Equipment utilization optimization method based on improved NSGA-III algorithm

Abstract

The invention belongs to the technical field of equipment utilization optimization, and discloses an equipment utilization optimization method based on an improved NSGA-III algorithm, which aims at the maximum equipment in-place rate, the maximum equipment combat readiness reserve reaching rate, the maximum equipment perfectness rate and the minimum equipment maintenance cost. The invention relates to a multi-objective optimization model with the hourly revenue and expenditure balance of a motorcycle as a constraint. According to the characteristics of high dimension and large scale difference of an established model target, an improved NSGA-III algorithm is designed for solving. An algorithm-improved crossover and mutation evolution operation method based on a DNA structure improves the evolution efficiency of the population; the improved adaptive normalization method enhances the diversity of the population and the convergence speed of the algorithm. By taking annual equipment development optimization of a certain unit as an example, an improved NSGA-III algorithm and a traditional NSGA-III algorithm are compared and analyzed, and the feasibility and the high efficiency of the model and the algorithm in solving the problem are verified by experimental results.

Description

Technical Field

[0001] This invention belongs to the field of equipment mobilization optimization technology, and in particular relates to an equipment mobilization optimization method and system based on an improved NSGA-III algorithm. Background Technology

[0002] Armored equipment possesses powerful protective capabilities, firepower advantages, and assault capabilities, making it a primary weapon system in ground warfare. Armored equipment technical management standards determine maintenance time and methods based on vehicle hour consumption, highlighting a close coupling between equipment deployment and maintenance. Studying the patterns of armored equipment deployment and maintenance, and comprehensively optimizing deployment and maintenance plans, can effectively restore the equipment's combat and technical performance, steadily maintain its operational readiness status (including equipment integrity rate, availability rate, and vehicle hour reserve rate), meet the needs of daily combat readiness training and wartime mission deployment, and also provide a reference for strengthening the technical management of other types of equipment, thus being of great significance for improving the overall level of military construction.

[0003] Currently, there is limited research on the correlation and optimization between the deployment and maintenance of armored equipment. NATO forces, represented by the US military, use two sets of equipment for training and combat, without considering the balance and optimization of equipment deployment and maintenance; such research is rare internationally. Domestically, Zhou Yunyan et al. aimed to create a tiered reserve of equipment based on its operational hours and to generate preventative maintenance equipment as early as possible, conducting simulation optimization for the deployment of newly deployed equipment; Mei Guojian et al. studied the deployment of armored equipment with long service lives, establishing a decision-making model between planned decommissioning time and the availability of additional equipment; Lü Huiqiang et al. established evaluation indicators based on the PDCA cycle to assess equipment use and proposed improvement methods; Meng Qingjun et al., combined with in-service equipment assessment work, established an evaluation indicator system to evaluate equipment deployment; Cao Junhai et al. described the equipment deployment process and used the OOPN method. Some studies have constructed object-oriented Petri net models to model and simulate equipment mobilization operations; Li Lingwei et al. categorized equipment into key vehicles, general vehicles, and control vehicles based on motorcycle hour reserves, and conducted simulation studies on equipment mobilization strategies based on preset mobilization sequences; Cai Sainan established an equipment mobilization optimization model based on motorcycle hour revenue and expenditure balance, aiming at balanced equipment repair and scientific resource allocation, and designed the BSO algorithm to solve for mobilization schemes; Li Dongjing et al., based on equipment mobilization and maintenance standards and following the perspective of life cycle management, established a multi-agent model to simulate and evaluate equipment mobilization and maintenance over a longer period. However, these studies still have several shortcomings: the scope of research is not comprehensive enough, with some focusing on newly deployed equipment and others on equipment about to be retired; the research is not in-depth enough, lacking quantitative analysis of the correlation between equipment mobilization and maintenance, and failing to derive mobilization strategies based on equipment motorcycle hour reserves and maintenance intervals; the research is not closely aligned with reality, failing to fully consider many practical needs such as equipment use, combat readiness, and maintenance efficiency, and the assumptions and objectives of the research are too simplistic.

[0004] The NSGA-III algorithm is an effective algorithm for solving high-dimensional multi-objective optimization problems of 3D and above, but it still suffers from poor local search performance. Current improvements to the NSGA-III algorithm mainly focus on the following aspects: optimizing reference vectors (Asafuddoula et al. used an adaptive reinforcement learning algorithm to add and remove positive reference vectors, guiding the population towards the Pareto front, improving the evolution speed and population diversity); optimizing encoding (Chai et al. used a highly scalable encoding method to maximize the approximation of the optimal value in the first generation, improving the optimization capability); and optimizing the evolutionary strategy (Zhang et al. used a second-order difference strategy and a stochastic strategy to improve the individuals in the next generation population, and simulations verified the convergence and diversity of the improved algorithm). However, these improvements to the NSGA-III algorithm are all general theoretical methods and cannot fully adapt to equipment mobilization optimization problems.

[0005] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0006] Existing research is not comprehensive enough, with some focusing on newly deployed equipment and others on equipment about to be retired; the research is not in-depth enough, lacking quantitative analysis of the relationship between equipment deployment and maintenance, and failing to derive deployment strategies based on simulation calculations of equipment motorcycle hour reserves and maintenance intervals; the research is not closely aligned with reality, failing to fully consider many practical needs such as equipment use, combat readiness, and maintenance efficiency, and the research assumptions and objectives are too simplistic. Summary of the Invention

[0007] To address the problems existing in the prior art, this invention provides an equipment deployment optimization method based on an improved NSGA-III algorithm.

[0008] This invention is implemented as follows: an equipment mobilization optimization method based on an improved NSGA-III algorithm includes:

[0009] Step 1: Establish a multi-objective optimization model with the objectives of maximizing equipment availability, maximizing equipment combat readiness reserve compliance rate, maximizing equipment integrity rate, and minimizing equipment maintenance costs, and with motorcycle hourly revenue and expenditure balance as the constraint.

[0010] Step 2: Based on the characteristics of the established model target being high-dimensional and having large scale differences, an improved NSGA-III algorithm is designed to solve the problem.

[0011] Furthermore, the motorcycle's hourly operating income and expenditure are balanced:

[0012] The equipment maintenance and production hours for engine motorcycles are:

[0013]

[0014] Among them, T p The estimated production hours of motorcycles for the annual equipment are as follows. This represents the projected number of the i-th piece of equipment to return to base after mid-year maintenance. The rated service life of the i-th piece of equipment engine expected to return to base after the annual mid-term overhaul. This represents the number of the i-th piece of equipment expected to return to base after the annual major overhaul. The rated service life of the i-th equipment engine is expected to return to camp after the annual overhaul, and n is the number of equipment.

[0015] When formulating equipment deployment plans, the required number of motorcycle hours for maintenance and production at each equipment level must be considered to ensure a balance between revenue and expenditure per motorcycle hour.

[0016] |T p -Q|≤v (2)

[0017] Where Q represents the annual motorcycle hours consumed by the equipment, and v is the allowable deviation constant.

[0018] Furthermore, the multi-objective optimization model:

[0019] 1) Optimization Object

[0020] The unit has n armored vehicles, and each vehicle has R hours of reserve power. i The engine's motorcycle hour reserve is r i The major overhaul interval is 2 hours, and the intermediate overhaul interval is 1 hour; if r i =R i If the equipment's most recent preventative maintenance was a mid-level overhaul; if r i +l=R i If the equipment's most recent preventative maintenance was a major overhaul;

[0021] The annual training equipment usage requirement is Q engine-motorcycle hours, and the number of training months is m. Establish an equipment deployment time allocation matrix:

[0022]

[0023] d ij The number of engine motorcycle hours consumed in the j-th month is allocated to the i-th equipment, d ir ≤128 (calculated based on a maximum of 4 weeks of training per month, 4 days per week, 8 hours per day), d ij =0 indicates no allocation or use; the equipment deployment plan should meet the equipment usage needs of the troops, that is:

[0024]

[0025] This indicates that the number of motor hours consumed by the i-th piece of equipment cannot exceed its initial engine motor hour reserve, d. ij =0, b ij =0(r i =0), indicating that the i-th equipped engine motorcycle will be sent for repair after its hourly reserve is exhausted and will not be allocated for use again in the same year;

[0026] 2) Optimization Objective

[0027] 2.1) Equipment integrity rate

[0028] Using engine and vehicle motorcycle hour reserves and vehicle motorcycle hour consumption as indicators, and taking into account equipment failure patterns, calculate the availability rate of the i-th piece of equipment in month j:

[0029]

[0030] Equipment availability depends on the hourly consumption (r′) of the equipment's engine.ij Motorcycle hourly consumption R′ ij The changes follow a Weibull distribution; based on actual equipment failure data of the troops, α, β, δ, θ, η are fitted to obtain... Parameters such as γ; when the equipment engine and vehicle body reach the major and medium repair standards, preventive maintenance is carried out on the equipment, and the availability rate during the maintenance period is 0.

