Method and device for inverse location optimization of facilities without capacity constraints based on L1 norm

Abstract

The present invention discloses a reverse location optimization method for facilities without capacity constraints based on the L1 norm, comprising: respectively constructing a facility location model without capacity constraints and a reverse location model for facilities without capacity constraints based on the L1 norm; respectively solving the reverse location model and the location model according to preset feasible solutions to obtain an intermediate optimization solution of the reverse location model and an intermediate optimization solution of the location model; comparing the total cost of the preset feasible solution with the total cost of the intermediate optimization solution of the location model according to an objective function of the location model; updating the feasible solution restriction set of the reverse location model according to the comparison result; solving the optimized cost adjustment amount of the reverse location model according to the feasible solution restriction set of the updated reverse location model; iteratively performing solving operations, calculating operations, comparing operations and updating operations until the comparison result meets the preset conditions to obtain the optimal cost adjustment amount of the reverse location model; optimizing the facility location according to the optimal cost adjustment amount of the reverse location model.

Description

Technical Field

[0001] The present invention relates to the field of advance planning and facility site selection, and in particular to a method and device for reverse site selection optimization of facilities without capacity restrictions, electronic equipment and storage medium. Background Art

[0002] Ex ante planning is widely used in facility site selection issues, such as the site selection of distribution stations based on large regional logistics centers and the site selection of municipal livelihood projects.

[0003] The existing technical solutions usually use the forward optimization method of facility site selection to carry out ex ante facility site selection planning. However, the above forward site selection optimization method usually has the problems of low efficiency in obtaining feasible site selection solutions and high cost of the obtained feasible site selection solutions. Summary of the invention

[0004] In view of the above problems, the present invention provides a method and device for inverse location optimization of facilities without capacity constraints based on the L1 norm, an electronic device and a storage medium, in order to solve at least one of the above problems.

[0005] According to a first aspect of the present invention, a method for inverse location optimization of facilities without capacity constraints based on L1 norm is provided, comprising:

[0006] According to the number of facilities, the opening status of facilities, the opening cost of facilities, the number of users, the service tags, and the service cost of facilities-users, a facility location selection model without capacity constraints is constructed, wherein the location selection model includes a location selection objective function and location selection constraints;

[0007] According to the preset facility opening cost unit adjustment weight coefficient, the preset facility-user service cost unit adjustment weight coefficient, the number of facilities, the facility opening status, the facility opening cost, the number of users, the service tag, the facility-user service cost and the preset feasible solution, an inverse location model of facilities without capacity restriction under the L1 norm is constructed, wherein the inverse location model includes an inverse location objective function, inverse location constraints and a restricted set of feasible solutions;

[0008] Using the preset feasible solution, the inverse location model is solved to obtain the intermediate optimization solution of the inverse location model, and based on the intermediate optimization solution of the inverse location model, the location model is solved using the heuristic algorithm to obtain the intermediate optimization solution of the location model;

[0009] The objective function of the site selection model is used to calculate the total cost of the preset feasible solution and the intermediate optimization solution of the site selection model respectively, and the first site selection total cost and the second site selection total cost are obtained;

[0010] Compare the total cost of the first location selection with the total cost of the second location selection to obtain a comparison result, and update the restricted set of feasible solutions according to the comparison result;

[0011] Solve the inverse location model according to the updated restricted set of feasible solutions to obtain the cost adjustment of the inverse location model, wherein the cost adjustment of the inverse location model includes the adjustment of the facility start-up cost and the adjustment of the facility-user service cost;

[0012] Iterate the solving operation, calculating operation, comparing operation and updating operation until the comparison result meets the preset conditions, and obtain the optimized cost adjustment amount of the inverse site selection model;

[0013] The facility location is optimized based on the optimal cost adjustment of the inverse location model.

[0014] According to an embodiment of the present invention, the above-mentioned facility location model without capacity restriction is determined by formula (1) to formula (4):

[0015]

[0016]

[0017]

[0018]

[0019] Where m represents the number of facilities, n represents the number of users; r ij is the facility-user service cost, which is used to represent the cost of providing service to user j by facility i; u ij is a service tag, used to indicate the status of user j being served by facility i; i Indicates the facility is turned on, f i represents the facility opening cost;

[0020] Among them, formula (1) is the objective function of the site selection model, and formula (2) to formula (4) are the constraints of the site selection model.

[0021] According to an embodiment of the present invention, the above-mentioned inverse site selection model is determined by formula (5) to formula (7):

[0022]

[0023]

[0024] (v',u')∈γ (7),

[0025] in, Indicates the preset facility opening cost unit adjustment weight coefficient, represents the preset facility-user service cost unit adjustment weight coefficient, (v',u') represents the feasible solution, γ represents the number of feasible solution restriction sets, Indicates the default enabled facility status. Indicates the preset service mark, f i 0 represents the adjusted facility opening cost, represents the adjusted facility-user service cost;

[0026] Among them, formula (5) is the objective function of the inverse location model, formula (6) is the constraint condition of the inverse location model, and formula (7) is the restricted set of feasible solutions of the inverse location model.

[0027] According to an embodiment of the present invention, the above heuristic algorithm includes a linear relaxation algorithm and a neighborhood search algorithm.

[0028] According to an embodiment of the present invention, the method of solving the site selection model using a linear relaxation algorithm based on the intermediate optimization solution of the inverse site selection model to obtain the intermediate optimization solution of the site selection model includes:

[0029] The constraints of the site selection model are linearly relaxed using a linear relaxation algorithm to obtain the relaxed constraints of the site selection model;

[0030] According to the relaxed constraints of the site selection model and the objective function of the site selection model, the relaxed optimization solution of the site selection model is solved by using the intermediate optimization solution of the inverse site selection model;

[0031] According to the relaxed optimization solution of the site selection model, the feasible solution area of ​​the site selection model is obtained;

[0032] According to the constraints of the site selection model, the feasible solution area of ​​the site selection model is analyzed and screened to obtain the intermediate optimization solution of the site selection model.

[0033] According to an embodiment of the present invention, the intermediate optimization solution of the inverse site selection model is solved by using a neighborhood search algorithm to obtain the intermediate optimization solution of the site selection model, which includes:

[0034] According to the intermediate optimization solution of the inverse site selection model, the initial feasible solution of the site selection model is determined;

[0035] According to the neighborhood search method, facilities are randomly selected to update the initial feasible solution of the location selection model;

[0036] According to the updated initial feasible solution of the site selection model, the local optimal solution of the site selection model is calculated by using the neighborhood search method;

[0037] According to the objective function of the site selection model, the total cost of the local optimization solution of the site selection model and the total cost of the initial solution of the site selection model are compared, and according to the comparison result, the initial feasible solution of the site selection model is updated;

[0038] Iterate the random selection operation, calculation operation, comparison operation and update operation until the number of iterations meets the preset number of iterations to obtain the intermediate optimization solution of the site selection model.

