Regional guarantee scheduling method based on resource distribution view angle

Abstract

The invention belongs to the technical field of equipment guarantee, and particularly relates to a regional guarantee scheduling method based on a resource distribution view angle. According to the method, a regional guarantee scheduling model is established based on spatial distribution characteristics of resources by applying an optimal transmission theory, the regional guarantee scheduling model comprises a'combat marshalling-guarantee institution 'coarse-grained model of a regional task level and a'combat equipment-guarantee unit' fine-grained model of a specific task level, then expansion discussion of the model is carried out, and a regional guarantee scheduling model is established. And obtaining a method for guaranteeing scheduling under the perspective of resource distribution. The invention provides a regional guarantee scheduling model under the perspective of resource distribution, the prerequisite assumption of a traditional model is that the resource quantity is accurately predicted, the resource quantity in an actual task cannot be accurately predicted, but distribution characteristics can be obtained, and the optimal transmission theory is applied in the invention. The regional guarantee scheduling problem is converted into how to realize matching of guarantee demand distribution and guarantee supply distribution in the region in an optimal mode.

Description

Technical Field

[0001] The present invention belongs to the technical field of equipment support, and in particular relates to a regional support scheduling method based on a resource distribution perspective. Background Art

[0002] Equipment support is an activity that enables equipment systems to maintain and restore their specified functions by providing personnel, spare parts, facilities and equipment, technical information, laws and regulations, etc., including use support and maintenance support. [1] , in the operational implementation phase, the equipment support capability is mainly reflected in the support resource scheduling capability. Under joint combat conditions, multi-service joint and cross-regional operations have become the norm, and the "region-oriented" characteristics of equipment support are significant. In regional operations, combat missions, weapons and equipment, and support environments have stronger regional constraints and uncertainties, which are manifested as uncertain mission constraints, uncertain demand constraints, and uncertain environmental constraints. As the combat process advances, the positions of weapons and equipment and support units change dynamically, also showing uncertain position constraints. Support comes first in combat, so the support scheduling capability under uncertain conditions directly affects or even determines the outcome of regional combat.

[0003] Model-based equipment support is to better restore the functional status of a single device by improving the efficiency of the support system. The focus is mainly on the analysis and modeling of the support system. Usually, qualitative and quantitative models are constructed based on the components and relationships of the support system. Qualitative models mainly analyze the basic framework, main processes and operating mechanisms of the support system, and quantitative models mainly carry out support demand prediction, support resource allocation, support task scheduling and support resource scheduling. The difference between support task scheduling and support resource scheduling lies in the granularity of the support system. Task scheduling is a coarse-grained level, and resource scheduling is a fine-grained level. They can also be collectively referred to as support scheduling. There are four main types of quantitative models: considering system goals and resource constraints, a mathematical programming model can be established, which is suitable for simple systems; considering task hierarchies and domain knowledge, based on determining tasks and support requirements, a hierarchical task network model can be established, which makes full use of decision makers' cognition and is suitable for large-scale complex systems; considering manpower constraints and process scheduling, a resource-constrained project scheduling model can be established, which is suitable for systems with limited manpower and clear processes; considering intelligent agents and intelligent agent interactions, a simulation model can be established, which is suitable for systems where analytical models are difficult to establish and information is missing.

[0004] The common point of the above studies is that they believe that the demand for support resources is a known definite quantity or probability distribution, and is viewed from the time perspective of mission equipment. In the regional support problem, multiple equipment need to be supported by the support system at the same time. At this time, the support system needs to comprehensively consider the regional equipment tasks, technical status, environmental conditions, etc. to carry out regional support scheduling. Therefore, regional support scheduling reflects the resource interaction between the combat equipment system and the support organization system in a certain time and region. The demand for support resources has not only time attributes but also spatial attributes, that is, it has certain spatial distribution characteristics. The corresponding support resource supply also has certain spatial distribution characteristics as the mission progresses. At this time, the regional support scheduling problem is the optimal matching of distributed resources in the two systems.

