Nonlinear programming-based method and system for optimizing packing box groupings

Abstract

The application discloses a packaging box group optimization method and system based on nonlinear programming, relates to the technical field of optimization, and comprises the following steps: acquiring real-time environmental humidity data of a box and real-time weight data of the box; calculating and obtaining real-time moisture content data corresponding to the box according to the real-time environmental humidity data and the real-time weight data; calling a preset material mechanics performance database, performing mapping matching according to the real-time moisture content data, and extracting corresponding dynamic pressure threshold data and dynamic friction coefficient data; constructing a nonlinear programming group model, setting the dynamic pressure threshold data as a stress constraint boundary of vertical stacking, and setting the dynamic friction coefficient data as an anti-sliding constraint boundary of horizontal arrangement; using the nonlinear programming group model, solving and generating group scheme data under the premise of meeting the stress constraint boundary and the anti-sliding constraint boundary; and outputting the group scheme data to an execution terminal.

Description

Technical Field

[0001] This application relates to the field of optimization technology, and in particular to a method and system for optimizing the palletizing of packaging boxes based on nonlinear programming. Background Technology

[0002] Modern logistics and transportation widely employs automated palletizing technology to improve cargo loading efficiency and warehouse space utilization. Traditional palletizing optimization methods primarily rely on geometric constraints and combinatorial optimization algorithms, aiming to find the arrangement pattern with the highest volume utilization within a limited three-dimensional space. However, existing palletizing planning systems generally rely on idealized static assumptions, assuming that packaging boxes are primarily rigid objects throughout the logistics cycle, and that their physical parameters, such as compressive strength and surface friction characteristics, remain constant. This planning logic based on static parameters ignores the dynamic coupling relationship between packaging materials, especially hygroscopic materials, and the complex logistics environment, leading to theoretically optimal stacking schemes often facing serious safety hazards under harsh real-world conditions.

[0003] In actual supply chain operations, bamboo packaging materials exhibit significant hygroscopic properties, and their mechanical properties degrade non-linearly with increasing ambient humidity. Existing optimization models typically only input a fixed safety factor or maximum load-bearing value in the initial stage, failing to detect material softening caused by fluctuations in ambient humidity during transportation, nor monitor the increase in box weight due to moisture absorption. This means that a stacking scheme calculated correctly in a dry environment may find that the actual load-bearing capacity of the bottom boxes is far lower than its cumulative load capacity when transported in a high-humidity environment, leading to bottom box crushing deformation or even the collapse of the entire stack, causing irreversible cargo damage.

[0004] Furthermore, the frictional characteristics of the contact surfaces between bamboo packaging boxes are also dynamically affected by environmental factors, directly impacting the lateral stability of the stack during transportation. Existing technologies lack a dynamic correction mechanism for the surface friction coefficient, relying solely on fixed geometric interlocking logic for stacking. This makes it difficult to automatically adjust the stacking strategy when environmental changes cause a decrease in friction. For example, when humidity reduces the surface friction of the bamboo boxes, cantilever stacking or high-level stacking schemes calculated based on fixed parameters will not provide sufficient anti-slip resistance, making them highly susceptible to interlayer slippage or tipping under the inertial forces generated by the vehicle's starting, braking, or turning. Existing technologies cannot dynamically reduce stacking height or forcibly increase interlocking structures based on real-time environmental feedback at the planning level, resulting in an irreconcilable conflict between space utilization and cargo safety.

[0005] To address the aforementioned issues, there is an urgent need in this field to develop an optimization method for bamboo packaging box stacking that integrates environmental perception and dynamic mechanical constraints. This method should be able to invert the current physical state of the material based on real-time environmental data and adaptively adjust the stacking structure and constraints accordingly to achieve proactive protection of cargo safety in complex and ever-changing environments. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this application provides a method and system for optimizing the pallet assembly of packaging boxes based on nonlinear programming.

[0007] In a first aspect, this application provides a packaging box palletizing optimization method based on nonlinear programming, comprising the following steps:

[0008] Acquire real-time ambient humidity data of the environment in which the enclosure is located, as well as real-time weight data of the enclosure;

[0009] Based on the real-time ambient humidity data and the real-time weight data, the real-time moisture content data corresponding to the box is calculated.

[0010] The system calls a preset material mechanical properties database, performs mapping and matching based on the real-time moisture content data, and extracts the corresponding dynamic pressure threshold data and dynamic friction coefficient data.

[0011] A nonlinear programming model is constructed, in which the dynamic pressure threshold data is set as a vertically stacked force constraint boundary, and the dynamic friction coefficient data is set as a horizontally arranged anti-slip constraint boundary.

[0012] Using the nonlinear programming assembly model, under the premise of satisfying the force constraint boundary and the anti-slip constraint boundary, the assembly scheme data containing the three-dimensional coordinate information of all boxes is generated;

[0013] Output the group hosting scheme data to the execution terminal.

[0014] Preferably, the real-time moisture content data corresponding to the box is calculated based on the real-time ambient humidity data and the real-time weight data, specifically including:

[0015] Obtain the initial dry weight data corresponding to the chamber;

[0016] The difference between the real-time weight data and the initial dry weight data is calculated to obtain the moisture absorption weight gain data;

[0017] Substituting the moisture absorption weight gain data and the real-time ambient humidity data into the preset moisture absorption balance equation, the real-time moisture content data corresponding to the box is calculated.

[0018] Preferably, a preset material mechanical property database is invoked, and mapping and matching are performed based on the real-time moisture content data, specifically including:

[0019] Read the preset material mechanical properties database, which stores the corresponding relationship curves between different moisture content nodes and compressive strength values ​​and surface friction coefficient values;

[0020] An interpolation algorithm is used to find the value corresponding to the real-time moisture content data in the corresponding relationship curve, and generate the corresponding dynamic pressure threshold data and dynamic friction coefficient data.

[0021] Preferably, the nonlinear programming model includes an objective function, which is constructed as follows:

[0022] Establish a weighted function with maximizing space utilization as a positive indicator and the bottom-level crush risk index and the overall collapse risk index as negative penalty terms;

[0023] The underlying crush risk index is determined based on the ratio of the estimated load data of the underlying tank to the dynamic pressure threshold data.

[0024] The overall tipping risk index is determined based on the correlation between the overall center of gravity position data of the stack and the dynamic friction coefficient data.

[0025] Preferably, setting the dynamic bearing capacity threshold data as a vertically stacked force constraint boundary specifically includes:

[0026] In the nonlinear programming group model, a vertical constraint condition is set, which requires that the cumulative weight data of all boxes above any Nth layer box must be less than the dynamic pressure bearing threshold data corresponding to the Nth layer box.

[0027] When the real-time moisture content data increases, causing the dynamic pressure threshold data to decrease, the vertical constraint condition automatically limits the maximum number of stacking layers in the group support scheme data.