[0031] The unit's overall annual equipment readiness rate is the average of the monthly equipment readiness rates:

[0032]

[0033] 2.2) Equipment availability rate

[0034] After the reserve engine hours are depleted, a mid-term overhaul is performed; after the reserve chassis hours are depleted, a major overhaul is performed. During the mid-term overhaul period... m Overhaul period t h Internal equipment is not in place; initialize the equipment in-place matrix:

[0035]

[0036] b ij For the i-th piece of equipment in month j, 1 indicates in-service; 0 indicates out-of-service. Calculate the reserve consumption of engine motorcycle hours and chassis motorcycle hours. If the corresponding standards are reached, send the equipment for major or intermediate repair and adjust the equipment in-service matrix.

[0037] b ij =0(r ik =0,k <j≤k+t m (8)

[0038] b ij =0(R) is =0,s <j≤s+t h (9)

[0039] Equation (8) indicates that the equipment engine is sent for intermediate repair after its motorcycle hour reserve is depleted, and the equipment is not in place during the intermediate repair period; Equation (9) indicates that the equipment body is sent for major repair after its motorcycle hour reserve is depleted, and the equipment is not in place during the major repair period; the number of equipment in the camp is the total number of equipment minus the number of equipment sent for repair; the equipment availability rate of the troops is calculated by the average of the ratio of the number of equipment in place to the number of organized equipment in each month:

[0040]

[0041] Among them, E aTo allocate equipment quantity; similar to equipment readiness rate, maintaining a high equipment availability rate is an important foundation for troops to be in a state of high alert at all times, improve emergency response capabilities, and effectively perform diversified military tasks.

[0042] 2.3) Compliance rate of combat readiness reserves

[0043] 2.4) Repair costs.

[0044] Furthermore, the compliance rate of the aforementioned combat readiness reserves:

[0045] In order to adapt to various complex and arduous combat missions, the military must ensure the continuous combat capability of its equipment. This requires the engine motor hours reserve of the equipment to meet certain standards, which is measured by the ratio of the engine motor hours reserve to the rated service life of the engine after major and medium overhauls.

[0046]

[0047] Where u is a standard constant; the equipment combat readiness reserve that satisfies equation (11) meets the standard, and the equipment combat readiness reserve compliance rate of the entire force is measured by the average ratio of the number of equipment that meets the combat readiness reserve standard to the number of organized equipment in each month:

[0048]

[0049] E c To ensure the monthly combat readiness reserve meets the required equipment quantity, E a To optimize equipment usage, it is crucial to allocate equipment quantities, rationally distribute equipment usage hours, scientifically maintain equipment production hours, and improve the equipment's combat readiness reserve compliance rate.

[0050] Furthermore, the repair costs are as follows:

[0051] The cost of restorative repair is calculated using average values; the costs of restorative repair C1, preventative repair C2, and total repair cost C are calculated as follows:

[0052]

[0053] C2=n m ·e m +n h ·e h (14)

[0054] C = C1 + C2 (15)

[0055] Where, n m n h These represent the number of equipment undergoing medium and major repairs annually, e r e m e hThese are the average cost of restorative repair, the standard cost of intermediate repair, and the standard cost of major repair for a single piece of equipment; when planning the use of equipment, efforts should be made to reduce equipment maintenance costs;

[0056] In summary, the optimization objective for the planned equipment use is:

[0057] max:A,O,S(16)

[0058] min:C(17)

[0059] The constraints are:

[0060]

[0061] d ij =0, b ij =0 (r i =0) (19)

[0062] Equation (18) indicates that the number of motorcycle hours consumed by the i-th piece of equipment cannot exceed its motorcycle hour reserve. Equation (19) indicates that the i-th piece of equipment will be sent for repair after its reserve motorcycle hours are used up. The equipment will not be in place during the repair period, and will not be allocated for use again in the same year after the repair is completed and the equipment is returned to the camp.

[0063] Furthermore, the improved NSGA-III algorithm:

[0064] Step 1: Set the basic parameters of the algorithm, including population size Npop, crossover probability Pc, mutation probability Pm, number of algorithm loops MaxIt, and number of reference points p.

[0065] Step 2: Initialize the population. Based on the equipment training time requirements, equipment quantity, equipment motorcycle hour reserves, monthly motorcycle hour allocation limit, etc., randomly generate a chromosome population of Npop.

[0066] Step 3: Calculate the target function values ​​f1, f2, f3, f4 for each chromosome according to equations (6), (10), (12), and (15);

[0067] Step 4: Based on Pareto dominance, perform a rapid non-dominated sort of chromosomes, calculate the number of dominated chromosomes and the set of dominant chromosomes for each chromosome, and determine the Pareto rank R for each chromosome. i ;

[0068] Step 5: Select the top-ranked chromosomes to enter the parent population; the number of top-ranked chromosomes... And the number of chromosomes in the first l+1 level

[0069] Step 5: Generate reference points;

[0070] Step 6: Using the method of calculating the distance between the hyperplane and the coordinate axes of the multidimensional solution, for the (l+1)th level F l+1 Normalize the solutions for each chromosome;

[0071] Step 7: Establish the connection between level 1+1 chromosomes and the reference point, and select chromosomes from them using the niche preservation method. One chromosome enters the parent population;

[0072] Step 8: [To be continued] Crossover and mutation operations are performed on the parent population to obtain the offspring population. The parent population and the offspring population are then merged to generate a new generation population.

[0073] Step 9: Repeat steps 3-8 until the iteration ends, and the Pareto level R in the population is determined. i The set of chromosomes with a value of 1 is the optimal solution set.

[0074] Another objective of this invention is to provide an equipment mobilization optimization system based on an improved NSGA-III algorithm, comprising:

[0075] The model building module is used to build a multi-objective optimization model with the objectives of maximizing equipment availability, maximizing equipment combat readiness reserve compliance rate, maximizing equipment integrity rate, and minimizing equipment maintenance costs, and with motorcycle hour revenue and expenditure balance as the constraint.

[0076] The solver module is used to design an improved NSGA-III algorithm to solve the problem, taking into account the characteristics of the established model's high-dimensional target and large scale differences.

[0077] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the equipment mobilization optimization method based on the improved NSGA-III algorithm.

[0078] Another object of the present invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the steps of the equipment mobilization optimization method based on the improved NSGA-III algorithm.

[0079] Another objective of this invention is to provide an information data processing terminal for implementing the equipment mobilization optimization system based on the improved NSGA-III algorithm.

[0080] Based on the above technical solutions and the technical problems solved, please analyze the advantages and positive effects of the technical solution to be protected by this invention from the following aspects:

[0081] First, addressing the technical problems existing in the prior art and the difficulty in solving them, this paper closely analyzes, in conjunction with the technical solution to be protected by this invention and the results and data obtained during the research and development process, how the technical solution of this invention solves the technical problems, and the inventive technical effects brought about by solving these problems. The specific description is as follows:

[0082] This invention takes equipment deployment schemes as the research object, establishes an equipment deployment optimization model based on preventive maintenance theory and the actual situation of the troops, proposes an improved NSGA-III algorithm adapted to the model for solving the problem, and analyzes the simulation results to obtain equipment deployment optimization strategies with different preferences. The main innovations of this invention are as follows: (1) Mathematical descriptions are made of equipment motorcycle hour reserves and consumption, in-situ status, failure occurrence, and maintenance costs. A multi-objective optimization model is established with the objectives of maximizing equipment in-situ rate, maximizing equipment combat readiness reserve compliance rate, maximizing equipment integrity rate, and minimizing equipment maintenance costs, and with motorcycle hour revenue and expenditure balance as a constraint; (2) Based on the characteristics of the established model objectives being high-dimensional and having large scale differences, a population individual crossover and mutation evolution operation method based on DNA structure is proposed on the basis of the traditional NSGA-III algorithm. An adaptive normalization method is designed to normalize the objective function, further enhancing the diversity of the population and the convergence speed of the algorithm; (3) The advantages of the improved NSGA-III algorithm compared with the traditional NSGA-III algorithm are verified through case simulation. Based on the simulation calculation results, through trend analysis and extreme value analysis of each objective function of the equipment mobilization scheme, four equipment mobilization optimization strategies with different preferences are derived.

