A facility location method in uncertain environment based on double-layer optimization

Abstract

The application discloses a facility location method in uncertain environment based on double-layer optimization, which is applied to a location scene composed of a customer demand point set I and a candidate facility set J and comprises the following steps: 1, initializing an upper-layer location population; 2, performing lower-layer optimization on all location individuals, finding a matching optimal radius, and performing evaluation; 3, performing cross and mutation operations on the upper-layer population to generate temporary offspring; 4, selecting good offspring for lower-layer optimization according to the number of facilities and the dispersion degree of each individual in the offspring; 5, comparing the parent population and the offspring which are subjected to lower-layer optimization according to an environment selection strategy to obtain a next generation population; 6, if a termination condition is reached, outputting a final population; otherwise, returning to step 3; 7, sorting all individuals of the final population in descending order according to evaluation values to select a facility location scheme with the minimum evaluation value. The application can effectively improve the reliability of location, thereby obtaining a higher-quality location scheme.

Description

Technical Field

[0001] This invention belongs to the field of facility location problems, specifically a facility location method based on two-level optimization under uncertain environments. Background Technology

[0002] Facility location decisions, as one of the fundamental decisions in logistics, are a crucial node in modern logistics systems. Scientifically selecting facility locations and determining their radii can effectively reduce transportation costs and ensure service levels.

[0003] Methods for solving facility location problems mainly focus on exact algorithms, heuristics, and metaheuristic algorithms. Exact algorithms, such as branch and bound, can find the optimal solution, but they suffer from high time complexity. This indicates that exact algorithms are generally only suitable for small-scale facility location problems. Heuristic and metaheuristic algorithms, such as simulated annealing, ant colony optimization, and evolutionary algorithms, can find a set of optimal solutions within a finite acceptable time. Evolutionary algorithms, inspired by biological evolution, have shown strong competitiveness in solving facility location problems. Therefore, many scholars have devoted considerable effort to evolutionary algorithms for solving facility location problems. It is precisely because of the continuous in-depth research on facility location problems that scholars have proposed many algorithms. However, most existing algorithms still have shortcomings in performance and efficiency when dealing with facility location problems under uncertain environments, and their overall performance declines as the problem size increases.

[0004] Real-world facility location problems involve many uncertainties such as facility interruptions and changing demand. Strengthening research on facility location problems under uncertain environments has significant practical application value. Most existing models typically assume that facilities are always available once built. However, in many practical applications, due to natural disasters, system failures, and other reasons, some established facilities may become unusable, thus every established facility carries the risk of interruption. Facility interruptions often lead to increased transportation costs or untimely service, thereby reducing the reliability of the location system. Summary of the Invention

[0005] The present invention aims to address the shortcomings of the existing technology by proposing a facility site selection method based on two-layer optimization under uncertain environments. This method is intended to effectively solve the problem of simultaneously optimizing facility site selection and coverage radius, and reduce the time complexity of dual-species interaction, thereby obtaining the site selection scheme with the minimum total distance and its coverage radius.

[0006] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0007] This invention discloses a facility location method based on two-level optimization under uncertain environments. It is applied to a location scenario consisting of a set of customer demand points I and a set of candidate facilities J, where i represents any customer demand point and j represents any candidate facility point. The method obtains the location coordinates of each customer demand point and candidate facility point in the location scenario and records the distance from candidate facility point j to its farthest customer i. max The distance is Record the candidate facility point j to its nearest customer i min The distance is Its characteristic lies in that the facility site selection method is carried out according to the following steps:

[0008] Step 1: Initialize the upper-level addressing population;

[0009] Step 1.0: Define the generation number of the current population as gen, and initialize gen = 1. Let the population of generation gen be... in, Let represent the location scheme of the num-th individual in the gen-th generation, and Indicates whether the num-th individual selects candidate facility point j. This indicates that the num-th individual did not select candidate facility point j, when This indicates that the num-th individual selects candidate facility point j; N u Indicates the population size, where L represents the number of candidate facilities;

[0010] Step 1.1: Initialize num = 1;

[0011] Step 1.2: Randomly generate the num-th individual. And as the current individual, the num-th individual Placed into the gen generation population Y gen middle;

[0012] Step 1.3: After assigning num+1 to num, check if num > N. u Whether it holds true or not, if it does, it means that the population Y of generation gen has been obtained. gen Otherwise, return to step 1.2 and execute sequentially.