[0039] According to an embodiment of the present invention, the above-mentioned neighborhood search method includes adding open facilities, exchanging open facilities or reducing open facilities.

[0040] According to a second aspect of the present invention, there is provided a device for inverse location optimization of facilities without capacity constraints based on L1 norm, comprising:

[0041] The first construction module is used to construct a facility location model without capacity constraints according to the number of facilities, the facility opening status, the facility opening cost, the number of users, the service tag, and the facility-user service cost, wherein the location model includes a location objective function and location constraints;

[0042] The second construction module is used to construct an inverse location model of facilities without capacity constraints under the L1 norm according to a preset facility opening cost unit adjustment weight coefficient, a preset facility-user service cost unit adjustment weight coefficient, the number of facilities, the facility opening status, the facility opening cost, the number of users, the service tag, the facility-user service cost, and a preset feasible solution, wherein the inverse location model includes an inverse location objective function, an inverse location constraint condition, and a feasible solution restriction set;

[0043] The first solving module is used to solve the inverse site selection model by using a preset feasible solution to obtain an intermediate optimization solution of the inverse site selection model, and solve the site selection model by using a heuristic algorithm according to the intermediate optimization solution of the inverse site selection model to obtain an intermediate optimization solution of the site selection model;

[0044] A calculation module, used to calculate the total cost of the preset feasible solution and the intermediate optimization solution of the location selection model respectively by using the objective function of the location selection model to obtain a first location selection total cost and a second location selection total cost;

[0045] A comparison and update module, used for comparing the first site selection total cost with the second site selection total cost, obtaining a comparison result, and updating the feasible solution restriction set according to the comparison result;

[0046] The second solving module is used to solve the inverse site selection model according to the updated feasible solution restriction set to obtain the cost adjustment of the inverse site selection model, wherein the cost adjustment of the inverse site selection includes the adjustment of the facility start-up cost and the adjustment of the facility-user service cost;

[0047] An iteration module is used to iteratively perform solving operations, calculation operations, comparison operations, and update operations until the comparison result meets the preset conditions, thereby obtaining the optimized cost adjustment amount of the inverse site selection model;

[0048] The site selection optimization module is used to optimize the facility site selection based on the optimal cost adjustment of the inverse site selection model.

[0049] According to a third aspect of the present invention, there is provided an electronic device, comprising:

[0050] one or more processors;

[0051] a storage device for storing one or more programs,

[0052] When one or more programs are executed by one or more processors, the one or more processors execute a reverse location optimization method for facilities without capacity constraints.

[0053] According to a fourth aspect of the present invention, there is provided a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, causes the processor to execute a method for inverse location optimization of facilities without capacity constraints.

[0054] The reverse location optimization method for facilities without capacity constraints provided by the present invention can efficiently obtain the optimized adjustment amount of the reverse location model by utilizing a row generation algorithm and a heuristic algorithm, and use the optimized adjustment amount of the reverse location model to carry out location planning for the facilities, thereby improving the efficiency of location decision-making and reducing the cost of location decision-making. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is a flow chart of a classic row generation algorithm according to an embodiment of the present invention;

[0056] Figure 2 is a flow chart of a method for inverse location optimization of facilities without capacity constraints based on L1 norm according to an embodiment of the present invention;

[0057] Figure 3 is a flow chart of obtaining an intermediate optimization solution of a site selection model by using a linear relaxation algorithm according to an embodiment of the present invention;

[0058] Figure 4 is a flow chart of obtaining an intermediate optimization solution of a site selection model by using a neighborhood search algorithm according to an embodiment of the present invention;

[0059] Figure 5 3 are schematic diagrams of operations of a neighborhood search method according to an embodiment of the present invention;

[0060] Figure 6 is a schematic flow chart of an improved row generation algorithm according to an embodiment of the present invention;

[0061] Figure 7 is a schematic diagram of a UFLP according to an embodiment of the present invention;

[0062] Figure 8is a schematic diagram of an IUFLP of a given feasible solution according to an embodiment of the present invention;

[0063] Fig. 9 is a structural schematic diagram of a reverse location optimization device for facilities without capacity constraints based on L1 norm according to an embodiment of the present invention;

[0064] Fig.10 The block diagram of an electronic device suitable for implementing a reverse site selection method for facilities without capacity constraints according to an embodiment of the present invention is schematically shown. DETAILED DESCRIPTION

[0065] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings.

[0066] In order to make those skilled in the art more clearly aware of the technical solution of the present invention, the present invention takes the advance site selection planning of logistics distribution sites based on large regional logistics centers as an example to illustrate the main points of the technical solution of the present invention.

[0067] The large-scale regional logistics center described in the present invention refers to the site selection of logistics distribution stations through reasonable advance planning without changing the location of the large-scale regional logistics center, so as to achieve the optimization of transportation costs. Since the above-mentioned large-scale regional logistics center has the characteristics of high regional radiation capacity and high construction cost, once it is built and put into use, the location of the logistics center warehouse will not be changed at will. Based on the above background, logistics companies usually transport according to the established transportation routes when completing logistics transportation tasks; when adjusting the transportation routes, it usually brings about problems such as increased transportation costs and operating costs, and decreased service satisfaction. Therefore, how to adjust the original starting point-end transportation cost plan as little as possible so that the new plan has the least disturbance to the original plan is a difficult problem that needs to be solved urgently, and it is also a problem that the technical solution provided by the present invention is intended to solve.

[0068] Compared with the forward optimization method, the inverse optimization method has obvious advantages and applicability in solving the readjustment of road transport costs. Traditional forward optimization is to seek the theoretically optimal decision-making plan within the feasible domain when the model and its parameters are known. Forward optimization is a "search for optimization" problem of seeking the output result with a known input. It can be seen that the forward optimization method is not suitable for solving the transportation plan result of the known optimization model, and the problem of inversely seeking the optimal transportation cost parameters of the transportation plan. On the contrary, inverse optimization is a problem of inversely seeking the parameters that cause the result when the result is known. Given that multiple inputs can get the same output, when inversely seeking the cause from the result, not only the feasible range of parameter adjustment is added, but also the objective function of the smaller the adjustment amount is, the better, based on the initial parameters. According to the definition of inverse optimization, combined with the specific practical problems to be solved in this study, the new starting-end distribution plan after changes due to natural disasters, the original starting-end distribution plan, and the transportation costs of different routes on the transportation network are known, and the transportation cost adjustment plan of the new starting-end distribution plan is sought on the basis of the original transportation costs of different routes, and the smaller the adjustment amount is, the better.

