A method for solving the maximum coverage problem based on an improved symbiotic organism search algorithm

Abstract

The present application discloses a method for solving the maximum coverage problem based on an improved symbiotic search algorithm. The method for solving the maximum coverage problem based on the improved symbiotic search algorithm includes the steps of: S110, constructing a mathematical model of the maximum coverage problem, and then determining the objective function of the mathematical model of the maximum coverage problem; and S120, constructing a symbiotic search algorithm based on the mathematical model of the maximum coverage problem, wherein step S120 includes entering a binary decision stage; wherein, in the binary decision stage, each dimension of the new organism is first converted to the (0,1) interval by a Sigmoid function, a random vector between the (0,1) interval is generated, the new organism is subtracted from the random vector, and the binary decision value of the organism corresponding to the absolute value of the difference between the new organism and the random vector ranked from large to small is 1, and the binary decision value of other organisms is 0.

Description

Technical Field

[0001] The present application relates to the fields of computer science and optimization algorithms, and specifically to a method for solving the maximum coverage problem based on an improved symbiotic organism search algorithm. Background Art

[0002] The Maximum Covering Problem (MCP) is a classic discrete problem in the field of combinatorial optimization, and is widely used in a variety of practical scenarios such as resource allocation, facility site selection, and network optimization. The core goal of the maximum covering problem is to select p locations so that the number of covered demand points is the largest or the demand volume is the largest under the constraints of given limited resources or budget. The maximum covering problem is an NP-hard problem, and the difficulty of solving it increases exponentially as the scale of the problem increases.

[0003] Traditional methods for solving the maximum cover problem mainly include Lagrangian relaxation, column generation method, etc. Such traditional algorithms have high algorithm design and computational complexity. As the scale of the problem increases, the computing time and memory requirements increase dramatically, making it difficult to solve large-scale problems within an acceptable time. To overcome the above difficulties, researchers have introduced various meta-heuristic algorithms, such as genetic algorithms, particle swarm optimization algorithms, and ant colony algorithms. These algorithms achieve a balance between global search and local optimization by simulating biological evolution or group behavior in nature, and have achieved certain results in solving complex optimization problems. However, these algorithms still have the following shortcomings when dealing with the maximum cover problem: some algorithms are not efficient in searching in high-dimensional solution spaces, resulting in slow convergence; they are highly sensitive to parameters and require a large number of parameters to be adjusted. Improper parameter selection will affect the performance of the algorithm and increase the difficulty of applying the algorithm; lack of an effective global exploration mechanism, the algorithm is prone to converge prematurely and fall into a local optimal solution, and the quality of the solution cannot be further improved.

[0004] The Symbiotic Organisms Search (SOS) algorithm is an optimization algorithm based on biological symbiosis. The Symbiotic Organisms Search algorithm simulates the symbiotic interactions in paired biological relationships to find the most suitable organisms. Symbiotic interactions include three stages: mutualism, commensalism, and parasitism. The Symbiotic Organisms Search algorithm was originally designed for continuous optimization problems. The Symbiotic Organisms Search algorithm has the advantages of few parameters, easy implementation, and balance between global and local searches, and shows good performance on continuous optimization problems. However, when solving some discrete combinatorial optimization problems, the traditional Symbiotic Organisms Search algorithm has limitations such as mismatched encoding methods and illegal generated solutions, which affect the ability of the algorithm. Later, researchers improved the original Symbiotic Organisms Search algorithm to make it applicable to binary discrete optimization problems, thus forming a binary version of the Symbiotic Organisms Search algorithm. However, compared with other binary discrete optimization problems, the maximum covering problem has its own unique constraints. The current binary version of the symbiotic organism search algorithm has difficulty solving the maximum coverage problem, and the search efficiency is low in the high-dimensional solution space, resulting in slow convergence; it is highly sensitive to parameters and requires a large number of parameters to be adjusted. Improper parameter selection will affect the algorithm performance and increase the difficulty of algorithm application; it lacks an effective global exploration mechanism, and the algorithm is prone to converge prematurely and fall into a local optimal solution, making it impossible to further improve the quality of the solution.