[0005] At present, the research on regional support mainly focuses on qualitative analysis of system structure, support process, support mechanism, etc., and quantitative research includes task allocation model. There are three problems:

[0006] (1) The time-based security demand cannot reflect the spatial distribution characteristics of regional security demand, and the model lacks a regional overall perspective;

[0007] (2) The existing assurance model does not have macro- and micro-structural consistency and cannot meet the needs of model conversion when interacting between different levels;

[0008] (3) In traditional scheduling problems, accurate knowledge of the number of support resources is a prerequisite for model calculation. However, due to the large amount of uncertainty in actual tasks, it is often impossible to accurately predict the number of resources. Therefore, how to establish a support scheduling model based on resource distribution characteristics has become a key issue in mission-oriented equipment support.

[0009] Demand characteristics can be analyzed from the time interval and scale of demand arrival, and can be divided into unstable demand, smooth demand, block demand, and intermittent demand. In regional missions, support demand is closely related to regional characteristics, equipment characteristics, organizational functions, usage intensity, and mission environment. It is a comprehensive reflection of the above four types of demand, showing certain distribution characteristics, and support supply also shows certain distribution characteristics.

[0010] The essence of the regional security scheduling problem is how to match the supply distribution of resources to the demand distribution of resources in an optimal way. The optimal transmission theory, which has attracted widespread attention in recent years, provides a distance measure between two distributions, describes the optimal way of data transmission between two distributions, and provides information transmission paths for data distributed at different levels, providing new ideas for regional security scheduling problems. Optimal Transport comes from the bulldozer problem and considers how to transport mass from the source distribution to the target distribution with the lowest cost. Given two non-negative masses u and v, when the total mass is equal, seek a transmission diagram that moves mass from distribution u To v makes the transportation cost ∫C(x, y)dx the lowest, and the optimal transmission is denoted by T # u=v。 Here C(x, y) is the transportation cost per unit mass from point x to y. In 2013, Marco Cuturi proposed the optimal transport problem with entropy regularization and proposed the approximate algorithm sinkhorn. Since then, the optimal transport theory has been widely used in image processing, machine learning, statistics, fault diagnosis, resource allocation and other fields. Summary of the invention

[0011] Based on the spatial distribution characteristics of resources and using the optimal transmission theory, this paper establishes a regional support scheduling model, including a coarse-grained model of "combat formation-support organization" at the regional task level and a fine-grained model of "combat equipment-support unit" at the specific task level. Then, an extended discussion of the model is carried out to derive a method of support scheduling from the perspective of resource distribution.

[0012] In order to achieve the above object, the present invention provides a regional guarantee scheduling method based on resource distribution perspective, comprising:

[0013] Step 1: Get Security Unit X ik , Equipment Unit Y jl , the number of resources of the guarantee unit h ik and the resource quantity g of the equipment unit jl , probabilistic processing h ik , g jl Get the probability vector ph of each supply and demand point i , pg j .

[0014] Step 2: Calculate the assurance unit X based on the fine-grained model ik To equipment unit Y jl The distribution distance d w (h i , g j ) and its guaranteed dispatch probability scheme PT ij , and calculate from the guarantee unit X according to the fine-grained model ik Transport to equipment unit Y jl Cost

[0015] Step 3: Get resources from security agency X i Transport to the target Y j The cost of C ij , Resource Supply i and resource requirements j , probabilistic processing u i , v j Get the probability vector u, v;

[0016] Step 4: Calculate the resource supply u based on the coarse-grained model i To resource requirements v j The distance of the distribution d w (u, v) and its guaranteed scheduling probability scheme PT;

[0017] Step 5: Combined with step 4, calculate the coarse-grained model guarantee scheduling solution T:

[0018] Step 6: Combined with step 2, calculate the fine-grained model guarantee scheduling solution T ij :

[0019] Step 7: Output the coarse-grained model guarantee scheduling solution T and the fine-grained model guarantee scheduling solution T ij .

[0020] Preferably, the fine-grained model of step 2 is as follows:

[0021]

[0022]

[0023]

[0024]

[0025] Among them, d w (h i , g j ) is the protection institution X i To the protected object Y j The distribution distance of For resources from the security unit X ik Transport to equipment unit Y jl The cost, For resources from the security unit X ik Transport to equipment unit Y jl The number of

[0026] Preferably, the guaranteed scheduling probability scheme PT in step 2 is ij for:.