[0069] In summary, the inverse problem of an optimization problem is a type of problem that, given a feasible solution to the optimization problem, minimizes the change in the parameters in the objective function in order to achieve the theoretical optimal result of the model output under the original transportation optimization model and new parameters as the feasible solution.

[0070] The most basic facility location problem is divided into two types: no capacity restriction and capacity restriction. Among them, no capacity restriction means that the number of services that each facility can provide is greater than or equal to the sum of the number of services required by users. The present invention provides a new row generation algorithm and a heuristic algorithm for solving the inverse optimization problem of the facility location problem without capacity restriction.

[0071] Existing technologies often use enumeration methods to solve the inverse site selection model of facilities without capacity constraints. However, the enumeration method is relatively inefficient and time-sensitive, and is not suitable for site selection of facilities such as logistics sites and municipal livelihood projects.

[0072] Figure 1 is a flowchart of a classic row generation algorithm according to an embodiment of the present invention.

[0073] like Figure 1As shown in the figure, the classic row generation algorithm refers to an algorithm that continuously adds constraints. Because in the solution matrix, one constraint corresponds to one row, so the method of adding constraints is naturally called a row generation algorithm. Correspondingly, the method of adding variables is called a column generation algorithm. This section first looks at the row generation algorithm, which is used when there are not many variables to solve, but there are many constraints. When solving the inverse optimization problem of UFLP (Uncapacitated Facility Location Problem, UFLP, uncapacitated facility location problem), the row generation algorithm has a slow calculation speed and cannot be used directly. When solving similar problems, the row generation algorithm needs to design different methods according to different problems, and it cannot solve large-scale problems.

[0074] The core of the row generation algorithm is to reduce the number of rows. Since rows grow exponentially, reducing the number of rows can reduce the number of calculations. When using the row generation algorithm, a subproblem needs to be solved, and based on the solved subproblem, the optimal solution to the entire problem is obtained.

[0075] Figure 2 It is a flowchart of a method for inverse location optimization of facilities without capacity constraints based on L1 norm according to an embodiment of the present invention.

[0076] like Figure 2 As shown, the above-mentioned inverse location optimization method for facilities without capacity constraints based on the L1 norm includes operations S210 to S280.

[0077] In operation S210, a facility location model without capacity constraints is constructed according to the number of facilities, facility start-up status, facility start-up cost, number of users, service tags, and facility-user service cost, wherein the location model includes a location objective function and location constraints.

[0078] In operation S220, according to the preset facility activation cost unit adjustment weight coefficient, the preset facility-user service cost unit adjustment weight coefficient, the number of facilities, the facility activation status, the facility activation cost, the number of users, the service tag, the facility-user service cost and the preset feasible solution, a capacity-free facility inverse location model based on the L1 norm is constructed, wherein the inverse location model includes an inverse location objective function, inverse location constraints and a restricted set of feasible solutions.

[0079] In operation S230, the inverse site selection model is solved using a preset feasible solution to obtain an intermediate optimization solution of the inverse site selection model, and the site selection model is solved using a heuristic algorithm based on the intermediate optimization solution of the inverse site selection model to obtain an intermediate optimization solution of the site selection model.

[0080] In operation S240, the total costs of the preset feasible solution and the intermediate optimization solution of the site selection model are calculated respectively by using the objective function of the site selection model to obtain a first site selection total cost and a second site selection total cost.

[0081] In operation S250, the first site selection total cost and the second site selection total cost are compared to obtain a comparison result, and the feasible solution restriction set is updated according to the comparison result.

[0082] Updating the restricted set of feasible solutions is essentially to continuously add constraints. Because in the solution matrix, one constraint corresponds to one row, so the method of adding constraints is called the row generation algorithm. Correspondingly, the method of adding variables is called the column generation algorithm.

[0083] In operation S260, the inverse site selection model is solved according to the updated restricted set of feasible solutions to obtain a cost adjustment of the inverse site selection model, wherein the cost adjustment of the inverse site selection includes an adjustment of the facility startup cost and an adjustment of the facility-user service cost.

[0084] In operation S270, the solving operation, the calculating operation, the comparing operation, and the updating operation are iterated until the comparison result satisfies a preset condition, thereby obtaining an optimized cost adjustment amount of the inverse site selection model.

[0085] In operation S280, the facility location is optimized according to the optimized cost adjustment amount of the inverse location model.

[0086] The reverse location optimization method for facilities without capacity constraints provided by the present invention can efficiently obtain the optimized adjustment amount of the reverse location model by utilizing a row generation algorithm and a heuristic algorithm, and use the optimized adjustment amount of the reverse location model to carry out location planning for the facilities, thereby improving the efficiency of location decision-making and reducing the cost of location decision-making.

[0087] According to an embodiment of the present invention, the above-mentioned facility location model without capacity restriction is determined by formula (1) to formula (4):

[0088]

[0089]

[0090]

[0091]

[0092] Where m represents the number of facilities, n represents the number of users; r ij is the facility-user service cost, which is used to represent the cost of providing service to user j by facility i; u ij is a service tag, used to indicate the status of user j being served by facility i; iIndicates the facility is turned on, f i represents the facility opening cost;

[0093] Among them, formula (1) is the objective function of the site selection model, and formula (2) to formula (4) are the constraints of the site selection model.

[0094] According to an embodiment of the present invention, the above-mentioned inverse site selection model is determined by formula (5) to formula (7):

[0095]

[0096]

[0097] (v',u')∈γ (7),

[0098] in, Indicates the preset facility opening cost unit adjustment weight coefficient, represents the preset facility-user service cost unit adjustment weight coefficient, (v',u') represents the feasible solution, γ represents the number of feasible solution restriction sets, Indicates the default facility is turned on. Indicates the preset service mark, f i 0 represents the adjusted facility opening cost, represents the adjusted facility-user service cost;

[0099] Among them, formula (5) is the objective function of the inverse location model, formula (6) is the constraint condition of the inverse location model, and formula (7) is the restricted set of feasible solutions of the inverse location model.

[0100] In order to better illustrate the above-mentioned site selection model and inverse site selection model of the present invention, the above-mentioned models are further explained below in combination with specific implementation methods.

[0101] The facility location problem is usually defined as follows: Assuming there are m facilities and n users, choose which facilities to open and which users to serve in order to meet demand at the lowest cost. Introduce the following notation, let f i represents the fixed cost of opening facility i, i∈M, M={1,…,m}. ij is the facility-user service cost, which is used in this embodiment to represent the cost of transporting goods from facility i to user j, j∈N, N={1,…,n}. No capacity restriction means that the capacity K that each facility can provide is sufficiently large, that is, the service capacity that any facility can provide is greater than or equal to the sum of the number of services required by all users.