[0028] Preferably, the dynamic friction coefficient data is set as horizontally arranged anti-slip constraint boundaries, specifically including:

[0029] In the nonlinear programming group model, horizontal constraints are set, and the horizontal constraints define the minimum contact area threshold between the boxes.

[0030] The minimum contact area threshold is negatively correlated with the dynamic friction coefficient data. When the dynamic friction coefficient data is lower than the preset safe friction threshold, the horizontal constraint condition forcibly increases the minimum contact area threshold to limit the cantilever stacking ratio of the box.

[0031] Preferably, the assembly scheme data containing the three-dimensional coordinate information of all the boxes is generated by solving the solution, specifically including:

[0032] A heuristic search algorithm is used to iteratively solve the nonlinear programming group model;

[0033] During the iteration process, if the optimal solution under the current stacking layer number cannot satisfy the force constraint boundary, the stacking layer number variable is automatically reduced, and the search is repeated in the reduced layer space until a group support scheme data that satisfies all constraints is generated.

[0034] Preferably, after outputting the group hosting scheme data to the execution terminal, the method further includes:

[0035] Determine whether the dynamic friction coefficient data is less than a preset reinforcement warning threshold;

[0036] If it is less than, additional stability reinforcement instruction data is generated, which includes operational suggestions for increasing interlayer anti-slip medium or increasing the tension of the external winding film;

[0037] The stability reinforcement instruction data is associated with the group support scheme data and output synchronously.

[0038] Secondly, this application provides a packaging box palletizing optimization system based on nonlinear programming, including:

[0039] The data acquisition module is used to acquire real-time ambient humidity data of the environment in which the enclosure is located and real-time weight data of the enclosure.

[0040] The calculation module is used to calculate the real-time moisture content data corresponding to the box based on the real-time ambient humidity data and the real-time weight data.

[0041] The matching module is used to call a preset material mechanical property database, perform mapping matching based on the real-time moisture content data, and extract the corresponding dynamic pressure threshold data and dynamic friction coefficient data.

[0042] The construction module is used to construct a nonlinear programming group model, setting the dynamic pressure threshold data as vertically stacked force constraint boundaries and the dynamic friction coefficient data as horizontally arranged anti-slip constraint boundaries.

[0043] The solution module is used to generate assembly scheme data containing the three-dimensional coordinate information of all boxes by using the nonlinear programming assembly model, under the premise of satisfying the force constraint boundary and the anti-slip constraint boundary.

[0044] The output module is used to output the group support scheme data to the execution terminal.

[0045] Thirdly, this application provides a computer-readable storage medium storing instructions that, when executed on a computer, cause the computer to perform the packaging box palletizing optimization method based on nonlinear programming described above.

[0046] In summary, this application includes at least one of the following beneficial technical effects:

[0047] 1. This application provides a nonlinear programming-based optimization method for packaging box palletizing. By collecting real-time environmental humidity and box weight data, the moisture content of the boxes is calculated inversely. Furthermore, by linking with a material mechanical property database, the pressure threshold and friction coefficient under the current environment are dynamically obtained. This allows the palletizing scheme to respond in real-time to changes in material properties, overcoming the environmental limitations of traditional static parameter optimization models. This fundamentally improves the reliability and safety of the scheme under complex actual working conditions. The dynamic pressure threshold is used as a constraint boundary for vertical stacking, automatically limiting the bearing pressure of the bottom box in high humidity environments and preventing crushing failure due to material softening. Simultaneously, horizontal anti-slip constraints are set based on the dynamic friction coefficient, automatically adjusting the box arrangement and contact requirements when friction performance decreases. This effectively prevents interlayer slippage or overall tipping caused by inertial forces during transportation, achieving proactive defense against cargo damage risks.

[0048] 2. By establishing a nonlinear programming model with the goal of maximizing space utilization and the penalty of crushing and tipping risks, intelligent search is performed under the premise of satisfying dynamic mechanical constraints. This achieves the optimal balance between safety and space utilization efficiency. Furthermore, it can adaptively adjust the number of stacking layers and arrangement according to environmental changes, avoiding space waste caused by conservative fixed stacking height and preventing safety from being ignored due to excessive pursuit of utilization, thereby improving the overall economy of logistics loading.

[0049] 3. While outputting palletizing solutions, it can automatically generate stability reinforcement instructions based on whether the dynamic friction coefficient is below the safety threshold, providing clear auxiliary decision support for on-site operations, and further improving the stability of stacking under extreme working conditions and the control level of the entire logistics process. Attached Figure Description

[0050] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0051] Figure 1 This is a flowchart of a method for optimizing packaging box pallet assembly based on nonlinear programming, as described in this application.

[0052] Figure 2 This is a schematic diagram of a system for optimizing packaging box pallet assembly based on nonlinear programming, according to an embodiment of this application. Detailed Implementation

[0053] The following description, in conjunction with the implementation of this invention, is merely an example and illustration of the concept of this invention. Those skilled in the art can make various modifications or additions to the specific embodiments described, or use similar methods to replace them, as long as they do not deviate from the inventive concept or exceed the scope defined in these claims, all of which should fall within the protection scope of this invention.

[0054] Application Overview:

[0055] In existing technologies, packaging box stacking optimization largely relies on static geometric combination algorithms, focusing on maximizing volume utilization within limited space, making it difficult to consider physical safety in complex transportation environments. Traditional methods are usually based on rigid assumptions, assuming that the compressive strength and surface friction coefficient of the packaging materials remain constant throughout the transportation process, leading to a serious disconnect between the solution design and actual working conditions. Existing equipment cannot dynamically sense the nonlinear impact of changes in environmental humidity on the mechanical properties of hygroscopic materials. Especially in humid environments, when bamboo boxes soften due to moisture absorption or become slippery, stacking solutions calculated based on fixed parameters may face the risk of bottom layer crushing or lateral tipping, making it difficult to meet the stringent requirements of the supply chain for cargo integrity.

[0056] To address the aforementioned issues, the inventors discovered a significant dynamic coupling between environmental humidity and the real-time load-bearing capacity and contact surface friction characteristics of packaging materials. By establishing a closed-loop feedback mechanism of "environment-property-constraint," dynamic defense for stacking safety can be achieved. During the research, it was found that a slight increase in material moisture content leads to an exponential decrease in compressive strength, while the surface friction coefficient also undergoes abrupt changes. Therefore, the researchers proposed transforming the invisible "environmental humidity" into a dynamically changing "mechanical constraint boundary" in a mathematical model. Further experimental verification involved introducing the mechanical parameters derived from real-time moisture content into a nonlinear programming model to replace traditional fixed height and fixed stability constraints, forming an environmentally adaptive optimization system.