[0083] This invention proposes an equipment deployment optimization method based on preventive maintenance theory. It establishes a multi-objective optimization model with the objectives of maximizing equipment availability, maximizing equipment readiness and reserve compliance, maximizing equipment integrity, and minimizing equipment maintenance costs, constrained by a balance of revenue and expenditure per motor vehicle hour. Based on the high-dimensionality and large scale differences of the established model's objectives, an improved NSGA-III algorithm is designed for solving the problem. The improved algorithm employs a DNA-structure-based crossover and mutation evolution method, increasing the population's evolutionary efficiency; the improved adaptive normalization method enhances population diversity and algorithm convergence speed. Taking the annual equipment deployment optimization of a certain unit as an example, the improved NSGA-III algorithm and the traditional NSGA-III algorithm are compared and analyzed. Experimental results verify the feasibility and efficiency of the proposed model and algorithm in solving this problem. Through the analysis of the objective function value trends of a large number of equipment deployment schemes and detailed index analysis of schemes that achieve extreme values ​​for single-objective functions, different equipment deployment optimization schemes with different preferences are proposed, which can provide a reference for optimizing equipment use in the armed forces.

[0084] This invention, based on the analysis of the relationship between equipment deployment and maintenance, and combined with the needs of troop combat readiness training, comprehensively considers preventive and restorative maintenance types, and establishes an equipment deployment optimization model with objectives of equipment availability rate, combat readiness reserve compliance rate, maintenance cost, and operational readiness rate. The improved NSGA-III algorithm performs excellently in high-dimensional multi-objective optimization problems, exhibiting superior convergence and optimization performance compared to the traditional NSGA-III algorithm, providing multiple balanced solutions for equipment deployment. Based on simulation results, optimization strategies for equipment deployment with different preferences are proposed. The research results have significant practical implications for guiding the military in the scientific and rational deployment of equipment, improving equipment deployment efficiency and maintenance efficiency. Future research will focus on further in-depth studies of preventive maintenance influencing factors and multi-year analysis of equipment deployment.

[0085] Secondly, as supplementary evidence of the inventive step of the claims of this invention, it is also reflected in the following important aspects:

[0086] (1) The technical solution of this invention fills the technical gap in the domestic and foreign industry: Based on the analysis of the relationship between equipment deployment and maintenance, this paper combines the needs of the troops' combat readiness training, comprehensively considers the types of preventive maintenance and repair maintenance, and establishes an equipment deployment optimization model with the equipment availability rate, combat readiness reserve compliance rate, maintenance cost and integrity rate as the objectives.

[0087] (2) Does the technical solution of this invention overcome technical bias? In the process of population evolution, the traditional NSGA-III algorithm performs crossover and mutation operations on a single code unit, which will destroy the correlation between codes within the code group and generate a large number of unreasonable equipment deployment schemes. In view of the characteristics of close connection within the model code group and relative independence between groups, inspired by the structure of human chromosomes, DNA, and genes, a method for individual initial coding and crossover and mutation evolution operations based on DNA structure is proposed to improve the evolutionary efficiency of the population. Attached Figure Description

[0088] Figure 1 This is a flowchart of the equipment mobilization optimization method based on the improved NSGA-III algorithm provided in the embodiments of the present invention.

[0089] Figure 2 This is a block diagram of the equipment mobilization optimization system based on the improved NSGA-III algorithm provided in an embodiment of the present invention.

[0090] Figure 3 This is an algorithm flowchart provided in an embodiment of the present invention.

[0091] Figure 4 This is a diagram of the chromosome initial coding method provided in an embodiment of the present invention.

[0092] Figure 5 This is a diagram of the cross-operation method provided in an embodiment of the present invention.

[0093] Figure 6 This is a diagram of the mutation operation method provided in an embodiment of the present invention.

[0094] Figure 7 This is a graph showing the results of calculating the in-situ rate and the combat readiness reserve compliance rate after 50 iterations of the two algorithms provided in this embodiment of the invention.

[0095] Figure 8 The graph shows the results of calculating the integrity rate and maintenance cost after 50 iterations of the two algorithms provided in this embodiment of the invention.

[0096] Figure 9 This is a complete picture of the Pareto front calculation using two algorithms with 500 iterations provided in the embodiments of the present invention.

[0097] Figure 10 The graph shows the results of calculating the in-situ rate and the combat readiness reserve compliance rate using two algorithms iterated 500 times according to the embodiments of the present invention.

[0098] Figure 11 The graph shows the results of calculating the integrity rate and maintenance cost using two algorithms iterated 500 times according to embodiments of the present invention.

[0099] Figure 12 This is a graph showing the change of the objective function with the number of equipment deployed, provided in an embodiment of the present invention.

[0100] Figure 13 This is a graph showing the change in the objective function as a function of the reserve rate of the operating equipment's motor hours, provided in an embodiment of the present invention.

[0101] Figure 14 This is a graph showing the change of the objective function as a function of the ratio of equipment that has undergone intermediate repair and equipment that has not.

[0102] Figure 15 This is a graph showing the change of the objective function as a function of the cross-year equipment maintenance period ratio, provided in an embodiment of the present invention.

[0103] Figure 16 This is a graph showing the number of preventive maintenance starts each month when the in-situ rate reaches its extreme value, provided by an embodiment of the present invention.

[0104] Figure 17 This is a graph showing the number of equipment deployed each month when the in-service rate reaches its extreme value, provided by an embodiment of the present invention.

[0105] Figure 18 This is a graph showing the number of motorcycle hours used in each month when the in-situ rate reaches an extreme value, as provided in an embodiment of the present invention.

[0106] Figure 19 This is a graph showing the number of preventive maintenance operations started each month when the combat readiness reserve compliance rate reaches its extreme value, as provided in this embodiment of the invention.

[0107] Figure 20 This is a chart showing the number of equipment deployed each month when the combat readiness reserve compliance rate reaches its extreme value, as provided in this embodiment of the invention.

[0108] Figure 21 This is a graph showing the number of motorcycle hours used in each month when the combat readiness reserve compliance rate reaches its extreme value, as provided in this embodiment of the invention.

[0109] Figure 22 This is a graph showing the number of equipment used each month when maintenance costs reach their extreme values, provided by an embodiment of the present invention.

[0110] Figure 23 This is a graph showing the number of motorcycle hours used in each month when the maintenance cost reaches its extreme value, as provided in an embodiment of the present invention. Detailed Implementation

[0111] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0112] like Figure 1 As shown, an equipment mobilization optimization method based on an improved NSGA-III algorithm provided by an embodiment of the present invention includes the following steps:

[0113] S101. Establish a multi-objective optimization model with the objectives of maximizing equipment availability, maximizing equipment combat readiness reserve compliance rate, maximizing equipment integrity rate, and minimizing equipment maintenance costs, and with motorcycle hour revenue and expenditure balance as the constraint.

[0114] S102. Based on the characteristics of the established model target being high-dimensional and having large scale differences, an improved NSGA-III algorithm is designed for solving the problem.

[0115] like Figure 2 As shown, an equipment mobilization optimization system based on an improved NSGA-III algorithm provided in this embodiment of the invention includes:

[0116] The model building module is used to build a multi-objective optimization model with the objectives of maximizing equipment availability, maximizing equipment combat readiness reserve compliance rate, maximizing equipment integrity rate, and minimizing equipment maintenance costs, and with motorcycle hour revenue and expenditure balance as the constraint.

[0117] The solver module is used to design an improved NSGA-III algorithm to solve the problem, taking into account the characteristics of the established model's high-dimensional target and large scale differences.

[0118] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the equipment mobilization optimization method based on the improved NSGA-III algorithm.

[0119] Another object of the present invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the steps of the equipment mobilization optimization method based on the improved NSGA-III algorithm.

[0120] Another objective of this invention is to provide an information data processing terminal for implementing the equipment mobilization optimization system based on the improved NSGA-III algorithm.

[0121] Specific implementation of the present invention:

[0122] 1. Problem Description

[0123] Equipment deployment refers to the management of equipment use. Guided by the goal of meeting the annual training requirements of the armed forces, and based on the technical condition information such as the remaining motorcycle hours of the equipment, and following certain regulations, each deployment task is assigned to a single piece of equipment. The expected service life of the deployed equipment is then used to predict its technical condition at the end of its service life and the types of preventative maintenance required. On the one hand, developing equipment deployment plans ensures the availability of usable equipment for completing combat training missions. On the other hand, equipment deployment determines the motorcycle hours consumed and component wear and tear. Based on maintenance interval standards and equipment failure probabilities, the timing and workload of preventative maintenance can be determined, random equipment failures can be predicted, and a basis for proactively procuring various maintenance resources.