[0102] Let f i is an m-dimensional row vector, r ijIf the rows are connected end to end to form an (m×n)-dimensional row vector, then a (m+m×n)-dimensional row vector, c=(f,r), can be used to represent the cost.

[0103] The definition of the uncapacitated facility location problem (UFLP) is as shown in formula (1), formula (2), formula (8) and formula (4):

[0104]

[0105]

[0106]

[0107]

[0108] Rewriting the above formula with a sufficiently large capacity K in a more concise way, we obtain the site selection model shown in formulas (1) to (4):

[0109]

[0110]

[0111]

[0112]

[0113] The above site selection model belongs to the integer programming model. In the integer programming model, u ij Indicates whether user j is served by facility i. If so, then u ij =1, otherwise u ij =0;v i Indicates whether facility i is turned on. If it is turned on, then v i =1, otherwise v i = 0. Formula (1) is the objective function of UFLP, which is to minimize the total cost of opening facilities and transporting goods; Formula (2) indicates that each user j∈N must be served by a facility, and Formula (3) indicates that if user j is served by facility i, then facility i must be opened.

[0114] The inverse problem is usually defined as follows: given a weighted optimization problem and an instance of a fixed feasible solution, the corresponding inverse problem is to modify the weighting parameters as little as possible (under a fixed norm) so that the given solution becomes the optimal solution to the original optimization problem in this instance.

[0115] According to the definition of the inverse problem, the inverse problem of the general optimization problem has the following form, as shown in formula (9) to formula (10):

[0116]

[0117] std∈G(x 0 ) (10),

[0118] G(x 0 )={d∈R n |min{g(d,x)|x∈D}=g(d,x 0)} (11),

[0119] Where g(c,x) is the objective function of the original optimization problem, c∈R n is the parameter vector, D is the feasible domain of x, d∈R n is the adjusted parameter vector. G(x 0 ) means that the given feasible solution x 0 becomes g(d,x 0 ) is the set of parameter vectors d of the optimal solution.

[0120] For convenience and to be closer to reality, we take the L1 norm as an example, which means the sum of the adjustments is the smallest. The weights of the facility cost and transportation cost adjustments are often different. They can be set as and

[0121] Then the inverse problem of facility location without capacity constraints (IUFLP) under the L1 norm can be defined as shown in formula (12) to formula (14):

[0122] Min w×|dc| T (12)

[0123] Stdx 0 =U(d) (13),

[0124] d∈R m+mn (14)

[0125] Where w=(w f ,w r ) is the (m+mn)-dimensional unit cost adjustment vector, f 0 ,r 0 denote the adjusted facility cost and transportation cost respectively, c = (f, r) is the original cost parameter mentioned above, |dc| T is the (m+mn)-dimensional column vector of the cost adjustment amount (absolute value), x 0 is a feasible solution to the original problem, and U(d) is the minimum value corresponding to the parameter d in formula (1).

[0126] It can be seen from the constraint that x 0is the optimal solution that satisfies all constraints of UFLP after adjusting costs. For each user j∈N, there are |M|=m choices that can be served by any facility. Therefore, there are m choices for all users. n There are different situations, namely, m that satisfy the UFLP constraint n The solution set consisting of feasible solutions is γ. Therefore, the solution model is established based on the definition of the inverse problem, and the number of feasible solutions contained in γ is exponential.

[0127] From the definition of the inverse problem of facility location without capacity constraints, it can be seen that the original optimization problem and its inverse problem have a certain connection, that is, the cost corresponding to the given solution in the inverse problem needs to be less than or equal to the cost corresponding to all solutions that meet the constraints of the original problem. As an effective method for solving large-scale linear programming problems, the row generation algorithm can be applied to this problem, and it is easy to find that the subproblem at this time is the original UFLP problem. Therefore, the row generation algorithm can be used to solve the inverse problem of facility location without capacity constraints.

[0128] The inverse location model for the location problem of uncapacitated facilities is shown in formula (5) to formula (7):

[0129]

[0130]

[0131] (v',u')∈γ (7),

[0132] Among them, γ is the same as above, which is the set of all feasible solutions x'=(v',u') that satisfy the original problem. To facilitate the display of results, we mainly consider the inverse optimal solution problem, that is, the inverse problem. For the inverse optimal value problem, that is, given V 0 Instead of x 0 , according to the formula V 0 =cx 0 The same idea can also be used to solve the problem.

[0133] According to an embodiment of the present invention, the above heuristic algorithm includes a linear relaxation algorithm and a neighborhood search algorithm.

[0134] Figure 3 It is a flow chart of obtaining an intermediate optimization solution of a site selection model by using a linear relaxation algorithm according to an embodiment of the present invention.

[0135] like Figure 3 As shown, according to the intermediate optimization solution of the inverse site selection model, the site selection model is solved by using a linear relaxation algorithm to obtain the intermediate optimization solution of the site selection model, including operations S310 to S340.

[0136] In operation S310, a linear relaxation algorithm is used to perform linear relaxation on the constraint conditions of the site selection model to obtain relaxed constraint conditions of the site selection model.

[0137] In operation S320, a relaxed optimization solution of the site selection model is obtained by using an intermediate optimization solution of the inverse site selection model according to the relaxed constraint conditions of the site selection model and the objective function of the site selection model.

[0138] In operation S330, a feasible solution region of the site selection model is obtained according to the relaxed optimization solution of the site selection model.

[0139] In operation S340, according to the constraints of the site selection model, the feasible solution region of the site selection model is analyzed and screened to obtain an intermediate optimization solution of the site selection model.

[0140] Figure 4 It is a flow chart of obtaining an intermediate optimization solution of a site selection model by using a neighborhood search algorithm according to an embodiment of the present invention.

[0141] like Figure 4 As shown, according to the intermediate optimization solution of the inverse site selection model, the site selection model is solved by using a neighborhood search algorithm to obtain the intermediate optimization solution of the site selection model, including operations S410 to S450.

[0142] In operation S410, an initial feasible solution of the site selection model is determined according to an intermediate optimization solution of the inverse site selection model.

[0143] In operation S420, a facility is randomly selected to update an initial feasible solution of the site selection model according to a neighborhood search method.

[0144] In operation S430, a local optimal solution of the site selection model is calculated using a neighborhood search method according to the updated initial feasible solution of the site selection model.

[0145] In operation S440, according to the objective function of the site selection model, the total cost of the local optimization solution of the site selection model and the total cost of the initial solution of the site selection model are compared, and according to the comparison result, the initial feasible solution of the site selection model is updated.

[0146] In operation S450, the random selection operation, the calculation operation, the comparison operation, and the update operation are iterated until the number of iterations meets the preset number of iterations, thereby obtaining an intermediate optimization solution of the site selection model.