[0057] Specifically, the detection system first simultaneously collects temperature and humidity data of the environment surrounding the bamboo box, as well as real-time total weight data of the bottom of the tray. By calculating the coupling relationship between the box's moisture absorption and weight gain and the ambient humidity, it obtains the real-time moisture content that accurately reflects the material's internal moisture saturation state. Then, it calls upon a pre-set material mechanical property database to map the real-time moisture content to the current dynamic pressure threshold and dynamic friction coefficient. When constructing the nonlinear programming tray assembly model, it no longer uses simple layer height limitations as boundaries, but rather uses the core constraint that the pressure on the bottom box does not exceed the dynamic pressure threshold. Simultaneously, it adjusts the minimum contact area and interlocking pattern between boxes in real-time based on the dynamic friction coefficient. When the ambient humidity causes the material performance to deteriorate to the warning line, the algorithm automatically converges the solution space and outputs an optimized solution to reduce the number of stacking layers or increase the amount of anti-slip material between layers. For dry environments, it restores the number of stacking layers to improve the loading rate.

[0058] Compared to existing technologies, traditional methods only focus on the filling efficiency of geometric space and lack compensation mechanisms for changes in environmental physical quantities, making them highly susceptible to irreversible cargo damage in high-humidity transportation environments. This solution innovatively integrates multi-source environmental perception and nonlinear programming theory, achieving proactive risk avoidance by establishing a dynamic mapping model between environmental humidity and pallet constraints. Unlike existing static planning models that remain unchanged, this solution can intelligently adjust the stacking structure based on the real-time physical state of the materials, and significantly improves the transportation stability of hygroscopic packaging materials under complex weather conditions through dual dynamic constraints on pressure and friction.

[0059] Through the above technical solution, this application effectively overcomes the problems of bottom-layer crushing and side slippage caused by the degradation of mechanical properties of packaging materials due to fluctuations in environmental humidity. It dynamically seeks the optimal solution for space utilization while ensuring transportation safety. The dynamic mechanical constraint mechanism balances high loading rates in dry environments with high stability in humid environments, and the adaptive adjustment function based on real-time material property inversion ensures cargo safety throughout the entire supply chain.

[0060] Example 1

[0061] This application discloses an optimization method for packaging box palletizing based on nonlinear programming.

[0062] Reference Figure 1 The packaging box pallet grouping optimization method based on nonlinear programming includes the following steps:

[0063] Acquire real-time ambient humidity data of the environment in which the enclosure is located, as well as real-time weight data of the enclosure;

[0064] Based on the real-time ambient humidity data and the real-time weight data, the real-time moisture content data corresponding to the box is calculated.

[0065] The system calls a preset material mechanical properties database, performs mapping and matching based on the real-time moisture content data, and extracts the corresponding dynamic pressure threshold data and dynamic friction coefficient data.

[0066] A nonlinear programming model is constructed, in which the dynamic pressure threshold data is set as a vertically stacked force constraint boundary, and the dynamic friction coefficient data is set as a horizontally arranged anti-slip constraint boundary.

[0067] Using the nonlinear programming assembly model, under the premise of satisfying the force constraint boundary and the anti-slip constraint boundary, the assembly scheme data containing the three-dimensional coordinate information of all boxes is generated;

[0068] Output the group hosting scheme data to the execution terminal.

[0069] In a specific embodiment, real-time ambient humidity data and real-time weight data refer to physical quantities collected by micro-environment sensing devices and load-bearing devices deployed in storage or transportation units. Specifically, an integrated temperature and humidity sensor can be used to obtain the relative humidity of the environment, and an industrial-grade weighing sensor installed at the bottom of the pallet can be used to obtain the total load change, so as to perceive the potential impact of the external environment on the packaging material and the actual quality status of the box after absorbing moisture in real time.

[0070] Among them, real-time moisture content data refers to a quantitative indicator that reflects the degree of moisture saturation inside the packaging material. Specifically, it can be achieved by substituting the increase in real-time weight relative to the initial dry weight into the preset material moisture absorption balance equation for inversion calculation. This is used to accurately quantify the degree of physical performance degradation of the packaging material due to moisture absorption under the current environment.

[0071] The pre-set material mechanical properties database refers to a collection of mechanical test data for specific packaging materials (such as bamboo) under different moisture content gradients. Specifically, it can be constructed by fitting compression test and friction test data conducted in a laboratory environment using a universal testing machine, serving as a mapping benchmark for transforming abstract moisture content indicators into specific engineering mechanical parameters.

[0072] Among them, the dynamic pressure bearing threshold data refers to the maximum vertical load limit that a single box can withstand under the current moisture content. Specifically, it can be obtained by interpolation in the "moisture content-compressive strength" curve in the database. It is used to dynamically define the safe upper limit of the number of stacked layers in the vertical direction in the nonlinear programming model to prevent the bottom box from being crushed.

[0073] Among them, the dynamic friction coefficient data refers to the sliding friction resistance coefficient between the surfaces of the box at the current moisture content. Specifically, it can be obtained by matching and extracting from the "moisture content-friction coefficient" curve in the database. It is used to dynamically define the minimum contact area or interlocking tightness when arranged horizontally in the nonlinear programming model to prevent lateral slippage during transportation.

[0074] Among them, the nonlinear programming grouping model refers to a mathematical optimization model with space utilization and overall stability as objective functions and dynamically changing mechanical parameters as constraints. Specifically, it can be solved using genetic algorithms, simulated annealing algorithms, or particle swarm optimization algorithms to find the optimal arrangement of box spaces under the premise of satisfying physical safety boundaries.

[0075] Among them, the palletization scheme data refers to the set of instructions containing the three-dimensional position coordinates and rotation angles of all boxes to be stacked in the pallet coordinate system. Specifically, it can be encapsulated in JSON or XML format data packets, which are used to directly drive the palletizing robot or guide manual visual safe stacking operations.

[0076] The core innovation of this application lies in constructing a dynamic constraint assembly optimization system based on environmental perception and material property inversion. By transforming the mechanical performance degradation caused by real-time moisture content into dynamic boundary conditions in a nonlinear programming model, it solves the problem that traditional static assembly algorithms cannot adapt to the safety hazards caused by the performance degradation of hygroscopic materials in humid environments.

[0077] The working process and principle of this application are as follows: First, real-time environmental humidity data and real-time weight data of the container are acquired. Then, based on the real-time environmental humidity data and the real-time weight data, the real-time moisture content data corresponding to the container is calculated through the moisture absorption balance equation. Next, a preset material mechanical property database is called, and mapping and matching are performed based on the real-time moisture content data to extract the corresponding dynamic pressure threshold data and dynamic friction coefficient data. Subsequently, a nonlinear programming stacking model is constructed, setting the dynamic pressure threshold data as the force constraint boundary for vertical stacking and the dynamic friction coefficient data as the anti-slip constraint boundary for horizontal arrangement. Using the nonlinear programming stacking model, under the premise of satisfying the force constraint boundary and the anti-slip constraint boundary, a heuristic algorithm is used to solve and generate stacking scheme data containing the three-dimensional coordinate information of all containers. Finally, the stacking scheme data is output to the execution terminal. Through the above method, the transformation from "geometric stacking" to "physical safety stacking" is realized, ensuring that when changes in environmental humidity cause materials to soften or become slippery, the system can automatically adjust the stacking structure to ensure the safety of cargo transportation.

