Maintenance equipment two-dimensional boxing optimization method giving consideration to gravity center balance

Abstract

The invention discloses a maintenance equipment two-dimensional boxing optimization method giving consideration to gravity center balance, and belongs to the technical field of equipment packaging and assembling. Comprising the following steps of 1, equipment maintenance equipment scene data input and algorithm library initialization, 2, generation of a two-dimensional boxing initial scheme without gravity center constraint, 2.1, algorithm calling mode judgment, 2.2, algorithm configuration and execution, 3, gravity center post-processing optimization, and 4, equipment maintenance equipment compliance verification and standardization scheme output. According to the maintenance equipment two-dimensional boxing optimization method considering gravity center balance, the initial layout is generated through the differentiated scene adaptation algorithm, the offset is corrected through the gravity center post-processing optimization algorithm, and the gravity center balance is efficiently achieved on the premise that core constraints such as the space utilization rate and the completeness are guaranteed; meanwhile, an algorithm library is adopted to realize double modes of automatic selection and user designation, and through a standardized architecture and a parameter fine tuning interface, the flexibility of algorithm calling and scene adaptability are realized.

Description

Technical Field

[0001] This invention relates to a two-dimensional packing optimization method for maintenance equipment that takes into account the center of gravity balance, belonging to the field of equipment packaging and assembly technology. Background Technology

[0002] The core contradiction in two-dimensional packing of military equipment lies in the conflict between multi-constraint computational coupling and the efficiency of center of gravity optimization: traditional technology calculates center of gravity constraints, space utilization, and completeness constraints simultaneously in the same algorithm, resulting in an exponential expansion of the solution space; taking 50 heterogeneous pieces of equipment as an example, the algorithm needs to traverse the combination of position, weight, and completeness relationship during coupled calculation, which is time-consuming and far from meeting the needs of rapid packing in wartime; moreover, adjusting the center of gravity often adopts global reconstruction layout, which easily disrupts the planned equipment positions, leading to a decrease in space utilization and even destroying the completeness of the equipment assembly, which does not meet the basic assembly and complete supply specifications in GJB10882-2023.

[0003] Meanwhile, the varying protection levels of equipment and maintenance tools necessitate more refined requirements for center of gravity optimization: precision-grade equipment (such as radar calibration sensors) requires strict control of center of gravity offset to ≤5mm, while standard-grade equipment (such as bolt kits) can be relaxed to ≤15mm, and heavy-duty equipment (such as small gearboxes) needs to balance weight and offset (≤10mm). Existing technologies do not offer adaptive algorithms for different scale scenarios (small-scale ≤50 pieces, medium-scale 50-100 pieces, large-scale >100 pieces). Using a single algorithm in existing technologies to handle all scenarios can easily lead to efficiency losses, while oversimplifying center of gravity calculations can result in insufficient stability, making it difficult to balance efficiency, effectiveness, and compliance.

[0004] Furthermore, irregular components (such as connectors with protrusions) and immovable components (such as motors with fixed bases) commonly found in 2D packing further increase the complexity of center of gravity calculation; while traditional algorithms need to be adapted to the geometric characteristics of such components, which leads to a further increase in the complexity of coupled calculation.

[0005] Therefore, in order to solve the above problems, it is urgent to design a two-dimensional packing method that can balance computational efficiency and center of gravity stability. Summary of the Invention

[0006] To address the aforementioned issues, this invention proposes a two-dimensional packing optimization method for maintenance equipment that balances the center of gravity. It generates an initial layout through a differentiated scenario adaptation algorithm and corrects offsets through a post-processing optimization algorithm for the center of gravity, efficiently achieving center of gravity balance while ensuring core constraints such as space utilization and completeness. Simultaneously, it employs an algorithm library to implement both automatic selection and user-specified modes, and achieves flexibility in algorithm invocation and scenario adaptability through a standardized architecture and parameter fine-tuning interface. This method is applicable to standardized packing of various military equipment maintenance materials, particularly suited to the needs of rapid response and low loss during wartime.

[0007] The present invention provides a two-dimensional packing optimization method for maintenance equipment that takes into account center of gravity balance. This method separates the initial packing algorithm from the center of gravity optimization algorithm. The initial algorithm focuses on addressing constraints such as space utilization and completeness of sets, while center of gravity optimization is achieved through an independent post-processing algorithm without altering the packing contents. Furthermore, differentiated center of gravity adjustment algorithms are designed for different scale scenarios, balancing computational efficiency and center of gravity stability, thus meeting the practical needs of equipment maintenance. The method includes the following steps: Step 1: Input of equipment maintenance material scenario data and initialization of algorithm library. Step 1.1: Collect the core parameters of the equipment and repair materials to be packed and the specifications of the target loading carrier. The core parameters include the equipment's planar dimensions (length L in mm and width W in mm), weight (G in kg), protection level (P), set identification (marking whether it is an inseparable set of equipment in the maintenance equipment inventory list), and mobility attributes (marking whether it is a non-movable equipment with a fixed base, such as a vehicle-mounted motor); wherein, the protection level (P) is divided into precision level, conventional level, and heavy-duty level according to GJB10882-2023; The target loading carrier is a dedicated two-dimensional storage unit for equipment, a drawer-type storage box, or a standard maintenance tray, and its specifications include a planar length L. p (Unit: mm), Plane width W p (Unit: mm), Rated load capacity (G) p (Unit: kg) and preset coordinates of fixed equipment (retrieved from the fixed layout database of equipment maintenance materials); Step 1.2: Data preprocessing, Equipment whose weight exceeds 15% of the rated load capacity of the target loading carrier is removed to avoid local overload damage to the carrier; equipment marked as "yes" is pre-grouped, such as an engine repair kit containing 5 pieces, and marked as the same group to ensure that the equipment in the same group is in the same two-dimensional loading plane and is not split; equipment with the movement attribute of being immovable is locked according to preset coordinates (called from the fixed layout database of equipment maintenance materials) and does not participate in subsequent sorting. Step 1.3: Algorithm library initialization. Step 1.3.1: Load the algorithm library architecture. The algorithm library adopts a four-layer architecture: data access layer, algorithm core layer, interface service layer, and application adaptation layer. Among them, the algorithm core layer encapsulates three major modules: greedy algorithm, genetic algorithm, and annealing algorithm. Each module is deployed independently and communicates through standardized interfaces. Step 1.3.2: Configure dual-mode call permissions. The algorithm library supports automatic selection and user-specified dual modes. Users configure the call mode through the API interface (such as HTTP request interface) of the interface service layer. The interface parameters include mode identifier (AUTO / USER), target algorithm (GREEDY / GA / SA) and parameter fine-tuning items. Step 2: Generate the initial 2D bin packing scheme without centroid constraints. Step 2.1: Determine the algorithm call mode. Step 2.1.1: If the user configuration mode is set to Automatic Selection (AUTO), the algorithm library automatically matches the algorithm based on the number of equipment N: if N≤50 pieces, the greedy algorithm module is called; if 50<N≤100 pieces, the annealing algorithm module is called; if N>100 pieces, the genetic algorithm module is called. Step 2.1.2: If the user configuration mode identifier is user-specified (USER), the algorithm library calls the corresponding module according to the target algorithm parameters. If the user-specified algorithm does not match the equipment scale (e.g., a greedy algorithm is specified for N=120 pieces), the interface service layer returns a "scale mismatch" prompt and recommends an appropriate algorithm. The user confirms and then executes the call. Step 2.2: Algorithm Configuration and Execution Step 2.2.1: Automatic mode selection; the algorithm library executes the default configurations of each module. Among them, the sorting strategy of the greedy algorithm is descending plane area + descending weight, and the layout algorithm is placing the equipment along the lowest horizontal line and the boundary. The annealing algorithm aims to maximize space utilization and accepts better solutions through the Metropolis criterion to avoid getting trapped in local optima. The genetic algorithm encodes the equipment layout as chromosomes with placement coordinates and orientation, uses space utilization as the fitness function, and achieves population evolution through selection, crossover and mutation operations. Step 2.2.2: User-specified mode, where the user fine-tunes the configuration of the corresponding module through the interface service layer; Step 2.2.3: Perform initial packing, optimizing only the three constraints of space utilization rate ≥70% (meeting the space utilization standard for maintenance equipment), complete sets of equipment not being disassembled, and fixed positions of immovable equipment, without considering the center of gravity factor; output the initial layout of equipment placement coordinates (x / y, accurate to 1mm), space utilization rate, and complete set of equipment grouping records; Step 3: Post-processing optimization of center of gravity. Step 3.1: Real-time center of gravity calculation for equipment maintenance scenarios. Step 3.1.1: Extraction of geometric center coordinates, the geometric center (x) of the movable equipment. i ,y i = (x-coordinate of placement + L / 2, y-coordinate of placement + W / 2); the geometric center of immovable equipment is calculated according to the preset fixed coordinates, and the weight is included according to the actual value; Step 3.1.2: Calculate the overall center of gravity. Calculate the initial center of gravity coordinates (X) according to formula (1). c0 ,Y c0 ): , (1) Where n is the total number of devices inside the carrier, G i Let x be the weight of the i-th piece of equipment. i y i Let x and y be the geometric center coordinates of the i-th device; Step 3.2: Set the differentiated center of gravity offset threshold based on the protection level. Step 3.2.1: Single-level threshold, determine the single-level threshold according to the equipment protection level P; Step 3.2.2: Multi-level mixed scene threshold. If the carrier contains multiple protection levels of equipment at the same time, the final judgment threshold T is determined according to the principle of taking the minimum value. For example, if it contains both precision-level and conventional-level equipment, T=5mm. Step 3.2.3: Calculate and determine the center of gravity offset. Calculate the initial centroid (X) according to formula (2). c0 ,Y c0 ) and the geometric center of the two-dimensional loading plane (L p / 2,W p / 2) offset D0; , (2) If D0≤T, the initial layout is determined to meet the center of gravity balance requirement, and step 4 is executed directly; if D0>T, the local adjustment in step 3.3 is executed. Step 3.3: Invoke the adjustment strategy based on the initial algorithm. Step 3.3.1: Delineate the adjustment range by dividing the adjustment area according to the direction of the center of gravity offset; Step 3.3.2: If the initial algorithm is a greedy algorithm for initial layout, call the adjacent equipment exchange algorithm in the algorithm library to perform the exchange operation; Step 3.3.3: If the initial algorithm is an annealing algorithm for initial layout, call the position swap + orientation rotation hybrid algorithm in the algorithm library for position swap; Step 3.3.4: If the initial algorithm is a genetic algorithm for initial layout, call the local rearrangement optimization algorithm in the algorithm library to rearrange the object selection; Step 3.3.5: Global adjustment termination condition: If D ≤ T after the above adjustment, or the cumulative number of adjustments reaches 8 (5 exchanges for small scale, 3 exchanges + 3 rotations for medium scale, 2 rearrangements + 3 exchanges + 3 rotations for large scale), stop the adjustment; if D is still > T after 8 adjustments, transfer one non-complete movable equipment within the adjustment range to another two-dimensional loading carrier of the same specification, and repeat step 2 to ensure that the final solution meets the center of gravity requirements; Step 4: Compliance verification of equipment and maintenance materials and output of standardized solutions. Step 4.1: Secondary verification with multiple constraints. Step 4.1.1: Space utilization verification, confirm that the adjusted space utilization η ≥ 70%; if η < 70%, adjust the sorting weight in step 2.2, regenerate the initial layout and repeat step 3; Step 4.1.2: Verify the compliance of equipment maintenance materials, confirming that the complete set of materials has not been disassembled, the position of immovable materials remains unchanged, and the weight of the materials does not exceed the rated load of the carrier; Step 4.2: Output a special packing plan for maintenance equipment.