[0147] In order to better understand the present invention, the above two heuristic algorithms of the present invention are further described in detail below in conjunction with specific embodiments.

[0148] The row generation algorithm is applied to IUFLP, and the facility and transportation parts corresponding to c are represented by (f, r) respectively. Let c = (f, r) be the original cost vector, d = (f 0 ,r0 ) is the adjusted cost vector. Let

[0149]

[0150]

[0151] Then a i ,h ij Respectively represent the relative cost f i , r ij The increase in b i , l ij Respectively represent the relative original cost f i , r ij of reduction.

[0152] The main problem of IUFIP can be obtained as shown in formula (17) to formula (21):

[0153]

[0154]

[0155]

[0156]

[0157] (v',u')∈Ⅱ (21),

[0158] Among them, (v',u') belongs to a feasible solution restricted set II∈γ, and the elements in the restricted set are continuously generated and added to it by the sub-problem. The (a',b',h',l') obtained from the main problem is brought into the sub-problem for solution in each iteration cycle.

[0159] The sub-problems are shown in formula (22) to formula (25):

[0160]

[0161]

[0162]

[0163]

[0164] The subproblem is solved to get (v' * ,u' * ), if the objective function value is less than 0, the obtained (v' * ,u' * ) is added to the constraint set of the main problem. If the objective function value is not less than 0, the program ends. Note that the subproblem is actually the UFLP.

[0165] The detailed steps of the row generation algorithm for solving the IUFLP problem are as follows:

[0166] Input: (1) Feasible solution: x 0 =(v 0 ,u 0 );(2) Original facility cost:c=(f,r);

[0167] Output: (1) Optimal solution: (a * ,b * ,h * ,l * ); (2) Minimum total cost change: (3) Change in the original cost:

[0168] Initialization: The initial restricted set only needs to contain the feasible solution to the original problem. For convenience and to avoid regenerating feasible solutions, the initial restricted set can be a set containing only the given feasible solution, that is, Ⅱ0 = {(v 0 ,u 0 )}.

[0169] Step 1: Solve the main problem at this time and obtain the optimal solution (a', b', h', l').

[0170] Step 2: Bring the optimal solution (a', b', h', l') obtained in step 1 into the subproblem, solve the integer programming of the subproblem and obtain the optimal solution x' * =(v' * +u' * ) and the objective function T.

[0171] Step 3: If the objective function T<0, the obtained x' * Add to the restricted set II = II ∪ {x' *}, return to step 1 and solve the main problem again. If the objective function T ≥ 0, the algorithm ends and the final restriction set is obtained, which is recorded as II Ⅰ According to this restriction set II Ⅰ Solve the main problem and get the optimal solution (a * ,b * ,h * ,l * ).

[0172] According to an embodiment of the present invention, the above-mentioned neighborhood search method includes adding open facilities, exchanging open facilities or reducing open facilities.

[0173] Figure 5 3 are schematic diagrams of operations of a neighborhood search method according to an embodiment of the present invention.

[0174] like Figure 5 As shown, let the number of unopened facilities be p and the number of opened facilities be (mp). Increase, that is, for the currently unopened facilities, open a facility as an increase neighborhood, with a total of p neighborhoods. Exchange, that is, for the currently unopened facilities, open a facility and close a facility in the opened facilities, with a total of p (m-p) neighborhoods. Decrease, that is, for the currently opened facilities, close a facility as a decrease neighborhood, with a total of p (m-p) neighborhoods.

[0175] From the above-mentioned row generation method, we can know that in order to obtain the optimal solution of the inverse problem, we need to obtain the most accurate restriction set of the main problem, that is, the constraints in the main problem. Since the restriction set of the main problem is continuously generated by sub-problems, it can be seen that the core of the row generation method is the efficiency of solving the sub-problems, that is, the more accurate the sub-problem solution, the more accurate the optimal solution of the inverse problem. However, since the sub-problem is the original problem of facility location selection, the solution process can be simplified by relaxing the sub-problem and sacrificing a certain degree of solution accuracy.

[0176] When strictly solving the subproblems, the optimal solution of IUFLP is obtained at the end of the loop. Note that the number of solutions selected from the subproblems depends on the given initial solution. Although the row generation method can greatly reduce the original constraints, it is impossible to determine how many solutions need to be selected. In fact, if it is possible to determine how many solutions can be selected, the IUFLP can be solved by directly solving the main problem based on the solution set composed of the selected solutions.

[0177] The subproblem (shown in formula (22)) is solved using the neighborhood search method, and a certain number of loops is set to terminate the solution of the subproblem in advance. At this time, the lower bound of the IUFLP is obtained. The neighborhood search method uses a basic local search method to obtain a local optimal integer solution for the current given solution by increasing, exchanging, and decreasing. In one solution process, the costs corresponding to the neighborhood solutions obtained by the three methods are compared, and the minimum value is taken to obtain the corresponding local optimal solution. The current given solution is transferred to the obtained local optimal solution, and the local optimal solution is added to the restricted set of the main problem before the next solution is performed.

[0178] The detailed steps of the row generation algorithm for solving the UFLP problem are as follows:

[0179] Input: (1) Feasible solution: x 0 =(v 0 ,u 0 );(2) Original facility cost:c=(f,r);

[0180] Output: (1) Optimal solution: (a * ,b * ,h* ,l * ); (2) Minimum total cost change: (3) Change in the original cost:

[0181] Initialization: The initial restricted set only needs to contain the feasible solution to the original problem. For convenience and to avoid regenerating feasible solutions, the initial restricted set can be a set containing only the given feasible solution, that is, Ⅱ0 = {(v 0 ,u 0 )}.

[0182] Step 1: Solve the main problem at this time and obtain the optimal solution (a', b', h', l').

[0183] Step 2: Bring the optimal solution (a', b', h', l') obtained in step 1 into the subproblem, solve the integer programming of the subproblem and obtain the optimal solution x' * =(v' * ,u' * ) and the objective function T.

[0184] Step 3: If the objective function T<0, the obtained x' * Add to the restricted set II = II ∪ {x' *}, return to step 1 and solve the main problem again. If the objective function T ≥ 0, the algorithm ends. At this time, the optimal solution (a * ,b * ,h * ,l * ). Among them, the increase and exchange in the neighborhood search and the reduction operation are as follows Figure 5 shown.

[0185] The subproblem (shown in formula (22)) is linearly relaxed to obtain a linear programming problem. The upper bound of the corresponding inverse problem can be obtained by solving it using the row generation algorithm. At this time, the corresponding subproblem model (i.e., the location selection model) is shown in formulas (26) to (28):

[0186]

[0187]

[0188]

[0189] Combine the following Figure 6 to Figure 8 Tables 1 and 2 further illustrate the method provided by the present invention.

[0190] Figure 6 4 is a flow chart of an improved row generation algorithm according to an embodiment of the present invention.