[0078] For example, based on the real-time ambient humidity data and the real-time weight data, the real-time moisture content data corresponding to the box is calculated, specifically including:

[0079] Obtain the initial dry weight data corresponding to the chamber;

[0080] The difference between the real-time weight data and the initial dry weight data is calculated to obtain the moisture absorption weight gain data;

[0081] Substituting the moisture absorption weight gain data and the real-time ambient humidity data into the preset moisture absorption balance equation, the real-time moisture content data corresponding to the box is calculated.

[0082] In a specific embodiment, during the calculation of the real-time moisture content data of the box, the total moisture gain is first calculated based on the real-time weight data and initial dry weight data of the box. This calculation aims to eliminate the self-weight of the pallet and the basic mass of the bamboo packaging box, and simply extract the moisture mass generated by environmental heat and humidity exchange. The core calculation formula is ΔWabs = Wrt - (Wdry + Wpal), where ΔWabs is the moisture gain data, Wrt is the real-time weight data (from the real-time sampling value of the weighing sensor at the bottom of the pallet), Wdry is the initial dry weight of the box, and Wpal is the tare weight of the pallet, all obtained by reading the pre-stored factory parameters in the RFID electronic tag attached to the pallet. This step generates pure moisture increment data through differential operation. Next, based on the moisture gain data and the real-time environmental humidity data, a real-time moisture content inversion under non-uniform moisture distribution correction is performed. The moisture balance correction equation of the surface-core layer humidity gradient is adopted, and the inversion formula is as follows: Among them, MCreal is real-time moisture content data. Real-time moisture content data not only reflects the average moisture content, but also reflects the actual wetting state of the material's stressed surface through environmental humidity correction. The reference mass moisture content is λmat, the material's moisture absorption sensitivity coefficient, which is preset to a constant between 0.12 and 0.18 based on the porosity characteristics of bamboo. RHenv is the real-time ambient humidity data from an environmental sensor. RHeq is the material's moisture absorption equilibrium humidity threshold, set to 55% based on the material's physicochemical property library. ln(·) is the natural logarithm function, used to characterize the nonlinear mechanical decay characteristics caused by moisture accumulation on the material surface under high humidity conditions. This inversion process integrates full moisture detection in the gravity dimension and surface moisture activity analysis in the environmental dimension, outputting real-time moisture content data that can truly characterize the current load-bearing capacity of the packaging box, providing a physically corrected input benchmark for the accurate mapping of the subsequent dynamic pressure threshold.

[0083] For example, a preset material mechanical property database is invoked, and mapping and matching are performed based on the real-time moisture content data, specifically including:

[0084] Read the preset material mechanical properties database, which stores the corresponding relationship curves between different moisture content nodes and compressive strength values ​​and surface friction coefficient values;

[0085] An interpolation algorithm is used to find the value corresponding to the real-time moisture content data in the corresponding relationship curve, and generate the corresponding dynamic pressure threshold data and dynamic friction coefficient data.

[0086] Specifically, a pre-defined database of material mechanical properties stores the compressive strength and surface friction coefficient of materials at different moisture contents in the form of spectral curves, forming a full-range mechanical response benchmark from dry to saturated states. When real-time moisture content data is input, the system immediately initiates an interpolation matching mechanism. By performing high-resolution interpolation calculations on the corresponding relationship curves, it quickly locates the precise mechanical property coordinates corresponding to the current moisture content and outputs the dynamic bearing capacity threshold and dynamic friction coefficient in real time. In this process, the database serves as a static benchmark to provide a full-condition mechanical image, while the interpolation algorithm acts as a dynamic bridge to achieve continuous parameter mapping. The two collaborate through a high-speed query interface to ensure that a smooth and accurate mechanical parameter sequence can still be generated under conditions of continuous moisture content variation.

[0087] Compared to traditional static parameter lookup methods, existing technologies typically rely on fixed mechanical values ​​corresponding to discrete moisture content ranges. These methods are prone to parameter step errors when operating conditions change continuously and fail to reflect the true mechanical behavior of materials under transitional states. This solution, however, achieves uninterrupted calculation of mechanical parameters within the continuous moisture content domain through high-precision interpolation matching and real-time data stream processing, improving parameter response accuracy from discrete ranges to continuous numerical levels. Existing methods often cause control command oscillations due to lookup delays and data jumps when moisture content changes rapidly. This solution, through a built-in real-time interpolation engine and streaming data processing, controls parameter matching delays to within milliseconds and ensures the smoothness and physical rationality of the output curve. Existing systems often use piecewise constant approximations, which are difficult to adapt to high-dynamic humidity environments. This solution, by establishing a continuous mechanical response model across the entire range, improves the accuracy of material mechanical property evaluation to the same level as moisture content measurement accuracy.

[0088] Through the above technical solution, this application effectively solves the problem of lag and inaccuracy in mechanical property evaluation caused by changes in material moisture content. A pre-constructed material mechanical property database provides a benchmark mapping relationship covering all working conditions, and a real-time interpolation mechanism ensures accurate and smooth dynamic matching. The two work together to achieve real-time and precise monitoring, querying, and output closed-loop. This technical solution advances the evaluation method of material mechanical properties from static table lookup to dynamic tracking, ensuring that the parameter response speed is consistent with the measurement update frequency. It provides real-time and accurate mechanical input for applications such as structural pressure safety early warning and friction compensation of moving mechanisms, significantly improving the state perception and control accuracy of water-sensitive materials under varying working conditions.

[0089] For example, the nonlinear programming model includes an objective function, which is constructed as follows:

[0090] Establish a weighted function with maximizing space utilization as a positive indicator and the bottom-level crush risk index and the overall collapse risk index as negative penalty terms;

[0091] The underlying crush risk index is determined based on the ratio of the estimated load data of the underlying tank to the dynamic pressure threshold data.

[0092] The overall tipping risk index is determined based on the correlation between the overall center of gravity position data of the stack and the dynamic friction coefficient data.

