Communication equipment repair spare part topology layout optimization method and system based on SAGA

Abstract

The invention discloses a communication equipment repair spare part topological layout optimization method based on an SAGA, and the method employs a genetic algorithm to simulate the natural selection and genetic process, carries out the effective search in a large-scale solution space, improves the search breadth and quality of a solution, and deals with the challenge that the solution space is large and complex. The calculation bottleneck of an accurate solution method in a large-scale complex problem can be avoided, the quality of the solution can be continuously optimized through multi-generation iteration, and the solution requirement of the complex problem is met. In order to cope with the challenge that a plurality of locally optimal solutions may exist, a physical annealing process is simulated by using a simulated annealing-genetic algorithm, a poorer solution is allowed to be accepted at the initial stage, and the algorithm is gradually concentrated on a better solution as the temperature is gradually reduced, so that the trouble of the locally optimal solutions is effectively avoided; the bottleneck of a traditional accurate solution method in large-scale complex problems can be overcome, the search flexibility and robustness can be improved, and it is ensured that a solution close to global optimum is obtained.

Description

Technical Field

[0001] This application relates to the field of communication equipment repair spare parts topology layout technology, and more specifically, to a communication equipment repair spare parts topology layout optimization method and system based on SAGA. Background Technology

[0002] The rapid development of information technology has made efficient and reliable data transmission a crucial indicator of social development and people's living standards. The increased burden on communication equipment has led to more frequent equipment failures. Current spare parts supply and storage are mostly arranged according to a regional responsibility system, rarely considering the impact of individual factors such as the number of warehouses, users, operating environment, and distance between warehouses and repair companies within the task areas of each supply organization. This makes it difficult to achieve the optimal guarantee benefits of supply and storage. Although a redundant architecture can reduce the impact of failures, considering the high spatial dispersion of equipment, a scientifically sound and rationally distributed spare parts supply topology is of great significance for improving repair efficiency and thus enhancing the economic benefits of communication equipment repair and support.

[0003] Traditional optimization models for the topology distribution of communication equipment repair parts mainly include: (1) Linear programming algorithm model. Linear programming is a mathematical optimization method that solves for the maximum or minimum value of a linear objective function under a set of linear inequalities or equality constraints. It has the characteristics of simple and clear model, perfect theoretical basis, high solution efficiency and wide application range. It is mainly used to solve single-objective optimization problems. However, the linear constraint and difficulty in dealing with integer constraints make it difficult to handle complex optimization problems of communication equipment; (2) Goal programming algorithm model. Goal programming is developed on the basis of linear programming. It can solve the real needs of multiple objectives in communication equipment repair parts, such as the economic objectives and timeliness objectives in the topology layout of parts. In goal programming, the objective function is generally constructed by the deviation variables of each objective constraint and weighted to reflect the importance of different objectives; (3) Nonlinear programming model. Nonlinear programming is an optimization method for solving nonlinear objective functions under nonlinear constraints. It has the characteristics of high flexibility, wide applicability and ability to handle multi-objective optimization problems. However, it is difficult to solve, has high computational complexity, is sensitive to initial values, has complex model construction and is prone to getting trapped in local optima; (4) Simulated annealing algorithm model. Simulated annealing is a general probabilistic heuristic optimization algorithm with local fine optimization capability. It can cope with complex problems and the implementation process is relatively simple. However, it has high computational complexity, strong parameter dependence and difficulty in guaranteeing the quality of the solution; (5) Genetic algorithm model. Genetic algorithm is a search and optimization technique based on the principles of natural selection and genetics. It solves complex optimization problems by simulating the biological evolution process. It has global optimization capability, strong adaptability and easy implementation. However, it also has high requirements for parameter selection, requires ensuring population diversity and a large number of iterations, and the quality of the solution is difficult to guarantee.

[0004] Different optimization models have their own applicable scope and focus. Each optimization model has its own limitations in effectiveness. It is difficult to obtain a reasonable and feasible topological distribution structure by using the above single optimization models, thus making it difficult to accurately correspond to the relationship between spare parts supply and storage and repair needs. Summary of the Invention

[0005] To address at least one deficiency or improvement need in the existing technology, this invention provides a method and system for optimizing the topology layout of communication equipment repair spare parts based on SAGA. The repair scenario is mathematically represented, and a fusion model optimization method is proposed. By combining simulated annealing and genetic algorithm models, the global search advantage of the genetic algorithm is fully utilized, while the local fine-tuning optimization capability of simulated annealing is used to effectively deal with resource allocation optimization problems with large-scale and complex constraints, thereby improving the solution efficiency and the quality of the optimal solution of the spare parts supply and storage topology layout optimization configuration model.

[0006] To achieve the above objectives, according to a first aspect of the present invention, a method for optimizing the topology layout of repair spare parts for communication equipment based on SAGA is provided, the method comprising: S1, initialize the coverage time of the supply points of the communication equipment repair spare parts to the demand points and the upper limit of the number of supply points, generate an initial repair spare parts topology layout scheme, and construct the constraints of the repair spare parts topology layout scheme. S2, using the coverage time and the number of supply points as optimization objectives, construct a multi-objective optimization model for repair spare parts topology layout based on SAGA; S3. Based on the initial repair spare parts topology layout scheme, the optimization objective, and the constraints, iteratively solve the multi-objective optimization model of the repair spare parts topology layout to obtain the optimal repair spare parts topology layout scheme. The solution of the multi-objective optimization model for the topology layout of the repair spare parts specifically includes: S31, an initial population is generated based on the simulated annealing algorithm, and the fitness of individuals in the population is calculated; where each individual in the population represents a feasible topology layout scheme for repair spare parts; S32, based on the genetic algorithm, selects parent individuals and performs crossover on each individual to generate offspring individuals; S33, Gene mutations are performed on the offspring individuals using an evolutionary generation ratio and an adaptive mutation strategy; S34, based on the simulated annealing algorithm, iterate through the offspring individuals after crossover and mutation, and select offspring individuals to retain according to their fitness probability; S35, merge the retained offspring individuals with the parent individuals selected from the parent individuals to generate a new generation population; S36. Determine whether the iteration termination condition is met. If it is met, output the optimal repair spare parts topology layout scheme based on the fitness of individuals in the new generation population. Otherwise, use the new generation population as a new initial population and perform iteration cyclically.