[0027] Preferably, the coarse-grained model is:

[0028] d w (u, v) = inf T∈U(u,v) E x，y～T [d(x i ,y j )]

[0029] Among them, d(x i ,y j ) is x i andj Distance, x i is X i Position, y j is Y j Position.

[0030] Preferably, the guaranteed scheduling probability scheme PT in step 4 is as follows:

[0031] Preferably, the coarse-grained model guaranteed scheduling scheme T in step 5 is specifically: the minimum resource allocation T 1 = PT * sum(v) and the maximum resource delivery T 2 = PT * sum(u);

[0032] If sum(u) ≥ sum(v) and the demand can be met at this time, the optimal guarantee scheme is T 1 ;

[0033] If sum(u) < sum(v) and the demand is partially met at this time, the optimal guarantee scheme includes two parts, the front scheduling scheme T 2 and the rear scheduling scheme sum(T 1 - T 2 , 2).

[0034] Preferably, the fine-grained model guaranteed scheduling scheme T in step 6 ij is specifically:

[0035] The minimum resource allocation and the maximum resource delivery

[0036] If sum(h i ) ≥ sum(g j ), and the demand can be met at this time, the optimal guarantee scheme is

[0037] If sum(h i ) < sum(g j ), and the demand is partially met at this time, the optimal guarantee scheme includes two parts, the front scheduling scheme and the rear scheduling scheme

[0038] Compared with the prior art, the beneficial effects of the present invention are:

[0039] (1) The present invention proposes a regional guarantee scheduling model from the perspective of resource distribution. The premise assumption of the traditional model is that the resource quantity has been accurately predicted. In actual tasks, the resource quantity cannot be accurately predicted, but the distribution characteristics can be obtained. In this paper, the optimal transport theory is used to transform the regional guarantee scheduling problem into how to optimally match the guarantee demand distribution and the guarantee supply distribution in the region.

[0040] (2) The present invention solves the problem of hierarchical structure consistency of the regional support scheduling model. The coarse-grained and fine-grained models of the traditional model have large differences in structure and complex information transmission, which makes it difficult to solve the hierarchical scheduling problem of complex systems. The coarse-grained and fine-grained regional support scheduling models established by this model have the characteristics of structural consistency, convenient conversion of distribution distance and cost structure, and can switch models freely when the resolution is converted.

[0041] (3) Based on the case analysis of the established model, this paper draws some new conclusions about security scheduling. When there is an exponential distribution in supply and demand, a separate plan needs to be formulated; when there is no exponential distribution in supply and demand, the security plan is stable, especially under large-scale conditions; when the fixed combination security relationship is used, the security plan is more sensitive under small-scale conditions, and when there is a free competition security relationship, the security plan is stable under large and small scale conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0043] In the attached picture:

[0044] Figure 1 Calculate the results of the coarse-grained model for the three algorithms;

[0045] Figure 2 Calculation results for the fine-grained model of the sinkhorn algorithm;

[0046] Figure 3 Iteration curves for both algorithms;

[0047] Figure 4 is the calculation result of two kinds of guarantee relations;

[0048] Figure 5 The calculation results are for "supply distribution fixed - demand distribution changing";

[0049] Figure 6 The calculation results are for "fixed demand distribution - variable supply distribution";

[0050] Figure 7 Comprehensive analysis of the guarantee scheme errors based on supply and demand distribution;

[0051] Figure 8 The figure is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0052] The following combination Figure 1-Figure 8The preferred embodiments of the present invention are described. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0053] Example:

[0054] 1 Model construction

[0055] 1.1 Basic model of regional support scheduling from the perspective of resource distribution

[0056] Assuming that there are m security agencies and n security objects in the region, how to dispatch a certain resource from the security agencies in the best way to meet the task needs of the security objects. Among them, the security agency set is {X1, X2…X m}, the distribution of resources provided by the security agency is {(x1,u1)…(x i ,u i )...(x m ,u m )],x i and u i X i The location and quantity of resources; the set of guaranteed objects is {Y1, Y2…Y n}, the resource distribution required by the protection object is {(y1, v1)…(y j , v j )…(y n , v n )},y j and v j Y j Location and quantity of resources; resources from X i Transport to Y j The cost is C ij , resources from x i Transport to Y j The number is T ij .