[0013] Step 2: For the current generation Y population... gen The site selection schemes of all individuals are optimized at the next level to find the optimal matching radius and then evaluated.

[0014] Step 2.1: Initialize num = 1;

[0015] Step 2.2: For the current generation Y population (generation gen), gen The num-th individual Perform lower-level optimization to find the optimal matching radius and evaluate it;

[0016] Step 2.2.1, for the current individual All elements with a value of "1" are reassigned and used as the radius of the site selection facility;

[0017] Step 2.2.2: For the current individual A local search is performed to optimize the radius of the site selection facility, resulting in an updated value for the current individual, which is then assigned to... And obtain the current individual fitness rating

[0018] Step 2.3: After assigning num+1 to num, check if num > N. u If the condition is met, it indicates that the lower-level optimization of all individual location schemes is complete, and the population Y of generation gen is obtained. gen The set of fitness evaluation values ​​for all individual site selection schemes is as follows: Otherwise, return to step 2.2 and execute sequentially;

[0019] Step 3: For the gen generation population Y gen All individual location selection schemes in the population undergo upper-level crossover and mutation operations to generate a temporary offspring population;

[0020] Step 3.1: Define the temporary offspring population of generation gen as Child. gen and initialized to Define a size of N u The zero vector Flag is used to record the population Y in the gen generation. gen The selection of individuals as parents; define M as the number of crossover mutations, and initialize M = 1;

[0021] Step 3.2, in [1, N] u Two integers P are randomly generated within the interval for the Mth crossover mutation. 1,M P 2,M ;

[0022] Step 3.3, Determine P 1,M ≠P 2,M And Flag[P 1,M ] = 0, Flag[P 2,M If Flag[P] = 0, proceed to step 3.4; otherwise, return to step 3.2. 1,M ] = 0 indicates that the population Y in the gen generation is 0. gen P in the middle 1,M individual Not selected as a parent, Flag[P 2,M] = 0 indicates that the population Y in the gen generation is 0. gen P in the middle 2,M individual Not selected as a parent generation;

[0023] Step 3.4: Match the vector Flag with P 1,M and Setting the element at the corresponding position to "1" indicates that the population Y in the gen generation is... gen P in the middle 1,M individual and P 2,M individual It has been selected as the parent generation and used to generate offspring; among them, Represents an individual Whether candidate facility point j is selected. Represents an individual Whether candidate facility point j has been selected;

[0024] Step 3.5: Use the crossover operator on the Pth... 1,M individual and P 2,M individual Process and generate crossover individuals.

[0025] Step 3.6: For overlapping individuals Perform mutation operations to obtain mutated individuals.

[0026] Generate a random number ra. If ra > 0.5, then... middle The candidate facility point at the location is selected; otherwise, make middle The candidate facility location was not selected.

[0027] Step 3.7: Transfer the mutated individuals As a sub-generation individual site selection scheme And put into the temporary offspring population of generation gen. gen ;

[0028] Step 3.8, Judgment If true, it means that a temporary offspring population of generation gen has been obtained. Otherwise, after assigning M+1 to M, return to step 3.2 and execute sequentially;

[0029] Step 4: Based on the temporary offspring population of generation gen (Child) genThe number and dispersion of facilities corresponding to the site selection scheme of each offspring individual are analyzed, and good offspring are selected for further optimization at the next level.

[0030] Step 4.0: Define the temporary offspring population Child in generation gen. gen Number of facilities corresponding to each sub-generation site selection scheme in, This represents the location selection scheme for the Mth offspring individual. The number of facilities;

[0031] Define the temporary offspring population of generation gen as Child gen The degree of dispersion corresponding to each child generation location scheme in, This represents the location selection scheme for the Mth offspring individual. The degree of dispersion;

[0032] Step 4.1: Calculate the temporary offspring population Child in generation gen. gen Number of facilities corresponding to each individual site selection scheme in, This represents the location selection scheme for the Mth offspring individual. Whether candidate facility point j has been selected;

[0033] Step 4.2, Calculation The negative of the sum of the Euclidean distances between the location coordinates of all candidate facility points with a value of "1" is used as... Dispersion

[0034] Step 4.3, let This represents the set of non-dominant children and is initialized to empty.