[0005] In view of the above problems, it is urgent to improve the symbiotic search algorithm and design a solution method suitable for the maximum cover problem to improve the convergence speed of the algorithm, the quality and robustness of the solution. This is of great significance for solving large-scale and complex maximum cover problems in practical applications. Summary of the invention

[0006] One advantage of the present application is that it provides a method for solving the maximum coverage problem based on an improved symbiotic organism search algorithm, wherein the method for solving the maximum coverage problem based on an improved symbiotic organism search algorithm is suitable for scenarios such as resource allocation, facility site selection, and network optimization that require maximizing coverage, and can effectively improve problem-solving efficiency and reduce computing costs.

[0007] Another advantage of the present application is that it provides a method for solving the maximum coverage problem based on an improved symbiotic organism search algorithm, wherein the method for solving the maximum coverage problem based on an improved symbiotic organism search algorithm optimizes the encoding method and binary decision method of the solution to ensure that the number of 1s in all solution vectors in each stage of the algorithm meets the requirements of the maximum coverage problem.

[0008] Another advantage of the present application is that it provides a method for solving the maximum coverage problem based on an improved symbiotic organism search algorithm, wherein the method for solving the maximum coverage problem based on the improved symbiotic organism search algorithm redesigns the encoding method of the organism, adapts the continuous symbiotic organism search algorithm to a discrete binary form suitable for the maximum coverage problem, so that the symbiotic organism search algorithm can accurately represent the selection state and ensure the feasibility and effectiveness of the solution.

[0009] Another advantage of the present application is that it provides a method for solving the maximum coverage problem based on an improved symbiotic organism search algorithm, wherein the method for solving the maximum coverage problem based on an improved symbiotic organism search algorithm adjusts the strategy of the parasitic stage in the symbiotic organism search algorithm according to the characteristics of the maximum coverage problem, thereby enhancing the diversity of the population and improving the global search capability of the algorithm, thereby maintaining the legitimacy of the solution vector and enhancing the exploration capability of the entire population, avoiding falling into local optimality and premature convergence problems.

[0010] Another advantage of the present application is that it provides a method for solving the maximum coverage problem based on an improved symbiotic organism search algorithm, wherein the method for solving the maximum coverage problem based on an improved symbiotic organism search algorithm uses fewer parameters and is simple to operate, thereby reducing the difficulty of parameter tuning and the complexity of algorithm implementation and application, making it easier to promote and apply it in actual engineering projects.

[0011] According to one aspect of the present application, a method for solving the maximum coverage problem based on an improved symbiotic organism search algorithm is provided, which includes the steps of: S110, constructing a mathematical model of the maximum coverage problem, and then determining the objective function of the mathematical model of the maximum coverage problem; and S120, constructing a symbiotic organism search algorithm based on the mathematical model of the maximum coverage problem, wherein the objective function of the mathematical model of the maximum coverage problem is used as the fitness function of the solution of the symbiotic organism search algorithm; wherein, in step S120, the population of the symbiotic organism search algorithm is first initialized, and the organism with the best fitness in the current population is calculated, and then the mutual benefit stage, the binary decision stage, the commensal stage, the binary decision stage, and the parasitic stage are successively entered, and then the solution is iteratively updated until the algorithm is terminated; wherein, in the binary decision stage, the new organism is first converted into a new organism through the Sigmoid function Each dimension of is transformed into the interval (0, 1), generating a random vector between the interval (0, 1) , the new organism With random vector Subtraction, new organism The absolute value of the difference with the random vector is ranked from large to small of The binary decision value of the corresponding organism is 1, and the binary decision value of other organisms is 0, where The total number of facilities representing the mathematical model of the maximum coverage problem.

[0012] According to an embodiment of the method for solving the maximum coverage problem based on the improved symbiotic organism search algorithm described in the present application, in the parasitic stage, an organism is randomly selected. A position with a value of 1 and a position with a value of 0 in the , the two positions are exchanged to produce a new organism , calculate the fitness, and compare it with another randomly selected organism Compare and determine whether to use new organisms Replaces randomly selected organisms .

[0013] According to an embodiment of the method for solving the maximum coverage problem based on the improved symbiotic organism search algorithm described in the present application, when the new fitness is better than the original fitness, the new organism is used Replaces randomly selected organisms .