[0057] From the perspective of regional resource distribution, the supply distribution of resources is The resource demand distribution is is the Dirac function, and its meaning is as follows.

[0058]

[0059]

[0060] The basic model of security scheduling from the perspective of regional resource distribution is established as follows:

[0061]

[0062]

[0063]

[0064] Resource supply u in the model i ; Resource requirementsv j ; Transportation cost C ij ; Delivery quantity T ij are all non-negative numbers; U(u, v) is the joint distribution of u and v, where u and v are the supply distribution vector and demand distribution vector of the resource respectively.

[0065] Obviously, this is a typical linear programming problem in form, but it is different from the classical linear programming. Here, u and v are the marginal distributions of the joint distribution U(u, v) at u and v. The distribution of u is related to the division of the support area, the location of the regional organization and the allocation of resources, and the distribution of v is related to the division of the support area, the location of the regional equipment and the probability of being hit.

[0066] 1.2 Connotation of regional support scheduling model from the perspective of resource distribution

[0067] According to the guaranteed scheduling model and combined with the optimal transmission theory, the connotation of the model is interpreted from four aspects: cost structure, distribution distance, distribution characteristics and calculation results.

[0068] (1) Cost structure

[0069] Cost C ij Factors such as transport distance, security relationship and importance can be considered. When considering distance, define C ij =d(x i ,y j ) p , d(x i ,y j )=|x i -y j |, p is a positive integer, usually 1 and 2; if we also consider X i and Y j The guarantee relationship between ij ,definition θ ij If the value set is set to {1e-3, 1, 1e3}, 1e-3 means no relationship, 1 means relationship, and 1e3 means Y j In X i Has a higher priority; if Y is also considered j Importance j ,definition e j Experts can give scores to obtain corresponding importance scores.

[0070] (2) Distribution distance

[0071] In this paper, considering the resource distribution characteristics, it is necessary to measure the distance between the two distributions. The distance measurement between the two distributions generally uses KL divergence and JS divergence. KL divergence describes the measurement of the asymmetry of the difference between two probability distributions. JS divergence is a variant of KL divergence, which solves the problem of KL divergence asymmetry. However, when the two distributions do not overlap, the KL divergence value is meaningless, and the JS divergence is a constant, and the gradient disappears. At this time, these two divergences cannot measure the distance between the distributions, while the Wasserstein distance in the optimal transmission theory can still reflect the distance between the two distributions when the two distributions do not overlap or overlap very little.

[0072] According to the optimal transmission theory, the distribution distance is the distance between two point clouds, measured by the expected minimum value of the distance between any pair of points after sampling according to a joint distribution. The mathematical definition is as follows:

[0073] d w (u, v) = inf T∈U(u，v) E x，y～T [d(x i ,y j )] (4)

[0074] At this time, the distribution T that makes this expectation reach the minimum value is the optimal transmission solution. i ,y j ) is x i and j distance.

[0075] Therefore, the distance from the supply distribution to the demand distribution of resources in the regional security scheduling model is defined as

[0076]

[0077] When the optimal transmission T is found * The distance that minimizes the objective function of the model is L c (u, v), called the Wasserstein distance. ij =d(X i , Y j ) p hour, W p (u, v) is the p-wasserstein distance.

[0078] (3) Distribution characteristics

[0079] Supply distribution reflects the allocation of security resources, which is related to the regional organizations and their attributes. Demand distribution reflects the demand for security resources, which is related to the regional equipment and its attributes. When the attributes change, u and v change, and the cost C ijChanges have occurred, and the guarantee scheduling plan has changed.