[0124] 1.1 Preventive Maintenance Methods

[0125] According to the Reliability-Centered Maintenance (RCM) theory, compared to corrective maintenance after equipment failure, preventative maintenance, performed on armored equipment according to scheduled procedures, is a more economical approach. Maintenance intervals are determined based on the reserve of vehicle hull and engine motorcycle hours, categorizing maintenance into three levels: major overhaul, intermediate overhaul, and minor overhaul. As vehicle hull and engine motorcycle hours decrease during use, maintenance is performed at the corresponding level once the required interval is reached. Equipment cannot be used during preventative maintenance. After major or intermediate overhauls, the hull and engine are refurbished or replaced. Major overhauls generate new hull and engine motorcycle hours, while intermediate overhauls generate new engine motorcycle hours. The number of preventative maintenance units should remain relatively stable annually, avoiding a large concentration of units reaching their maintenance intervals. Therefore, maintenance conditions must be fully considered when developing equipment deployment plans.

[0126] 1.2 Motorcycle hourly break-even requirements

[0127] To ensure the military is prepared for missions at any time, it must maintain a sufficient reserve of engine hours for its equipment to guarantee sustainable use. To maintain a long-term, stable reserve of engine hours, the annual engine hours consumed in equipment use and the engine hours produced through preventative maintenance must be roughly balanced. The annual engine hours consumed in equipment use are calculated based on training equipment requirements. The engine hours produced through equipment maintenance are:

[0128]

[0129] Among them, T p The estimated production hours of motorcycles for the annual equipment are as follows. This represents the projected number of the i-th piece of equipment to return to base after mid-year maintenance. The rated service life of the i-th piece of equipment engine expected to return to base after the annual mid-term overhaul. This represents the number of the i-th piece of equipment expected to return to base after the annual major overhaul. The rated service life of the i-th equipment engine is expected to return to camp after the annual overhaul, and n is the number of equipment.

[0130] When formulating equipment deployment plans, the required number of motorcycle hours for maintenance and production at each equipment level must be considered to ensure a balance between revenue and expenditure per motorcycle hour.

[0131] |T p -Q|≤v (2)

[0132] Where Q represents the annual motorcycle hours consumed by the equipment, and v is the allowable deviation constant.

[0133] 2 Optimization Model

[0134] 2.1 Optimization Target

[0135] The unit has n armored vehicles, and each vehicle has R hours of reserve power. i The engine's motorcycle hour reserve is r i The major overhaul interval is 2 hours, and the intermediate overhaul interval is 1 hour. (e.g., r) i =R i If the equipment's most recent preventative maintenance was a mid-level overhaul; if r i +l=R i If the equipment's most recent preventative maintenance was a major overhaul.

[0136] The annual training equipment usage requirement is Q engine-motorcycle hours, and the number of training months is m. Establish an equipment deployment time allocation matrix:

[0137]

[0138] d ij The number of engine motorcycle hours consumed in the j-th month is allocated to the i-th equipment, d ir ≤128 (calculated based on a maximum of 4 weeks of training per month, 4 days per week, 8 hours per day), d ij =0 indicates no allocation or use. The equipment deployment plan should meet the equipment usage needs of the troops, that is:

[0139]

[0140] This indicates that the number of motor hours consumed by the i-th piece of equipment cannot exceed its initial engine motor hour reserve, d. ij =0, b ij =0(r i =0), indicating that the i-th equipped engine motorcycle will be sent for repair after its hourly reserve is exhausted and will not be allocated for use again in the current year.

[0141] 2.2 Optimization Objectives

[0142] 2.2.1 Equipment integrity rate

[0143] Equipment in good working order refers to equipment whose technical condition meets the standards of "cleanliness, completeness, proper lubrication, correct adjustment, appropriate tightening, and no malfunctions," and whose main functions, such as mobility, firepower, information, protection, and support, are intact and can be used to perform daily combat readiness training missions. The equipment readiness rate is the ratio of the number of in-service equipment to the number of deployed equipment. Due to the complex structure of modern weapon systems, judging whether equipment is in good working order involves multiple technical methods and steps, including data collection, fault diagnosis, and condition assessment of various systems. This presents significant theoretical and practical challenges, and currently, a unified and operable technical means, evaluation standard, and methodology have not yet been established. To simplify the research, the Weibull distribution is applied to calculate the equipment readiness rate. Using engine and vehicle motorcycle hour reserves and vehicle motorcycle hour consumption as indicators, and comprehensively considering equipment failure patterns, the readiness rate of the i-th piece of equipment in month j is calculated:

[0144]

[0145] Equipment availability depends on the hourly consumption (r′) of the equipment's engine. ij Motorcycle hourly consumption R′ ij The variations exhibit a Weibull distribution. Based on actual equipment failure data from the military, α, β, δ, θ, η, and other parameters are fitted to obtain... Parameters such as γ. When the engine and chassis wear levels reach the standards for major and medium repairs, preventative maintenance is performed on the equipment, with an availability rate of 0% during the maintenance period.

[0146] The unit's overall annual equipment readiness rate is the average of the monthly equipment readiness rates:

[0147]

[0148] During equipment use, as engine and vehicle hours increase, the failure rate rises and the availability rate declines. While corrective repairs are performed when equipment malfunctions occur during use and do not affect task allocation, a decrease in the overall availability rate of the unit will impact the combat capability of the troops. During major and medium-scale equipment overhauls, the availability rate is defined as zero, but after repairs and return to base, performance improves, and the availability rate increases significantly. Therefore, when planning equipment use, efforts should be focused on improving the overall equipment availability rate of the unit.

[0149] 2.2.2 Equipment availability rate

[0150] Equipment in place refers to equipment being in a state of control and management by the troops, such as within the barracks, at temporary deployment points, or while carrying out missions. The equipment in place rate is the ratio of the number of in-place equipment to the number of allocated equipment. This invention studies equipment not in place, primarily considering situations where equipment is sent to relevant repair facilities for major or medium-scale repairs. Medium-scale repairs are performed after the reserve engine's motorcycle hours are depleted, and major repairs are performed after the reserve vehicle's motorcycle hours are depleted. During the medium-scale repair period (t...),... m Overhaul period t hInternal equipment is not in place. Initialize the equipment in-place matrix:

[0151]

[0152] b ij This represents the availability status of the i-th piece of equipment in month j, where 1 indicates it is in place and 0 indicates it is not. Calculate the reserve consumption of the equipment's engine motorcycle hours and chassis motorcycle hours. Once the corresponding standards are met, send the equipment for major or intermediate repair and adjust the equipment availability matrix.

[0153] b ij =0(r ik =0,k <j≤k+t m (8)

[0154] b ij =0(R) is =0,s <j≤s+t h (9)

[0155] Equation (8) indicates that the equipment engine is sent for intermediate repair after its motorcycle hour reserve is depleted, and the equipment is not in place during the intermediate repair period; Equation (9) indicates that the equipment body is sent for major repair after its motorcycle hour reserve is depleted, and the equipment is not in place during the major repair period. The number of equipment in the camp is the total number of equipment minus the number of equipment sent for repair. The equipment availability rate of the troops is calculated by the average of the ratio of the number of equipment in place to the number of organized equipment in each month:

[0156]

[0157] Among them, E a The number of equipment allocated. Similar to equipment readiness rate, maintaining a high equipment availability rate is an important foundation for troops to be on high alert at all times, improve emergency response capabilities, and effectively perform diversified military tasks.

[0158] 2.2.3 Compliance rate of combat readiness reserves

[0159] In order to adapt to various complex and arduous combat missions, the military must ensure the continuous combat capability of its equipment. This requires the engine motor hours reserve of the equipment to meet certain standards, which is measured by the ratio of the engine motor hours reserve to the rated service life of the engine after major and medium overhauls.

[0160]

[0161] Where u is a standard constant. The equipment readiness reserve compliance rate of the entire force, satisfying equation (11), is measured by the average ratio of the number of equipment meeting the readiness reserve standard to the total number of organized equipment in each month.

[0162]

[0163] E c To ensure the monthly combat readiness reserve meets the required equipment quantity, E a To optimize equipment usage, it is crucial to allocate equipment quantities, rationally distribute equipment usage hours, scientifically maintain equipment production hours, and improve the equipment's combat readiness reserve compliance rate.

[0164] 2.2.4 Repair Costs

[0165] Equipment maintenance incurs significant costs in terms of manpower, materials, and consumables, as well as wear and tear on facilities and equipment. These costs primarily include preventative maintenance and restorative maintenance. Preventative maintenance, such as major and intermediate overhauls, is planned maintenance focused on improving equipment reliability. It is implemented according to standardized processes, with specific and clearly defined items for component disassembly, testing, maintenance, and replacement, regardless of the equipment's technical condition. The cost per unit is fixed. Restorative maintenance, on the other hand, is on-the-spot maintenance following equipment failure. Appropriate testing items, methods, and component replacements are performed based on the equipment's technical condition. Since similar equipment often exhibits similar failure types, average values ​​are used to calculate restorative maintenance costs to simplify the analysis. The restorative maintenance cost C1, preventative maintenance cost C2, and total maintenance cost C are calculated as follows:

[0166]

[0167] C2=n m ·e m +n h ·e h (14)

[0168] C = C1 + C2 (15)

[0169] Where, n m n h These represent the number of equipment undergoing medium and major repairs annually, e r e m e h These are the average cost of restorative repair, the standard cost of intermediate repair, and the standard cost of major repair for a single piece of equipment. When planning equipment use, efforts should be made to reduce equipment maintenance costs.