[0014] According to an implementation of the method for solving the maximum coverage problem based on the improved symbiotic biological search algorithm described in the present application, step S110 includes the following steps: S111, obtaining a set of demand points, a total number of facilities, a facility coverage radius, a weight of each demand point, and a distance between any two demand points; wherein, represents the set of demand points; represents the facility coverage radius; represents the weight of each demand point; Represents the coordinates of a demand point; represents the coordinates of another demand point; represents the distance between any two demand points; S112, defining a binary solution vector, where Represents the algorithm dimensional binary solution vector; express No. Dimension value; Indicated in Point construction facilities; represents the decision variable matrix; Indicated in No facilities have been built at the point or The facilities built at the point failed to cover point; when or hour, ,otherwise ; S113, establish an objective function, wherein the objective function is: ;in, , the constraints are .

[0015] According to an implementation of the method for solving the maximum coverage problem based on the improved symbiotic search algorithm described in the present application, in the process of initializing the population of the symbiotic search algorithm, the initial population size of the symbiotic search algorithm is set to eco_size, each organism in the population represents a solution of the algorithm, and eco_size binary initial solutions are randomly generated. , the number of dimensions 1 in the initial solution is equal to the total number of facilities in the mathematical model of the maximum covering problem , the organism with the best fitness in the current population is recorded as .

[0016] According to an implementation of the method for solving the maximum coverage problem based on the improved symbiotic organism search algorithm described in the present application, in the mutual benefit stage, the current organism with another randomly selected organism The interaction creates two new organisms , , where the interest factors of the two new organisms are denoted as BF1 and BF2 respectively; ; ; .

[0017] According to one embodiment of the method for solving the maximum coverage problem based on the improved symbiotic organism search algorithm described in the present application, the benefit factor of each organism is 1 or 2.

[0018] According to an implementation of the method for solving the maximum coverage problem based on the improved symbiotic organism search algorithm described in the present application, in the symbiotic stage, the current organism with another randomly selected organism Interaction, so that the current organism benefit, while another randomly selected organism Neither benefit nor suffer; in which the new organism The expression is: .

[0019] According to one implementation method of the method for solving the maximum coverage problem based on the improved symbiotic organism search algorithm described in the present application, the mutual benefit stage, binary decision stage, commensal stage, binary decision stage, and parasitic stage are repeated in the process of iteratively updating the solution until the algorithm is terminated. When the fitness reaches a preset range or the number of iterations reaches a set upper limit, the algorithm is terminated.

[0020] Further objectives and advantages of the present application will be fully reflected through understanding of the following description and drawings.

[0021] These and other objects, features and advantages of the present application are fully reflected in the following detailed description, drawings and claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] By describing the embodiments of the present application in more detail in conjunction with the accompanying drawings, the above and other purposes, features and advantages of the present application will become more apparent. The accompanying drawings are used to provide a further understanding of the embodiments of the present application and constitute a part of the specification. Together with the embodiments of the present application, they are used to explain the present application and do not constitute a limitation of the present application. In the drawings, the same reference numerals generally represent the same components or.

[0023] Figure 1 A flowchart schematic diagram of a method for solving the maximum coverage problem based on an improved symbiotic organism search algorithm according to an embodiment of the present application is illustrated.

[0024] Figure 2 A flowchart schematic diagram of an example of a method for solving the maximum coverage problem based on an improved symbiotic organism search algorithm according to an embodiment of the present application is illustrated. DETAILED DESCRIPTION

[0025] Below, the exemplary embodiments according to the present application will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application, and it should be understood that the present application is not limited to the exemplary embodiments described here.

[0026] It is understood that the term "one" should be understood as "at least one" or "one or more", that is, in one embodiment, the number of an element can be one, while in another embodiment, the number of the element can be multiple, and the term "one" cannot be understood as a limitation on the number. "Multiple" means greater than or equal to two.

[0027] Although ordinals such as "first," "second," and the like will be used to describe various components, those components are not limited herein. The term is used only to distinguish one component from another. For example, a first component may be referred to as a second component, and likewise, a second component may be referred to as a first component without departing from the teachings of the present application. The term "and / or" as used herein includes any and all combinations of one or more associated listed items.

[0028] The terms used herein are only used for the purpose of describing various embodiments and are not intended to be limiting. As used herein, the singular form is intended to include the plural form, unless the context clearly indicates an exception. It will also be understood that the terms "including" and / or "having" when used in this specification specify the presence of the described features, numbers, operations, components, elements, or combinations thereof, without excluding the presence or addition of one or more other features, numbers, operations, components, elements, or combinations thereof.