[0080] 1.3 Multi-resolution model of regional support scheduling from the perspective of resource distribution

[0081] In regional missions, decision makers at different levels need to establish support scheduling models at corresponding levels. In the context of the above problem, we further obtain expanded high-resolution information: the location and resource quantity of all support units of the support organization, and the location and resource quantity of all equipment units of the support object. The problem is further described as follows: Support organization X i It is a protection unit A collection of security agencies X i The resource distribution of supply is x ik and h ik X ik The location and quantity of resources, h i For X i Resource supply vector of Y; security object Y j It is an equipment unit A collection of protection objects Y j The required resource distribution is y jl and g jl Y jl The location and quantity of resources, g j Y j The resource demand vector of . Similarly, for is the Dirac function. M and N are the total number of support units and equipment units respectively. ik Transport to Y jl The cost is Resources from X ik Transport to Y jl The number of

[0082] A multi-resolution model for regional support dispatch is further established, including a coarse-grained model and a fine-grained model. The coarse-grained model is the same as above, and the fine-grained model is as follows:

[0083]

[0084]

[0085]

[0086]

[0087] Among them, C in the coarse-grained model ij Can no longer use Xi To Y j The Euclidean distance d(x i ,y h ) calculation, because they each contain multiple units, and each unit has different locations, supply and demand conditions. In this case, the distribution distance of the optimal transmission theory can be used as C ij ,Right now X The supply distribution of the security unit in i to Y j The Wasserstein distance d of the demand distribution of equipment units in w (h i , g j ). It can be seen that this conversion relationship between distribution distance and cost structure enables good information transmission between coarse-grained and fine-grained models. At the same time, due to the structural consistency of coarse-grained and fine-grained models, this model has obvious advantages in hierarchical scheduling of complex systems.

[0088] Therefore, the regional security scheduling problem is interpreted using the optimal transmission theory, and its essence is to find the optimal transmission plan from the supply-side resource distribution to the demand-side resource distribution.

[0089] 2 Algorithm Design

[0090] 2.1 Sinkhorn Algorithm

[0091] The high computational complexity of optimal transmission has limited its application. There are three main types of algorithms for solving optimal transmission. The first is to use linear programming to obtain an exact solution. Since the optimal solution of linear programming is to find the vertices on the feasible domain polyhedron, there are no optimal solutions and multiple optimal solutions. Especially in large-scale complex linear programming models, the optimal solution is sparse and the computational efficiency is low. At the same time, the computational complexity is O(n3). The second is to use the standard optimization algorithm under the optimal transmission setting, including the accelerated gradient descent method and the quasi-Newton method. This algorithm is very effective, but theoretical analysis needs to be developed. The third is the entropy regularization method. This method can make the problem smoother in the solution space by regularizing the entropy of the objective function, increase the convexity of the problem, and ensure that there is a unique optimal solution. It is currently the most widely used. Taking the coarse-grained model as an example, the objective function is regularized through the transmission plan, that is, the entropy regularization term is added on the basis of the wasserstein distance to obtain the sinkhorn distance, that is:

[0092]

[0093] in H(T) is the information entropy of T. The more evenly distributed T is, the greater the information entropy is. The entropy regularization parameter λ is responsible for adjusting the influence of information entropy. The larger the λ is, the smaller the influence of information entropy is, and the greater the influence of the cost matrix is ​​on the final result, which means that it tends to be centralized. On the contrary, the larger the λ is, the more it tends to be distributed.

[0094] Sinkhorn distance The partial derivative is get make get Thus, an approximate algorithm for the optimal transmission model is obtained, namely the sinkhorn algorithm, and the basic process is shown in Table 1. Obviously, the algorithm process is simple, efficient and convergent, and it shows superior performance in solving large-scale problems.

[0095] Table 1 Basic process of sinkhorn algorithm

[0096]

[0097] 2.2 Regional Support Scheduling Multi-resolution Model Algorithm

[0098] When solving the multi-resolution model of regional security scheduling, it is also necessary to consider dimensional differences and unbalanced scheduling problems. In view of the dimensional differences in the transmission of information between coarse-grained and fine-grained models, such as Euclidean distance and distribution distance, normalization processing is adopted; in view of the unbalanced scheduling of resource quantities in coarse-grained and fine-grained models, probabilistic processing is adopted to convert it into a balanced scheduling problem at the probability level, that is, the supply quantity distribution is converted into the spatial probability density distribution of supply, and the demand quantity distribution is converted into the spatial probability density distribution of demand. After probabilistic processing, the probability scheme of security scheduling is first calculated by the sinkhorn algorithm, and then multiplied by the total demand and total configuration of resources to obtain the corresponding security scheduling scheme.