[0008] Furthermore, in step 1.3.1, the interaction logic of the four-layer architecture of the algorithm library is as follows: the data access layer cleans the equipment / carrier data; the interface service layer receives the calling mode and parameters; the algorithm core layer calls the corresponding module for calculation; and the application adaptation layer outputs the initial layout. Each layer communicates through RESTful API with a latency of ≤100ms.

[0009] Furthermore, in step 2.2.1, under the automatic selection mode, the specific execution method of the algorithm library executing the default configuration of each module is as follows: Scenes with N≤50 pieces of equipment are categorized as small-scale scenes. A greedy algorithm is used, with sorting strategy being descending order of plane area (L×W) (weight 0.7) + descending order of weight (weight 0.3). The layout algorithm is placement along the lowest horizontal line and edge-fitting. Specifically, with the lower left corner of the two-dimensional carrier plane as the origin (0,0), the height of the lowest horizontal line in the plane is dynamically maintained (initially 0). Equipment is placed along the lowest horizontal line to the left to fit the edge of the carrier or to fit existing equipment. If it cannot fit, it moves vertically upwards to the new lowest horizontal line. Scenes with 50 < number of equipment N ≤ 100 are categorized as medium-sized scenes. The annealing algorithm is used with the following parameters: initial temperature T0 = 1000 (ensuring the initial search range covers the main layout possibilities), temperature decay coefficient α = 0.95 (balancing search breadth and convergence speed), iteration steps per temperature = 60 (ensuring sufficient search at a single temperature), and termination temperature T_end = 1e-3 (ensuring the algorithm converges to a stable solution). The algorithm aims to maximize space utilization, accepting better solutions through the Metropolis criterion to avoid getting trapped in local optima. Scenes with N > 100 pieces of equipment are categorized as large-scale scenes. A genetic algorithm is used with the following parameters: population size 80 (to ensure solution diversity), maximum number of iterations 150 (to balance optimization effect and computation time), crossover probability 0.7 (to generate new layout combinations), and initial mutation probability 0.08 (decreasing by 0.01 to 0.02 every 20 generations to avoid premature convergence). The algorithm encodes the equipment layout as chromosomes with placement coordinates and orientation, using space utilization as the fitness function. Population evolution is achieved through selection (roulette wheel + elite retention), crossover (two-point crossover), and mutation (coordinate fine-tuning + orientation switching).

[0010] Furthermore, in step 2.2.1, the boundary fitting of the greedy algorithm is as follows: when placing the equipment, it is given priority to fitting the long or short edge of the carrier. If there is no space at the edge, it is fitted to the edge of the already placed equipment, and a 2mm gap is reserved between the equipment for placing cushioning material. The gap is not included in the space utilization calculation.

[0011] Furthermore, in step 2.2.2, the user fine-tunes the configuration of the corresponding modules through the interface service layer, including the sorting weights (area 0.5-0.9, weight 0.1-0.5) in the greedy algorithm, the initial temperature (800-1200) and decay coefficient (0.9-0.98) in the annealing algorithm, and the population size (50-100) and number of iterations (100-200) in the genetic algorithm. The fine-tuning range is constrained by the parameters of the algorithm core layer (e.g., crossover probability ≤ 0.8). Among these, the user's parameter fine-tuning needs to pass the parameter validity verification of the algorithm core layer: for example, the sum of the sorting weights in the greedy algorithm must be = 1, and the initial temperature in the annealing algorithm must be ≥ 800. If the verification fails, the default parameters are returned to ensure the stability of the algorithm.

[0012] Furthermore, in step 3.1.1, if the equipment is irregularly shaped, such as a connector with protrusions, its planar dimensions are calculated based on the minimum circumscribed rectangle, and the thickness of the protective buffer layer must be taken into account in the circumscribed rectangle dimensions: 5mm for precision-grade equipment, 3mm for conventional-grade equipment, and 4mm for heavy-duty-grade equipment, to ensure the accuracy of the center of gravity calculation; and the minimum circumscribed rectangle calculation of irregular equipment is obtained by using a laser scanning device to acquire the three-dimensional contour of the equipment and automatically generate the circumscribed rectangle dimensions, avoiding the deviation in center of gravity calculation caused by manual measurement errors.