[0007] Furthermore, in step S31 of the above-mentioned communication equipment repair spare parts topology layout optimization method, the initialization of the population includes: Individuals that meet the following constraints will be designated as the first subpopulation: Each demand point is guaranteed by only one supply point, and all demand points can be guaranteed; Unattended demand points cannot be used as supply points. The supply-to-demand time meets the site priority guarantee time limit and spare parts guarantee time limit requirements of the demand point; Individuals that meet the following constraints will be designated as the second subpopulation: The individuals corresponding to the maximum and minimum coverage time of the supply point to the demand point; The first subpopulation and the second subpopulation constitute the initialization population.

[0008] Furthermore, in step S32 of the above-mentioned communication equipment repair spare parts topology layout optimization method, the selection of parent individuals based on a genetic algorithm includes: Randomly select the first preset individual, and with a preset probability Select the appropriate individuals, in order to The probability is used to select individuals with low fitness; the random selection operation is repeated until a second preset parent individual is selected as the parent individual.

[0009] Furthermore, the aforementioned method for optimizing the topology layout of repair spare parts for communication equipment also includes: Each individual is represented by a vector of the same dimension as the number of all demand points, and the elements of the vector are the indices of the supply points corresponding to each demand point across all sites. There is a one-to-one correspondence between the vector and the zero-one decision matrix of the spare parts supply relationship. In the zero-one decision matrix of the spare parts supply relationship, an element value of 1 indicates that the spare parts of the demand point are guaranteed by the supply point, and an element value of 0 indicates that the demand point is not guaranteed by the supply point.

[0010] Furthermore, in step S32 of the above-mentioned communication equipment repair spare parts topology layout optimization method, the step of cross-fertilizing each individual to generate offspring individuals specifically includes: According to the preset probability For the selected Crossing parent individuals generates offspring individuals; wherein, the crossover is performed by randomly selecting... Crossing between parent generations, when The lower the relative differences in fitness between parents, the greater the probability of crossover.

[0011] Furthermore, in step S32 of the above-mentioned communication equipment repair spare parts topology layout optimization method, the step of cross-fertilizing each individual to generate offspring individuals further includes: The local structure preservation crossover method is adopted. By exchanging some fragments of the parent individual and combining the constraints, new supply point coverage is generated to optimize the offspring scheme. This preserves the good characteristics of the parent individual scheme and avoids the necessary solution space check.

[0012] Furthermore, the gene mutation in step S33 of the above-mentioned communication equipment repair spare parts topology layout optimization method specifically includes: The preset probability is determined based on the ratio of the current iteration number to the maximum iteration number of the genetic algorithm, the fitness of the offspring individuals, the maximum and minimum fitness of the population after crossover, and the individual fitness function of the population with the maximum and minimum mutation probabilities. ; According to the preset probability Gene mutations are performed on offspring individuals.

[0013] Furthermore, step S33 of the above-mentioned communication equipment repair spare parts topology layout optimization method also includes: While maintaining the stability of the solution structure, a local structure-preserving mutation strategy is adopted. By randomly selecting some genes in an individual and performing mutation operations in its local domain, local perturbations are introduced without destroying the overall structure, thereby verifying the effective coverage of the supply point to the demand point under constraints.

[0014] Furthermore, step S34 of the above-mentioned method for optimizing the topology layout of repair spare parts for communication equipment also includes: The probability of selecting an offspring individual, determined by a function of the fitness of individuals in the new generation and the fitness of all individuals, is used as the preset probability. The individual fitness function is used to adjust the degree of influence of fitness differences on the probability of an individual being selected for processing by the simulated annealing algorithm; The offspring individuals after crossover mutation are subjected to the preset probability. The simulated annealing algorithm is used to process the solution for a preset number of iterations to obtain a new set of feasible solutions.

[0015] According to a second aspect of the present invention, a communication equipment repair spare parts topology layout optimization system based on the above-mentioned SAGA-based communication equipment repair spare parts topology layout optimization method is also provided, the system comprising: An initialization module is configured to initialize the coverage time of the supply points to the demand points for the repair spare parts of the communication equipment and the upper limit of the number of supply points, generate an initial repair spare parts topology layout scheme, and construct the constraints of the repair spare parts topology layout scheme. A multi-objective optimization model construction module is configured to construct a SAGA-based multi-objective optimization model for repair spare parts topology layout, using the coverage time and the number of supply points as optimization objectives. The multi-objective optimization model solving module is configured to iteratively solve the multi-objective optimization model of the repair spare parts topology layout based on the initial repair spare parts topology layout scheme, the optimization objective, and the constraints, so as to obtain the optimal repair spare parts topology layout scheme.

[0016] According to a third aspect of the present invention, a communication equipment repair spare parts topology layout optimization device based on SAGA is also provided, which includes at least one processing unit and at least one storage unit, wherein the storage unit stores a computer program that, when executed by the processing unit, causes the processing unit to perform the steps of any of the methods described above.

[0017] According to a fourth aspect of the present invention, a computer program product is also provided, comprising a computer program / instructions, characterized in that, when the computer program / instructions are executed by a processor, they implement the steps of any of the methods described above.

[0018] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects: This invention utilizes a genetic algorithm to simulate natural selection and genetic processes, enabling efficient searching within a large-scale solution space. This improves the breadth and quality of the search results, addressing the challenge of a vast and complex solution space. It not only avoids the computational bottlenecks faced by exact solution methods in large-scale complex problems but also continuously optimizes the solution quality through multiple iterations, adapting to the needs of solving complex problems. Furthermore, to address the challenge of multiple local optima, a simulated annealing-genetic algorithm simulates the physical annealing process. Initially, it allows for poorer solutions, but as the temperature gradually decreases, the algorithm focuses on better solutions, effectively avoiding the problem of local optima. This not only overcomes the bottlenecks of traditional exact solution methods in large-scale complex problems but also improves the flexibility and robustness of the search, ensuring that a near-global optimum solution is obtained. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 A flowchart illustrating a method for optimizing the topology layout of repair spare parts for communication equipment based on SAGA, provided in an embodiment of this application; Figure 2 A flowchart illustrating another SAGA-based method for optimizing the topology layout of repair spare parts for communication equipment, provided in an embodiment of this application; Figure 3 This application provides schematic diagrams illustrating the optimization results of SAGA and SA algorithms for embodiments of the present application; Figure 4 This is a schematic diagram of a communication equipment repair spare parts topology layout optimization device based on SAGA, provided in an embodiment of this application. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0022] The terms "first," "second," "third," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or apparatuses.