[0029] like Figure 1 to Figure 2 As shown, the method for solving the maximum coverage problem based on the improved symbiotic organism search algorithm according to the embodiment of the present application is explained. The method for solving the maximum coverage problem based on the improved symbiotic organism search algorithm improves the existing binary version of the algorithm so that it can be applied to scenarios such as resource allocation, facility site selection, network optimization, etc. that require maximizing coverage, and can effectively improve the efficiency of problem solving and reduce computing costs. In addition, the method for solving the maximum coverage problem based on the improved symbiotic organism search algorithm uses fewer parameters and is simple to operate, which reduces the difficulty of parameter tuning, reduces the complexity of algorithm implementation and application, and is easy to promote and apply in actual engineering.

[0030] Specifically, Figure 1 As shown, the method for solving the maximum coverage problem based on the improved symbiotic organism search algorithm includes the steps of: S110, constructing a mathematical model of the maximum coverage problem, and then determining the objective function of the mathematical model of the maximum coverage problem; and S120, constructing a symbiotic organism search algorithm based on the mathematical model of the maximum coverage problem, wherein the objective function of the mathematical model of the maximum coverage problem is used as the fitness function of the solution of the symbiotic organism search algorithm.

[0031] In step S110, a mathematical model of the maximum coverage problem is constructed, wherein the mathematical model of the maximum coverage problem is constructed by the following steps: S111, obtaining a set of demand points, a total number of facilities, a facility coverage radius, a weight of each demand point, and a distance between any two demand points; S112, defining a binary solution vector; and, S113, establishing an objective function.

[0032] Specifically, in step S111, a set of demand points, the total number of facilities, the radius of facility coverage, the weight of each demand point, and the distance between any two demand points are obtained. The demand point represents the object that needs to be served or covered, which can be an actual geographical location (such as a city, community), a customer group, or other entity that needs resources. Each demand point has a location coordinate that is used to determine the distance between it and the potential facility. The weight of the demand point reflects the importance or priority of each demand point. When constructing a mathematical model, the weight is used to quantify the value of different demand points being covered. Therefore, during the optimization process, the algorithm tends to select facility configuration solutions that can cover more high-weight demand points.

[0033] Facilities refer to physical locations or entities that can provide certain services or resources. The main function of these facilities is to cover or serve demand points within a certain range. Specifically, facilities can be public facilities, commercial facilities, educational facilities, transportation facilities, communication facilities, entertainment and leisure facilities, logistics facilities, etc. Public facilities can be hospitals, fire stations, etc. Commercial facilities can be retail stores, gas stations, etc. Educational facilities can be schools, libraries, etc. Transportation facilities can be bus stations, subway stations, airports, railway stations, high-speed rail stations, etc. Communication facilities can be base stations, satellite ground stations, etc. Entertainment and leisure facilities can be parks, gymnasiums, etc. Logistics facilities can be warehouses, distribution centers, etc. Each facility usually has multiple key attributes, such as location, coverage radius, service capabilities, cost, etc.

[0034] by represents the set of demand points; Indicates the total number of facilities; represents the facility coverage radius; represents the weight of each demand point; Represents the coordinates of a demand point; represents the coordinates of another demand point; Represents the distance between any two demand points.

[0035] In step S112, a binary solution vector is defined. Specifically, a binary solution vector is a common way to represent candidate solutions. Each element in the solution vector corresponds to a possible facility location, indicating whether the location is selected to build a facility. Each element It is equal to a binary value, which can be 0 or 1. In the Maximum Covering Problem (MCP), the decision variable matrix is ​​a key component used to represent which facility locations are selected and how they cover the demand points.

[0036] In the embodiment of the present application, Represents the algorithm dimensional binary solution vector; express No. Dimension value; Indicated in Point construction facilities; Indicated in No facilities will be built at this point; represents the decision variable matrix; Indicated in No facilities have been built at the point or The facilities built at the point failed to cover point Indicated in Point construction facilities and The facilities built at the point can cover point; when or hour, ,otherwise .

[0037] In step S130, an objective function is established. Specifically, the objective function is: ,in, , the constraints are ; Since the objective function is a fixed value, the objective function can be converted to .