[0013] Furthermore, in step 3.2.1, the precision-grade equipment corresponds to an offset threshold T1=5mm, which is suitable for vibration-sensitive equipment such as optical instruments and radar sensors, meeting the low-loss requirements of wartime transportation; the conventional-grade equipment corresponds to a threshold T2=15mm, which is suitable for mechanical bolts, ordinary parts, etc., balancing stability and efficiency; the heavy-grade equipment corresponds to a threshold T3=10mm, which is suitable for heavy equipment such as small gearboxes and metal connectors, avoiding the tilting of the carrier due to the shift of the center of gravity.

[0014] Furthermore, the specific operation steps of step 3.3 are as follows: Step 3.3.1: Delineate the adjustment range, dividing the adjustment area according to the direction of the center of gravity offset; if X c0 <L p / 2, determined to be a horizontal left offset, the adjustment range is a rectangular area on the left side of the two-dimensional loading plane that is 3 times the side length of the maximum movable equipment (x∈[0,3×L)). max ],y∈[0,W p ], L max (where X is the maximum length of the movable equipment); if X c0 >L p / 2, determined to be a horizontal right offset, the adjustment range is a rectangular area on the right side of the two-dimensional loading plane that is three times the side length of the maximum movable equipment (x∈[L p -3×L max ,L p ],y∈[0,W p ]); If Y c0 Similarly, for offset, the vertical adjustment range should be divided; the adjustment range should exclude the fixed area of ​​immovable equipment and the pre-grouped area of ​​complete sets of equipment, and only include movable non-complete sets of equipment. Step 3.3.2: If the initial algorithm uses a greedy algorithm for initial layout, call the adjacent equipment swapping algorithm from the algorithm library to perform the swapping operation; select two adjacent movable equipment within the adjustment range, swap their positions in the two-dimensional plane, and recalculate the overall center of gravity coordinates (X). c1 ,Y c1 The adjustment is performed on the following parameters: D1 < D0 and D1 ≤ T; if D1 < D0 and D1 ≤ T, the adjustment result is retained; if D1 ≥ D0, the original position is restored and other adjacent equipment is selected for repeated exchange, with a maximum of 5 sets of adjacent equipment to be tried; termination condition: D ≤ T after exchange or the number of exchanges reaches 5, the adjustment is stopped; users can fine-tune the number of exchange groups (3-8 groups) through the interface; among them, the exchange of adjacent equipment should avoid the assembly area of ​​the complete set of equipment. Specifically, if the adjustment range includes the complete set of equipment, the area should be marked as an unadjustable buffer zone, and the exchange operation is only performed outside the buffer zone to ensure the assembly integrity of the complete set of equipment; Step 3.3.3: If the initial algorithm uses the annealing algorithm for initial layout, call the position swap + orientation rotation hybrid algorithm from the algorithm library for position swap; specifically, select 3 groups of adjacent equipment within the adjustment range and swap them sequentially, calculate the offset D2 after each swap, and retain the result with the smallest D2; orientation rotation: if D is still greater than T after the swap, select 1-2 movable equipment within the adjustment range and rotate them 90° around an axis perpendicular to the two-dimensional plane (only rotations in multiples of 90° are allowed to avoid damage to the equipment's protective structure), and recalculate the offset D3; use the Metropolis criterion to accept the better solution (if D3 < D0, retain it), and try rotating a maximum of 3 pieces of equipment; termination condition: if D ≤ T after adjustment or the cumulative number of adjustments reaches 6 (3 swaps + 3 rotations), stop the adjustment; the user can fine-tune the number of rotations (2-5 times). Step 3.3.4: If the initial algorithm uses a genetic algorithm for initial layout, call the local rearrangement optimization algorithm in the algorithm library to rearrange the selection of objects; specifically, within the adjustment range, prioritize the selection of movable equipment with a weight ≥ 5kg (heavy items have a more significant impact on the center of gravity), and select 3-5 items; the rearrangement strategy is: reorder according to the balanced weight distribution, specifically, place the heaviest items in the edge area of ​​the adjustment range, medium-weight items in the middle area, and lightest items in the other side area to disperse the local weight concentration; effect verification: calculate the offset D4 after rearrangement. If D4 ≤ T, retain the result; if D4 > T, readjust the rearrangement order, and try a maximum of 3 rearrangements; termination condition: stop the adjustment when D ≤ T after adjustment or the number of rearrangements reaches 3; the user can fine-tune the number of heavy items selected (2-6 items); among them, the local rearrangement optimization algorithm needs to be combined with the equipment weight distribution heat map to identify the weight concentration area within the adjustment range through the heat map, and prioritize the transfer of heavy items from the concentrated area to the weight sparse area to further reduce the risk of center of gravity shift; Step 3.3.5: Global adjustment termination condition: If D ≤ T after the above adjustment, or the cumulative number of adjustments reaches 8 (5 exchanges for small scale, 3 exchanges + 3 rotations for medium scale, 2 rearrangements + 3 exchanges + 3 rotations for large scale), stop the adjustment; if D is still > T after 8 times, transfer one non-complete movable equipment within the adjustment range to another two-dimensional loading carrier of the same specification, and repeat step 2 to ensure that the final solution meets the center of gravity requirements.

[0015] Furthermore, in step 4.2, the scheme includes equipment positioning information, center of gravity optimization results, equipment maintenance equipment protection scheme, and adjustment log; the equipment positioning information includes placement coordinates, geometric center coordinates (x...). i ,y i The centroid optimization results include the overall centroid coordinates (X...). c ,Y cThe equipment maintenance material protection scheme includes fixation suggestions for different protection levels, such as using 5mm thick silicone buffer pads for precision-grade equipment, using ratchet straps for heavy-duty equipment, and using elastic straps for conventional equipment; the adjustment log includes mode type, target algorithm, parameter fine-tuning items, and calculation time, which facilitates maintenance scenario traceability and algorithm optimization iteration.

[0016] Furthermore, in step 4.2, the scheme also includes equipment maintenance material identification information, which includes the material code, set number, and protection level identification of the material, so as to facilitate rapid identification and allocation of the material.

[0017] Compared with existing technologies, the two-dimensional packing optimization method for maintenance equipment in this invention, which takes into account the balance of the center of gravity, decouples the initial algorithm from the center of gravity optimization, avoiding the increase in complexity caused by multiple constraint coupling and improving computational efficiency. It can balance the stability of the center of gravity and the compatibility of constraints, and local adjustments do not change the packing contents, improving space utilization, ensuring the integrity of complete sets of equipment and the accuracy of the position of immovable equipment, and reducing the damage rate of precision equipment during transportation. It has strong scene adaptability, with differentiated algorithms designed for small, medium and large-scale scenarios, a center of gravity adjustment success rate of ≥95%, and can adapt to different specifications of carriers (drawers, trays) and different protection levels of equipment, covering more than 80% of two-dimensional packing scenarios for equipment maintenance equipment. At the same time, it complies with the basic array allocation, complete set supply and protection level adaptation requirements in GJB10882-2023, and the solution can be directly implemented, with high compliance of equipment maintenance equipment. In addition, through a standardized architecture and parameter fine-tuning interface, it realizes the flexibility of algorithm calling and scene adaptability, which not only meets the needs of rapid automatic decision-making in wartime, but also supports users to optimize algorithm parameters based on practical experience, improving the practicality and operability of two-dimensional packing. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the workflow of the present invention. Detailed Implementation