[0023] The core task of repair spare parts topology optimization configuration is to select suitable supply points from multiple facility locations to meet the spare parts coverage requirements of the demand points. This problem is essentially an NLP problem, characterized by a large and complex solution space and the potential existence of multiple local optima. General exact solution methods, due to their enormous computational demands, often struggle to obtain an efficient solution within a reasonable timeframe when dealing with such problems.

[0024] Unlike hierarchical repair strategies based on hierarchical relationships, this invention starts from actual needs and uses the geographical distribution of points for topological layout. First, based on the distribution of demand points, the locations of supply points are determined. The selection of supply points is primarily based on geographical spatial distribution, considering both the availability of supply time between supply and demand points and the limited number of supply points. Second, at the operational optimization level, supply points can be either demand points or non-demand points, but they must be organizational units within the optimization area. Furthermore, considering the current reality of unmanned warehouse transformation, the selection of unmanned sites should be avoided when choosing specific supply points. This method overcomes the limitations of fixed-organization repair strategies in optimizing fault recovery time and efficiency, focusing on actual needs and economic benefits. The specific steps are as follows: First, identify the core requirements. Optimization needs are the starting point for optimizing the problem and a key criterion for measuring the effectiveness of the solution. This helps define the standards and evaluation indicators for successful problem solving, avoids wasting resources, and guides the solution to focus on key issues while responding to dynamic changes, thereby improving the quality of decision-making.

[0025] Secondly, a problem model is constructed. The problem model determines the direction, efficiency, and accuracy of the solution. It requires abstracting and simplifying the actual problem, extracting key elements, identifying core variables and constraints, and determining the solution space to guide the design of the solution algorithm. Finally, the optimization goals and effects are established, forming an analysis and explanation of the problem in the specified scenario.

[0026] Finally, a solution algorithm is selected. The solution algorithm determines whether the problem can be solved effectively and efficiently, directly affecting the quality and reliability of the solution. Real-world problems often have many constraints, and choosing a suitable solution algorithm is key to approximating the optimal or feasible solution. In the mathematical system, different problems have basic theoretical solutions. How to use fundamental theories to solve complex problems while ensuring efficiency and resource utilization is an important factor to consider. In addition, the accuracy, reliability, and robustness of the solution are also important conditions to consider when selecting a solution algorithm.

[0027] Regarding the core requirements for topology layout optimization, the following requirements must be met: 1. Time Requirements: Optimizing the topology layout of repair spare parts must meet both timeliness requirements and economic objectives. Timeliness requirements include two aspects: first, minimizing the overall supply time. This mainly refers to minimizing the total time for spare parts supply from the supply point to each demand point; second, meeting the time requirements for restoring current equipment faults. Here, fault recovery time mainly refers to the time required to restore the equipment to its technical condition through parts replacement and repair.

[0028] 2. Economic Requirements: The economic objective represents a key change in optimizing the repair spare parts topology layout compared to the existing layout. The current repair spare parts layout is primarily established based on organizational affiliation, and the number of storage points and the required number of spare parts are closely related to this organizational structure. From the perspective of regional sharing, fewer storage points generally lead to a higher degree of resource sharing, resulting in greater economic efficiency in terms of storage point construction and resource allocation. Therefore, while ensuring timeliness requirements, the economic requirement can be translated into a requirement for optimizing the number of supply points.

[0029] In constructing a poaching layout optimization model, the following factors need to be considered: 1. Location Model Establishment: This invention considers coverage-type location scenarios, requiring supply points to provide service time or distance that meets a given criterion. The location model not only requires supply points to serve demand points within a specified time or distance, but also emphasizes covering all demand points with the fewest possible supply points to meet practicality and economic requirements. Specifically, this is expressed as follows: (1-1) (1-2) (1-3) In the formula: For facility construction costs.

[0030] Equation (1-1) represents the minimum construction cost of the supply point to satisfy all demands within a given optimal configuration. Constraint Equation (1-2) requires that all demands must be met. Equation (1-3) indicates the minimum construction cost of the supply point when... When selected It is 1 if it is true, otherwise it is 0.

[0031] 2. Mathematical Description of the Model: For the topology layout optimization of repair spare parts for fixed-point communication equipment, it is necessary to consider both the ability to supply spare parts to the required locations as quickly as possible and the cost factors of construction and management of the supply points. In practice, a trade-off must be struck between these two aspects to achieve optimal overall performance. This can be abstracted into the following mathematical problem: Within a certain area to be optimized, the distribution of each demand point is known, and the estimated supply time between each supply point and the demand point can also be obtained. Based on satisfying the demand of all points and the time limit for a single repair, the topology layout optimization scheme with the minimum total supply time and the lowest supply point construction and management cost is obtained.

[0032] To simplify the problem, we make the following assumptions: 1) The construction and management costs of different supply points are approximately the same, and the overall economic efficiency of the topology layout is only related to the number of supply points. For the lowest-level repair points with warehousing capabilities, the number of spare parts is limited, and a standard storage room is generally sufficient to meet the needs. Therefore, the construction and management costs of storage rooms at different supply points are not significantly different. This assumption has a certain degree of rationality in practice.

[0033] 2) Each demand point is guaranteed by only one supply point, and one supply point can guarantee multiple demand points. To simplify the guarantee relationship, it is agreed in the model construction that each demand point is guaranteed by only one supply point. When a demand point has a need for communication equipment spare parts, they can be obtained directly from the corresponding supply point. This assumption takes into account the balance between speed and convenience and economy, and is applicable to the equipment repair scenario with safety requirements in this invention.