[0038] In step S120, a symbiotic organism search algorithm is constructed based on the maximum coverage problem mathematical model, wherein the objective function of the maximum coverage problem mathematical model is used as the fitness of the solution of the symbiotic organism search algorithm. Specifically, Figure 2 As shown in the figure, in the process of constructing the symbiotic organism search algorithm based on the mathematical model of the maximum coverage problem, the population of the symbiotic organism search algorithm is first initialized, and the organism with the best fitness in the current population is calculated, and then the mutualism stage, binary decision stage, commensal stage, binary decision stage, and parasitic stage are entered in sequence, and then the solution is iteratively updated until the algorithm is terminated.

[0039] Accordingly, step S120 includes the steps of: S121, initializing the population of the symbiotic organism search algorithm and calculating the organism with the best fitness in the current population; S122, entering the mutual benefit stage; S123, entering the binary decision stage; S124, entering the commensal stage; S125, entering the binary decision stage; S126, entering the parasitic stage; S127, iteratively updating the solution until the algorithm is terminated.

[0040] In step S121, the population of the symbiotic search algorithm is initialized, and the organism with the best fitness in the current population is calculated. Specifically, in the symbiotic search algorithm, the initial population size refers to the number of a set of candidate solutions randomly generated when the algorithm starts. Each candidate solution represents a possible solution to a problem. These candidate solutions form the basis for the algorithm to explore the solution space. By continuously updating and improving the candidate solutions in the iterative process, the optimal or approximately optimal solution to the problem can be found. A larger initial population size can increase the diversity of solutions, allowing the symbiotic search algorithm to explore the solution space more widely, thereby reducing the risk of falling into a local optimal solution. However, an excessively large population size will also increase the computational cost and time complexity. A smaller initial population size may cause the algorithm to converge faster, but this rapid convergence may be at the expense of the quality of the solution because it reduces the opportunity for global exploration. An appropriate initial population size helps to improve the robustness of the algorithm, that is, it can perform well under different problem instances and parameter settings.

[0041] In the embodiment of the present application, the initial population size of the symbiotic organism search algorithm is set to eco_size, and each organism in the population represents a solution of the algorithm. In order to ensure the legitimacy of the solution, the number of initial solutions equal to 1 in the initial solution must be strictly equal to the total number of facilities in the mathematical model of the maximum coverage problem ; Calculate the organism with the best fitness in the current population. The organism with the best fitness in the current population is recorded as .

[0042] In step S122, the mutualism phase is entered. Specifically, in the symbiotic biological search algorithm, the mutualism phase is a process that simulates the mutual benefit between different species in nature through cooperation and resource sharing. The purpose of this phase is to improve the quality of the solution and accelerate convergence by promoting cooperation between organisms in the population.

[0043] In the embodiment of the present application, in the mutual benefit stage, the current organism with another randomly selected organism The interaction creates two new organisms , , where the interest factors of the two new organisms are denoted as BF1 and BF2 respectively; ; ; .

[0044] In the symbiotic search algorithm, the benefit factor for new organisms is a key parameter used to control the degree of improvement of new organisms in the mutualistic stage and the parasitic stage. The benefit factor of the new organism determines the extent of improvement of the new organism relative to the original organism, thereby affecting the exploration and development capabilities of the algorithm. Usually, the benefit factor of the new organism is a randomly generated value used to adjust the position of the new organism. By introducing the benefit factor, the algorithm can strike a balance between exploring new solution space and developing existing solutions. A larger benefit factor means a larger improvement step, which helps global exploration; a smaller benefit factor means a smaller improvement step, which helps local development. In one example of the present application, the benefit factor of each new organism can be set to 1 or 2.

[0045] In step S123, the binary decision stage is entered. In the embodiment of the present application, the method for solving the maximum coverage problem based on the improved symbiotic search algorithm adapts the continuous symbiotic search algorithm to a discrete binary form suitable for the maximum coverage problem by redesigning the encoding method of the organism, so that the symbiotic search algorithm can accurately represent the selection state and ensure the feasibility and effectiveness of the solution. Furthermore, the method for solving the maximum coverage problem based on the improved symbiotic search algorithm optimizes the encoding method and the binary decision method of the solution to ensure that the number of 1s in all solution vectors in each stage of the algorithm meets the requirements of the maximum coverage problem.