[0019] like Figure 1 The two-dimensional packing optimization method for maintenance equipment that takes into account the center of gravity balance, as shown, includes the following steps: Step 1: Input the scene data of equipment maintenance materials and initialize the algorithm library to generate an initial two-dimensional packing scheme without center of gravity constraints. Without considering the center of gravity, select the optimal algorithm for different equipment scales to quickly generate an initial layout that meets the three major constraints of space utilization, completeness, and fixation of immovable equipment, laying the foundation for subsequent center of gravity optimization. Step 1.1: Basic Data Acquisition and Preprocessing. Collect the core parameters of the equipment and repair materials to be packed and the specifications of the target loading carrier. The core parameters include the equipment's planar dimensions (length L, mm) and width W, weight G, protection level P, set identification (marking whether it is an inseparable set of equipment in the maintenance equipment inventory list), and mobility attributes (movable / immovable, marking whether it is immovable equipment with a fixed base, such as a vehicle-mounted motor); wherein, the protection level P is divided into precision level, conventional level, and heavy-duty level according to GJB10882-2023; The target loading carrier is a dedicated two-dimensional storage unit for equipment, a drawer-type storage box, or a standard maintenance tray, and its specifications include a planar length L. p (Unit: mm), Plane width W p (Unit: mm), Rated load capacity (G) p (Unit: kg) and preset coordinates of fixed equipment (retrieved from the fixed layout database of equipment maintenance materials); Step 1.2: Data preprocessing, Equipment whose weight exceeds 15% of the rated load capacity of the target loading carrier is removed to avoid local overload damage to the carrier; equipment marked as "yes" is pre-grouped, such as an engine repair kit containing 5 pieces, and marked as the same group to ensure that the equipment in the same group is in the same two-dimensional loading plane and is not split; equipment with the movement attribute of being immovable is locked according to preset coordinates (called from the fixed layout database of equipment maintenance materials) and does not participate in subsequent sorting. Step 1.3: Algorithm library initialization. Step 1.3.1: Load the algorithm library architecture. The algorithm library adopts a four-layer architecture: data access layer, algorithm core layer, interface service layer, and application adaptation layer. Among them, the algorithm core layer encapsulates three major modules: greedy algorithm, genetic algorithm, and annealing algorithm. Each module is deployed independently and communicates through standardized interfaces. The interaction logic of the four-layer architecture of the algorithm library is as follows: the data access layer cleans the equipment / carrier data; the interface service layer receives the call mode and parameters; the algorithm core layer calls the corresponding module for calculation; and the application adaptation layer outputs the initial layout. Each layer communicates through RESTful API with a latency of ≤100ms. Specifically, the algorithm library adopts a four-layer architecture plus three core modules. The four layers, from bottom to top, are: data access layer, algorithm core layer, interface service layer, and application adaptation layer. The three core modules correspond to the independent encapsulation of three algorithms. The modules communicate and collaborate with each other through the interface service layer. The overall architecture is as follows: Data access layer: responsible for receiving basic data (equipment dimensions, weight, constraints, container parameters, etc.) from the business system, performing data cleaning and standardization (such as unit unification and outlier filtering), and outputting structured data for algorithm calls; The core algorithm layer encapsulates three main modules: greedy algorithm (including sorting and layout sub-modules), genetic algorithm (including encoding and evolution sub-modules), and annealing algorithm (including temperature control and Metropolis criterion sub-modules). Each module contains algorithm logic, parameter configuration, and result processing sub-modules, enabling independent computation and parameter adjustment of the algorithm. Interface Service Layer: Provides standardized API interfaces, including algorithm selection interface (automatic selection / user specified), parameter configuration interface, and calculation result return interface, to decouple the business system from the algorithm library; Application Adaptation Layer: For 2D packing scenarios, a dedicated adaptation module is provided to adapt the output format of each algorithm module, uniformly convert it into a standard structure of equipment coordinates + space utilization, integrate scenario-based constraint rules, and achieve accurate matching between the algorithm and the scenario; Step 1.3.2: Configure dual-mode call permissions. The algorithm library supports automatic selection and user-specified dual modes. Users configure the call mode through the API interface (such as HTTP request interface) of the interface service layer. The interface parameters include mode identifier (AUTO / USER), target algorithm (GREEDY / GA / SA) and parameter fine-tuning items. Step 2: Generate the initial 2D bin packing scheme without centroid constraints. Step 2.1: Determine the algorithm call mode. Step 2.1.1: If the user-configured mode is set to Automatic Selection (AUTO), the algorithm library automatically matches the algorithm based on the number of equipment N: for N≤50 pieces, the greedy algorithm module is called; for 50<N≤100 pieces, the annealing algorithm module is called; for N>100 pieces, the genetic algorithm module is called. Specifically, in Automatic Selection mode, the algorithm library has built-in scale determination logic. It queries the number of equipment N through SQL and automatically matches the algorithm (e.g., the greedy algorithm is used when N=30 pieces), without user intervention, which is suitable for wartime emergency scenarios. Step 2.1.2: If the user configuration mode is set to User-Specified (USER), the algorithm library calls the corresponding module based on the target algorithm parameters. If the user-specified algorithm does not match the equipment scale (e.g., specifying a greedy algorithm for N=120 pieces), the interface service layer returns a "Scale mismatch" prompt and recommends a suitable algorithm. The user confirms and the call is executed. Specifically, in User-Specified mode, the user selects the target algorithm through the system's visual interface or API interface. For example, for 120 pieces of heavy equipment, the user can specify a genetic algorithm and adjust the population size from 80 to 90 to improve the global optimization effect. If the specified algorithm conflicts with the scale (e.g., specifying a greedy algorithm for N=150 pieces), the interface returns "Scale mismatch, recommend genetic algorithm," and the user confirms and the call is executed. Step 2.2: Algorithm Configuration and Execution Step 2.2.1: Automatic mode selection; the algorithm library executes the default configurations of each module. Scenes with N≤50 pieces of equipment are categorized as small-scale scenes. A greedy algorithm is used, with sorting strategy based on descending plane area (L×W) (weight 0.7) + descending weight (weight 0.3). The layout algorithm is based on the lowest horizontal line + boundary-fitting placement. Specifically, with the lower left corner of the two-dimensional carrier plane as the origin (0,0), the height of the lowest horizontal line in the plane is dynamically maintained (initially 0). Equipment is placed along the lowest horizontal line to the left, fitting to the edge of the carrier or existing equipment. If there is no space, it moves vertically upwards to the new lowest horizontal line. The boundary-fitting in the greedy algorithm is as follows: when placing equipment, priority is given to fitting to the long or short edge of the carrier. If there is no space at the edge, it fits to the edge of existing equipment. A 2mm gap is reserved between equipment for placing cushioning material. The gap is not included in the space utilization calculation. Scenes with 50 < number of equipment N ≤ 100 are categorized as medium-sized scenes. The annealing algorithm is used with the following parameters: initial temperature T0 = 1000 (ensuring the initial search range covers the main layout possibilities), temperature decay coefficient α = 0.95 (balancing search breadth and convergence speed), iteration steps per temperature = 60 (ensuring sufficient search at a single temperature), and termination temperature T_end = 1e-3 (ensuring the algorithm converges to a stable solution). The algorithm aims to maximize space utilization, accepting better solutions through the Metropolis criterion to avoid getting trapped in local optima. Scenes with N > 100 pieces of equipment are categorized as large-scale scenes. A genetic algorithm is used with the following parameters: population size 80 (to ensure solution diversity), maximum number of iterations 150 (to balance optimization effect and computation time), crossover probability 0.7 (to generate new layout combinations), and initial mutation probability 0.08 (decreasing by 0.01 to 0.02 every 20 generations to avoid premature convergence). The algorithm encodes the equipment layout as chromosomes with placement coordinates and orientation, using space utilization as the fitness function. Population evolution is achieved through selection (roulette wheel + elite retention), crossover (two-point crossover), and mutation (coordinate fine-tuning + orientation switching). Step 2.2.2: User-specified mode. The user fine-tunes the configuration of the corresponding modules through the interface service layer; including the sorting weights in the greedy algorithm (area 0.5-0.9, weight 0.1-0.5), the initial temperature (800-1200) and decay coefficient (0.9-0.98) in the annealing algorithm, and the population size (50-100) and number of iterations (100-200) in the genetic algorithm; the fine-tuning range is constrained by the parameters of the algorithm core layer (e.g., crossover probability ≤ 0.8); among them, the user's parameter fine-tuning must pass the parameter validity verification of the algorithm core layer: for example, the sum of the sorting weights in the greedy algorithm must be = 1, and the initial temperature in the annealing algorithm must be ≥ 800. If the verification fails, the default parameters are returned to ensure the stability of the algorithm; Step 2.2.3: Perform initial packing, optimizing only the three constraints of space utilization ≥70%, complete sets of equipment not being disassembled, and fixed positions of immovable equipment, without considering the center of gravity factor; output the equipment placement coordinates, space utilization, and grouping records of complete sets of equipment in the initial layout; Step 3: Post-processing optimization of center of gravity. Using an independent post-processing algorithm, the center of gravity shift is corrected without adjusting the number of equipment, splitting up equipment sets, or moving fixed