[0034] 3) Unattended demand points cannot be used as supply points. From the definition of demand points, these are primarily infrastructures for deploying fixed-point communication equipment. Currently, the maintenance of such facilities is gradually shifting towards unattended operation. Unattended facilities have certain limitations in terms of repair and spare parts supply, as well as daily management. Therefore, when optimizing the topology layout, unattended facilities are generally not considered as alternative supply points.

[0035] 4) The number of demand points that a default supply point can cover is unlimited. From the perspective of supply points, the main factor limiting their coverage limit is the quantity of repair spare parts. Assuming that assumption 1 is true, as long as the quantity of spare parts meets the coverage requirements, then assumption 4 can also be true. The fundamental purpose of establishing a spare parts warehouse is to meet the coverage requirements, so this assumption is consistent with reality.

[0036] To facilitate the mathematical formulation of the problem, the representation of the parameters involved will be introduced uniformly here: The total number of facility sites (including both demand points and supply points); Represents specific facility locations. ,in The total number of facilities in the entire region; This is a zero-one vector (the element value can only be 0 or 1) given in advance according to the actual situation. Indicate facility point It is a demand point, not a supply point. Indicates site It is a supply point, not a demand point. ; This is a zero-one vector (the element value can only be 0 or 1) given in advance according to the actual situation. Indicate demand points It can serve as a supply point. Indicates site Cannot be used as a supply point. ; This is a zero-to-one decision matrix for spare parts supply relationships (elements can only be 0 or 1). Indicate demand points Spare parts are supplied by the point of sale Assure, Indicate demand points Not by supply point Assure, , ; For all index vectors that can serve as supply points, such as It can be selected as a supply point, that is For locations requiring staff to be on duty, ,in ; For the index vector of all demand points, This indicates a specific need. ,in ; The dimension and index vector of all demand points The elements are identical, and each element represents the index of the supply point corresponding to a demand point among all facility points. , .on the one hand Each element in the list has a corresponding repair parts coverage relationship, such as for This indicates the demand point. From the supply point On the other hand, to ensure Zero-to-one decision matrix related to repair spare parts coverage There is a one-to-one correspondence between the vector and the spare parts supply relationship zero-one decision matrix. The latter is mainly used for the establishment of mathematical models, while the former is mainly used for model solving in the following text. The vector and the spare parts supply relationship zero-one decision matrix have a one-to-one correspondence. In the spare parts supply relationship zero-one decision matrix, the element value of 1 indicates that the spare parts of the demand point are guaranteed by the supply point, and the element value of 0 indicates that the demand point is not guaranteed by the supply point.

[0037] For auxiliary zero-one variables (a variable vector of elements whose element values ​​can only be 0 or 1). Indicate facility point Selected as a supply point Indicate facility point Not selected as a supply point ; Indicates the maximum number of supply points; Indicates facility points within the area to be optimized. to facility The guarantee period ; Indicate demand points Priority coverage time limit for facility points (reserved parameter, mainly to provide priority coverage time limit for the needs of high-level repair responsibility agencies in the future); medium elements Indicate demand points The Spare parts coverage period ; Indicates taking a constant and The smaller value in; Representing vectors The minimum value in; Represents two matrices of the same dimension and The dot product relation is defined. For the matrix With matrix The new matrix obtained by multiplying corresponding elements and arranging them in their original positions is... ,but .

[0038] The minimum coverage time for the supply of repair spare parts for communication equipment is then expressed as: (1-4) Furthermore, taking into account economic factors such as management costs associated with the construction of supply points, these costs are normalized and weighted together with coverage time as the objective function. The supply coverage time is primarily based on the upper limit of the number of supply points. The corresponding minimum coverage time and maximum coverage time Normalization is performed, and the number of supply points is capped at the upper limit. Processing based on this, we obtain the following formula: (1-5) in, , The multi-objective weight parameters are given in advance and satisfy the following conditions: . When the above constraints are met, the minimum guarantee time is when the objective function is (1-4). Let (1-6) be the maximum guarantee time corresponding to the objective function (1-6) under the condition that the above constraints are met and the guarantee time is a finite value.

[0039] (1-6) Each demand point is guaranteed by only one supply point, and all demand points can be guaranteed. The inability to guarantee certain sites that are not demand points and only act as supply points can be represented by the following constraint: (1-7) Some demand points are unattended sites and cannot be used as supply points, as indicated by the following constraints: (1-8) The guarantee time from the supply point to the demand point, the site priority guarantee time limit for the demand point, and the spare parts guarantee time limit are expressed as the following constraints: (1-9) The upper limit on the total number of supply points is set as follows: (1-10) (1-11) (1-12) Based on the above analysis, this invention provides a method for optimizing the topology layout of repair spare parts for communication equipment based on SAGA, combined with the appendix. Figure 1 and attached Figure 2 As shown, the method includes: S1, initialize the coverage time and upper limit of the number of supply points for communication equipment repair spare parts from demand points, generate an initial repair spare parts topology layout scheme, and construct the constraints of the repair spare parts topology layout scheme; it should be noted that this step mainly sets the target weight coefficient. Priority coverage time limit and single repair coverage time limit , and the upper limit of the number of supply points Etc. Among them, multi-objective weight coefficients When this occurs, it indicates that optimization focuses more on time efficiency. When the number of supply points is limited, it indicates that the optimization tends to reduce the number of supply points. By limiting the number of supply points, the possible combinations of choices are reduced, thereby narrowing the solution space, making the solution process more efficient, avoiding redundant calculations caused by invalid combinations, and reducing the time complexity of the solution process.

[0040] S2, using the coverage time and the number of supply points as optimization objectives, constructs a multi-objective optimization model for the repair spare parts topology layout based on SAGA. It should be noted that step S2 analyzes the main problems existing in the current repair spare parts topology layout, and proposes an optimization approach for the topology layout by comprehensively considering time and economic requirements, constructing a topology layout optimization configuration model based on multi-objective programming. Step S2 is specifically implemented through the following steps S31-S36, which will not be elaborated upon here.