[0035] Step 4.4: Based on the number and dispersion of facilities corresponding to the site selection scheme of each offspring individual, determine the temporary offspring population of generation gen. gen Perform a non-dominated sort on all offspring individuals, and then select and store the non-dominated offspring. middle;

[0036] Step 4.5: Follow the process in Step 2 to process the non-dominated child set. All non-dominated offspring are subjected to lower-level optimization and evaluation to obtain a set of fitness evaluation values. in, This represents the fitness score of the dom-th non-dominated offspring, where dom represents the number of non-dominated offspring.

[0037] Step 5: Select the population Y in generation gen based on the environmental selection strategy. genand its non-dominated child set By comparison, the population Y of generation gen+1 is obtained. gen+1 ;

[0038] Step 5.1, merge F gen and Then sort them in ascending order to select the top N with the smallest evaluation values. u The individual site selection schemes constitute the population Y of generation gen+1. gen+1 ;

[0039] Step 6: After assigning gen+1 to gen, check if gen has reached the maximum number of iterations. max If so, then stop iterating and obtain the gen-th iteration. max Generation population N u If the optimal radius of each site selection scheme and its site selection facility is not found, return to step three and execute sequentially.

[0040] Step 7: For the genth... max Generation population All individual site selection schemes are sorted in descending order of fitness evaluation value, and the facility site selection scheme with the smallest evaluation value is output.

[0041] The facility location method based on two-layer optimization under uncertain environments described in this invention is also characterized in that step 1.2 includes:

[0042] Step 1.2.1: Initialize j = 1;

[0043] Step 1.2.2, in the interval A real number d is randomly generated inside. j If d j Not in the range The innermost element represents the num-th individual. No candidate facility point j was selected, and Set to 0; otherwise, Set to 1;

[0044] Step 1.2.3: After assigning j+1 to j, check if j>L is true. If true, it means that the num-th individual has been obtained. Otherwise, return to step 1.2.2 and execute sequentially.

[0045] Step 2.2.1 includes:

[0046] Step 2.2.1.1: Initialize j = 1;

[0047] Step 2.2.1.2, if If so, proceed to step 2.2.1.3; otherwise, proceed within the interval. After randomly generating a real number and using it as the radius of the site selection facility, assign it to...

[0048] Step 2.2.1.3: After assigning j+1 to j, check if j>L is true. If true, it represents the location scheme of the num-th individual in the gen-th generation. Once the location facility radius of all elements is assigned, proceed with step 2.2.1.2 sequentially.

[0049] Step 2.2.2 includes:

[0050] Step 2.2.2.1: Define the current local search count as Len, initialize Len = 1, and set the maximum local search count as Len. max ; This represents the num-th individual in the gen-th generation of the population. Individual location schemes after the Lenth perturbation;

[0051] Step 2.2.2.2: Use equation (1) to analyze the current individual. To evaluate and obtain the current individual Evaluation value of total location distance

[0052]

[0053] In equation (1), Represents the fixed distance from candidate facility point j; using This represents the variable distance of candidate facility point j with a coverage radius r;

[0054] Step 2.2.2.3: Use equation (2) to analyze the current individual. Perform the Lenth perturbation to obtain the individual after the Lenth perturbation. Thus, the current individual can be obtained using equation (1). Evaluation value of total location distance And used as a fitness evaluation value:

[0055]

[0056] In equation (2), Δ represents the proportionality coefficient, and Δ∈(0,1);

[0057] Step 2.2.2.4, if Less than Then the current individual Updated to Conversely, maintain the current individual constant;

[0058] Step 2.2.2.5: After assigning Len+1 to Len, determine if Len > Len. max Whether it is true or false; if true, it indicates that the current individual... Update complete; otherwise, repeat steps 2.2.2.3 sequentially.

[0059] Step 3.5 includes:

[0060] Step 3.5.1, Take an individual and The intersection yields new individuals

[0061] Step 3.5.2, from In the set, randomly select a position j, and let Candidate facility point j is selected, thus obtaining the cross-individual. in, express Inverse of.

[0062] The present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing any of the facility addressing methods, and the processor is configured to execute the program stored in the memory.

[0063] The present invention discloses a computer-readable storage medium on which a computer program is stored, wherein the computer program, when executed by a processor, performs any step of the facility addressing method.