[0093] In this embodiment, the objective function of the nonlinear programming model is designed as a weighted form of multi-objective fusion. Its positive driving force stems from maximizing the container's space volume ratio, while two key negative penalty terms—the bottom-level crushing risk index and the overall tipping risk index—constitute the core of the dynamic safety constraints. The bottom-level crushing risk index takes effect in real time. It compares the estimated load on the bottom container calculated based on the current layout with the dynamic pressure threshold sensed by the material at the current moisture content. Once the load approaches or exceeds the threshold, the penalty term increases sharply, forcing the optimization direction away from the high-risk layout. At the same time, the overall tipping risk index continuously monitors the stability of the stack. Based on the dynamically calculated overall center of gravity position of the stack and combined with the dynamic surface friction coefficient sensed from the current environment, it accurately assesses the stack's anti-slip and anti-tipping margins under different stress conditions. The instability trend caused by an excessively high center of gravity or an excessively low friction coefficient will be significantly reflected in the objective function through this penalty term, thereby guiding the optimization search towards a stack configuration with a low center of gravity and high stability.

[0094] Compared to existing technologies, traditional load cell optimization models typically simplify bearing and friction constraints to static thresholds with fixed safety factors. This fails to respond to the drift in material mechanical properties caused by changes in environmental humidity, potentially leading to crushing or tipping risks in actual working conditions, or excessive sacrifice of space efficiency for the sake of conservatism. Our proposed solution, however, introduces dynamic bearing thresholds and dynamic friction coefficients as real-time calculation bases for penalty terms, achieving synchronous adaptive adjustment of safety constraints and physical reality. This elevates risk control from static, empirical prevention to dynamic, perceptual, and precise management. Existing methods often decouple mechanical constraints from the layout optimization process, employing piecewise verification or a posteriori correction. This makes it difficult to avoid high-risk areas in the early stages of optimization, resulting in low solution efficiency and the potential for getting trapped in local suboptimal solutions. Our solution deeply embeds the dynamic risk index into the objective function as a continuous penalty function, ensuring that physical safety and space efficiency are simultaneously quantified and weighed in each iteration. This guides the solution process to efficiently search for the globally optimal solution within a safe and feasible solution space. Existing systems often neglect the impact of environmental factors on material properties, which leads to a surge in the actual failure risk of schemes optimized according to drying parameters in humid environments. This scheme, however, establishes a real-time closed loop from environmental perception to mechanical mapping and then to optimization decision-making, ensuring that the support structure has structural reliability consistent with physical reality under any working conditions.

[0095] Through the above technical solution, this application effectively solves the decision-making challenge of balancing space utilization objectives and dynamic physical safety constraints in palletizing optimization. A positive drive oriented towards maximizing space utilization, coupled with a risk penalty mechanism based on real-time mechanical data, forms a dynamic balance in the objective function. During the optimization algorithm's solution process, each round of layout adjustment triggers an immediate reassessment of the two risk indices, thus forming an automated closed-loop decision-making flow of "layout proposal - risk calculation - objective feedback - solution iteration." This technical solution upgrades palletizing decision-making from experience-based planning relying on static safety coefficients to precise dynamic optimization responding to real-time physical conditions. While ensuring that stacking structure risks are strictly controlled below thresholds, it increases warehouse space utilization to near physical limits, significantly improving the reliability of automated palletizing operations in complex and variable environments.

[0096] For example, setting the dynamic bearing capacity threshold data as a vertically stacked force constraint boundary specifically includes:

[0097] In the nonlinear programming group model, a vertical constraint condition is set, which requires that the cumulative weight data of all boxes above any Nth layer box must be less than the dynamic pressure bearing threshold data corresponding to the Nth layer box.

[0098] When the real-time moisture content data increases, causing the dynamic pressure threshold data to decrease, the vertical constraint condition automatically limits the maximum number of stacking layers in the group support scheme data.

[0099] Specifically, this application further proposes an adaptive vertical safety constraint mechanism based on dynamic pressure-bearing capacity perception. By deeply integrating the real-time perceived material pressure-bearing capacity threshold into the geometric constraint system of the stacking optimization model, and establishing an instant response path from mechanical performance degradation to dynamic adjustment of the stacking topology, this mechanism achieves source assurance and adaptive optimization of the vertical stability of the stack. The core of this mechanism lies in establishing the dynamic pressure-bearing threshold as an insurmountable physical boundary for vertical stacking. This ensures that when the optimization algorithm searches the feasible solution space, the stacking probability of each layer of boxes undergoes real-time mechanical safety verification, thereby ensuring that the generated stacking scheme always satisfies the fundamental physical law that the load-bearing capacity of the bottom layer is greater than the cumulative load of the upper layer in the vertical dimension, and dynamically adjusts the safe stacking limit according to changes in material properties.

[0100] Specifically, in the nonlinear programming stacking model, vertical stability is transformed into a set of strict mathematical constraints. These constraints require that for any Nth layer in the stack, the sum of the estimated weights of all boxes above it (i.e., from the N+1th layer to the top layer) must be less than the dynamic pressure-bearing threshold of that layer, determined by the current moisture content. This constraint is not a static parameter, but a dynamic expression bound to the real-time mechanical data stream. When the environmental monitoring system detects an increase in moisture content and calculates a corresponding decrease in the dynamic pressure-bearing threshold through interpolation, this constraint immediately takes effect: during the iterative optimization process, any stacking scheme that would cause the estimated load of the bottom or intermediate layers to exceed the latest threshold is deemed infeasible and excluded. This process directly and automatically limits the maximum number of stacking layers that the mathematical model can explore, ensuring that the final generated "stacking scheme data" inherently possesses a safety margin in its vertical configuration that matches the current material mechanical state, eliminating the need for post-hoc verification.

[0101] Compared to existing technologies, traditional stacking schemes rely on fixed maximum allowable layers or empirical maximum load-bearing standards for vertical safety. This fails to address the softening and time-varying load-bearing capacity of materials like bamboo boxes due to moisture, and stacking them according to dry standards under high humidity conditions carries the potential risk of bottom-layer collapse. This solution, however, establishes a real-time binding between dynamic load-bearing thresholds and vertical constraints. This upgrades the vertical safety standard from a static, uniform empirical value to a dynamic, personalized threshold strictly synchronized with the material's current physical state, achieving adaptive contraction and expansion of the safety boundary. Existing optimization methods typically perform independent load-bearing checks after the geometric layout is completed, a post-hoc inspection. Failure to pass necessitates complete rework and reconstruction, resulting in low decision-making efficiency. This solution places mechanical constraints at the core of the optimization search process, directly participating in the selection of the solution space as a feasibility criterion. This prevents layout schemes that do not meet load-bearing requirements from entering the candidate set, making "safety" an inherent attribute of the optimization path. Existing systems often require manual intervention to reset safety parameters when the environment changes, resulting in a delayed response. In contrast, this solution achieves instantaneous response to material performance degradation and millisecond-level autonomous adjustment of stacking strategies through an automated closed loop of "sensing-mapping-constraint".