[0170] In summary, the optimization objective for the planned equipment use is:

[0171] max:A,O,S(16)

[0172] min:C(17)

[0173] The constraints are:

[0174]

[0175] dij =0, b ij =0 (r i =0) (19)

[0176] Equation (18) indicates that the number of motorcycle hours consumed by the i-th piece of equipment cannot exceed its motorcycle hour reserve. Equation (19) indicates that the i-th piece of equipment will be sent for repair after its reserve motorcycle hours are used up. The equipment will not be in place during the repair period, and will not be allocated for use again in the same year after the repair is completed and the equipment is returned to the camp.

[0177] 3. Improved NSGA-III Algorithm

[0178] The NSGA-III algorithm is a multi-objective optimization algorithm proposed by Deb and improved upon the NSGA-II

[16] . NSGA-II is used to handle low-dimensional optimization problems with no more than 3 objectives. In high-dimensional multi-objective optimization problems with more than 4 dimensions, the number of non-dominated individuals in the population increases exponentially, and it is difficult to sort and distinguish between good and bad individuals by crowding in the same Pareto level

[17] . The NSGA-III algorithm proposes a sorting mechanism based on reference points and uses a niche selection strategy to make the Pareto solution distribution more uniform, providing multiple balanced solutions for high-dimensional multi-objective optimization problems

[18] . However, it also has problems such as high complexity, single mutation strategy, and lack of adaptive adjustment mechanism, and does not have the dynamic characteristics to adapt to different problems

[19] . The equipment mobilization optimization model belongs to high-dimensional multi-objective optimization and can be solved by the NSGA-III algorithm. However, the optimization model has the characteristics of complex logical relationship, strong internal correlation of individual encoding, and large difference in objective function scale, so the traditional NSGA-III algorithm cannot be directly applied. Based on the characteristics of the optimization model, this invention improves the process, individual evolution method, and adaptive normalization method of the NSGA-III algorithm, thereby improving the algorithm's running speed and accuracy.

[0179] 3.1 Algorithm flow, as follows Figure 3 ;

[0180] Step 1: Set the basic parameters of the algorithm, including population size Npop, crossover probability Pc, mutation probability Pm, number of algorithm loops MaxIt, and number of reference points p.

[0181] Step 2: Initialize the population. Based on the equipment training time requirements, equipment quantity, equipment motorcycle hour reserves, monthly motorcycle hour allocation limit, etc., randomly generate a chromosome population of Npop.

[0182] Step 3: Calculate the target function values ​​f1, f2, f3, f4 for each chromosome according to equations (6), (10), (12), and (15).

[0183] Step 4: Based on Pareto dominance, perform a rapid non-dominated sort of chromosomes, calculate the number of dominated chromosomes and the set of dominant chromosomes for each chromosome, and determine the Pareto rank R for each chromosome. i .

[0184] Step 5: Select the top-ranked chromosomes to enter the parent population; the number of top-ranked chromosomes... And the number of chromosomes in the first l+1 level

[0185] Step 5: Generate reference points.

[0186] Step 6: Using the method of calculating the distance between the hyperplane and the coordinate axes of the multidimensional solution, for the (l+1)th level F l+1 The solutions for each chromosome are normalized.

[0187] Step 7: Establish the connection between level 1+1 chromosomes and the reference point, and select chromosomes from them using the niche preservation method. One chromosome enters the parent population.

[0188] Step 8: [To be continued] Crossover and mutation operations are performed on the parent population to obtain the offspring population. The parent population and the offspring population are then merged to generate a new generation population.

[0189] Step 9: Repeat steps 3-8 until the iteration ends, and the Pareto level R in the population is determined. i The set of chromosomes with a value of 1 is the optimal solution set.

[0190] 3.2 DNA structure-based crossover and mutation operations

[0191] The optimization model established in Section 2 takes all equipment deployment schemes as the optimization object. When using the NSGA-III algorithm for optimization calculation, a set of codes is needed to represent the motorcycle hour usage scheme of one piece of equipment. Multiple code sets are combined to represent the overall equipment deployment scheme, constituting an individual in the population. Since the usage scheme of a single piece of equipment is subject to many constraints such as motorcycle hour reserves and monthly allocation limits, the codes within a code set are highly correlated. During population evolution, the traditional NSGA-III algorithm performs crossover and mutation operations on a per-code basis, which disrupts the correlation between codes within a code set, resulting in a large number of unreasonable equipment deployment schemes. To address the characteristics of tightly connected codes within the model and relatively independent codes between sets, inspired by the structure of human chromosomes, DNA, and genes, a method based on DNA structure for initial individual coding and crossover / mutation evolution operations is proposed to improve the evolutionary efficiency of the population.

[0192] 3.2.1 Initial Encoding Method

[0193] Equipment was selected one by one in a random order, and its monthly usage hours were randomly assigned. ij The sum of motorcycle hours allocated to a single piece of equipment It must be less than its motorcycle hour reserve. When allocated to the kth piece of equipment, if the total allocated motorcycle hours are... If the annual training demand Q is greater than the demand Q, the k-th piece of equipment is reallocated to allocate t motorcycle hours. k =QT k-1 .like Figure 4 As shown, the monthly allocation of motorcycle hours for a single piece of equipment is t. ij Each piece of equipment is allocated one DNA, and the entire equipment uses one chromosome.

[0194] 3.2.2 Cross-operation method

[0195] To improve the accuracy and efficiency of the algorithm in light of practical business needs, the traditional NSGA-III algorithm, which uses genes as units for crossover and mutation, is modified to use DNA as the unit for parent-child chromosome inheritance. During the crossover operation, the parent chromosomes are shuffled and divided into two equal groups, with corresponding chromosomes then undergoing crossover sequentially. For example... Figure 5 As shown, C chromosomes from two randomly selected parent chromosomes were used. n Two DNA molecules are exchanged at corresponding positions to generate offspring chromosomes.

[0196] 3.2.3 Mutation Operation Method

[0197] During mutation inheritance, for each parent chromosome, its DNA is divided into two groups: all zero (unallocated time equipment) and non-all zero (allocated time equipment). M is randomly selected from each group. n Each DNA molecule is assigned a time allocation code using all-zero DNA and a full-zero DNA molecule is assigned a time allocation code to generate offspring chromosomes, such as... Figure 6 As shown.

[0198] 3.2.4 Evolutionary Adjustment Methods

[0199] Crossover operation converts C chromosomes into two chromosomes. n The corresponding DNA is exchanged, and the mutation operation randomly selects M within the chromosome. n Encode M with all zeros for each non-all-zero DNA. nEncoding motorcycle hour usage with all-zero DNA sequences, after two evolutionary operations, the single-equipment usage scheme represented by the DNA is reasonable. However, the total number of motorcycle hours allocated to the entire equipment, represented by the chromosome, will change, becoming inconsistent with the equipment motorcycle hour usage requirements, resulting in an infeasible chromosome. Therefore, the offspring chromosomes need to be adjusted. The time allocation of non-all-zero DNA sequences in the offspring chromosomes is added together one by one. When the nth DNA sequence is added, the equipment usage time and T are allocated... n If the annual training time requirement Q is greater than the requirement, the nth DNA is re-encoded so that its time allocation is t. n =QT n-1 If the sum of the allocation times of all non-zero DNA is still less than Q, then encode each zero DNA one by one until the allocation time equals Q.

[0200] 3.3 Improved Adaptive Normalization Method

[0201] The traditional NSGA-III algorithm uses fixed parameters for normalization, which cannot adapt to various optimization problems with different characteristics. When the scale difference of the objective function is large, some objectives will be overemphasized or ignored during the optimization process. Especially when there are extreme values ​​in the objective function, the normalized objective function value will be unevenly distributed, thus affecting the algorithm performance. Since the maintenance cost and other objective functions in the equipment use optimization model objective function differ by three orders of magnitude, when the traditional NSGA-III algorithm is used to calculate the distance between the hyperplane of the objective function and the coordinate axis, a singular matrix will be generated, and a unique solution cannot be obtained. The normalization process is interrupted, causing the algorithm to fail

[20] . In this regard, an adaptive normalization method is used to improve it. The improved NSGA-III algorithm can effectively handle this scale difference, dynamically adjust the weight of each objective, and will not favor a certain objective during the search process. On the one hand, it reduces the premature elimination of some solutions due to the difference in the numerical range of the objective function, and maintains the diversity of the population; on the other hand, it can quickly locate the Pareto front and improve the convergence of the algorithm.