[0046] Specifically, since the new organisms generated in the mutualistic stage are continuous, the fitness can only be calculated by converting the continuous organisms into discrete organisms. Therefore, the continuous organisms generated in the mutualistic stage are converted into discrete organisms. The new organisms are updated only when their new fitness is better than the original fitness, that is, when When using new organisms Successive organisms that replace mutually beneficial stages Since not only the discreteness but also the legality of the solution to the maximum coverage problem must be satisfied, the traditional decision-making method cannot be used.

[0047] In the embodiment of the present application, the new organism is first transformed into Each dimension of is transformed into the interval (0,1), generating a random vector between the interval (0, 1) , the new organism With random vector Subtraction, new organism The absolute value of the difference with the random vector is ranked from large to small of The binary decision of the corresponding organism has a value of 1, and the binary decision of the other organisms has a value of 0.

[0048] In step S124, the commensalism phase is entered. In the commensalism search algorithm, the commensalism phase simulates a symbiotic relationship in nature, in which one species (beneficiary) benefits from another species (provider) while the latter is not affected. The main purpose of this phase is to help the organisms in the population improve their solutions while maintaining the diversity of the population by imitating this mutually beneficial relationship without negatively affecting the provider. In this way, the beneficiary organisms can obtain better fitness values, thereby improving the quality of the overall population while avoiding premature convergence to the local optimal solution. The mutual benefit phase involves a two-way information exchange between the two organisms, from which both parties can benefit; while in the commensalism phase, only one party (beneficiary) benefits from the other party (provider), and the provider is not affected.

[0049] In the present embodiment, in the symbiotic stage, the current organism with another randomly selected organism Interaction, so that the current organism benefit, while another randomly selected organism Neither benefit nor suffer; in which the new organism The expression is: .

[0050] In step S125, the binary decision stage is entered. Since not only the discreteness but also the legality of the solution to the maximum coverage problem must be satisfied, the traditional decision method cannot be used. In the embodiment of the present application, the new organism is firstly transformed into Each dimension of is transformed into the interval (0, 1), generating a random vector between the interval (0, 1) , the new organism With random vector Subtraction, new organism The absolute value of the difference with the random vector is ranked from large to small of The binary decision of the corresponding organism has a value of 1, and the binary decision of the other organisms has a value of 0.

[0051] In step S126, the parasitic phase is entered. Due to the characteristics of the maximum coverage problem, the traditional parasitic phase operation cannot be used directly. The method for solving the maximum coverage problem based on the improved symbiotic search algorithm of the present application adjusts the strategy of the parasitic phase in the symbiotic search algorithm according to the characteristics of the maximum coverage problem, enhances the diversity of the population, improves the global search capability of the algorithm, maintains the legitimacy of the solution vector, and enhances the exploration capability of the entire population, avoiding falling into local optimality and premature convergence problems.

[0052] Specifically, in the embodiment of the present application, in the parasitic stage, randomly select an organism A position with a value of 1 and a position with a value of 0 in the , the two positions are exchanged to produce a new organism , calculate the fitness, and compare it with another randomly selected organism Compare and determine whether to use new organisms Replaces randomly selected organisms When the new fitness is better than the original fitness, use the new organism Replaces randomly selected organisms .

[0053] In step S127, the solution is iteratively updated until the algorithm ends. Specifically, steps S122 to S126 are repeatedly executed, and the algorithm ends when the fitness reaches a preset range or the number of iterations reaches a set upper limit. In other words, in the process of iteratively updating the solution until the algorithm ends, the mutual benefit stage, the binary decision stage, the commensal stage, the binary decision stage, and the parasitic stage are repeated, and the algorithm ends when the fitness reaches a preset range or the number of iterations reaches a set upper limit.

[0054] In summary, the method for solving the maximum coverage problem based on the improved symbiotic search algorithm according to the embodiment of the present application is explained. The method for solving the maximum coverage problem based on the improved symbiotic search algorithm is suitable for scenarios such as resource allocation, facility site selection, and network optimization that require maximizing coverage, and can effectively improve problem solving efficiency and reduce computing costs.

[0055] The present application and its implementation methods are described above, and such description is not restrictive. The drawings show only one implementation method of the present application, and the actual structure is not limited thereto. In short, if ordinary technicians in the field are inspired by it and design structural methods and embodiments similar to the technical solution without creative design without departing from the inventive purpose of the present application, they should all fall within the protection scope of the present application.