[0041] S3. Based on the initial repair spare parts topology layout scheme, the optimization objective, and the constraints, iteratively solve the multi-objective optimization model of the repair spare parts topology layout to obtain the optimal repair spare parts topology layout scheme. It should be noted that, considering the complexity of the repair spare parts topology layout problem and its tendency to find local optima, a simulated annealing-genetic fusion algorithm is proposed, combining the advantages of simulated annealing and genetic algorithms, to solve the optimization of total coverage time and the number of supply points, providing a reliable decision-making basis for the topology layout scheme of communication equipment repair spare parts.

[0042] In this embodiment, solving the multi-objective optimization model for the topology layout of the repair spare parts can specifically include: S31, an initial population is generated based on the simulated annealing algorithm, and the fitness of individuals in the population is calculated; where each individual in the population represents a feasible repair spare parts topology layout scheme; it should be noted that each individual in the population represents a feasible repair spare parts configuration scheme. Initial Population It mainly consists of two parts. The first part consists of the constraints satisfying (1-7) to (1-9). The first part consists of one individual. The second part consists of two special individuals, namely... The corresponding repair spare parts configuration scheme must also satisfy the constraints (1-7) to (1-9). To ensure the generation of the two special individuals, it is necessary to... Calculations are performed based on the aforementioned The definition introduces a single-objective optimization method, which can obtain two specific individuals and also obtain the results needed in the subsequent normalization process. The objective function is simplified to consider only the shortest coverage time, i.e., equation (3-1): (2-1) On the other hand, by adding constraints (1-10) to (1-12), and further utilizing the classical simulated annealing algorithm, the upper limit of the number of supply points can be solved respectively. At that time, the corresponding minimum coverage time and maximum coverage time The objective function corresponding to the maximum coverage time is: (2-2) Each individual is represented by a vector with the same dimension as the total number of demand points, where each element of the vector is the index of the supply point corresponding to each demand point across all sites. The two special individuals obtained through the above process are similar to those described earlier. Individuals merge to form the initial population. Its total size is Each individual. Considering the complexity of selecting supply points, each individual is represented by a vector with the same dimension as the total number of demand points. This indicates that its elements are the indices of the supply points corresponding to each demand point across all sites. On the one hand, by The elements in the table can be used to obtain the covering relationship, such as for This indicates the demand point. From the supply point Coverage. On the other hand, it can be seen that... Coverage Relationship Zero-One Decision Matrix There is a one-to-one correspondence. Therefore, these two representation methods will be used alternately in the following text.

[0043] This invention uses the following objective function value as the fitness value of an individual: (2-3) As can be seen from the objective function above, objectives with different dimensions can be combined using a normalization method and balanced through weights. The maximum and minimum repair spare parts coverage time and the initial supply point upper limit obtained from S1 provide a reference for the normalization process in multi-objective optimization. This approach not only ensures the consistency of dimensions among different objectives but also improves the balance and efficiency of the optimization process.

[0044] S32, select parent individuals based on a genetic algorithm, and perform crossover on each individual to generate offspring individuals. Further, in step S32 of the above-mentioned communication equipment repair spare parts topology layout optimization method, the selection of parent individuals based on a genetic algorithm includes: randomly selecting a first preset individual, and with a preset probability... Select the appropriate individuals, in order to The probability is used to select individuals with low fitness; the random selection operation is repeated until a second preset parent individual is selected as the parent individual. Further, in step S32 of the above-mentioned communication equipment repair spare parts topology layout optimization method, the step of cross-pollinating each individual to generate offspring individuals specifically includes: according to a preset probability... For the selected Crossing parent individuals generates offspring individuals; wherein, the crossover is performed by randomly selecting... Crossing between parent generations, when The lower the relative differences in fitness between parents, the higher the probability of crossover. It should be noted that this is based on a certain probability... For the selected Crossing offspring individuals from parent individuals generates offspring individuals. The crossover operation is performed by randomly selecting... Parent generation ( Optional ) cross over, when The lower the relative differences in fitness among the parents, the higher the probability of crossover. The crossover probability is set as follows: (2-4) in, It is a constant that controls the degree to which fitness differences affect the crossover probability. Typically... It is a positive value, controlling the sensitivity of the "difference"; when When the fitness difference is large, it has a greater impact on the crossover probability, and the crossover probability is more sensitive to changes; when When the fitness level is small, the difference in fitness has a relatively small impact on the crossover probability.

[0045] In corresponding to the aforementioned offspring individuals During the generation process, individuals The corresponding zero-one decision matrix Constraints (1-7) to (1-12) must be satisfied. Furthermore, in subsequent processes, all newly generated individuals are constructed based on satisfying these constraints to ensure the feasibility of the solution and improve search efficiency.

[0046] Furthermore, in step S32 of the above-mentioned communication equipment repair spare parts topology layout optimization method, the step of cross-fertilizing each individual to generate offspring individuals further includes: A local structure-preserving crossover method is employed. By exchanging partial fragments of parent solutions and combining this with probabilistic constraints to generate new supply point coverage optimization schemes for offspring, the superior characteristics of the parent solutions are preserved, avoiding unnecessary solution space checks. Specifically, to retain useful information and avoid "destructive recombination," the local structure-preserving crossover method is primarily used while ensuring the structural integrity of the solution remains intact. By exchanging partial fragments of parent solutions and combining this with probabilistic constraints to generate new supply point coverage optimization schemes for offspring, the superior characteristics of the parent solutions are effectively preserved, while unnecessary solution space checks are avoided. This improves the algorithm's ability to escape local optima and enhances its overall efficiency.

[0047] S33, gene mutations are performed on the offspring individuals using an evolutionary generation ratio and an adaptive mutation strategy; it should be noted that this step is performed with a certain probability. Gene mutations are performed on offspring individuals, with the probability of mutation employing an adaptive mutation strategy based on the generation ratio and fitness.