[0099] Based on the above content, a regional guarantee scheduling method based on the perspective of resource distribution is finally proposed, including:

[0100] Step 1: Get the guarantee agency X i 、Guarantee object Y j , Security Unit X ik , Equipment Unit Y jl , the number of resources of the guarantee unit h ik and the resource quantity g of the equipment unit jl , probabilistic processing Get the probability vector ph of each supply and demand point i , pg j ;

[0101] Step 2: Establish a fine-grained model for regional support scheduling based on resource distribution, and calculate the support organization X according to the fine-grained model. i To the protected object Y j The distribution distance d w (h i , g j ) and its guaranteed dispatch probability scheme PT ij , and calculate from the security unit X ik Transport to equipment unit Y jl Cost

[0102] The fine-grained model of step 2 is as follows:

[0103]

[0104]

[0105]

[0106]

[0107] Among them, d w (h i , g j ) is the protection institution X i To the protected object Y j The distribution distance of For resources from the security unit X ik Transport to equipment unit Y jl The cost, For resources from the security unit X ik Transport to equipment unit Y jl The number of

[0108] Step 3: Combined with step 2, obtain resource supply u i and resource requirements j , probabilistic processing u i , v j Get the probability vector u, v;

[0109] Step 4: Establish a coarse-grained model for regional security scheduling based on the perspective of resource distribution, and calculate the resource supply u according to the coarse-grained model i To resource requirements v j Distribution distance and its guaranteed dispatch probability scheme PT;

[0110] The coarse-grained cost is:

[0111] C ij =d w (ph i, pg j )。

[0112] The coarse-grained model is as follows:

[0113]

[0114] Among them, the entropy regularization parameter is λ,

[0115] Step 5: Combining Step 4, calculate the guaranteed scheduling plan T of the coarse-grained model: Specifically: the minimum resource allocation T 1 = PT * sum(v) and the maximum resource delivery T 2 = PT * sum(u);

[0116] If sum(u) ≥ sum(v), the demand can be met at this time, and the optimal guaranteed plan is T 1 ;

[0117] If sum(u) < sum(v), the demand is partially met at this time, and the optimal guaranteed plan includes two parts, the front scheduling plan T 2 and the rear scheduling plan sum(T 1 - T 2 , 2).

[0118] Step 6: Combining Step 2, calculate the guaranteed scheduling plan T of the fine-grained model ij . Specifically:

[0119] The minimum resource allocation and the maximum resource delivery

[0120] If sum(h i ) ≥ sum(g j ), the demand can be met at this time, and the optimal guaranteed plan is

[0121] If sum(h i ) < sum(g j ), the demand is partially met at this time, and the optimal guaranteed plan includes two parts, the front scheduling plan and the rear scheduling plan

[0122] Step 7: Output the guaranteed scheduling plan T of the coarse-grained model and the guaranteed scheduling plan T of the fine-grained model ij .

[0123] Simulation verification:

[0124] 1 Case background

[0125] Before a mission, according to the plan, there are 4 formations and 20 types of equipment to perform combat missions, and 5 support organizations and 12 support units to participate in support missions. The information of formations and organizations, their units, positions, resource supply and demand, etc. are shown in Tables 2 and 3, and the support relationship is shown in Table 4. A pre-mission support scheduling plan is formulated. The first two data in square brackets in Tables 2 and 3 are position coordinates, and the last one is the resource quantity.

[0126] Table 2 Related information of guarantee institutions and guarantee units

[0127]

[0128] Table 3 Related information of equipment group and equipment unit

[0129]

[0130] Table 4 Support relationship between support organizations and equipment groups

[0131]

[0132] Further support relationships are obtained from Table 4. The support relationships between all support units and equipment units within each support organization and equipment formation are the same, and are the support relationship values ​​of the organization and formation. For example, the support relationships of X1 and Y1 are both 1e-3.