[0202] 3.3.1 Determine the reference point

[0203] To ensure a uniform distribution of solutions to high-dimensional multi-objective optimization problems, the NSGA-III algorithm predefines a set of reference points to select and retain solutions. For M-dimensional multi-objective problems, the reference points are uniformly distributed on an M-1 dimensional hyperplane, forming a simplex equidistant from all objective axes. By setting the partition number p for each objective value, the total number of reference points H can be determined:

[0204]

[0205] 3.3.2 Adaptive Normalization

[0206] To facilitate comparison between the solution and the reference point, the objective function is normalized. The objective function f i (x), i = 1, 2, ..., M are replaced by:

[0207]

[0208] The smallest f i value, The calculation is more complex. First, find the target axis f. j Extreme point g in the direction j

[0209]

[0210] w j =(w j,1 ,w j,1 ,…,w j,M ) T The target value f j The direction, if i≠j, w j,i =0, otherwise w j,i =1. For w j,i =0, using a very small value of 10 -6 To replace it. It is the i-th dimension of the objective value of the worst-case scenario calculated in the previous generation. The extreme point is the objective vector of the found solution x, i.e., g. j = f(x).

[0211] Calculate all target axes to obtain M extreme points g1, g2, ..., g m Construct a hyperplane. Let a1, a2, ..., a m They represent the hyperplane in The intercept on the vector u = (1,1,…,1) is obtained using the vector u = (1,1,…,1). T Matrix E = (g1-z) * g2-z * ,…,g M -z * ) T Calculate the intercept:

[0212]

[0213] The value is updated to a i The objective function is updated using equation (21). If the rank of matrix E is less than M, the intercept may not be obtained in some directions, or the intercept may be... At this time Updated to include all solutions in target f i The maximum value on.

[0214] 4. Case Simulation

[0215] 4.1 Simulation Conditions

[0216] A unit is allocating armored equipment, and the deployment of this equipment must meet annual combat readiness requirements and training needs. Relevant data is extracted based on actual operational data, and simulation experiments are conducted. The initial conditions for equipment deployment optimization are set as shown in Tables 1 and 2.

[0217] Table 1 Simulation parameter settings

[0218]

[0219]

[0220] Table 2 Initial Motor Hour Reserves for Equipped Engines

[0221]

[0222] The initial parameters for the algorithm were set as follows: Npop = 500, crossover probability Pc = 0.07, mutation probability Pm = 0.1, and the number of crossover DNAs C. n =6, number of mutated DNA M n =4, Algorithm loop count MaxIt = 500, Number of equal divisions of reference points N r =10.

[0223] 4.2 Algorithm Comparison and Analysis

[0224] Based on the established optimization model, with the optimization objectives of high equipment availability rate, high equipment combat readiness reserve compliance rate, low maintenance cost, and high equipment integrity rate, 500 iterations of simulation calculations were performed using the improved NSGA-III algorithm and the NSGA-III algorithm respectively, and the simulation results were compared and analyzed.

[0225] In the 50th iteration, the two algorithms were compared to obtain chromosome results with a Pareto rank of 1, as follows: Figure 7 , Figure 8 The blue text on the left shows the results calculated by the NSGA-III algorithm, while the red text on the right shows the results calculated by the improved NSGA-III algorithm. It can be seen that the convergence of the two algorithms is almost identical, but the improved NSGA-III algorithm exhibits better optimization performance.

[0226] The NSGA-III algorithm completed 500 simulation calculations in 21 minutes and 43 seconds, while the improved NSGA-III algorithm completed the same task in 38 minutes and 10 seconds, demonstrating faster computation speed. Using a combination of 3D projection and color mapping, the complete image of a chromosome with a Pareto level of 1 was observed after 500 iterations of both algorithms. Figure 9As shown, the left side shows the NSGA-III algorithm, and the right side shows the improved NSGA-III algorithm.

[0227] like Figure 10 , Figure 11 Table 3 shows the results of the NSGA-III algorithm (blue on the left) and the results of the improved NSGA-III algorithm (red on the right). The extreme values ​​of each objective function are shown in Table 3. The improved NSGA-III algorithm is better at calculating the extreme values ​​of single objective functions and has stronger optimization performance.

[0228] Table 3 shows the optimal solutions for each function after 500 iterations of the two algorithms.

[0229]

[0230] 5. Analysis of Equipment Deployment Strategy

[0231] 5.1 Trend of the objective function value of the optimization scheme with the key indicator values

[0232] The improved NSGA-III algorithm iteratively calculated 500 times to obtain 250 chromosomes with a Pareto level of 1. These chromosomes represent optimized deployment plans with different preferences. For each of these 250 optimized plans, four key indicators were calculated: the number of equipment deployed, the engine and motor hours reserve rate of deployed equipment, the ratio of deployed equipment that has undergone intermediate repair to those that have not, and the ratio of equipment maintenance period across fiscal years.

[0233] The number of equipment used, i.e. the number of equipment allocated and used, i.e. the number of equipment whose DNA code corresponding to the equipment in the chromosome is not all zero, is calculated using formula (20).

[0234] n u =|D u |,D u ={d i ∈D|d ij ≠0} (20)

[0235] The engine motor hours reserve rate for a single piece of equipment is the ratio of its total engine motor hours reserve to the rated service life of the engine, which measures the equipment's sustainable operational capability. The engine motor hours reserve rate of operational equipment is the sum of all n... u The average value of the engine and motor hours reserve rate of the equipment at the beginning of the year can reflect the overall situation of the engine and motor hours reserve of the equipment, and can be calculated using formula (21).

[0236]

[0237] The next preventative maintenance for equipment that has undergone intermediate repair is a major overhaul, while the next preventative maintenance for equipment that has not undergone intermediate repair is an intermediate repair. The ratio of the number of equipment that has undergone intermediate repair to those that has not is n. u The ratio of the number of equipment that has undergone intermediate maintenance to the number of equipment that has not undergone intermediate maintenance can reflect the type of preventive maintenance that will be carried out on the next batch of equipment.

[0238] The cross-year maintenance period refers to the number of months in the following year that a piece of equipment reaches its maintenance standard within the current year's usage hours and falls within the preventive maintenance period. For example, if a piece of equipment reaches its engine's remaining motorcycle hours of 0 by November of the current year, reaching the intermediate maintenance standard, with an intermediate maintenance period of 2 months (December of the current year and January of the following year), then the cross-year maintenance period is 1. The cross-year equipment maintenance period ratio is the ratio of the sum of the maintenance periods in the following year for all equipment that reaches the preventive maintenance standard within the current year to the sum of all maintenance periods.

[0239] The improved NSGA-III algorithm was iterated 500 times, resulting in 250 optimized equipment deployment schemes. These schemes were then sorted in ascending order based on four indicators: the number of deployed equipment, the engine and motor hour reserve rate of deployed equipment, the ratio of deployed equipment that has undergone intermediate repair to those that have not, and the ratio of equipment maintenance periods spanning multiple years. Using the objective function values ​​of maintenance cost, on-site rate, combat readiness reserve compliance rate, and operational readiness rate as the ordinate for each equipment deployment scheme, and the four indicator values ​​as the abscissa for each scheme, curves showing the change of the objective function value with each indicator can be plotted. For ease of observation, the objective function values ​​of on-site rate, combat readiness reserve compliance rate, and operational readiness rate were multiplied by 1000 when plotting, while the maintenance cost function value remained unchanged.

[0240] like Figure 12-15 The figures show the curves of how the objective function value of the scheme changes with the indicator values: the number of equipment deployed, the engine and motor hours reserve rate of deployed equipment, the ratio of deployed equipment that has undergone intermediate repair to equipment that has not undergone intermediate repair, and the ratio of equipment maintenance period across years.

[0241] 5.2 Optimization scheme index for the extreme values ​​of a single objective function

[0242] Four equipment deployment schemes that achieved extreme values ​​for each objective function from 250 chromosome results were selected. Seventeen index values, including the number of equipment used, motorcycle hour reserves, number of preventive maintenance levels, and annual maintenance period, were calculated for each scheme, as shown in Table 4.

[0243] Table 4. Relevant Indicators of the Improved NSGA-III Algorithm for Calculating the Extreme Values ​​of Each Objective Function.