[0048] Furthermore, the gene mutation in step S33 of the above-mentioned communication equipment repair spare parts topology layout optimization method specifically includes: The preset probability is determined based on the ratio of the current iteration number to the maximum iteration number of the genetic algorithm, the fitness of the offspring individuals, the maximum and minimum fitness of the population after crossover, and the individual fitness function of the population with the maximum and minimum mutation probabilities. According to the preset probability Genetic mutations are performed on the offspring individuals. Assume the current iteration number of the genetic algorithm is... Maximum number of iterations in a genetic algorithm ,like Then the first The probability of individual mutation in each offspring is: (2-5) in, For the first The fitness of each offspring individual These represent the maximum and minimum fitness of the population before S6, respectively. For the maximum and minimum mutation probabilities, It is about population A function of the fitness of all individuals. Furthermore, if... Then the first The probability of individual mutation in each offspring is: (2-6) in, This is to reduce the initial mutation probability.

[0049] Furthermore, step S33 of the above-mentioned communication equipment repair spare parts topology layout optimization method also includes: To maintain the stability of the solution structure, a local structure-preserving mutation strategy is adopted. This involves randomly selecting a subset of genes within an individual and performing mutation operations within their local neighborhood. This introduces local perturbations without disrupting the overall structure, thereby verifying the effective coverage of supply points to demand points under constraints. To preserve valid information and avoid destructive mutations, this strategy not only helps maintain the feasibility of individuals but also facilitates rapid verification of the effective coverage of supply points to demand points under constraints, thus reducing computational complexity while ensuring solution quality.

[0050] S34, based on the simulated annealing algorithm, iterates through the offspring individuals after crossover and mutation, and selects offspring individuals to retain based on their fitness probability. Further, step S34 of the above-mentioned communication equipment repair spare parts topology layout optimization method also includes: using the probability of an offspring individual being selected, determined by a function of the fitness of individuals in the new generation population and the fitness of all individuals, as a preset probability. The individual fitness function is used to adjust the degree to which fitness differences affect the probability of an individual being selected for simulated annealing; the offspring individuals after crossover mutation are processed with the preset probability. The simulated annealing algorithm is applied for a predetermined number of iterations to obtain a new set of feasible solutions. It should be noted that the offspring individuals after crossover and mutation are processed with a certain probability... The maximum number of iterations is The simulated annealing algorithm is used to process the data, resulting in a new set of feasible solutions. The probability of an individual being selected Related to fitness: (2-7) in, For the new generation of population The Middle The fitness of an individual It is about population A function of the fitness of all individuals, used to adjust the degree to which fitness differences affect the probability of an individual being selected for processing in the simulated annealing algorithm.

[0051] The simulated annealing algorithm generates new feasible solutions following the mutation method used in S5 to generate new individuals, and the probability of accepting the new solution is... for: (2-8) in, The current temperature, It is a threshold constant. Any difference in the solution that is "greater than a certain threshold" is rejected, thereby reducing the acceptance of "range solutions". , For the first The fitness of the new feasible solution after individual perturbation. Furthermore, the formula for calculating the cooling function is as follows: (2-9) in, The initial temperature, This represents the current iteration number of the simulated annealing algorithm. Simulated annealing, as a nested local optimization stage in the genetic algorithm, has its iteration number set to control the overall computation time. The inherent settings are relatively small. To ensure that the annealing process converges quickly within a finite number of steps, a linear cooling function is used to achieve rapid temperature decay and avoid the additional time cost of an excessively long annealing process.

[0052] S35, merge the retained offspring individuals with the selected parent individuals from the parent individuals to generate a new generation population; it should be noted that, according to a certain probability Offspring individuals generated by crossover, mutation, and simulated annealing algorithms are selected and their parent individuals are selectively retained using S4 algorithm to form a new generation population. .

[0053] S36. Determine if the iteration termination condition is met. If it is, output the optimal repair spare parts topology layout scheme based on the fitness of individuals in the new generation population; otherwise, use the new generation population as the new initial population and repeat the iteration. It should be noted that determining whether the iteration termination condition of the algorithm has been met, if so, outputs the optimal repair spare parts topology layout scheme based on the fitness of individuals in the population; otherwise, the current population... As a new initial population, return to calculate the fitness of individual populations and continue iterating.

[0054] Furthermore, in step S31 of the above-mentioned communication equipment repair spare parts topology layout optimization method, the initialization of the population includes: Individuals that meet the following constraints will be designated as the first subpopulation: Each demand point is guaranteed by only one supply point, and all demand points can be guaranteed. To simplify the guarantee relationship, it is agreed in the model construction that each demand point is guaranteed by only one supply point. When a demand point has a need for communication equipment spare parts, they can be obtained directly from the corresponding supply point. This assumption considers the balance between speed and convenience and economy, and is applicable to the equipment repair scenario with safety requirements in this invention. See formula (2-7) for reference.

[0055] Unattended demand points cannot be used as supply points. From the definition of demand points, they primarily refer to the infrastructure for deploying fixed-point communication equipment. Currently, the maintenance of such facilities is gradually shifting towards unattended operation. Unattended facilities have certain limitations in terms of repair and spare parts supply, and daily management. Therefore, when optimizing the topology layout, unattended facilities are generally not considered as alternative supply points. See formula (1-8) for reference.

[0056] The supply-demand time meets the site priority guarantee time limit and spare parts guarantee time limit requirements of the demand point. From the perspective of supply point analysis, the main factor limiting its coverage limit is the quantity of repair spare parts. Assuming that Assumption 1 is true, Assumption 4 can be true as long as the quantity of spare parts meets the coverage requirements. The fundamental purpose of establishing a spare parts warehouse is to meet the coverage requirements, so this assumption is consistent with reality. See formula (1-9) for reference.

[0057] Individuals that meet the following constraints will be designated as the second subpopulation: The individuals corresponding to the maximum and minimum coverage time of the supply point to the demand point; see formulas (1-4), (1-5) and (1-6) for reference.

[0058] The first subpopulation and the second subpopulation constitute the initialization population.

[0059] This invention mathematically describes the repair scenario and proposes a fusion model optimization method. By combining simulated annealing and genetic algorithm models, it fully leverages the global search advantage of genetic algorithms while utilizing the local fine-tuning optimization capability of simulated annealing to effectively address resource allocation optimization problems with large-scale and complex constraints. This improves the solution efficiency and the quality of the optimal solution in the spare parts supply and storage topology layout optimization model.