[0191] Figure 7 is a schematic diagram of a UFLP according to an embodiment of the present invention.

[0192] Figure 8 is a schematic diagram of an IUFLP of a given feasible solution according to an embodiment of the present invention.

[0193] like Figure 6 As shown in Figure 2, in the process of solving IUFLP, given the feasible solution and the original cost, the initial restriction set is selected, the inverse location model (i.e., the main problem) is solved according to the feasible solution, and then the feasible solution of the inverse location model is substituted into the location model (i.e., the sub-problem), and then the Figure 6 The three methods shown solve the site selection model and decide whether to update the restriction set or end the algorithm based on the value of T.

[0194] like Figure 7-Figure 8 As shown in the figure, Ⅰ, Ⅱ, Ⅲ, Ⅳ are facility numbers, and the activation cost of each facility is 10. a, b, c, d are user numbers. The connection between the facility and the user indicates that the user can be served by the corresponding facility, and the number on the connection indicates the corresponding transportation cost. The thin black line indicates all feasible service connections for this problem, and the thick line with an arrow indicates the service optimal solution connection. The corresponding facility activation cost and transportation cost are:

[0195]

[0196] Where M represents a sufficiently large number.

[0197] Figure 7 The optimal solution service connection given the facility opening cost and transportation cost is given in . Figure 8 Given a service connection as shown in the figure, it is necessary to adjust the facility startup cost or transportation cost to make the service connection the optimal service connection after adjustment.

[0198] It can be seen that the optimal solution to the original problem is Figure 7 As shown in the figure, the optimal cost corresponding to opening facility II to serve user b and opening facility III to serve users a, c, d is 27. When a feasible solution is given as Figure 8 As shown, when facility III is opened to serve users a and d and facility IV is opened to serve users b and c, the corresponding cost is 29. The transportation cost in the box needs to be changed to make the given feasible solution the optimal solution after the cost change, that is, change 1 in the box to 2 and 2 in the box to 3. At this time, the minimum change is 2, which can make the given feasible solution the optimal solution after the cost change.

[0199] In order to verify the effectiveness of the above method provided by the present invention, the present invention conducted relevant experiments.

[0200] All numerical experiments were performed on a PC with Windows 10 operating system and 8G memory and Intel Core i7-8700 processor. All algorithms were implemented by calling Gurobi solver in Matlab R2019a. In the numerical experiments, 20 possible instances of the corresponding scales were randomly generated for 6 different scales: (m, n) = (10, 10), (10, 20), (10, 30), (20, 20), (20, 40), (30, 30).

[0201] The facility opening cost and transportation cost are both randomly generated integer values, and their value ranges are: i =[100,200]; r i =[1,100],[100,200]. In practice, the cost of opening a facility cannot be changed. Therefore, in the following calculations, the weights for the adjustment of facility cost and transportation cost are set to be w f =∞,w r =1.

[0202] The following method will be used to compare the difference between the optimal change and the change calculated by the heuristic algorithm.

[0203] When the optimal change is not 0, the relative value (change in upper and lower bounds - optimal change) / (optimal change) is used to compare the size of the gap. The corresponding results are shown in Table 1. Since the given feasible solution is randomly generated, the possibility that the given feasible solution is exactly the optimal solution is almost zero. When the given feasible solution is exactly the optimal solution, according to the above algorithm, it can be known that whether it is an exact solution algorithm or a heuristic algorithm, the optimal change at this time is 0. However, in actual problems, it is almost impossible for a given feasible solution to be exactly the optimal solution, because this means that there is no need to make any changes to the original cost, and this extreme case is no longer considered here.

[0204] The results are as follows. In Table 1, (m,n)-1 represents the scale of the IUFLP problem. For example, (20,40)-1 represents 20 facilities and 40 users; -1 represents f i =[100,200]; r ij =[1,100]; -2 means f i =[100,200]; r ij=[100,200] represents the optimal value of the inverse problem obtained by strictly solving the subproblem. UB represents the upper bound of P obtained by linear relaxation. LB represents the lower bound of P obtained by neighborhood search. In Table 1, the gap calculation method is the relative ratio method. GAP1 represents the gap between UB and OS, and GAP2 represents the gap between LB and OS. T1, T2, and T3 are the calculation times for obtaining the optimal value, upper bound, and lower bound, respectively, in seconds. All the results in Table 1 are the average values ​​of 20 instances generated in one scale and are rounded off.

[0205] Table 1 Calculation results of IUFPL problem when the feasible solution is not the optimal solution

[0206]

[0207] Special note: When using processing method 2 to obtain the lower bound, the maximum number of loops is set to 1000. In processing methods 1 and 3, a larger maximum number of loops will not terminate the program early.

[0208] The calculation results show that the size of the problem (m, n) and the cost of setting up the facility f i and transportation cost ij The size relationship between them will not have much impact on the size of the gap. At the same time, since this problem is NP-hard, as the scale increases, the computational complexity and computational time both increase exponentially. According to the calculation results, it can be seen that the upper bound obtained by linear relaxation is close to the optimal change, but the solution efficiency has not been greatly improved. The reason is that when solving the optimal change, the integer programming model is used for solution, and the solver used has a high efficiency for integer programming; at the same time, the linear relaxation method produces non-integer solutions in each iterative cycle, and the relatively large number of iterative cycles also increases the time required for solution. The lower bound obtained by using the basic local search method is very close to the optimal change, and the solution efficiency is also greatly improved. Therefore, when the problem scale is not large, the optimal solution can be used for solution; when the problem scale is large, the heuristic method can be used in combination with a certain number of iterative cycles to obtain a good lower bound. The more iterative cycles, the more time it takes to calculate, but the better the lower bound obtained. In practice, specific analysis is performed on specific problems, and a good cost change can be obtained by using heuristic methods and setting a certain number of iterative cycles.

[0209] Table 2 Comparison between the original method and the improved method

[0210]

[0211] It can be seen from Table 2 that the optimization method provided by the present invention has greatly improved efficiency compared with the enumeration method in the prior art.

[0212] Fig. 9 4 is a schematic diagram of the structure of a reverse location optimization device for facilities without capacity constraints based on the L1 norm according to an embodiment of the present invention.

[0213] like Fig. 9 As shown, the reverse site selection optimization device 900 for facilities without capacity constraints includes a first construction module 910, a second construction module 920, a first solution module 930, a calculation module 940, a comparison and update module 950, a second solution module 960, an iteration module 970, and a site selection optimization module 980.

[0214] The first construction module 910 is used to construct a facility location model without capacity constraints according to the number of facilities, facility opening status, facility opening cost, number of users, service tags, and facility-user service cost, wherein the location model includes a location objective function and location constraints.