[0064] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0065] 1. This invention overcomes the difficulty of simultaneously optimizing facility location and determining facility radius in variable radius facility site selection by adopting a two-layer optimization framework. It solves the strong coupling problem between site selection and radius optimization in existing facility site selection technologies, thereby greatly reducing the difficulty of solving facility site selection and radius optimization problems and obtaining the optimal solution to the problem more quickly.

[0066] 2. This invention proposes an operator for crossover and mutation of binary variables in the site selection problem. The aim is to consider the correlation between each site location, fully utilize the geographical location information of the facilities, avoid overly sparse facility distribution, and serve customer needs over a wider area. Specifically, this operator considers the similarity between different site selection schemes, extracts common features, and then randomly selects some facilities to open or close.

[0067] 3. This invention proposes a novel solution selection optimization strategy that avoids the possibility of performing radius optimization for every location scheme. Specifically, this strategy selects a subset of non-dominated child location schemes from two perspectives: the number of facilities and their dispersion in each child location scheme, and performs radius optimization at the lower level. This reduces time complexity and, while saving computational resources, finds a good location scheme and the optimal matching radius more quickly. Attached Figure Description

[0068] Figure 1 This is a flowchart of the method of the present invention;

[0069] Figure 2 This is an example diagram of the crossover and mutation operator for binary variables according to the present invention;

[0070] Figure 3 This is an example diagram of the solution selection optimization strategy of the present invention. Detailed Implementation

[0071] This example presents a facility location method based on bi-level optimization under uncertain environments. It aims to address the problem of constructing facilities and determining their radii in practical facility location issues where demand and facilities are uncertain. By transforming the problem into a bi-level optimization problem, the two optimization problems are decoupled, reducing time complexity and overcoming the difficulty of simultaneous optimization. Furthermore, this method proposes a crossover mutation operator for binary variables, avoiding blind search and improving convergence speed. Moreover, by selecting good offspring individuals for lower-level optimization through two objectives, computational resources are saved, thereby obtaining the optimal location scheme and its matching optimal radius. Specifically, this method is applied to a location scenario consisting of a set of customer demand points I and a set of candidate facilities J, where i represents any customer demand point and j represents any candidate facility point. The method obtains the position coordinates of each customer demand point and candidate facility point in the location scenario and records the distance from candidate facility point j to its farthest customer i. max The distance is Record the candidate facility point j to its nearest customer i min The distance is like Figure 1 As shown, the site selection method for this facility is carried out according to the following steps:

[0072] Step 1: Initialize the upper-level addressing population;

[0073] Step 1.0: Define the generation number of the current population as gen, and initialize gen = 1. Let the population of generation gen be... in, Let represent the location scheme of the num-th individual in the gen-th generation, and Indicates whether the num-th individual selects candidate facility point j. This indicates that the num-th individual did not select candidate facility point j, when This indicates that the num-th individual selects candidate facility point j; N u Indicates the population size, where L represents the number of candidate facilities;

[0074] Step 1.1: Initialize num = 1;

[0075] Step 1.2: Randomly generate the num-th individual. And as the current individual, the num-th individual Placed into the gen generation population Y gen middle;

[0076] Step 1.2.1: Initialize j = 1;

[0077] Step 1.2.2, in the interval A real number d is randomly generated inside. j If d j Not in the range The innermost element represents the num-th individual. No candidate facility point j was selected, and Set to 0; otherwise, Set to 1;

[0078] Step 1.2.3: After assigning j+1 to j, check if j>L is true. If true, it means that the num-th individual has been obtained. Otherwise, return to step 1.2.2 and execute sequentially.

[0079] Step 1.3: After assigning num+1 to num, check if num > N. u Whether it holds true or not, if it does, it means that the population Y of generation gen has been obtained. gen Otherwise, return to step 1.2 and execute sequentially.

[0080] like Figure 2 As shown, 6 individuals were randomly generated in the initial population, and each individual represents a site selection scheme. For example, individual 1 indicates that among the 5 candidate facilities, facilities 1 and 4 are selected for construction, with a value of 1 at the corresponding position, and 0 at the other positions, indicating that the facilities are not selected.

[0081] Step 2: For the current generation Y population... gen The site selection schemes of all individuals are optimized at the next level to find the optimal matching radius and then evaluated.