equipment. Different adjustment algorithms are designed for different scale scenarios, specifically consisting of three steps: Step 3.1: Real-time center of gravity calculation for equipment maintenance scenario adaptation, extracting the geometric center coordinates and weight of all equipment in the initial layout, and accurately quantifying the initial center of gravity position; Step 3.1.1: Extraction of geometric center coordinates, the geometric center (x) of the movable equipment. i ,y i = (x-coordinate of placement + L / 2, y-coordinate of placement + W / 2); For immovable equipment, the geometric center is calculated according to the preset fixed coordinates, and the weight is included according to the actual value; if the equipment is irregularly shaped, such as a connector with protrusions, its planar dimensions are calculated based on the minimum circumscribed rectangle, and the thickness of the protective buffer layer must be included in the circumscribed rectangle dimensions: 5mm for precision equipment, 3mm for conventional equipment, and 4mm for heavy-duty equipment, to ensure the accuracy of the center of gravity calculation; and the minimum circumscribed rectangle calculation for irregular equipment is obtained by using a laser scanning device to obtain the three-dimensional contour of the equipment and automatically generate the circumscribed rectangle dimensions, avoiding the deviation in center of gravity calculation caused by manual measurement errors; Step 3.1.2: Calculate the overall center of gravity. Calculate the initial center of gravity coordinates (X) according to formula (1). c0 ,Y c0 ): , (1) Where n is the total number of devices inside the carrier, G i Let x be the weight of the i-th piece of equipment. i y i Let x and y be the geometric center coordinates of the i-th device; Step 3.2: Set the differentiated center of gravity offset threshold based on the protection level. Step 3.2.1: Single-level threshold. Determine the single-level threshold based on the equipment protection level P. The corresponding offset threshold T1=5mm for precision-level equipment is suitable for vibration-sensitive equipment such as optical instruments and radar sensors, meeting the low-loss requirements for wartime transportation. The corresponding threshold T2=15mm for conventional-level equipment is suitable for mechanical bolts, ordinary parts, etc., balancing stability and efficiency. The corresponding threshold T3=10mm for heavy-duty equipment is suitable for heavy equipment such as small gearboxes and metal connectors, avoiding the tilting of the carrier due to the shift of the center of gravity. Step 3.2.2: Multi-level mixed scene threshold. If the carrier contains equipment of multiple protection levels at the same time, the final judgment threshold T is determined according to the principle of taking the minimum value. For example, if the carrier contains both precision-level and conventional-level equipment, T=5mm. Step 3.2.3: Calculate and determine the center of gravity offset. Calculate the initial centroid (X) according to formula (2). c0 ,Y c0 ) and the geometric center of the two-dimensional loading plane (L p / 2,W p / 2) offset D0; , (2) If D0≤T, the initial layout is determined to meet the center of gravity balance requirement, and step 4 is executed directly; if D0>T, the local adjustment in step 3.3 is executed. Step 3.3: Based on the initial algorithm, the adjustment strategy is invoked, and an adaptation algorithm is designed for different scale scenarios to ensure adjustment efficiency and effectiveness; Step 3.3.1: Delineate the adjustment range, dividing the adjustment area according to the direction of the center of gravity offset; if X c0 <L p / 2, determined to be a horizontal left offset, the adjustment range is a rectangular area on the left side of the two-dimensional loading plane that is 3 times the side length of the maximum movable equipment (x∈[0,3×L)). max ],y∈[0,W p ], L max (where X is the maximum length of the movable equipment); if X c0 >L p / 2, determined to be a horizontal right offset, the adjustment range is a rectangular area on the right side of the two-dimensional loading plane that is three times the side length of the maximum movable equipment (x∈[L p -3×L max ,L p ],y∈[0,W p ]); If Y c0 Similarly, for offset, the vertical adjustment range should be divided; the adjustment range should exclude the fixed area of ​​immovable equipment and the pre-grouped area of ​​complete sets of equipment, and only include movable non-complete sets of equipment. Step 3.3.2: Small-scale scene adjustment. The initial layout uses a greedy algorithm, and the adjacent equipment swapping algorithm from the algorithm library is called to perform the swapping operation. Within the adjustment range, two adjacent movable equipment are selected, and their positions in the two-dimensional plane are swapped. The overall center of gravity coordinates (X) are recalculated. c1 ,Y c1 The adjustment result is set as follows: ) and offset D1; if D1 < D0 and D1 ≤ T, retain the adjustment result; if D1 ≥ D0, restore the original position and select other adjacent equipment to repeat the exchange, with a maximum of 5 sets of adjacent equipment to be tried; termination condition: if D ≤ T after the exchange or the number of exchanges reaches 5, stop the adjustment. In small-scale scenarios, the exchange of adjacent equipment should avoid the assembly area of ​​complete sets of equipment. Specifically, if the adjustment range includes complete sets of equipment, the area should be marked as an unadjustable buffer zone, and the exchange operation should only be performed outside the buffer zone to ensure the integrity of the assembly of complete sets of equipment. Step 3.3.3: Medium-scale scene adjustment. The initial algorithm uses the annealing algorithm for initial layout, and then calls the position swap + orientation rotation hybrid algorithm from the algorithm library for position swap. Specifically, within the adjustment range, select 3 groups of adjacent equipment and swap them sequentially, calculating the offset D2 after each swap, and retaining the result with the smallest D2. Orientation rotation: If D is still greater than T after the swap, select 1-2 movable equipment within the adjustment range and rotate them 90° around an axis perpendicular to the 2D carrier plane (only multiples of 90° are allowed to avoid damage to the equipment's protective structure), and recalculate the offset D3. The Metropolis criterion is used to accept the better solution (if D3 < D0, it is retained). Even if D3 does not drop below T after rotation, but D3 < the current minimum value, the solution is still accepted. A maximum of 3 equipment rotations are tried to ensure adjustment flexibility. Termination condition: When D ≤ T after adjustment or the cumulative number of adjustments reaches 6 (3 swaps + 3 rotations), the adjustment stops. Step 3.3.4: Large-scale scene adjustment. The initial algorithm uses a genetic algorithm for initial layout, and then calls the local rearrangement optimization algorithm in the algorithm library to rearrange the selection of objects. Specifically, within the adjustment range, movable equipment weighing ≥5kg is selected first, as heavy items have a more significant impact on the center of gravity, and the number of selected items is 3-5. The rearrangement strategy is to reorder according to the weight distribution. Specifically, the heaviest items are placed in the edge area of ​​the adjustment range, medium-weight items are placed in the middle area, and the lightest items are placed in the other side area to disperse the local weight concentration. Effect verification: After rearrangement, the offset D4 is calculated. If D4≤T, the result is retained; if D4>T, the rearrangement order is readjusted. A maximum of 3 rearrangements are tried to ensure that the center of gravity converges quickly in large-scale scenes. Termination condition: After adjustment, D≤T or the number of rearrangements reaches 3, the adjustment is stopped. Among them, the local rearrangement optimization algorithm for large-scale scenarios needs to be combined with the equipment weight distribution heat map. The heat map identifies the weight concentration area within the adjustment range, and prioritizes the transfer of heavy items from the concentrated area to the weight sparse area to further reduce the risk of center of gravity shift. Step 3.3.5: Global adjustment termination condition: If D ≤ T after the above adjustment, or the cumulative number of adjustments reaches 8 (5 exchanges for small scale, 3 exchanges + 3 rotations for medium scale, 2 rearrangements + 3 exchanges + 3 rotations for large scale), stop the adjustment; if D is still > T after 8 adjustments, transfer one non-complete movable equipment within the adjustment range to another two-dimensional loading carrier of the same specification, and repeat step 2 to ensure that the final solution meets the center of gravity requirements; Step 4: Compliance verification of equipment and maintenance materials and output of standardized solutions. Step 4.1: Secondary verification of multiple constraints to confirm that the adjusted layout meets all equipment maintenance material constraints; Step 4.1.1: Space utilization verification, confirm that the adjusted space utilization η ≥ 70%; if η < 70%, adjust the sorting weight in step 2.2, such as reducing the plane area weight to 0.5 and increasing the weight weight to 0.5, regenerate the initial layout and repeat step 3. Step 4.1.2: Verify the compliance of equipment maintenance materials, confirm that the complete set of materials has not been disassembled, check the grouping records to ensure that the materials in the same group are still on the same carrier; confirm that the position of immovable materials remains unchanged, compare with fixed coordinates to ensure there is no offset; and confirm that the weight of the materials does not exceed the rated load of the carrier. Step 4.2: Output a dedicated packing plan for maintenance equipment; the plan includes equipment positioning information, center of gravity optimization results, equipment maintenance equipment protection plan, and adjustment log; the equipment positioning information includes the x / y coordinates of each piece of equipment and the geometric center coordinates (x, y, y). i ,y i The centroid optimization results include the overall centroid coordinates (X...). c ,Y c The equipment maintenance material protection scheme includes: center of gravity offset D; adjustment algorithm type; and fixing suggestions for different protection levels, such as using 5mm thick silicone cushioning pads for precision-grade materials, using ratchet straps for heavy-duty materials, and using elastic straps for standard-grade materials. The adjustment log includes mode type, target algorithm, parameter fine-tuning items, and calculation time, facilitating maintenance scenario traceability and algorithm optimization iteration. It also includes equipment maintenance material identification information and constraint satisfaction status. The equipment maintenance material identification information includes the material code, set number, and protection level identifier, facilitating rapid identification and allocation of materials. Constraint satisfaction status includes space utilization rate η, completeness of the set of materials, and fixed status of immovable materials.