[0215] The second construction module 920 is used to construct an inverse location model for facilities with no capacity constraints under the L1 norm according to a preset facility activation cost unit adjustment weight coefficient, a preset facility-user service cost unit adjustment weight coefficient, the number of facilities, the facility activation status, the facility activation cost, the number of users, the service tag, the facility-user service cost and a preset feasible solution, wherein the inverse location model includes an inverse location objective function, inverse location constraints and a restricted set of feasible solutions.

[0216] The first solution module 930 is used to solve the inverse site selection model using a preset feasible solution to obtain an intermediate optimization solution of the inverse site selection model, and to solve the site selection model using a heuristic algorithm based on the intermediate optimization solution of the inverse site selection model to obtain an intermediate optimization solution of the site selection model.

[0217] A calculation module 940 is used to calculate the total cost of the preset feasible solution and the intermediate optimization solution of the site selection model respectively by using the objective function of the site selection model to obtain a first site selection total cost and a second site selection total cost;

[0218] The comparison and update module 950 is used to compare the first site selection total cost with the second site selection total cost to obtain a comparison result, and update the feasible solution restriction set according to the comparison result.

[0219] The second solution module 960 is used to solve the inverse site selection model according to the updated feasible solution restriction set to obtain the cost adjustment of the inverse site selection model, wherein the cost adjustment of the inverse site selection includes the adjustment of the facility startup cost and the adjustment of the facility-user service cost.

[0220] Iteration module 970, used for iteratively performing solving operation, calculating operation, comparing operation and updating operation until the comparison result meets the preset condition, and obtaining the optimized cost adjustment amount of the inverse site selection model;

[0221] The site selection optimization module 980 is used to optimize the facility site selection according to the optimization cost adjustment amount of the inverse site selection model.

[0222] The above method and device provided by the present invention conducts modeling analysis on the inverse problem of facility location selection without capacity constraints, and proposes to use a row generation algorithm to divide the inverse problem into a main problem and a sub-problem. The optimal solution of the inverse problem can be obtained by solving the integer programming model in the sub-problem. Analysis shows that the upper and lower bounds of the inverse problem can be obtained by using the linear relaxation method and the neighborhood search method for the sub-problem in the row generation algorithm. The numerical experimental results show that the upper bound obtained by the linear relaxation method is close to the optimal solution, but the solution efficiency is greatly improved; the heuristic algorithm has a relatively excellent performance in obtaining the lower bound, and the solution speed is fast, which illustrates the effectiveness of the heuristic algorithm. In fact, since the sub-problem is the original problem of facility location selection without capacity constraints, a more efficient approximate algorithm for solving the problem can be used in it, thereby improving the quality and solution efficiency of the lower bound solution. The sub-problem is the place with the most optimization space. The heuristic algorithm can be combined to find multiple solutions that are less than the objective function at one time and add them all to the main problem for solution at one time, thereby improving the solution efficiency.

[0223] Fig.10 The block diagram of an electronic device suitable for implementing a reverse site selection method for facilities without capacity constraints according to an embodiment of the present invention is schematically shown.

[0224] like Fig.10 As shown, the electronic device 1000 according to an embodiment of the present invention includes a processor 1001, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 1002 or a program loaded from a storage part 1008 into a random access memory (RAM) 1003. The processor 1001 may include, for example, a general-purpose microprocessor (e.g., a CPU), an instruction set processor and / or a related chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)), etc. The processor 1001 may also include an onboard memory for caching purposes. The processor 1001 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of the present invention.

[0225] In RAM 1003, various programs and data required for the operation of electronic device 1000 are stored. Processor 1001, ROM 1002 and RAM 1003 are connected to each other via bus 1004. Processor 1001 performs various operations of the method flow according to the embodiment of the present invention by executing the program in ROM 1002 and / or RAM 1003. It should be noted that the program can also be stored in one or more memories other than ROM 1002 and RAM 1003. Processor 1001 can also perform various operations of the method flow according to the embodiment of the present invention by executing the program stored in the one or more memories.

[0226] According to an embodiment of the present invention, the electronic device 1000 may further include an input / output (I / O) interface 1005, which is also connected to the bus 1004. The electronic device 1000 may further include one or more of the following components connected to the I / O interface 1005: an input portion 1006 including a keyboard, a mouse, etc.; an output portion 1007 including a cathode ray tube (CRT), a liquid crystal display (LCD), etc., and a speaker, etc.; a storage portion 1008 including a hard disk, etc.; and a communication portion 1009 including a network interface card such as a LAN card, a modem, etc. The communication portion 809 performs communication processing via a network such as the Internet. A drive 1010 is also connected to the I / O interface 1005 as needed. A removable medium 1011, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 1010 as needed, so that a computer program read therefrom is installed into the storage portion 1008 as needed.

[0227] The present invention also provides a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiment; or may exist independently without being assembled into the device / apparatus / system. The above computer-readable storage medium carries one or more programs, and when the above one or more programs are executed, the method according to the embodiment of the present invention is implemented.

[0228] According to an embodiment of the present invention, the computer-readable storage medium may be a non-volatile computer-readable storage medium, for example, may include but is not limited to: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In the present invention, the computer-readable storage medium may be any tangible medium containing or storing a program, which may be used by or in combination with an instruction execution system, an apparatus or a device. For example, according to an embodiment of the present invention, the computer-readable storage medium may include the ROM 1002 and / or RAM 1003 described above and / or one or more memories other than ROM 1002 and RAM 1003.