[0102] Through the above technical solution, this application effectively solves the problem of vertical overload risk caused by neglecting the time-varying characteristics of material strength in warehouse stacking. The dynamic bearing capacity threshold, as a key boundary value perceived from the physical world, is directly injected into the constraint core of the optimization model; the vertical constraint condition acts as the enforcer of this boundary value, continuously conducting a "one-vote veto" safety review of the intermediate results of each optimization iteration. The two form a tightly coupled "threshold input-constraint adjudication" interaction, ensuring that the entire stacking optimization process always operates within a safety shell defined by real-time physical laws. This technical solution transforms the guarantee of vertical stability of stacking from a back-end check relying on fixed rules to a dynamic intrinsic constraint embedded in the optimization front end, evolving synchronously with physical reality. This completely eliminates the decision-making source of crushing accidents in a dynamic environment, while ensuring that space utilization efficiency is continuously pushed to the extreme under the premise of absolute safety.

[0103] For example, setting the dynamic friction coefficient data as horizontally arranged anti-slip constraint boundaries specifically includes:

[0104] In the nonlinear programming group model, horizontal constraints are set, and the horizontal constraints define the minimum contact area threshold between the boxes.

[0105] The minimum contact area threshold is negatively correlated with the dynamic friction coefficient data. When the dynamic friction coefficient data is lower than the preset safe friction threshold, the horizontal constraint condition forcibly increases the minimum contact area threshold to limit the cantilever stacking ratio of the box.

[0106] Specifically, this application further proposes a horizontal anti-slip constraint mechanism that adapts to the material surface state. By converting the dynamic friction coefficient into a quantitative requirement for the minimum contact area between the boxes in real time, and establishing a closed-loop feedback from friction performance perception to real-time adjustment of the stacking geometry, the mechanism achieves dynamic assurance of the horizontal anti-slip and anti-overturning stability of the stacking scheme. The core of this mechanism is to establish the dynamic friction coefficient as the fundamental physical basis for the safety of the horizontal layout, and to dynamically adjust the bottom line standard of the contact area between the boxes accordingly. This drives the optimization algorithm to automatically balance spatial compactness and frictional reliability when constructing the stack, ensuring that the generated layout has a fixation capability that matches the current surface state under lateral stress conditions.

[0107] Specifically, this mechanism manifests as a key horizontal constraint in the nonlinear programming assembly model. The core variable of this constraint is defined as the minimum contact area threshold required between the boxes. This threshold is not a fixed value, but rather forms an intelligent response relationship with the dynamically measured and calculated friction coefficient data in real time: the two are negatively correlated. When environmental monitoring indicates that the material surface becomes slippery due to factors such as increased moisture content, causing the dynamic friction coefficient to decrease and fall below the preset safe friction threshold, the horizontal constraint will immediately activate an enhancement mode. Through a built-in response function, it automatically and forcibly increases the required minimum contact area threshold. This increase is directly transmitted to the optimization solution process: to meet the new and more stringent contact area requirements, the algorithm must reduce stacking methods such as cantilever and extension that rely on smaller support surfaces, thus significantly limiting the proportion and extent of cantilever stacking of boxes in the "assembly scheme data" and forcing the stacking structure to tend towards a compact layout with a larger contact surface and more stable support.

[0108] Compared to existing technologies, traditional cantilever optimization primarily relies on static friction coefficients and empirical safety clearances for horizontal stability considerations. This fails to adapt to the dynamic changes in material surface friction properties due to factors such as humidity and contamination. Designing cantilever structures based on dry friction coefficients in humid environments poses significant risks of slippage and overturning. This solution, however, establishes a dynamic negative correlation model between the friction coefficient and the minimum contact area. This allows horizontal safety constraints to automatically tighten as physical conditions deteriorate, upgrading anti-slip design from a static, one-size-fits-all standard to a dynamic, risk-adaptive elastic boundary. Existing methods often treat friction safety as a post-verification item or simply specify a fixed maximum cantilever length in the layout. This fails to precisely quantify the impact of friction decay on specific configurations during optimization, leading to solutions that are either conservative and inefficient or risky and uncontrollable. This solution transforms dynamic friction constraints into direct and continuous control of the contact area and embeds it into the core optimization loop. This ensures that every contact interface design in the layout undergoes real-time friction safety verification, achieving a shift in horizontal stability from "result checking" to "process control." When faced with a decrease in the friction coefficient, existing systems often only respond with alarms or globally disable the cantilever, resulting in a crude response and sacrificing efficiency. In contrast, this solution precisely increases the local contact area requirements, enabling the intelligent guidance algorithm to find a still usable and more robust alternative stacking mode while ensuring safety, thus achieving a refined balance between safety and efficiency.

[0109] Through the above technical solution, this application effectively solves the risk of horizontal slippage and overturning of stacks caused by neglecting the time-varying characteristics of surface friction properties. The dynamic friction coefficient, as a real-time perceived physical input, continuously provides a basis for risk assessment of horizontal constraints; the horizontal constraints, as an execution controller, directly transform physical risks into immediate and precise restrictions on the layout search space by dynamically adjusting the key geometric parameter of the minimum contact area threshold. The two constitute a real-time interactive closed loop of "perception-assessment-control." This technical solution enables pallet optimization to possess environmentally adaptive stability in the horizontal dimension, fundamentally eliminating slippage accidents caused by changes in material surface conditions, ensuring reliable lateral stability of stacks in various complex storage environments, and maximizing the rationality of spatial layout.

[0110] For example, the solution generates assembly scheme data containing the three-dimensional coordinate information of all the boxes, specifically including:

[0111] A heuristic search algorithm is used to iteratively solve the nonlinear programming group model;

[0112] During the iteration process, if the optimal solution under the current stacking layer number cannot satisfy the force constraint boundary, the stacking layer number variable is automatically reduced, and the search is repeated in the reduced layer space until a group support scheme data that satisfies all constraints is generated.

[0113] Specifically, this application further proposes an adaptive iterative solution mechanism that coordinates constraints and optimization search depth. By embedding dynamic mechanical constraints deep into the decision logic of the heuristic search algorithm and establishing a real-time feedback loop from constraint verification failure to automatic adjustment of key optimization variables, it achieves efficient and reliable solutions for complex nonlinear assembly models. The core of this mechanism lies in upgrading the traditional static, unidirectional optimization process into a dynamic search process driven by physical constraints in real time and possessing self-correction capabilities. This ensures that the final generated assembly scheme data not only mathematically satisfies optimality but also strictly adheres to the real-time perceived pressure and friction safety boundaries in physical essence.