[0020] Example 1: A two-dimensional box packing task was selected for the drawer model. The application performance of three algorithms was compared in terms of computational efficiency and solution effectiveness. The test results are shown in Table 1. Table 1. Application of two-dimensional packing in drawers

[0021] As shown in Table 1, for small-scale scenarios (≤50 pieces): the greedy algorithm meets the basic requirements. Although its stability is slightly worse, it has a shorter processing time and a smaller difference in operation path length (only 15cm different from the genetic algorithm), making it suitable for packing regular parts. For medium-scale scenarios (50-100 pieces): the annealing algorithm has the highest cost-effectiveness. Its processing time is 40.3% of that of the genetic algorithm, its space utilization is only 3.8% lower, and it reduces the number of drawers by one compared to the greedy algorithm (the cost of a single drawer is about 50 yuan, saving 50 yuan). The operation path is shortened by 32%. For large-scale scenarios (≥100 pieces): the genetic algorithm shows its advantages. It can pack 120 pieces in a single drawer, reducing the number of drawers by one compared to the greedy / annealing algorithm. Its space utilization is 6-15% higher, and the operation path is shortened by 90-110cm, making it suitable for scenarios with high density and high convenience requirements.

[0022] The present invention provides an optimized two-dimensional packing method for maintenance equipment that balances the center of gravity. Through a core design combining post-processing optimization of the center of gravity with a dual-mode algorithm library, it specifically addresses the pain points of existing technologies. Compared to traditional two-dimensional packing methods and general logistics packing technologies, it achieves significant breakthroughs in four dimensions: efficiency, effectiveness, compliance, and scalability, as detailed below: 1. Computational efficiency improved by over 40%, adapting to wartime rapid packing requirements. Multi-constraint decoupling reduces complexity: The center of gravity optimization is separated from the initial bin packing algorithm. The initial algorithm focuses on solving space utilization, completeness and fixed equipment constraints (time is reduced to 60% of the traditional coupled algorithm). The center of gravity post-processing is only adjusted in local areas (time ≤ 1 minute). The total calculation time for a single batch of 100 pieces of equipment is reduced from 20 minutes to 12 minutes, meeting the minute-level response in wartime. The algorithm library features a dual-mode efficiency improvement system: In emergency scenarios (such as Level 1 combat readiness), the automatic mode can complete algorithm matching within 10 seconds (e.g., using a greedy algorithm for N=30 items) without manual intervention; in routine scenarios, the user-specified mode directly calls the optimization parameters (e.g., genetic algorithm population size = 90), avoiding repeated trial and error and further improving efficiency by 25%. 2. The success rate of center of gravity optimization reached 98%, and the wear and tear rate of maintenance equipment was significantly reduced. Differentiated threshold and adjustment strategy adaptation: 5mm / 15mm / 10mm thresholds are set for precision-grade / standard-grade / heavy-grade equipment respectively. Combined with the initial algorithm, a dedicated adjustment submodule is matched (the greedy algorithm uses adjacent swapping, and the genetic algorithm uses local rearrangement). The success rate of centroid optimization is increased from 70% to 98%. Partial adjustments without disrupting compliant layout: The adjustment scope is limited to 3 times the maximum equipment side length, excluding immovable equipment areas and complete equipment areas, with space utilization loss ≤3%, complete equipment integrity rate 100%, immovable equipment position accuracy rate 100%, precision equipment transportation damage rate reduced from 8% to below 0.5%, and conventional equipment displacement rate reduced from 15% to 1%. 3. The algorithm library features dual-mode adaptation for multiple scenarios, significantly enhancing its practicality. Automatic mode handles emergency needs: The algorithm library uses an automatic matching algorithm based on the number of equipment (greedy algorithm for N≤50 pieces, annealing algorithm for 50<N≤100 pieces, and genetic algorithm for N>100 pieces), which is suitable for small-scale emergency allocation and large-scale batch assembly scenarios. No user judgment is required, reducing the operation threshold. User-defined mode incorporates practical experience: It allows users to fine-tune key parameters (such as the sorting weight of the greedy algorithm and the initial temperature of the annealing algorithm). For example, in high-altitude transportation scenarios, users can adjust the initial temperature of the annealing algorithm from 1000 to 1100 to expand the search range to adapt to bumpy environments, improving the center of gravity stability by 15%. Dedicated verification ensures compliance: The interface service layer has built-in GJB10882-2023 standard verification (such as complete sets of equipment not being disassembled, weight ≤ the rated load of the carrier), the compliance rate of the solution is 100%, avoiding wartime support risks caused by violations; 4. The architecture is highly scalable, reducing subsequent maintenance costs by 70%. The four-layer architecture supports flexible expansion: The algorithm library adopts a data access layer - algorithm core layer - interface service layer - application adaptation layer architecture. When adding a new exclusive algorithm (such as an algorithm for segmented packing of ultra-long equipment), only a module needs to be added to the algorithm core layer and the interface needs to be adapted. There is no need to reconstruct the entire process, and the expansion cost is reduced from 30% of the traditional technology to 9%. The entire process log supports traceability: the output solution includes maintenance-specific logs such as algorithm call mode, parameter fine-tuning items, center of gravity adjustment records and compliance verification results, which facilitates post-war review (such as analyzing equipment loss rate under different parameters), provides data support for algorithm iteration, and meets military audit requirements. 5. The project is highly feasible and has low implementation costs. Mature technology stack: The algorithm library is developed based on Java + Spring Boot, the parameter interface adopts RESTful API, and the data storage uses TiDB database. All of these are existing mature technologies that can be quickly implemented by those skilled in the art. Low hardware dependency: No dedicated hardware is required; data collection can be completed with just a conventional volume measuring instrument and a handheld barcode scanner. It is compatible with existing equipment in equipment maintenance warehouses, reducing implementation costs.

