is merely an optional embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformations made using the content of the present invention under the concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.
Claims
1. A center cube layout method based on intelligent heuristic algorithms, characterized in that, Includes the following steps: S1. Determine the size parameters of the space to be laid out, the number of objects to be laid out, the size parameters of each object to be laid out, and set the layout constraints and preset targets. The space to be laid out includes shipping containers. The layout constraints and preset targets are set according to the actual application scenario and demand response of the layout. The layout constraints include: Boundary constraints mean that in a real-world scenario, objects must not exceed the boundaries of the layable space. There are no interference constraints between objects, meaning there is no overlap or collision between them; Functional association constraints refer to the proximity layout of objects that are functionally related. The preset objectives include: The goal is to maximize space utilization, reduce space waste, and lower site occupancy costs. The center of gravity stability is optimal. Off-center gravity deviation of offshore platform equipment will affect the stability of the ship. If the center of gravity of the rack is too high, it will easily lead to collapse. The goal is safe operation. S2. Construct a mathematical model for the central cube layout problem, defining layout state, envelope box, central cube, arrangeable space, and envelope box fill rate. The arrangeable space is divided into complete space, space to be expanded, and dead zone space according to different object placement situations. The envelope box fill rate includes the volume fill rate and the area fill rate of the envelope box. In S2, the state of the object to be placed in the space at a certain moment is recorded as a layout state. The smallest cube that contains all the laid-out objects in a certain intermediate layout state is called the envelope box. The cube located in the center position is called the center cube; In a certain intermediate layout state, the difference between the already placed objects and the 3D layout space is denoted as the space that can be arranged. In S2, the space that can be arranged completely encompasses the object to be laid out is called the complete space; If the size of an object to be laid out exceeds the available space, it is considered as space to be expanded. The space where the size of all objects to be laid out exceeds the available space is called a dead zone. S3. Design an intelligent heuristic algorithm. The intelligent heuristic algorithm is designed according to the space calculation strategy, the space cube selection strategy, and the object placement strategy. The space calculation strategy in S3 is specifically as follows: set virtual seed points and establish a virtual space coordinate system, determine the filling step size, expand the seed points in multiple directions, and generate multiple space cubes. The specific strategy for selecting sortable space cubes is as follows: the sum of the minimum Manhattan distances between the eight vertices of the sortable space cube and the corresponding vertices of the envelope box is recorded as the anchor distance, and the sortable space cube corresponding to the minimum anchor distance is selected as the priority sorting space. The specific strategy for arranging objects to be laid out is as follows: determine the centerline matching degree, construct the spatial attitude matrix, calculate the envelope box expansion rate and the envelope box incremental volume filling rate, and perform the object placement operation. The centerline matching degree in the object placement strategy is: in a certain layout state, for a selected space cube that can be placed, the geometric center distance between the object to be placed and the already placed center block in a certain placement mode. The spatial attitude matrix uses Boolean variables. If any spatial attitude of the object to be laid out satisfies the constraint conditions, it is marked as 1, otherwise it is marked as 0. Under unconstrained conditions, the spatial pose matrix of the object to be laid out is represented as Sposei=[1, 1, 1, 1, 1, 1]; S4, based on the intelligent heuristic algorithm designed in S3, combines the parameters of S1 and the mathematical model of S2 to solve the layout of the central cube and output a layout scheme that meets the layout constraints and preset objectives.
2. The center cube layout method based on intelligent heuristic algorithm according to claim 1, characterized in that, In S2, the volume fill rate of the envelope box is the ratio of the volume of the laid-out objects to the volume of the envelope box in a certain layout state. The area fill rate of the envelope box is the ratio of the bottom area of the laid-out objects to the bottom area of the envelope box in a certain layout state.
3. The center cube layout method based on intelligent heuristic algorithm according to claim 1, characterized in that, In the aforementioned space calculation strategy, the specific process of establishing a virtual space coordinate system is as follows: Place a virtual seed point on any vertex of the already placed object. With the seed point O as the center, establish a virtual spatial coordinate system O-xyz for the seed point. The x, y, and z axes of the coordinate system are parallel to the length, width, and height directions of the space to be laid out, respectively.
4. The center cube layout method based on intelligent heuristic algorithm according to claim 1, characterized in that, When the seed point expands in multiple directions in the permissible space calculation strategy, the optimal expansion order is determined based on the whale optimization algorithm. The specific process is as follows: Initialize the position of the whale population, which records the expansion order of all seed points, and initialize the convergence factor, coefficient vector, spiral parameter and probability; Calculate the fitness value at different whale locations, using the envelope box filling rate as the evaluation index, and determine the current optimal location; Iteratively update the convergence factor, coefficient vector, spiral parameters, and probability, and select the whale position update method based on the probability. Check if the updated position exceeds the layout space. If it does, correct it, recalculate the fitness value and update the optimal position until the maximum number of iterations is reached, and output the optimal expansion order of the seed point.
5. The center cube layout method based on intelligent heuristic algorithm according to claim 1, characterized in that, In a certain intermediate layout state, after the objects to be laid out are placed, the selected space cube that can be placed changes from a complete space to a space to be expanded. The expansion rate of the envelope box is the ratio of the volume of the envelope box before and after expansion. When dead zones occur during the placement of objects, the envelope box needs to be expanded. The fill rate of the increased volume of the envelope box is the ratio of the volume of the objects to be placed to the increased volume of the envelope box.
6. The center cube layout method based on intelligent heuristic algorithm according to claim 1, characterized in that, When placing objects into the layout, the objects should be placed in the order of the least centerline matching degree, and then placed in the order of full space, space to be expanded, and dead zone space.