[0082] Step 2.1: Initialize num = 1;

[0083] Step 2.2: For the current generation Y population (generation gen), gen The num-th individual Perform lower-level optimization to find the optimal matching radius and evaluate it;

[0084] Step 2.2.1, for the current individual All elements with a value of "1" are reassigned and used as the radius of the site selection facility;

[0085] Step 2.2.1.1: Initialize j = 1;

[0086] Step 2.2.1.2, if If so, proceed to step 2.2.1.3; otherwise, proceed within the interval. After randomly generating a real number and using it as the radius of the site selection facility, assign it to...

[0087] Step 2.2.1.3: After assigning j+1 to j, check if j>L is true. If true, it represents the location scheme of the num-th individual in the gen-th generation. Once the location facility radius of all elements is assigned, proceed with step 2.2.1.2 sequentially.

[0088] Step 2.2.2: For the current individual A local search is performed to optimize the radius of the site selection facility, resulting in an updated value for the current individual, which is then assigned to... And obtain the current individual fitness rating

[0089] Step 2.2.2.1: Define the current local search count as Len, initialize Len = 1, and set the maximum local search count as Len. max ; This represents the num-th individual in the gen-th generation of the population. Individual location schemes after the Lenth perturbation;

[0090] Step 2.2.2.2: Use equation (1) to analyze the current individual. To evaluate and obtain the current individual Evaluation value of total location distance

[0091]

[0092] In equation (1), Represents the fixed distance from candidate facility point j; using This represents the variable distance of candidate facility point j with a coverage radius r;

[0093] Step 2.2.2.3: Use equation (2) to analyze the current individual. Perform the Lenth perturbation to obtain the individual after the Lenth perturbation. Thus, the current individual can be obtained using equation (1). Evaluation value of total location distance And used as a fitness evaluation value:

[0094]

[0095] In equation (2), Δ represents the proportionality coefficient, and Δ∈(0,1);

[0096] Step 2.2.2.4, if Less than Then the current individual Updated to Conversely, maintain the current individual constant;

[0097] Step 2.2.2.5: After assigning Len+1 to Len, determine if Len > Len. max Whether it is true or false; if true, it indicates that the current individual... Update complete; otherwise, repeat steps 2.2.2.3 sequentially.

[0098] Step 2.3: After assigning num+1 to num, check if num > N. u If the condition is met, it indicates that the lower-level optimization of all individual location schemes is complete, and the population Y of generation gen is obtained. gen The set of fitness evaluation values ​​for all individual site selection schemes is as follows: Otherwise, return to step 2.2 and execute sequentially;

[0099] Step 3: For the gen generation population Y gen All individual location selection schemes in the population undergo upper-level crossover and mutation operations to generate a temporary offspring population;

[0100] Step 3.1: Define the temporary offspring population of generation gen as Child. gen and initialized to Define a size of N u The zero vector Flag is used to record the population Y in the gen generation. gen In cases where an individual is selected as a parent, such as... Figure 2 As shown, the value of each dimension of the vector is 0, indicating that none of the parent individuals were initially selected; define M as the number of crossover mutations, and initialize M = 1;

[0101] Step 3.2, in [1, N] uTwo integers P are randomly generated within the interval for the Mth crossover mutation. 1,M P 2,M ;

[0102] Step 3.3, Determine P 1,M ≠P 2,M And Flag[P 1,M ] = 0, Flag[P 2,M If Flag[P] = 0, proceed to step 3.4; otherwise, return to step 3.2. 1,M ] = 0 indicates that the population Y in the gen generation is 0. gen P in the middle 1,M individual Not selected as a parent, Flag[P 2,M ] = 0 indicates that the population Y in the gen generation is 0. gen P in the middle 2,M individual Not selected as a parent; such as Figure 2 As shown, the two integers are 2 and 5, neither of which have been selected before, and they are not equal, thus satisfying the condition.

[0103] Step 3.4: Match the vector Flag with P 1,M and Setting the element at the corresponding position to "1" indicates that the population Y in the gen generation is... gen P in the middle 1,M individual and P 2,M individual It has been selected as the parent generation and used to generate offspring; among them, Represents an individual Whether candidate facility point j is selected. Represents an individual Whether candidate facility point j is selected; if Figure 2 As shown in the figure, the gene sequences of the two parents are displayed.

[0104] like Figure 2 As shown, the specific crossover operator process is as follows:

[0105] Step 3.5: Use the crossover operator on the Pth... 1,M individual and P 2,M individual Process and generate crossover individuals.