[0023] The above embodiments are merely preferred embodiments of the present invention. Therefore, all equivalent changes or modifications made to the structure, features and principles described in the claims of this patent application are included within the scope of this patent application.

Claims

1. A two-dimensional packing optimization method for maintenance equipment that takes into account center of gravity balance, characterized in that, Includes the following steps: Step 1: Input of equipment maintenance material scenario data and initialization of algorithm library. Step 1.1: Collect the core parameters of the equipment to be packed for maintenance and the specifications of the target loading carrier. The core parameters include the equipment's planar dimensions (length and width), weight, protection level, set identification, and mobility attributes. The protection level is classified into precision, conventional, and heavy-duty levels according to GJB10882-2023. The target loading carrier is a dedicated two-dimensional storage unit for the equipment, and its specifications include planar length, planar width, rated load capacity, and preset coordinates for fixing the equipment. Step 1.2: Data preprocessing, removing equipment whose single weight exceeds 15% of the rated load capacity of the target loading carrier; pre-grouping equipment marked as "yes" to ensure that equipment in the same group is in the same two-dimensional loading plane and is not split; locking equipment with the movement attribute of immovable according to preset coordinates and not participating in subsequent sorting. Step 1.3: Algorithm library initialization. Step 1.3.1: Load the algorithm library architecture. The algorithm library adopts a four-layer architecture: data access layer, algorithm core layer, interface service layer, and application adaptation layer. Among them, the algorithm core layer encapsulates three major modules: greedy algorithm, genetic algorithm, and annealing algorithm. Each module is deployed independently and communicates through standardized interfaces. Step 1.3.2: Configure dual-mode call permissions. The algorithm library supports automatic selection and user-specified dual modes. Users configure the call mode through the API interface of the interface service layer. The interface parameters include mode identifier, target algorithm and parameter fine-tuning items. Step 2: Generate the initial 2D bin packing scheme without centroid constraints. Step 2.1: Determine the algorithm call mode. Step 2.1.1: If the user configuration mode is set to automatic selection, the algorithm library automatically matches the algorithm based on the number of equipment N: if N ≤ 50 pieces, the greedy algorithm module is called; if 50 < N ≤ 100 pieces, the annealing algorithm module is called; if N > 100 pieces, the genetic algorithm module is called. Step 2.1.2: If the user-configured mode identifier is specified by the user, the algorithm library calls the corresponding module according to the target algorithm parameters. If the user-specified algorithm does not match the equipment scale, the interface service layer returns a "scale mismatch" prompt and recommends an adapted algorithm. The user confirms and then executes the call. Step 2.2: Algorithm Configuration and Execution Step 2.2.1: Automatic mode selection; the algorithm library executes the default configurations of each module. Among them, the sorting strategy of the greedy algorithm is descending plane area + descending weight, and the layout algorithm is placing the equipment along the lowest horizontal line and the boundary. The annealing algorithm aims to maximize space utilization and accepts better solutions through the Metropolis criterion to avoid getting trapped in local optima. The genetic algorithm encodes the equipment layout as chromosomes with placement coordinates and orientation, uses space utilization as the fitness function, and achieves population evolution through selection, crossover and mutation operations. Step 2.2.2: User-specified mode, where the user fine-tunes the configuration of the corresponding module through the interface service layer; Step 2.2.3: Perform initial packing, optimizing only the three constraints of space utilization ≥70%, complete sets of equipment not being disassembled, and fixed positions of immovable equipment, without considering the center of gravity factor; output the equipment placement coordinates, space utilization, and complete set of equipment grouping records of the initial layout; Step 3: Post-processing optimization of center of gravity. Step 3.1: Real-time center of gravity calculation for equipment maintenance scenarios. Step 3.1.1: Extraction of geometric center coordinates, the geometric center (x) of the movable equipment. i ,y i = (x-coordinate of placement + L / 2, y-coordinate of placement + W / 2); the geometric center of immovable equipment is calculated according to the preset fixed coordinates, and the weight is included according to the actual value; Step 3.1.2: Calculate the initial centroid coordinates (X) according to formula (1). c0 ,Y c0 ): ， （1） Where n is the total number of devices inside the carrier, G i Let x be the weight of the i-th piece of equipment. i y i Let x and y be the geometric center coordinates of the i-th device; Step 3.2: Set the differentiated center of gravity offset threshold based on the protection level. Step 3.2.1: Single-level threshold, determine the single-level threshold according to the equipment protection level P; Step 3.2.2: Multi-level mixed scene threshold. If the carrier contains multiple protection levels of equipment at the same time, the final judgment threshold T is determined according to the principle of taking the minimum value. Step 3.2.3: Calculate and determine the center of gravity offset. Calculate the initial centroid (X) according to formula (2). c0 ,Y c0 ) and the geometric center of the two-dimensional loading plane (L p / 2,W p / 2) offset D0; ， （2） If D0≤T, the initial layout is determined to meet the center of gravity balance requirement, and step 4 is executed directly; if D0>T, the local adjustment in step 3.3 is executed. Step 3.3: Invoke the adjustment strategy based on the initial algorithm. Step 3.3.1: Delineate the adjustment range by dividing the adjustment area according to the direction of the center of gravity offset; Step 3.3.2: If the initial algorithm is a greedy algorithm for initial layout, call the adjacent equipment exchange algorithm in the algorithm library to perform the exchange operation; Step 3.3.3: If the initial algorithm is an annealing algorithm for initial layout, call the position swap + orientation rotation hybrid algorithm in the algorithm library for position swap; Step 3.3.4: If the initial algorithm is a genetic algorithm for initial layout, call the local rearrangement optimization algorithm in the algorithm library to rearrange the object selection; Step 3.3.5: Global adjustment termination condition: If D ≤ T after the above adjustment, or the cumulative number of adjustments reaches 8, stop the adjustment; if D is still > T after 8 adjustments, transfer one piece of non-complete movable equipment within the adjustment range to another two-dimensional loading carrier of the same specification, and repeat step 2. Step 4: Compliance verification of equipment and maintenance materials and output of standardized solutions. Step 4.1: Secondary verification with multiple constraints. Step 4.1.1: Space utilization verification, confirm that the adjusted space utilization η ≥ 70%; if η < 70%, adjust the sorting weight in step 2.2, regenerate the initial layout and repeat step 3; Step 4.1.2: Verify the compliance of equipment maintenance materials, confirming that the complete set of materials has not been disassembled, the position of immovable materials remains unchanged, and the weight of the materials does not exceed the rated load of the carrier; Step 4.2: Output a special packing plan for maintenance equipment.

2. The optimized two-dimensional packing method for maintenance equipment that takes into account center of gravity balance according to claim 1, characterized in that, In step 1.3.1, the interaction logic of the four-layer architecture of the algorithm library is as follows: the data access layer cleans the equipment / carrier data; the interface service layer receives the call mode and parameters; the algorithm core layer calls the corresponding module for calculation; and the application adaptation layer outputs the initial layout. Each layer communicates through RESTful API with a latency of ≤100ms.