[0229] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for inverse location optimization of facilities without capacity constraints based on L1 norm, comprising: According to the number of facilities, the opening status of facilities, the opening cost of facilities, the number of users, the service tags, and the service cost of facilities-users, a facility location model without capacity constraints is constructed, wherein the location model includes a location objective function and location constraints; According to the preset facility activation cost unit adjustment weight coefficient, the preset facility-user service cost unit adjustment weight coefficient, the number of facilities, the facility activation status, the facility activation cost, the number of users, the service tag, the facility-user service cost and the preset feasible solution, a capacity-free facility inverse location model based on the L1 norm is constructed, wherein the inverse location model includes an inverse location objective function, inverse location constraints and a feasible solution restriction set; Using the preset feasible solution, solving the inverse site selection model to obtain an intermediate optimization solution of the inverse site selection model, and solving the site selection model using a heuristic algorithm based on the intermediate optimization solution of the inverse site selection model to obtain an intermediate optimization solution of the site selection model; Calculating the total costs of the preset feasible solution and the intermediate optimization solution of the site selection model respectively by using the objective function of the site selection model to obtain a first site selection total cost and a second site selection total cost; Comparing the first site selection total cost with the second site selection total cost to obtain a comparison result, and updating the feasible solution restriction set according to the comparison result; Solving the inverse site selection model according to the updated restricted set of feasible solutions to obtain a cost adjustment of the inverse site selection model, wherein the cost adjustment of the inverse site selection includes an adjustment of the facility startup cost and an adjustment of the facility-user service cost; Iteratively performing a solving operation, a calculating operation, a comparing operation, and an updating operation until the comparison result satisfies a preset condition, thereby obtaining an optimized cost adjustment amount of the inverse site selection model; Optimizing the facility location according to the optimal cost adjustment of the inverse location model; The location model of the facility without capacity restriction is determined by formula (1) to formula (4): （1）， （2）， （3）， （4）， in, represents the number of facilities in question, represents the number of said users; is the facility-user service cost, used to represent the facility For users the cost of providing services; is the service mark used to indicate that the user Facilities the status of the service; Indicates the facility is turned on. represents the cost of starting up the facility; Wherein, formula (1) is the objective function of the site selection model, and formula (2) to formula (4) are the constraints of the site selection model; The inverse site selection model is determined by formula (5) to formula (7): （5）， （6）， （7）， in, Indicates the weight coefficient of the preset facility opening cost unit adjustment, represents the preset facility-user service cost unit adjustment weight coefficient, represents a feasible solution, represents the number of the restricted set of feasible solutions, Indicates the default facility is turned on. Indicates a preset service mark, represents the adjusted facility opening cost, represents the adjusted facility-user service cost; Wherein, formula (5) is the objective function of the inverse site selection model, formula (6) is the constraint condition of the inverse site selection model, and formula (7) is the restricted set of feasible solutions of the inverse site selection model.

2. The method according to claim 1, wherein: The heuristic algorithm includes a linear relaxation algorithm and a neighborhood search algorithm.

3. The method according to claim 2, wherein: The step of solving the site selection model using the linear relaxation algorithm according to the intermediate optimization solution of the inverse site selection model to obtain the intermediate optimization solution of the site selection model comprises: Using the linear relaxation algorithm to linearly relax the constraint conditions of the site selection model to obtain the relaxed constraint conditions of the site selection model; According to the constraint conditions of the relaxed site selection model and the objective function of the site selection model, the relaxed optimization solution of the site selection model is solved by using the intermediate optimization solution of the inverse site selection model; Obtaining a feasible solution region of the site selection model according to a relaxed optimization solution of the site selection model; According to the constraint conditions of the site selection model, the feasible solution region of the site selection model is analyzed and screened to obtain an intermediate optimization solution of the site selection model.

4. The method according to claim 2, wherein: The step of solving the site selection model using the neighborhood search algorithm according to the intermediate optimization solution of the inverse site selection model to obtain the intermediate optimization solution of the site selection model comprises: Determining an initial feasible solution of the site selection model according to the intermediate optimization solution of the inverse site selection model; According to the neighborhood search method, randomly selecting facilities to update the initial feasible solution of the location model; According to the updated initial feasible solution of the site selection model, a local optimal solution of the site selection model is calculated using a neighborhood search method; According to the objective function of the site selection model, comparing the total cost of the local optimization solution of the site selection model with the total cost of the initial solution of the site selection model, and updating the initial feasible solution of the site selection model according to the comparison result; Iterate the random selection operation, calculation operation, comparison operation and update operation until the number of iterations meets the preset number of iterations to obtain the intermediate optimization solution of the site selection model.

5. The method according to claim 4, wherein: The neighborhood search method includes adding open facilities, exchanging open facilities or reducing open facilities.

6. A device for inverse location optimization of facilities without capacity constraints based on L1 norm, comprising: The first construction module is used to construct a facility location model without capacity constraints according to the number of facilities, the facility opening status, the facility opening cost, the number of users, the service tag, and the facility-user service cost, wherein the location model includes a location objective function and location constraints; The second construction module is used to construct an inverse location model of facilities without capacity constraints under the L1 norm according to a preset facility activation cost unit adjustment weight coefficient, a preset facility-user service cost unit adjustment weight coefficient, the number of facilities, the facility activation status, the facility activation cost, the number of users, the service tag, the facility-user service cost and a preset feasible solution, wherein the inverse location model includes an inverse location objective function, an inverse location constraint condition and a feasible solution restriction set; A first solving module is used to solve the inverse site selection model by using the preset feasible solution to obtain an intermediate optimization solution of the inverse site selection model, and solve the site selection model by using a heuristic algorithm according to the intermediate optimization solution of the inverse site selection model to obtain an intermediate optimization solution of the site selection model; A calculation module, used to calculate the total cost of the preset feasible solution and the intermediate optimization solution of the site selection model respectively by using the objective function of the site selection model to obtain a first site selection total cost and a second site selection total cost; A comparison and update module, used for comparing the first site selection total cost with the second site selection total cost to obtain a comparison result, and updating the feasible solution restriction set according to the comparison result; A second solving module is used to solve the inverse site selection model according to the updated feasible solution restriction set to obtain a cost adjustment amount of the inverse site selection model, wherein the cost adjustment amount of the inverse site selection includes an adjustment amount of a facility startup cost and an adjustment amount of a facility-user service cost; An iteration module, used for iteratively performing a solution operation, a calculation operation, a comparison operation, and an update operation until the comparison result satisfies a preset condition, thereby obtaining an optimized cost adjustment amount of the inverse site selection model; A site selection optimization module, used for optimizing the facility site selection according to the optimization cost adjustment amount of the inverse site selection model; The location model of the facility without capacity restriction is determined by formula (1) to formula (4): （1）， （2）， （3）， （4）， in, represents the number of facilities in question, represents the number of said users; is the facility-user service cost, used to represent the facility For users the cost of providing services; is the service mark used to indicate that the user Facilities the status of the service; Indicates the facility is turned on. represents the cost of starting up the facility; Wherein, formula (1) is the objective function of the site selection model, and formula (2) to formula (4) are the constraints of the site selection model; The inverse site selection model is determined by formula (5) to formula (7): （5）， （6）， （7）， in, Indicates the weight coefficient of the preset facility opening cost unit adjustment, represents the preset facility-user service cost unit adjustment weight coefficient, represents a feasible solution, represents the number of the restricted set of feasible solutions, Indicates the default facility is turned on. Indicates a preset service mark, represents the adjusted facility opening cost, represents the adjusted facility-user service cost; Wherein, formula (5) is the objective function of the inverse site selection model, formula (6) is the constraint condition of the inverse site selection model, and formula (7) is the restricted set of feasible solutions of the inverse site selection model.

7. An electronic device comprising: one or more processors; a storage device for storing one or more programs, When the one or more programs are executed by the one or more processors, the one or more processors execute the method according to any one of claims 1 to 5.

8. A computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, causes the processor to execute the method according to any one of claims 1 to 5.

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