[0244]

[0245] 5.3 Equipment Deployment Optimization Strategy

[0246] By comprehensively analyzing the trend graph of the objective function of the optimization scheme with the four key indicators, and the 17 indicator values ​​of the four schemes where the objective function reaches the extreme value, we can derive equipment deployment optimization strategies with different emphases.

[0247] 5.3.1 Equipment mobilization optimization strategy with an emphasis on availability

[0248] (1) Reduce the number of equipment used

[0249] like Figure 11 As shown in Table 4, the equipment availability rate decreases significantly with the increase in the number of equipment used; when the equipment availability rate reaches a maximum of 1, the minimum number of equipment used is 69 units.

[0250] (2) Ensure that the equipment undergoes preventative maintenance in the following year.

[0251] like Figure 14 As shown in Table 4, the equipment availability rate increases significantly with the increase of the cross-year maintenance period ratio. When the equipment availability rate reaches its maximum value of 1, the cross-year maintenance period ratio is also at its maximum of 1, meaning that all major and minor repairs of equipment are carried out in the following year. Under this mobilization plan, the start of preventative maintenance is as follows: Figure 16 As shown, there were no major or medium-scale equipment overhauls during the year. In the 13th month, which is January of the following year, 3 pieces of equipment began major overhauls and 25 pieces of equipment began medium-scale overhauls.

[0252] (3) Use equipment evenly

[0253] The quantity of equipment used each month and the engine / motorcycle hours of that equipment should be as evenly distributed as possible. For example... Figure 17 , Figure 18 As shown, when the equipment availability rate reaches a maximum of 1, the number of equipment used and the number of motorcycle hours used each month are relatively even, so that major and medium-sized equipment repairs can be concentrated in the next year.

[0254] 5.3.2 Equipment Utilization Optimization Strategy Emphasizing Combat Readiness Reserve Compliance Rate

[0255] (1) Increase the number of equipment deployed

[0256] like Figure 12 As shown in Table 4, the equipment readiness reserve compliance rate increases significantly with the number of equipment deployed. When the equipment readiness reserve compliance rate reaches its maximum value of 0.7575, the number of equipment deployed is the second highest at 96 units. Deploying a large number of equipment units results in fewer motorcycle hours consumed per unit, leading to a reduction in the motorcycle hour reserve of fewer units below the readiness reserve standard.

[0257] (2) Prioritize the use of equipment with limited motorcycle hours.

[0258] As shown in Table 4, when the combat readiness reserve compliance rate reaches its maximum value of 0.7575, the number of equipment deployed for different engine motorcycle hour reserves is 5, 14, 9, 18, and 50. This means that the initial motorcycle hour reserve is low, and all equipment with reserves between 0-100, 100-200, and 200-300 hours is deployed. This allows more equipment to deplete its motorcycle hour reserves for preventative maintenance and generate new motorcycle hours. Under this deployment plan, the maximum number of equipment required for major and medium repairs is also 32 units.

[0259] (3) Ensure that the equipment undergoes preventive maintenance within the current year.

[0260] like Figure 15 As shown in Table 4, the equipment readiness reserve compliance rate decreases significantly with the increase in the cross-year maintenance ratio. When the equipment readiness reserve compliance rate reaches its maximum value of 0.7575, the cross-year maintenance ratio reaches its minimum value of 0.1818. Under this scheme, only 18.18% of preventative maintenance occurs in the following year. The start of preventative maintenance is as follows: Figure 19 As shown, most of the work was completed within the year.

[0261] (4) Equipment was mobilized in a concentrated manner at the beginning of the year.

[0262] Equipment should be concentrated at the beginning of the year to ensure that more preventative maintenance is completed within the year, resulting in more motorcycle hours. When the equipment readiness reserve compliance rate reaches its maximum value of 0.7575, the quantity of equipment deployed and the number of motorcycle hours deployed should be considered. Figure 20 , Figure 21 As shown, the peak season is the beginning of the year.

[0263] 5.3.3 Equipment Utilization Optimization Strategies that Prioritize Maintenance Costs

[0264] (1) Reduce the number of equipment requiring major repairs

[0265] As shown in Table 4, when the maintenance cost reaches a minimum value of 595.2607, the number of equipment requiring major repairs reaches a minimum value of 0, indicating that the major repair cost has a significant impact on the maintenance cost.

[0266] (2) Prioritize the use of equipment that has not undergone intermediate repair.

[0267] like Figure 14 As shown, maintenance costs increase significantly with the increase in the ratio of equipment that has undergone intermediate repair to equipment that has not. This is because increasing the proportion of equipment that has undergone intermediate repair and decreasing the proportion of equipment that has not undergone intermediate repair increases the number of equipment requiring major repairs, thus increasing maintenance costs. As shown in Table 4, when the maintenance cost reaches its minimum value of 595.2607, the ratio of equipment that has undergone intermediate repair to equipment that has not undergone intermediate repair is relatively small, at 0.7778. Under this deployment plan, the number of equipment deployed and the number of motorcycle hours deployed are as follows: Figure 22 , Figure 23As shown, it can be seen that a larger proportion of equipment that has not undergone repairs is being used.

[0268] like Figure 12-15 As shown in Table 4, the curves of the availability rate changing with the four indicators are basically similar to those of the in-situ rate. When the availability rate reaches its maximum value of 0.9333, the in-situ rate reaches its maximum value of 1, and the equipment deployment plan remains the same. Therefore, the equipment deployment optimization strategy that prioritizes the availability rate is the same as the equipment deployment optimization strategy that prioritizes the in-situ rate.

[0269] in conclusion

[0270] This invention, based on the analysis of the relationship between equipment deployment and maintenance, and combined with the needs of troop combat readiness training, comprehensively considers preventive and restorative maintenance types, and establishes an equipment deployment optimization model with objectives of equipment availability rate, combat readiness reserve compliance rate, maintenance cost, and operational readiness rate. The improved NSGA-III algorithm performs excellently in high-dimensional multi-objective optimization problems, exhibiting superior convergence and optimization performance compared to the traditional NSGA-III algorithm, providing multiple balanced solutions for equipment deployment. Based on simulation results, optimization strategies for equipment deployment with different preferences are proposed. The research results have significant practical implications for guiding the military in the scientific and rational deployment of equipment, improving equipment deployment efficiency and maintenance efficiency. Future research will focus on further in-depth studies of preventive maintenance influencing factors and multi-year analysis of equipment deployment.

[0271] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0272] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for optimizing equipment deployment based on an improved NSGA-III algorithm, characterized in that, The equipment mobilization optimization method based on the improved NSGA-III algorithm includes the following steps: Step 1: Establish a multi-objective optimization model with the objectives of maximizing equipment availability, maximizing equipment combat readiness reserve compliance rate, maximizing equipment integrity rate, and minimizing equipment maintenance costs, and with motorcycle hourly revenue and expenditure balance as the constraint. Step 2: Based on the characteristics of the established model target being high-dimensional and having large scale differences, an improved NSGA-III algorithm is designed to solve the problem.

2. The equipment deployment optimization method based on the improved NSGA-III algorithm as described in claim 1, characterized in that, The motorcycle's hourly revenue and expenditure are balanced: The equipment maintenance and production hours for engine motorcycles are: Among them, T p The estimated production hours of motorcycles for the annual equipment are as follows. This represents the projected number of the i-th piece of equipment to return to base after mid-year maintenance. The rated service life of the i-th piece of equipment engine expected to return to base after the annual mid-term overhaul. This represents the number of the i-th piece of equipment expected to return to base after the annual major overhaul. The rated service life of the i-th equipment engine is expected to return to camp after the annual overhaul, and n is the number of equipment. When formulating equipment deployment plans, the required number of motorcycle hours for maintenance and production at each equipment level must be considered to ensure a balance between revenue and expenditure per motorcycle hour. |T p -Q|≤v (2) Where Q represents the annual motorcycle hours consumed by the equipment, and v is the allowable deviation constant.