[0106] Step 3.5.1, Take an individual and The intersection yields new individuals like Figure 2As shown, individual 2 chose facilities at locations 3, 4, and 5, while individual 5 chose facilities at locations 1, 4, and 5. Both individuals chose facilities at locations 4 and 5. Therefore, their intersection is facilities 4 and 5.

[0107] Step 3.5.2, from In the set, randomly select a position j, and let Candidate facility point j is selected, thus obtaining the cross-individual. in, express Inverse of. For example Figure 2 As shown, The set has two facility locations to choose from, number 1 and number 3. If number 1 is randomly selected, then number 1 will be added as the facility construction site.

[0108] Step 3.6: For overlapping individuals Perform mutation operations to obtain mutated individuals.

[0109] Generate a random number ra. If ra > 0.5, then... middle The candidate facility point at the location is selected; otherwise, make middle The candidate facility location was not selected.

[0110] Step 3.7: Transfer the mutated individuals As a sub-generation individual site selection scheme And put into the temporary offspring population of generation gen. gen ;

[0111] like Figure 2 As shown, in the mutation operation, by calculating Rounding up, we get 5. The diagram shows that facility number 5 is turned off, which means the value at position 5 is flipped to 0.

[0112] Step 3.8, Judgment If true, it means that a temporary offspring population of generation gen has been obtained. Otherwise, after assigning M+1 to M, return to step 3.2 and execute sequentially;

[0113] Step 4: Based on the temporary offspring population of generation gen (Child) gen The number and dispersion of facilities corresponding to the site selection scheme of each offspring individual are analyzed, and good offspring are selected for further optimization at the next level.

[0114] To conserve computational resources, a solution selection strategy was designed, choosing a subset of sub-solutions for lower-level optimization. For example... Figure 3 As shown, the number of facilities and the degree of dispersion corresponding to each offspring are calculated. Based on these two objectives, non-dominated sorting is performed to obtain the dominance level corresponding to each offspring. Offspring 1, 2, and 5 are located in the first level, indicating that they are non-dominated. These three offspring individuals are selected for lower-level optimization and allocated computing resources. The remaining offspring are discarded.

[0115] Step 4.0: Define the temporary offspring population Child in generation gen. gen Number of facilities corresponding to each sub-generation site selection scheme in, This represents the location selection scheme for the Mth offspring individual. The number of facilities;

[0116] Define the temporary offspring population of generation gen as Child gen The degree of dispersion corresponding to each child generation location scheme in, This represents the location selection scheme for the Mth offspring individual. The degree of dispersion;

[0117] Step 4.1: Calculate the temporary offspring population Child in generation gen. gen The number of facilities corresponding to each individual site selection scheme in, This represents the location selection scheme for the Mth offspring individual. Whether candidate facility point j has been selected;

[0118] Step 4.2, Calculation The negative of the sum of the Euclidean distances between the location coordinates of all candidate facility points with a value of "1" is used as... Dispersion

[0119] Step 4.3, let This represents the set of non-dominant children and is initialized to empty.

[0120] Step 4.4: Based on the number and dispersion of facilities corresponding to the site selection scheme of each offspring individual, determine the temporary offspring population of generation gen. gen Perform a non-dominated sort on all offspring individuals, and then select and store the non-dominated offspring. middle;

[0121] Step 4.5: Follow the process in Step 2 to process the non-dominated child set. All non-dominated offspring are subjected to lower-level optimization and evaluation to obtain a set of fitness evaluation values. in, This represents the fitness score of the dom-th non-dominated offspring, where dom represents the number of non-dominated offspring.

[0122] Step 5: Select the population Y in generation gen based on the environmental selection strategy. gen and its non-dominated child set By comparison, the population Y of generation gen+1 is obtained. gen+1 ;

[0123] Step 5.1, merge F gen and Then sort them in ascending order to select the top N with the smallest evaluation values. u The individual site selection schemes constitute the population Y of generation gen+1. gen+1 ;

[0124] Step 6: After assigning gen+1 to gen, check if gen has reached the maximum number of iterations. max If so, then stop iterating and obtain the gen-th iteration. max Generation population N u If the optimal radius of each site selection scheme and its site selection facility is not found, return to step three and execute sequentially.

[0125] Step 7: For the genth... max Generation population All individual site selection schemes are sorted in descending order of fitness evaluation value, and the facility site selection scheme with the smallest evaluation value is output.