Claims

1. A method for solving the maximum coverage problem based on an improved symbiotic organism search algorithm, characterized in that: The method comprises the following steps: S110, constructing a mathematical model of the maximum coverage problem, and then determining the objective function of the mathematical model of the maximum coverage problem; and S120, constructing a symbiotic organism search algorithm based on the mathematical model of the maximum coverage problem, wherein the objective function of the mathematical model of the maximum coverage problem is used as the fitness function of the solution of the symbiotic organism search algorithm; wherein, in step S120, the population of the symbiotic organism search algorithm is first initialized, and the organism with the best fitness in the current population is calculated, and then the mutual benefit stage, the binary decision stage, the commensal stage, the binary decision stage, and the parasitic stage are successively entered, and then the solution is iteratively updated until the algorithm is terminated; wherein, in the binary decision stage, the new organism is firstly converted into a new organism by the Sigmoid function. Each dimension of is transformed into the interval (0, 1), generating a random vector between the interval (0, 1) , the new organism With random vector Subtraction, new organism The absolute value of the difference with the random vector is ranked from large to small of The binary decision value of the corresponding organism is 1, and the binary decision value of other organisms is 0, where The total number of facilities representing the mathematical model of the maximum coverage problem; Wherein, step S110 includes the steps of: S111, obtaining a set of demand points, a total number of facilities, a facility coverage radius, a weight of each demand point, and a distance between any two demand points; wherein, represents the set of demand points; represents the facility coverage radius; represents the weight of each demand point; Represents the coordinates of a demand point; represents the coordinates of another demand point; represents the distance between any two demand points; S112, defining a binary solution vector, where Represents the algorithm dimensional binary solution vector; express No. Dimension value; Indicated in Point construction facilities; represents the decision variable matrix; Indicated in No facilities have been built at the point or The facilities built at the point failed to cover point; when or hour, ,otherwise ; S113, establish an objective function, wherein the objective function is: ;in, , the constraints are ; Among them, in the symbiotic search algorithm, the initial population size refers to the number of a set of candidate solutions randomly generated when the algorithm starts, each candidate solution represents a possible solution to a problem, and each organism in the population represents a solution of the algorithm.

2. The method for solving the maximum coverage problem based on the improved symbiotic organism search algorithm according to claim 1, wherein: During the parasitic phase, randomly selected organisms A position with a value of 1 and a position with a value of 0 in the , the two positions are exchanged to produce a new organism , calculate the fitness, and compare it with another randomly selected organism Compare and determine whether to use new organisms Replaces randomly selected organisms .

3. The method for solving the maximum coverage problem based on the improved symbiotic organism search algorithm according to claim 2, wherein: When the new fitness is better than the original fitness, use the new organism Replaces randomly selected organisms .

4. The method for solving the maximum coverage problem based on the improved symbiotic organism search algorithm according to claim 3, wherein: In the process of initializing the population of the symbiotic search algorithm, the initial population size of the symbiotic search algorithm is set to eco_size, and eco_size binary initial solutions are randomly generated. , the number of dimensions 1 in the initial solution is equal to the total number of facilities in the mathematical model of the maximum covering problem , the organism with the best fitness in the current population is recorded as .

5. The method for solving the maximum coverage problem based on the improved symbiotic organism search algorithm according to claim 4, wherein: In the mutualism stage, the current organism with another randomly selected organism The interaction creates two new organisms , , where the interest factors of the two new organisms are denoted as BF1 and BF2 respectively; ; ; .

6. The method for solving the maximum coverage problem based on the improved symbiotic organism search algorithm according to claim 5, wherein: The benefit factor for each organism is 1 or 2.

7. The method for solving the maximum coverage problem based on the improved symbiotic organism search algorithm according to claim 5, wherein: In the symbiotic stage, the current organism with another randomly selected organism Interaction, so that the current organism benefit, while another randomly selected organism Neither benefit nor suffer; in which the new organism The expression is: .

8. The method for solving the maximum coverage problem based on the improved symbiotic organism search algorithm according to claim 7, wherein: In the process of iteratively updating the solution until the algorithm ends, the mutual benefit stage, binary decision stage, commensal stage, binary decision stage, and parasitic stage are repeated. When the fitness reaches the preset range or the number of iterations reaches the set upper limit, the algorithm ends.

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