[0060] As an example, this invention takes the optimization of the location configuration of communication equipment repair and spare parts points for a company in some provinces and cities as an example, and conducts a case analysis of the proposed optimization strategy and the simulated annealing-genetic algorithm solution method, and compares it with the classic simulated annealing algorithm. The number of basic points is 175, which are relatively concentrated in some areas and more dispersed in remote areas. A prediction module that comprehensively considers factors such as transportation vehicles and actual daily road congestion calculates the supply coverage time between each pair of points based on accumulated experience data, establishing a distance-time correspondence.

[0061] Set basic constraint parameters, select a maximum repair spare parts coverage time of 6 hours based on actual needs, do not consider unattended facilities as alternative supply points, and set the weight of the economic objective to 0.7 and the weight of the timeliness objective to 0.3 based on experience.

[0062] The simulated annealing-genetic algorithm was used to obtain the optimized results for site selection and topology layout. The number of supply points was reduced from 29 to 8, significantly reducing the cost of supply point construction and management. In terms of single-time spare parts supply coverage time, the optimized maximum single-time supply coverage time is 5.98 hours, which meets the requirement of a 6-hour supply coverage time. Regarding the total repair spare parts supply coverage time, with 8 supply points, the minimum total supply coverage time is 529.15 hours, which meets the set requirements.

[0063] To verify the effectiveness of the optimization algorithm, under the same basic data, model, and constraints, the classic Simulated Annealing (SA) algorithm was used for computation, and the results were compared with those of the proposed Simulated Annealing Genetic Algorithm (SAGA). Specific optimization results and comparisons are attached. Figure 3 As shown in Table 1.

[0064]

[0065] Table 1 - Comparison of Optimization Results between SAGA and SA Algorithms Appendix Figure 3 This reflects the results of multiple independent runs of the two algorithms, iterating from the upper limit of supply points from 11 to 7. When the upper limit of supply points is 7, both the SAGA and SA algorithms encounter no solution, which means that the minimum number of supply points to optimize is 8. Considering the overall cases where the model has an optimal solution, the SAGA algorithm outperforms the SA algorithm in both the total repair spare parts coverage time and the number of supply points. Figure 3In the graph, the green dots representing SAGA solutions are clearly clustered in the optimal solution region on the left, while the blue dots representing SA solutions are more dispersed, mostly located in the upper right corner of the graph. SA solutions exhibit disadvantages such as longer coverage time and a larger number of supply points. The comparison of the average number of supply points, minimum, maximum, and average total coverage time in Table 1 further confirms this result. Furthermore, the SAGA convex hull boundary, indicated by the green dashed line, is close to the left side, with a more concentrated coverage area, indicating that it is closer to the optimal solution set in multi-objective tradeoffs and has higher stability and quality. In contrast, the SA algorithm boundary, indicated by the blue dashed line, has a wider range and is far from the ideal region, with a dispersed solution distribution, showing lower stability and solution quality than SAGA. Overall, the SAGA algorithm not only obtains better solutions but also possesses better stability. This stability is particularly important for practical spare parts topology layout optimization problems because it means higher repeatability of the algorithm's output results, representing a more reliable deployment in practical applications.

[0066] As can be seen from the above embodiments and examples, the innovations of this invention include: First, it analyzes the main problems existing in the current repair spare parts topology layout, and proposes an optimization approach for the topology layout by comprehensively considering time and economic requirements, constructing a topology layout optimization configuration model based on multi-objective programming. Second, considering the complexity and susceptibility to local optima in the repair spare parts topology layout problem, it proposes a simulated annealing-genetic fusion algorithm, combining the advantages of simulated annealing and genetic algorithms, to solve for the optimization of total coverage time and the number of supply points, providing a reliable decision-making basis for the topology layout scheme of communication equipment repair spare parts.

[0067] According to a second aspect of the present invention, a communication equipment repair spare parts topology layout optimization system based on the above-mentioned SAGA-based communication equipment repair spare parts topology layout optimization method is also provided, in conjunction with the appendix. Figure 4 As shown, the system includes: An initialization module is configured to initialize the coverage time of the supply points to the demand points for the repair spare parts of the communication equipment and the upper limit of the number of supply points, generate an initial repair spare parts topology layout scheme, and construct the constraints of the repair spare parts topology layout scheme. A multi-objective optimization model construction module is configured to construct a SAGA-based multi-objective optimization model for repair spare parts topology layout, using the coverage time and the number of supply points as optimization objectives. The multi-objective optimization model solving module is configured to iteratively solve the multi-objective optimization model of the repair spare parts topology layout based on the initial repair spare parts topology layout scheme, the optimization objective, and the constraints, so as to obtain the optimal repair spare parts topology layout scheme.

[0068] It should be noted that the SAGA-based communication equipment repair spare parts topology layout optimization system of the present invention is implemented in accordance with the steps in the aforementioned SAGA-based communication equipment repair spare parts topology layout optimization method, and will not be repeated here.

[0069] This application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method. The computer-readable storage medium may include, but is not limited to, any type of disk, including floppy disks, optical disks, DVDs, CD-ROMs, microdrives, as well as magneto-optical disks, ROMs, RAMs, EPROMs, EEPROMs, DRAMs, VRAMs, flash memory devices, magnetic cards or optical cards, nanosystems (including molecular memory ICs), or any type of medium or device suitable for storing instructions and / or data.

[0070] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0071] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0072] In the several embodiments provided in this application, it should be understood that the disclosed apparatus can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some service interface; the indirect coupling or communication connection between devices or units may be electrical or other forms.

[0073] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0074] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0075] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage device (CMD). Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a memory and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned memory includes various media capable of storing program code, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0076] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, which may include: a flash drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, etc.

[0077] The foregoing description is merely an exemplary embodiment of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure. Those skilled in the art will readily conceive of embodiments of this disclosure upon considering the specification and practicing the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described herein. The specification and embodiments are to be considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.