[0133] 2 Calculation results

[0134] In this case, the total supply and demand balance is taken, p = 2, λ = 1, the number of iterations is 300, and the calculation results are as follows.

[0135] (1) The coarse-grained model results T using the sinkhorn, admm, and LP algorithms are as follows Figure 1 shown.

[0136] (2) Sinkhorn algorithm fine-grained model results T ij like Figure 2 shown.

[0137] 3 Algorithm Performance and Related Discussion

[0138] (1) Performance comparison of different algorithms

[0139] The admm algorithm is an important method for solving separable convex optimization problems, with good processing speed and convergence performance. Although the model in this case is a convex optimization problem after regularization, the separability feature is not obvious, so a new algorithm needs to be found. The feasibility of the sinkhorn algorithm has been demonstrated before. Here, the admm algorithm is mainly used to verify the calculation accuracy of the sinkhorn algorithm. From the error iteration curve, the difference between the two is very small. From the calculation results, the coarse-grained models of the two are almost the same, and the fine-grained models have certain differences in local areas. The verification results show that the constructed model has a good advantage using the sinkhorn algorithm. The sinkhorn algorithm is used to solve the model and discuss it later.

[0140] (2) Comparison of different cost structures

[0141] In this case, when p = 1, the calculation result remains unchanged. When the guarantee relationship matrix is ​​adjusted from the existing data (guarantee relationship 1: fixed combination guarantee relationship) to the matrix elements are all 1 (guarantee relationship 2: free competition guarantee relationship), the calculation result is similar to Figure 4 The reason why p=1 and p=2 remain unchanged is that the cost matrix of the fine-grained model changes very slightly, which has no effect on the calculation results of the coarse-grained model. The latter change is because the diagonal elements of the first three rows in the cost matrix of the fine-grained model change greatly, resulting in a greater impact on the first three rows of the coarse-grained model calculation results, especially the diagonal elements. This shows that the cost matrix has a radiation effect on the calculation results, that is, a certain C ij Large changes, corresponding T ij The changes are also large, and the corresponding rows and columns have also undergone certain changes.

[0142] (3) Comparison of different distribution functions

[0143] Taking the coarse-grained model as an example, the calculation results of the fixed cost matrix under different supply and demand distribution conditions are analyzed.

[0144] Under the condition of a small-scale model, such as 5 supply points and 4 demand points in the case, the cost matrix is ​​C ij =d w (ph i , pg j ), respectively consider the model solution under two conditions: fixed supply distribution and fixed demand distribution. In the first case, the supply distribution is normal distribution, and the demand distribution is normal distribution, exponential distribution and uniform distribution respectively. The calculation results are as follows Figure 5 In the second case, the demand distribution is normal distribution, and the supply distribution is normal distribution, exponential distribution and uniform distribution respectively. The calculation results are shown in Figure 6 shown.

[0145] from Figure 5 and Figure 6 It can be seen that when there is an exponential distribution in the supply and demand distribution, the difference in the protection scheme is large. When the supply and demand distribution is a combination of normal distribution and uniform distribution, the change in the protection scheme is very small, especially when both supply and demand are normally distributed, the protection scheme is almost unchanged. Therefore, under the condition that the supply and demand position and the protection relationship remain unchanged, when both supply and demand are normally distributed, the protection scheme is stable; when there is no exponential distribution of supply and demand, the protection scheme is relatively stable; when there is an exponential distribution of supply and demand, the protection scheme has a large deviation. The mean error in the two cases is shown in Table 5.

[0146] Table 5 Mean error of guarantee schemes under different supply and demand distributions under small-scale conditions

[0147]

[0148] Under large-scale conditions, this case is expanded to 50 supply points and 40 demand points, and the cost matrix is ​​repmat(C ij , 10, 10), and the model solutions for the two cases of fixed supply distribution and fixed demand distribution are also considered. Due to space limitations, the error diagram of the calculation results is not given here. The mean error values ​​for the two cases are shown in Table 6. Three conclusions are drawn: (1) The impact of different supply and demand distribution functions on the security scheme is the same as the law under small-scale conditions; (2) As the scale increases, the error of the cosine distance remains basically unchanged, the error of the variance becomes significantly smaller, and the security scheme becomes more stable; (3) Although the error of the variance of the exponential distribution becomes significantly smaller under large-scale conditions, the error of the cosine distance does not change significantly and is still large, and the security scheme is not stable.