3. The optimized two-dimensional packing method for maintenance equipment that takes into account center of gravity balance according to claim 1, characterized in that, In step 2.2.1, under the automatic selection mode, the specific execution method of the algorithm library executing the default configuration of each module is as follows: Scenarios with N≤50 pieces of equipment are categorized as small-scale scenarios. A greedy algorithm is used, with sorting strategies of descending plane area and descending weight. The sorting weights are 70% for plane area and 30% for weight. The layout algorithm is placement along the lowest horizontal line and edge-fitting. Specifically, the origin (0,0) is taken as the lower left corner of the two-dimensional carrier plane. The height of the lowest horizontal line in the plane is dynamically maintained. Equipment is placed along the lowest horizontal line to the left to fit the edge of the carrier or to fit existing equipment. If the equipment cannot fit, it is moved vertically upwards to the new lowest horizontal line. Scenes with 50 < number of equipment N ≤ 100 are categorized as medium-sized scenes. The annealing algorithm is used with the following parameters: initial temperature T0 = 1000, temperature decay coefficient α = 0.95, number of iterations per temperature = 60, and termination temperature T_end = 1e-3. The algorithm aims to maximize space utilization and accepts better solutions through the Metropolis criterion to avoid getting trapped in local optima. Scenes with N > 100 pieces of equipment are categorized as large-scale scenes. A genetic algorithm is used with the following parameters: population size 80, maximum number of iterations 150, crossover probability 0.7, and initial mutation probability 0.

08. The algorithm encodes the equipment layout as chromosomes with placement coordinates and orientation, uses space utilization as the fitness function, and achieves population evolution through selection, crossover, and mutation operations.

4. The optimized two-dimensional packing method for maintenance equipment that takes into account center of gravity balance according to claim 3, characterized in that, In step 2.2.1, the boundary fitting of the greedy algorithm is as follows: when placing the equipment, it should first fit the long or short edge of the carrier. If there is no space at the edge, it should fit the edge of the already placed equipment. A 2mm gap should be reserved between the equipment. The gap is not included in the space utilization calculation.

5. The optimized two-dimensional packing method for maintenance equipment that takes into account center of gravity balance according to claim 1, characterized in that, In step 2.2.2, the user fine-tunes the configuration of the corresponding modules through the interface service layer, including the sorting weight in the greedy algorithm, the initial temperature and decay coefficient in the annealing algorithm, and the population size and number of iterations in the genetic algorithm; the fine-tuning range is constrained by the parameters of the algorithm's core layer.

6. The optimized two-dimensional packing method for maintenance equipment that takes into account center of gravity balance according to claim 1, characterized in that, In step 3.1.1, if the equipment is irregular in shape, its planar dimensions are calculated based on the minimum bounding rectangle, and the thickness of the protective buffer layer must be taken into account in the bounding rectangle dimensions to ensure the accuracy of the center of gravity calculation; and the minimum bounding rectangle of the irregular equipment is calculated by obtaining the three-dimensional contour of the equipment through a laser scanning device and automatically generating the bounding rectangle dimensions.

7. The optimized two-dimensional packing method for maintenance equipment that takes into account center of gravity balance according to claim 1, characterized in that, In step 3.2.1, the offset threshold T1 = 5mm corresponds to precision-grade equipment; the threshold T2 = 15mm corresponds to conventional-grade equipment; and the threshold T3 = 10mm corresponds to heavy-duty equipment.

8. The optimized two-dimensional packing method for maintenance equipment that takes into account center of gravity balance according to claim 1, characterized in that, The specific steps of step 3.3 are as follows: Step 3.3.1: Delineate the adjustment range, dividing the adjustment area according to the direction of the center of gravity offset; if X c0 <L p / 2, determined to be a horizontal left offset, the adjustment range is a rectangular area on the left side of the two-dimensional loading plane, three times the side length of the maximum movable equipment; if X c0 >L p / 2, determined to be a horizontal right offset, the adjustment range is a rectangular area on the right side of the two-dimensional loading plane, three times the side length of the maximum movable equipment; if Y c0 Similarly, for offset, the vertical adjustment range should be divided; the adjustment range should exclude the fixed area of ​​immovable equipment and the pre-grouped area of ​​complete sets of equipment, and only include movable non-complete sets of equipment. Step 3.3.2: If the initial algorithm uses a greedy algorithm for initial layout, call the adjacent equipment swapping algorithm from the algorithm library to perform the swapping operation; select two adjacent movable equipment within the adjustment range, swap their positions in the two-dimensional plane, and recalculate the overall center of gravity coordinates (X). c1 ,Y c1 The adjustment is performed on the following parameters: 1) and 2) offset D1; 3) if D1 < D0 and D1 ≤ T, retain the adjustment result; 4) if D1 ≥ D0, restore the original position and select other adjacent equipment to repeat the exchange, with a maximum of 5 sets of adjacent equipment to be tried; 5) termination condition: D ≤ T after the exchange or the number of exchanges reaches 5, stop the adjustment; 6) the exchange of adjacent equipment must avoid the assembly area of ​​the complete set of equipment. Specifically, if the adjustment range includes the complete set of equipment, the area must be marked as an unadjustable buffer zone, and the exchange operation is only performed outside the buffer zone to ensure the assembly integrity of the complete set of equipment. Step 3.3.3: If the initial algorithm uses the annealing algorithm for initial layout, call the position swap + orientation rotation hybrid algorithm from the algorithm library for position swap; specifically, select 3 groups of adjacent equipment within the adjustment range and swap them sequentially, calculate the offset D2 after each swap, and keep the result with the smallest D2; orientation rotation: if D is still greater than T after the swap, select 1-2 movable equipment within the adjustment range and rotate them 90° around an axis perpendicular to the two-dimensional plane, and recalculate the offset D3; use the Metropolis criterion to accept the better solution, and try rotating a maximum of 3 equipment; termination condition: stop adjusting when D ≤ T after adjustment or the cumulative number of adjustments reaches 6; Step 3.3.4: If the initial algorithm uses a genetic algorithm for initial layout, call the local rearrangement optimization algorithm in the algorithm library to rearrange the selection of objects; specifically, within the adjustment range, prioritize the selection of movable equipment with a weight ≥ 5kg, and select 3-5 pieces; the rearrangement strategy is: reorder according to the weight distribution, specifically, place the heaviest piece in the edge area of ​​the adjustment range, the medium-weight piece in the middle area, and the lightest piece in the other side area, to disperse the local weight concentration; effect verification: calculate the offset D4 after rearrangement. If D4 ≤ T, retain the result; if D4 > T, readjust the rearrangement order, and try a maximum of 3 rearrangements; termination condition: stop the adjustment when D ≤ T after adjustment or the number of rearrangements reaches 3; among them, the local rearrangement optimization algorithm needs to be combined with the equipment weight distribution heat map to identify the weight concentration area within the adjustment range through the heat map, and prioritize the transfer of heavy pieces from the concentrated area to the weight sparse area to further reduce the risk of center of gravity shift; Step 3.3.5: Global adjustment termination condition: If D ≤ T after the above adjustment, or the cumulative number of adjustments reaches 8, stop the adjustment; if D is still > T after 8 adjustments, transfer one piece of non-complete movable equipment within the adjustment range to another two-dimensional loading carrier of the same specification, and repeat step 2.

9. The optimized two-dimensional packing method for maintenance equipment that takes into account center of gravity balance according to claim 1, characterized in that, In step 4.2, the scheme includes equipment positioning information, center of gravity optimization results, equipment maintenance equipment protection scheme, and adjustment log; the equipment positioning information includes placement coordinates, geometric center coordinates (x, y, y). i ,y i The centroid optimization results include the overall centroid coordinates (X...). c ,Y c The equipment maintenance and material protection scheme includes fixed recommendations for different protection levels; the adjustment log includes mode type, target algorithm, parameter fine-tuning items, and calculation time.

10. The optimized two-dimensional packing method for maintenance equipment that takes into account center of gravity balance according to claim 9, characterized in that, In step 4.2, the scheme also includes equipment maintenance material identification information, which includes the material code, set number, and protection level identification of the material.

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