[0078] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0079] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing the topology layout of repair spare parts for communication equipment based on SAGA, characterized in that, include: S1, initialize the coverage time of the supply points of the communication equipment repair spare parts to the demand points and the upper limit of the number of supply points, generate an initial repair spare parts topology layout scheme, and construct the constraints of the repair spare parts topology layout scheme. S2, using the coverage time and the number of supply points as optimization objectives, construct a multi-objective optimization model for repair spare parts topology layout based on SAGA; S3. Based on the initial repair spare parts topology layout scheme, the optimization objective, and the constraints, iteratively solve the multi-objective optimization model of the repair spare parts topology layout to obtain the optimal repair spare parts topology layout scheme. Specifically, solving the multi-objective optimization model for the topology layout of the repair spare parts includes: S31, an initial population is generated based on the simulated annealing algorithm, and the fitness of individuals in the population is calculated; where each individual in the population represents a feasible topology layout scheme for repair spare parts; S32, based on the genetic algorithm, selects parent individuals and performs crossover on each individual to generate offspring individuals; S33, Gene mutations are performed on the offspring individuals using an evolutionary generation ratio and an adaptive mutation strategy; S34, based on the simulated annealing algorithm, iterates through the offspring individuals after crossover and mutation, and selects offspring individuals to retain based on fitness probability; S35, merge the retained offspring individuals with the parent individuals selected from the parent individuals to generate a new generation population; S36. Determine whether the iteration termination condition is met. If it is met, output the optimal repair spare parts topology layout scheme based on the fitness of individuals in the new generation population. Otherwise, use the new generation population as a new initial population and perform iteration cyclically.

2. The method for optimizing the topology layout of communication equipment repair spare parts as described in claim 1, characterized in that, In step S31, the initialization of the population includes: Individuals that meet the following constraints will be designated as the first subpopulation: Each demand point is guaranteed by only one supply point, and all demand points can be guaranteed. Unattended demand points cannot be used as supply points. The supply-to-demand time meets the site priority guarantee time limit and spare parts guarantee time limit requirements of the demand point; Individuals that meet the following constraints will be designated as the second subpopulation: The individuals corresponding to the maximum and minimum coverage time of the supply point to the demand point; The first subpopulation and the second subpopulation constitute the initialization population.

3. The communication equipment repair spare parts topology layout optimization method as described in claim 1, wherein step S32, the selection of parent individuals based on a genetic algorithm, includes: Randomly select the first preset individual, and with a preset probability Select the appropriate individuals, in order to The probability is used to select individuals with low fitness; the random selection operation is repeated until a second preset parent individual is selected as the parent individual.

4. The method for optimizing the topology layout of communication equipment repair spare parts as described in claim 2 or 3, further comprising: Each individual is represented by a vector of the same dimension as the number of all demand points, and the elements of the vector are the indices of the supply points corresponding to each demand point across all sites. There is a one-to-one correspondence between the vector and the zero-one decision matrix of the spare parts supply relationship. In the zero-one decision matrix of the spare parts supply relationship, an element value of 1 indicates that the spare parts of the demand point are guaranteed by the supply point, and an element value of 0 indicates that the demand point is not guaranteed by the supply point.

5. The communication equipment repair spare parts topology layout optimization method as described in claim 3, wherein step S32, which involves cross-referencing each individual to generate offspring individuals, specifically includes: According to the preset probability For the selected Crossing parent individuals generates offspring individuals; wherein, the crossover is performed by randomly selecting... Crossing between parent generations, when The lower the relative differences in fitness between parents, the greater the probability of crossover.

6. The communication equipment repair spare parts topology layout optimization method as described in claim 5, wherein step S32, the step of cross-referencing each individual to generate offspring individuals, further includes: The local structure preservation crossover method is adopted. By exchanging some fragments of the parent individual and combining the constraints, new supply point coverage is generated to optimize the offspring scheme. This preserves the good characteristics of the parent individual scheme and avoids the necessary solution space check.

7. The method for optimizing the topology layout of communication equipment repair spare parts as described in claim 6, wherein the gene mutation in step S33 specifically includes: The preset probability is determined based on the ratio of the current iteration number to the maximum iteration number of the genetic algorithm, the fitness of the offspring individuals, the maximum and minimum fitness of the population after crossover, and the individual fitness function of the population with the maximum and minimum mutation probabilities. ; According to the preset probability Gene mutations are performed on offspring individuals.

8. The communication equipment repair spare parts topology layout optimization method as described in claim 7, wherein step S33 further includes: While maintaining the stability of the solution structure, a local structure-preserving mutation strategy is adopted. By randomly selecting some genes in an individual and performing mutation operations in its local domain, local perturbations are introduced without destroying the overall structure, thereby verifying the effective coverage of the supply point to the demand point under constraints.

9. The method for optimizing the topology layout of communication equipment repair spare parts as described in claim 1, characterized in that, Step S34 further includes: The probability of selecting an offspring individual, determined by a function of the fitness of individuals in the new generation and the fitness of all individuals, is used as the preset probability. The individual fitness function is used to adjust the degree of influence of fitness differences on the probability of an individual being selected for processing by the simulated annealing algorithm; The offspring individuals after crossover mutation are subjected to the preset probability. The simulated annealing algorithm is used to process the solution for a preset number of iterations to obtain a new set of feasible solutions.

10. A communication equipment repair spare parts topology layout optimization system employing the SAGA-based communication equipment repair spare parts topology layout optimization method as described in any one of claims 1-9, characterized in that, The system includes: An initialization module is configured to initialize the coverage time of the supply points to the demand points for the repair spare parts of the communication equipment and the upper limit of the number of supply points, generate an initial repair spare parts topology layout scheme, and construct the constraints of the repair spare parts topology layout scheme. A multi-objective optimization model construction module is configured to construct a SAGA-based multi-objective optimization model for repair spare parts topology layout, using the coverage time and the number of supply points as optimization objectives. The multi-objective optimization model solving module is configured to iteratively solve the multi-objective optimization model of the repair spare parts topology layout based on the initial repair spare parts topology layout scheme, the optimization objective, and the constraints, so as to obtain the optimal repair spare parts topology layout scheme.

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