[0149] Table 6 Mean error of guarantee schemes under different supply and demand distributions under large-scale conditions

[0150]

[0151] (4) Comprehensive analysis

[0152] Further expansion, when the cost matrix is ​​adjusted to all elements are 1 (free competition guarantee relationship), the calculation results of different supply and demand distributions are analyzed under small-scale and large-scale conditions. The comprehensive analysis is as follows: Figure 7 shown.

[0153] from Figure 7 The following conclusions can be drawn: (1) The error of the guarantee plan caused by the supply and demand distribution is smaller under large-scale conditions than under small-scale conditions. The errors are in the order of normal distribution, uniform distribution, and exponential distribution from small to large. The errors of normal distribution and uniform distribution are similar, while the error of exponential distribution is much larger than the first two. (2) The error of the guarantee plan caused by the guarantee relationship is that guarantee relationship 1 is generally larger than guarantee relationship 2, and the error is larger under small-scale conditions.

[0154] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A regional security scheduling method based on the perspective of resource distribution, characterized by: include: Step 1: Get the guarantee agency X i 、Guarantee object Y j , Security Unit X ik , Equipment Unit Y jl , the number of resources of the guarantee unit h ik and the resource quantity g of the equipment unit jl , probabilistic processing h ik , g jl Get the probability vector ph of each supply and demand point i , pg j ; Step 2: Establish a fine-grained model for regional support scheduling based on resource distribution, and calculate the support organization X according to the fine-grained model. i To the protected object Y j The distribution distance d w (h i , g j ) and its guaranteed dispatch probability scheme PT ij , and calculate from the security unit X ik Transport to equipment unit Y jl Cost Step 3: Combined with step 2, obtain resource supply u i and resource requirements j , probabilistic processing u i , v j Get the probability vector u, v; Step 4: Based on step 3, a coarse-grained model for regional security scheduling based on the perspective of resource distribution is established, and the resource supply u is calculated according to the coarse-grained model. i To resource requirements v j Distribution distance and its guaranteed dispatch probability scheme PT; Step 5: Combined with step 4, calculate the coarse-grained model guarantee scheduling solution T: Step 6: Combined with step 2, calculate the fine-grained model guarantee scheduling solution T ij : Step 7: Output the coarse-grained model guarantee scheduling solution T and the fine-grained model guarantee scheduling solution T ij .

2. A regional security scheduling method based on resource distribution perspective according to claim 1, characterized in that: The fine-grained model of step 2 is as follows: Among them, d w (h i , g j ) is the protection institution X i To the protected object Y j The distribution distance of For resources from the security unit X ik Transport to equipment unit Y jl The cost, For resources from the security unit X ik Transport to equipment unit Y jl The number of 3. A regional security scheduling method based on resource distribution perspective according to claim 2, characterized in that: The coarse-grained model is: Among them, the entropy regularization parameter is λ, 4. The regional security scheduling method based on resource distribution perspective according to claim 3 is characterized by: The coarse-grained model guarantee scheduling solution T in step 5 is as follows: minimum resource configuration T 1 =PT*sum(v) and maximum resource delivery T 2 =PT*sum(u); If sum(u)≥sum(v), the demand can be met, and the optimal guarantee solution is T 1 ; If sum(u)<sum(v), the demand is partially met. The optimal guarantee solution includes two parts: the forward scheduling solution T 2 and the rear scheduling plan sum(T 1 -T 2 , 2).

5. The regional security scheduling method based on resource distribution perspective according to claim 4 is characterized in that: The fine-grained model in step 6 guarantees the scheduling solution T ij Specifically: Minimum resource allocation and the most resource delivery If sum(h i )≥sum(g j ), at this time, the demand can be met, then the optimal guarantee solution is If sum(h i )<sum(g j ), at this time, the demand is partially met, and the optimal guarantee solution includes two parts: the front scheduling solution and rear dispatch plan

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