[0114] Specifically, this mechanism uses a heuristic search algorithm as its main execution mechanism, iteratively optimizing within a high-dimensional solution space defined by box dimensions, pallet specifications, and dynamic mechanical parameters. Each iteration is not simply a matter of scoring and improving solutions, but rather a deep dialogue with the constraint system embedded within the model. When the algorithm searches at a preset stacking layer number, dynamic bearing capacity and dynamic friction constraints continuously review the physical feasibility of the generated candidate solutions. If, after sufficient searching, the optimal solution at the current layer level still fails to meet the force constraint boundary defined by the dynamic bearing capacity threshold—that is, if the estimated load of a certain layer exceeds its dynamic bearing capacity—an adaptive layer adjustment mechanism is triggered. This mechanism does not simply declare failure, but rather acts as an intelligent feedback loop, proactively and automatically reducing the key optimization variable of "stacking layer number." Subsequently, the search algorithm immediately restarts the optimization process within the reduced, physically safer layer space. This closed loop of "search-verification-adjustment-research" continues until the algorithm finds a feasible optimal solution that satisfies all dynamic mechanical and geometric constraints and maximizes space utilization under a given number of layers. Finally, it outputs assembly scheme data containing the precise three-dimensional coordinates of all boxes.

[0115] Compared to existing technologies, traditional group optimization solutions often employ a fixed number of layers or rely on manual experience to reset parameters and perform multiple independent solutions when constraints are not met. This process is cumbersome, slow, and prone to prolonged unsolvable searches due to improper layer settings. Our proposed solution, however, treats the number of layers as an endogenous variable that can be dynamically adjusted by constraint violation signals, forming a closed loop with the search algorithm. This achieves adaptive dimensionality reduction and self-guidance in the solution process, upgrading the solution strategy from mechanical repetition to intelligent progression. Existing methods often cause the algorithm to blindly search in infeasible regions due to constraint conflicts when dealing with complex constraints, leading to convergence difficulties or even failure. Our solution, through constraint-triggered layer adjustment, effectively shrinks the solution space boundary during the solution process, guiding the algorithm to quickly escape physically infeasible regions, significantly improving convergence efficiency and success rate. Existing systems often require post-hoc verification of the safety of the output solution in simulations, incurring iterative costs of repeated modifications. Our solution, by embedding dynamic safety constraint depth into the solution loop, ensures that safety verification and solution generation are completed simultaneously, guaranteeing the physical reliability of the output solution from its inception.

[0116] Through the above technical solution, this application effectively solves the problems of low solution efficiency and difficulty in ensuring feasibility of stacking optimization models under complex dynamic constraints. The heuristic search algorithm, dynamic constraint set, and adaptive layer adjustment mechanism constitute a closely collaborative intelligent solution consortium: the algorithm is responsible for exploration, the constraints for judgment, and the adjustment mechanism provides crucial decision-making for dimensionality reduction and restart when judgment is rejected. This collaborative working mode enables the entire solution process to possess a keen awareness of physical limits and the ability to autonomously avoid them. This technical solution transforms the generation of stacking schemes from offline calculations relying on extensive trial and error and manual intervention into a highly automated, adaptive, and reliable online optimization process. While ensuring absolute stacking safety, it significantly improves the decision-making speed and scheme output quality of automated stacking systems in complex and variable environments.

[0117] For example, after outputting the group hosting scheme data to the execution terminal, the method further includes:

[0118] Determine whether the dynamic friction coefficient data is less than a preset reinforcement warning threshold;

[0119] If it is less than, additional stability reinforcement instruction data is generated, which includes operational suggestions for increasing interlayer anti-slip medium or increasing the tension of the external winding film;

[0120] The stability reinforcement instruction data is associated with the group support scheme data and output synchronously.

[0121] In this embodiment, the mechanism is activated immediately after the assembly plan data is output to the execution terminal. An independent monitoring and decision-making module continuously monitors the dynamic friction coefficient data issued along with the plan and compares it in real time with a preset reinforcement warning threshold representing a critical safety state. This comparison is the core of risk assessment: if the current friction coefficient is determined to be lower than the warning threshold, it indicates that the optimized geometric layout alone may not be sufficient to resist the risk of horizontal slippage. At this time, the system will automatically trigger the reinforcement process. This process is not a simple alarm, but rather a structured stability reinforcement instruction data actively generated by an instruction generation module. This instruction data precisely corresponds to low friction risk, and its content is not a general warning, but includes specific and actionable suggestions such as "inserting anti-slip pads between specific layers" or "increasing the overall tension of the wrapping film." Finally, this set of generated reinforcement instructions will be intelligently associated and bound with the original assembly plan data to form a composite data package of "basic layout + reinforcement suggestions," which is synchronously output to the execution terminal, providing complete guidance from placement to reinforcement for on-site operations.

[0122] Compared to existing technologies, traditional automated assembly systems consider the task complete once the solution is output, lacking subsequent support for extreme conditions that the solution may face during deployment in the actual physical environment. This leaves the responsibility for risk identification and response entirely to on-site personnel, relying on their experience and vigilance, which carries the risk of missed risk assessments and untimely handling. This solution, however, embeds an intelligent risk filter and instruction generator at the end of the output pipeline, enabling automatic assessment and proactive intervention of potential risks during the solution implementation phase. This extends the system's responsibilities from simple "layout design" to "construction safety guidance." Existing methods, when dealing with known environmental degradation, often employ modified and optimized model parameters to regenerate conservative solutions, resulting in a lengthy and inefficient process that cannot quickly enhance and adapt already qualified solutions. This solution, by adding a lightweight, fast-responding hardening decision layer after output, achieves risk-compensatory enhancement of existing solutions without backtracking or recalculation, resulting in faster response times and lower resource consumption. Existing systems often limit human-computer interaction to displaying the final layout diagram, requiring operators to determine whether and how reinforcement is needed. This solution extends the system's intelligent output from the geometric domain to the operational domain by outputting related and specific reinforcement instructions, providing clear and timely decision support for on-site operations, reducing personnel workload, and improving operational standardization and safety.

[0123] Through the above technical solution, this application effectively addresses the problem of insufficient stability assurance faced by the palletizing optimization scheme due to dynamic environmental changes during actual deployment. Real-time monitoring of the dynamic friction coefficient constitutes the nerve endings of risk perception, comparison of the reinforcement warning threshold constitutes the decision-making center of risk judgment, and the generation and associated output of stability reinforcement instructions constitute the prelude to risk response. These three elements are interconnected, forming a "monitoring-judgment-enhancement" safety value-added link that is independent of, yet closely connected to, the core optimization loop. This technical solution enables the entire palletizing decision-making system to not only generate a stable digital scheme under ideal conditions, but also further ensures that the scheme has a feasible and risk-resistant capability in the complex real physical world, significantly improving the overall robustness and operational safety of the automated warehousing system in the face of uncertain environmental factors.

[0124] Example 2

[0125] This application also discloses a packaging box pallet optimization system based on nonlinear programming.

[0126] Reference Figure 2 A nonlinear programming-based optimization system for packaging box palletizing includes:

[0127] The data acquisition module is used to acquire real-time ambient humidity data of the environment in which the enclosure is located and real-time weight data of the enclosure.