[0126] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the facility addressing method described above. The processor is configured to execute the program stored in the memory.

[0127] In this embodiment, a computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of the facility location method described above.

Claims

1. A facility location method based on two-level optimization in uncertain environments, applicable to a set of customer demand points. and candidate facility collection In the site selection scenario that is constituted, using To represent any single customer demand point; using Represent any candidate facility point; obtain the location coordinates of each customer demand point and candidate facility point in the site selection scenario; record the candidate facility points. To its farthest customer The distance is Record candidate facility sites To its most recent customers The distance is Its characteristics are, The facility site selection method is carried out according to the following steps: Step 1: Initialize the upper-level addressing population; Step 1.0: Define the generation number of the current population as... and initialize , order the Generation population ,in, Indicates the first The generation Individual site selection schemes, and , Indicates the first Whether an individual selects a candidate facility site ,when , indicating the first Individuals did not select candidate facility sites. ,when , indicating the first Individuals select candidate facility sites ; Indicates population size, The number of candidate facilities; Step 1.1, Initialization ; Step 1.2: Randomly generate the first... individual And as the current individual, the first individual Put into the first Generation population middle; Step 1.3, Assign to Then, make a judgment Whether it is true or false; if it is true, then it means that the first... Generation population Otherwise, return to step 1.2 and execute sequentially. Step 2: For the current... Generation population The site selection schemes of all individuals are optimized at the next level to find the optimal matching radius and then evaluated. Step 2.1, Initialization ; Step 2.2, for the current... Generation population The Middle individual Perform lower-level optimization to find the optimal matching radius and evaluate it; Step 2.2.1, for the current individual All elements with a value of "1" are reassigned and used as the radius of the site selection facility; Step 2.2.2: For the current individual A local search is performed to optimize the radius of the site selection facility, resulting in an updated value for the current individual, which is then assigned to... and obtain the current individual fitness rating ; Step 2.2.2.1: Define the current local search count as... and initialize Set the maximum number of local searches. ; Indicates the first The first generation of the population individual In the Individual location selection schemes after the second disturbance; Step 2.2.2.2: Use equation (1) to analyze the current individual. To evaluate and obtain the current individual Evaluation value of total location distance : (1) In equation (1), Indicates candidate facility points A fixed distance; Indicates coverage radius Candidate facility sites Variable distance; Step 2.2.2.3: Use equation (2) to analyze the current individual. Proceed to the first The perturbation yields the first... Individual after the second perturbation Thus, the current individual can be obtained using equation (1). Evaluation value of total location distance And used as a fitness evaluation value: (2) In equation (2), This represents the proportionality coefficient. ; Step 2.2.2.4, if Then the current individual Updated to Conversely, maintain the current individual constant; Step 2.2.2.5, will Assign to Then, make a judgment Whether it is true or false; if true, it indicates that the current individual... Update complete; otherwise, repeat step 2.2.2.3 sequentially. Step 2.3, Assign to Then, make a judgment If the condition is met, it indicates that the lower-level optimization of all individual location schemes is complete, and the result is obtained. Generation population The set of fitness evaluation values ​​for all individual site selection schemes is as follows: Otherwise, return to step 2.2 and execute sequentially. Step 3, for the first Generation population All individual location selection schemes in the population undergo upper-level crossover and mutation operations to generate a temporary offspring population; Step 3.1, Define the first The temporary progeny population is and initialized to Define a size of zero vector Used to record the first Generation population The situation where an individual is selected as a parent; definition Let this be the number of crossover mutations, and initialize it. ; Step 3.2, in Randomly generate the first interval Two integers from the second crossover mutation , ; Step 3.3, Judgment ,and , If the condition is met, proceed to step 3.4; otherwise, return to step 3.