3. The equipment deployment optimization method based on the improved NSGA-III algorithm as described in claim 1, characterized in that, The multi-objective optimization model: 1) Optimization Object The unit has n armored vehicles, and each vehicle has R hours of reserve power. i The engine's motorcycle hour reserve is r i The major overhaul interval is 2 hours, and the intermediate overhaul interval is 1 hour; if r i =R i If the equipment's most recent preventative maintenance was a mid-level overhaul; if r i +l=R i If the equipment's most recent preventative maintenance was a major overhaul; The annual training equipment usage requirement is Q engine-motorcycle hours, and the number of training months is m. Establish an equipment deployment time allocation matrix: d ij The number of engine motorcycle hours consumed in the j-th month is allocated to the i-th equipment, d ir ≤128 (calculated based on a maximum of 4 weeks of training per month, 4 days per week, 8 hours per day), d ij =0 indicates no allocation or use; the equipment deployment plan should meet the equipment usage needs of the troops, that is: This indicates that the number of motor hours consumed by the i-th piece of equipment cannot exceed its initial engine motor hour reserve, d. ij =0, b ij =0(r i =0), indicating that the i-th equipped engine motorcycle will be sent for repair after its hourly reserve is exhausted and will not be allocated for use again in the same year; 2) Optimization Objective 2.1) Equipment integrity rate Using engine and vehicle motorcycle hour reserves and vehicle motorcycle hour consumption as indicators, and taking into account equipment failure patterns, calculate the availability rate of the i-th piece of equipment in month j: Equipment availability depends on the hourly consumption (r′) of the equipment's engine. ij Motorcycle hourly consumption R′ ij The changes follow a Weibull distribution; based on actual equipment failure data of the troops, α, β, δ, θ, η are fitted to obtain... Parameters such as γ; when the equipment engine and vehicle body reach the major and medium repair standards, preventive maintenance is carried out on the equipment, and the availability rate during the maintenance period is 0. The unit's overall annual equipment readiness rate is the average of the monthly equipment readiness rates: 2.2) Equipment availability rate After the reserve engine hours are depleted, a mid-term overhaul is performed; after the reserve chassis hours are depleted, a major overhaul is performed. During the mid-term overhaul period... m Overhaul period t h Internal equipment is not in place; initialize the equipment in-place matrix: b ij For the i-th piece of equipment in month j, 1 indicates in-service; 0 indicates out-of-service. Calculate the reserve consumption of engine motorcycle hours and chassis motorcycle hours. If the corresponding standards are reached, send the equipment for major or intermediate repair and adjust the equipment in-service matrix. b ij =0(r ik =0,k<j≤k+t m )(8) b ij =0(R is =0,s<j≤s+t h )(9) Equation (8) indicates that the equipment engine is sent for intermediate repair after its motorcycle hour reserve is depleted, and the equipment is not in place during the intermediate repair period; Equation (9) indicates that the equipment body is sent for major repair after its motorcycle hour reserve is depleted, and the equipment is not in place during the major repair period; the number of equipment in the camp is the total number of equipment minus the number of equipment sent for repair; the equipment availability rate of the troops is calculated by the average of the ratio of the number of equipment in place to the number of organized equipment in each month: Among them, E a To allocate equipment quantity; similar to equipment readiness rate, maintaining a high equipment availability rate is an important foundation for troops to be in a state of high alert at all times, improve emergency response capabilities, and effectively perform diversified military tasks. 2.3) Compliance rate of combat readiness reserves 2.4) Repair costs.

4. The equipment deployment optimization method based on the improved NSGA-III algorithm as described in claim 3, characterized in that, The mentioned combat readiness reserve compliance rate: In order to adapt to various complex and arduous combat missions, the military must ensure the continuous combat capability of its equipment. This requires the engine motor hours reserve of the equipment to meet certain standards, which is measured by the ratio of the engine motor hours reserve to the rated service life of the engine after major and medium overhauls. Where u is a standard constant; the equipment combat readiness reserve that satisfies equation (11) meets the standard, and the equipment combat readiness reserve compliance rate of the entire force is measured by the average ratio of the number of equipment that meets the combat readiness reserve standard to the number of organized equipment in each month: E c To ensure the monthly combat readiness reserve meets the required equipment quantity, E a To optimize equipment usage, it is crucial to allocate equipment quantities, rationally distribute equipment usage hours, scientifically maintain equipment production hours, and improve the equipment's combat readiness reserve compliance rate.

5. The equipment deployment optimization method based on the improved NSGA-III algorithm as described in claim 3, characterized in that, The repair cost is as follows: The cost of restorative repair is calculated using average values; the costs of restorative repair C1, preventative repair C2, and total repair cost C are calculated as follows: C2=n m ·e m +n h ·e h (14) C = C1 + C2 (15) Where, n m n h These represent the number of equipment undergoing medium and major repairs annually, e r e m e h These are the average cost of restorative repair, the standard cost of intermediate repair, and the standard cost of major repair for a single piece of equipment; when planning the use of equipment, efforts should be made to reduce equipment maintenance costs; In summary, the optimization objective for the planned equipment use is: max:A,O,S (16) min:C (17) The constraints are: d ij =0,b ij =0 (r i =0) (19) Equation (18) indicates that the number of motorcycle hours consumed by the i-th piece of equipment cannot exceed its motorcycle hour reserve. Equation (19) indicates that the i-th piece of equipment will be sent for repair after its reserve motorcycle hours are used up. The equipment will not be in place during the repair period, and will not be allocated for use again in the same year after the repair is completed and the equipment is returned to the camp.

6. The equipment deployment optimization method based on the improved NSGA-III algorithm as described in claim 1, characterized in that, The improved NSGA-III algorithm: Step 1: Set the basic parameters of the algorithm, including population size Npop, crossover probability Pc, mutation probability Pm, number of algorithm loops MaxIt, and number of reference points p. Step 2: Initialize the population. Based on the equipment training time requirements, equipment quantity, equipment motorcycle hour reserves, monthly motorcycle hour allocation limit, etc., randomly generate a chromosome population of Npop. Step 3: Calculate the target function values ​​f1, f2, f3, f4 for each chromosome according to equations (6), (10), (12), and (15); Step 4: Based on Pareto dominance, perform a rapid non-dominated sort of chromosomes, calculate the number of dominated chromosomes and the set of dominant chromosomes for each chromosome, and determine the Pareto rank R for each chromosome. i ; Step 5: Select the top-ranked chromosomes to enter the parent population; the number of top-ranked chromosomes... And the number of chromosomes in the first l+1 level Step 5: Generate reference points; Step 6: Using the method of calculating the distance between the hyperplane and the coordinate axes of the multidimensional solution, for the (l+1)th level F l+1 Normalize the solutions for each chromosome; Step 7: Establish the connection between level 1+1 chromosomes and the reference point, and select chromosomes from them using the niche preservation method. One chromosome enters the parent population; Step 8: [To be continued] Crossover and mutation operations are performed on the parent population to obtain the offspring population. The parent population and the offspring population are then merged to generate a new generation population. Step 9: Repeat steps 3-8 until the iteration ends, and the Pareto level R in the population is determined. i The set of chromosomes with a value of 1 is the optimal solution set.

7. The equipment deployment optimization method based on the improved NSGA-III algorithm as described in claim 1, characterized in that, It also includes a DNA-based equipment deployment optimization method, which uses DNA structure encoding methods to represent and evolve equipment deployment schemes, including the following steps: 1) Initial coding method: The monthly usage hours of each piece of equipment are treated as a gene, the usage plan of a single piece of equipment is treated as DNA, and the usage plans of all equipment are combined into a chromosome; during the initialization process, the usage hours of each piece of equipment are randomly assigned to ensure that the total number of motorcycle hours of each piece of equipment is less than its motorcycle hour reserve and meets the annual training requirements. 2) Crossover operation method: Instead of the traditional crossover method based on genes, this method uses DNA as the unit for crossover of parent chromosomes. By shuffling the order of parent chromosomes and grouping them, DNA is randomly selected and the corresponding positions are exchanged to generate new offspring chromosomes. 3) Mutation operation method: Divide the DNA in each parent chromosome into two groups: all-zero DNA and non-all-zero DNA. All-zero DNA is assigned time encoding, and non-all-zero DNA is encoded as all-zero, thus generating new offspring chromosomes. 4) Evolutionary adjustment method: Adjust the offspring chromosomes by detecting the difference between the total non-zero DNA allocation time and the annual training requirements, and adjust the coding values ​​of some DNA to make the total meet the training requirements, thus ensuring the rationality and feasibility of the evolutionary results.

8. An equipment mobilization optimization system based on the improved NSGA-III algorithm, implementing the equipment mobilization optimization method based on the improved NSGA-III algorithm as described in any one of claims 1-7, characterized in that, The equipment mobilization optimization system based on the improved NSGA-III algorithm includes: The model building module is used to build a multi-objective optimization model with the objectives of maximizing equipment availability, maximizing equipment combat readiness reserve compliance rate, maximizing equipment integrity rate, and minimizing equipment maintenance costs, and with motorcycle hour revenue and expenditure balance as the constraint. The solver module is used to design an improved NSGA-III algorithm to solve the problem, taking into account the characteristics of the established model's high-dimensional target and large scale differences.

9. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the equipment mobilization optimization method based on the improved NSGA-III algorithm as described in any one of claims 1-6.

10. An information data processing terminal, characterized in that, The information data processing terminal is used to implement the equipment mobilization optimization system based on the improved NSGA-III algorithm as described in claim 8.

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