[0128] The calculation module is used to calculate the real-time moisture content data corresponding to the box based on the real-time ambient humidity data and the real-time weight data.

[0129] The matching module is used to call a preset material mechanical property database, perform mapping matching based on the real-time moisture content data, and extract the corresponding dynamic pressure threshold data and dynamic friction coefficient data.

[0130] The construction module is used to construct a nonlinear programming group model, setting the dynamic pressure threshold data as vertically stacked force constraint boundaries and the dynamic friction coefficient data as horizontally arranged anti-slip constraint boundaries.

[0131] The solution module is used to generate assembly scheme data containing the three-dimensional coordinate information of all boxes by using the nonlinear programming assembly model, under the premise of satisfying the force constraint boundary and the anti-slip constraint boundary.

[0132] The output module is used to output the group support scheme data to the execution terminal.

[0133] The above content is merely an example and illustration of the concept of the present invention. Those skilled in the art can make various modifications or additions to the specific embodiments described or use similar methods to replace them, as long as they do not deviate from the concept of the invention, they should all fall within the protection scope of the present invention.

[0134] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0135] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to any specific implementation. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention.

Claims

1. A packaging box pallet grouping optimization method based on nonlinear programming, characterized in that, Includes the following steps: Acquire real-time ambient humidity data of the environment in which the enclosure is located, as well as real-time weight data of the enclosure; Based on the real-time ambient humidity data and the real-time weight data, the real-time moisture content data corresponding to the box is calculated. The system calls a preset material mechanical properties database, performs mapping and matching based on the real-time moisture content data, and extracts the corresponding dynamic pressure threshold data and dynamic friction coefficient data. Calling a preset material mechanical property database and performing mapping and matching based on the real-time moisture content data specifically includes: Read the preset material mechanical properties database, which stores the corresponding relationship curves between different moisture content nodes and compressive strength values ​​and surface friction coefficient values; An interpolation algorithm is used to find the value corresponding to the real-time moisture content data in the corresponding relationship curve, and generate the corresponding dynamic pressure threshold data and dynamic friction coefficient data. A nonlinear programming model is constructed, in which the dynamic pressure threshold data is set as a vertically stacked force constraint boundary, and the dynamic friction coefficient data is set as a horizontally arranged anti-slip constraint boundary. Using the nonlinear programming assembly model, under the premise of satisfying the force constraint boundary and the anti-slip constraint boundary, the assembly scheme data containing the three-dimensional coordinate information of all boxes is generated; Output the group hosting scheme data to the execution terminal.

2. The packaging box pallet optimization method based on nonlinear programming according to claim 1, characterized in that, Based on the real-time ambient humidity data and the real-time weight data, the real-time moisture content data corresponding to the box is calculated, specifically including: Obtain the initial dry weight data corresponding to the chamber; The difference between the real-time weight data and the initial dry weight data is calculated to obtain the moisture absorption weight gain data; Substituting the moisture absorption weight gain data and the real-time ambient humidity data into the preset moisture absorption balance equation, the real-time moisture content data corresponding to the box is calculated.

3. The packaging box pallet grouping optimization method based on nonlinear programming according to claim 1, characterized in that, The nonlinear programming model includes an objective function, which is constructed as follows: Establish a weighted function with maximizing space utilization as a positive indicator and the bottom-level crush risk index and the overall collapse risk index as negative penalty terms; The underlying crush risk index is determined based on the ratio of the estimated load data of the underlying tank to the dynamic pressure threshold data. The overall tipping risk index is determined based on the correlation between the overall center of gravity position data of the stack and the dynamic friction coefficient data.

4. The packaging box pallet grouping optimization method based on nonlinear programming according to claim 1, characterized in that, Setting the dynamic pressure-bearing threshold data as a vertically stacked force constraint boundary specifically includes: In the nonlinear programming group model, a vertical constraint condition is set, which requires that the cumulative weight data of all boxes above any Nth layer box must be less than the dynamic pressure bearing threshold data corresponding to the Nth layer box. When the real-time moisture content data increases, causing the dynamic pressure threshold data to decrease, the vertical constraint condition automatically limits the maximum number of stacking layers in the group support scheme data.

5. The packaging box pallet optimization method based on nonlinear programming according to claim 1, characterized in that, Setting the dynamic friction coefficient data as horizontally arranged anti-slip constraint boundaries specifically includes: In the nonlinear programming group model, horizontal constraints are set, and the horizontal constraints define the minimum contact area threshold between the boxes. The minimum contact area threshold is negatively correlated with the dynamic friction coefficient data. When the dynamic friction coefficient data is lower than the preset safe friction threshold, the horizontal constraint condition forcibly increases the minimum contact area threshold to limit the cantilever stacking ratio of the box.

6. The packaging box pallet grouping optimization method based on nonlinear programming according to claim 1, characterized in that, The solution generates assembly scheme data containing the three-dimensional coordinate information of all the boxes, specifically including: A heuristic search algorithm is used to iteratively solve the nonlinear programming group model; During the iteration process, if the optimal solution under the current stacking layer number cannot satisfy the force constraint boundary, the stacking layer number variable is automatically reduced, and the search is repeated in the reduced layer space until a group support scheme data that satisfies all constraints is generated.

7. The packaging box pallet grouping optimization method based on nonlinear programming according to claim 1, characterized in that, After outputting the group hosting scheme data to the execution terminal, it also includes: Determine whether the dynamic friction coefficient data is less than a preset reinforcement warning threshold; If it is less than, additional stability reinforcement instruction data is generated, which includes operational suggestions for increasing interlayer anti-slip medium or increasing the tension of the external winding film; The stability reinforcement instruction data is associated with the group support scheme data and output synchronously.

8. A packaging box palletizing optimization system based on nonlinear programming, applied to the packaging box palletizing optimization method based on nonlinear programming as described in any one of claims 1-7, characterized in that, include: The data acquisition module is used to acquire real-time ambient humidity data of the environment in which the enclosure is located and real-time weight data of the enclosure. The calculation module is used to calculate the real-time moisture content data corresponding to the box based on the real-time ambient humidity data and the real-time weight data. The matching module is used to call a preset material mechanical property database, perform mapping matching based on the real-time moisture content data, and extract the corresponding dynamic pressure threshold data and dynamic friction coefficient data. The construction module is used to construct a nonlinear programming group model, setting the dynamic pressure threshold data as vertically stacked force constraint boundaries and the dynamic friction coefficient data as horizontally arranged anti-slip constraint boundaries. The solution module is used to generate assembly scheme data containing the three-dimensional coordinate information of all boxes by using the nonlinear programming assembly model, under the premise of satisfying the force constraint boundary and the anti-slip constraint boundary. The output module is used to output the group support scheme data to the execution terminal.

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