2. Indicates the first Generation population The Middle individual Not selected as a parent generation Indicates the first Generation population The Middle individual Not selected as a parent generation; Step 3.4: Transfer the vector Zhongyu and Setting the element at the corresponding position to "1" indicates that the first element is... Generation population The Middle individual and the individual It has been selected as the parent generation and used to generate offspring; among them, Represents an individual Candidate facility sites Whether or not to be selected, Represents an individual Candidate facility sites Whether or not it was selected; Step 3.5: Use the crossover operator to apply the first... individual and the individual Process and generate crossover individuals. ; Step 3.6: For overlapping individuals Perform mutation operations to obtain mutated individuals. ; Generate a random number ,like Then make middle The candidate facility point at the location is selected; otherwise, make middle The candidate facility location was not selected. Step 3.7: Transfer the mutated individuals As a sub-generation individual site selection scheme And put it in the first Temporary progeny population ; Step 3.8, Judgment Whether it is true or false, if true, it means that the first... Temporary progeny population Otherwise, Assign to Then, return to step 3.2 and execute sequentially; Step 4, according to the... Temporary progeny population The number and dispersion of facilities corresponding to the site selection scheme of each offspring individual are analyzed, and good offspring are selected for further optimization at the next level. Step 4.0, Define the first Temporary progeny population Number of facilities corresponding to each sub-generation site selection scheme ,in, Indicates the first Individual site selection scheme for offspring The number of facilities; Definition of the first Temporary progeny population The degree of dispersion corresponding to each child generation location scheme ,in, Indicates the first Individual site selection scheme for offspring The degree of dispersion; Step 4.1, calculate the first... Temporary progeny population The number of facilities corresponding to each individual site selection scheme ;in, Indicates the first Individual site selection scheme for offspring Candidate facility sites Whether or not it was selected; Step 4.2, Calculation The negative of the sum of the Euclidean distances between the location coordinates of all candidate facility points with a value of "1" is used as... Dispersion ; Step 4.3, let This represents the set of non-dominant children and is initialized to empty. Step 4.4: Based on the number and dispersion of facilities corresponding to the site selection scheme of each offspring individual, the [specific steps are missing]. Temporary progeny population Perform a non-dominated sort on all offspring individuals, and then select and store the non-dominated offspring. middle; Step 4.5: Follow the process in Step 2 to process the non-dominated child set. All non-dominated offspring are subjected to lower-level optimization and evaluation to obtain a set of fitness evaluation values. ;in, Indicates the first The fitness evaluation value of each non-dominant offspring. Indicates the number of non-dominant offspring; Step 5: Select the appropriate strategy based on the environment. Generations of population and its non-dominated child set Compare and obtain the first Generations of population ; Step 5.1, Merge and Then sort them in ascending order to select the top ones with the smallest evaluation values. The individual site selection schemes constitute the first Generation population ; Step Six: Assign to Then, make a judgment Has the maximum number of iterations been reached? If so, then stop iterating and obtain the first iteration. Generation population of If the optimal radius of each site selection scheme and its site selection facility is not found, return to step three and execute sequentially. Step 7, for the first Generation population All individual site selection schemes are sorted in descending order of fitness evaluation value, and the facility site selection scheme with the smallest evaluation value is output.

2. The facility location method based on two-layer optimization under uncertain environments according to claim 1, characterized in that, Step 1.2 includes: Step 1.2.1, Initialization =1; Step 1.2.2, in the interval A real number is randomly generated inside. ;like Not in the range Inside, it means the first individual No candidate facility sites were selected in China and will Set to 0; otherwise, Set to 1; Steps 1, 2, and 3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] Assign to Then, make a judgment Whether it is true or false; if it is true, then it means that the first... individual Otherwise, return to step 1.2.2 and execute sequentially.

3. The facility location method based on two-layer optimization under uncertain environments according to claim 2, characterized in that, Step 2.2.1 includes: Step 2.2.1.1 Initialization ; Step 2.2.1.2, if If so, proceed to step 2.2.1.3; otherwise, within the interval... After randomly generating a real number and using it as the radius of the site selection facility, assign it to... ; Step 2.2.1.3, will Assign to Then, make a judgment Whether it is true or false; if true, then it means that the first... The generation Individual site selection scheme Once the location facility radius of all elements is assigned, proceed with step 2.2.1.2 sequentially.

4. The facility location method based on two-layer optimization under uncertain environments according to claim 3, characterized in that, Step 3.5 includes: Step 3.5.1, Take an individual and The intersection yields new individuals ; Step 3.5.2, from Randomly select a position from the set. and order Candidate facility sites Selected, thus obtaining crossover individuals ;in, express Inverse of.

5. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing any of the facility addressing methods of claims 1-4, the processor being configured to execute the program stored in the memory.

6. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program, when executed by a processor, performs the steps of any of the facility location methods described in claims 1-4.

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