Method and device for evaluating reliability of multi-state flow network of state heterogeneous component

Abstract

The invention relates to a multi-state flow network reliability evaluation method and device for state heterogeneous components. The method comprises the following steps: acquiring a multi-state flow network containing state heterogeneous components and component state probability distribution of the multi-state flow network, and acquiring a candidate state vector set of a minimum cut vector according to a constraint condition of a demand level by adopting an implicit enumeration method; and according to the candidate state vector set, generating a state combination of components in a minimum cut vector corresponding to the candidate state vector meeting a preset first constraint condition, and generating a candidate multi-state minimum cut vector set by adopting a minimum cut state combination comparison method and a preset second constraint condition. And judging the sizes of each candidate multi-state minimum cut vector and all derived vectors of the candidate multi-state minimum cut vector according to the candidate multi-state minimum cut vector set, and obtaining a real multi-state minimum cut vector set according to a judgment result. By adopting the method, the searching efficiency of the minimum cut vector in the multi-state flow network of the state heterogeneous component can be effectively improved.

Description

Technical Field

[0001] The present application relates to the technical field of vector search for reliability assessment of multi-state flow networks, and in particular to a reliability assessment method and device for a multi-state flow network of state-heterogeneous components. Background Art

[0002] As a more practical abstraction tool, the multi-state network model is widely used in the modeling and analysis of real-world network systems that cannot be fully covered by the two-state network, such as communication networks, distribution networks, power networks, road traffic networks, and drone cluster networks. Multi-state networks believe that the system and its nodes or components will be in multiple states due to design factors or performance degradation, and have network flow characteristics. They are also called multi-state flow networks (MFNs). Reliability is an important attribute and indicator for the safe operation of complex systems and is the focus of designers and managers. MFN reliability refers to its ability to complete the transmission of a given physical quantity under specified conditions and time. The probability R of transporting d+1 units of demand flow from the source point s to the sink point t is d+1 It is the key performance indicator of MFN reliability search. Searching for the exact solution of MFN reliability is an NP-hard problem. The reliability exact solution algorithm based on the minimum cut set vector (d-MC) is an effective method. However, the existing d-MC search methods only obtain d-MC in networks where the component state space is a set of integers that increases sequentially from 0. If there are one or more state heterogeneous components (SHC), the existing d-MC search algorithm cannot be used directly. Therefore, it is of great significance to propose an accurate and efficient algorithm to search for all d-MC* in MFNs containing SHC.

[0003] The ultimate goal of searching for d-MC or d-MC* is to obtain the reliability of MFN under the d demand level. Among the existing methods for the d-MC search problem, the algorithm proposed by "Niu YF, Xu X ZA new solution algorithm for the multistate minimal cut problem[J].IEEE Transactions on Reliability, 2019, 69(3):1064-1076" has the highest solution efficiency. It supplements the missing state between two adjacent integer states of the network component and sets the corresponding probability value to 0 in the state probability distribution. Then, the algorithm is used to solve all d-MCs and obtain the correct network reliability.

[0004] The objects of the existing minimum cut set vector d-MC search methods are mainly concentrated in multi-state flow networks (MFNs) without state heterogeneous components (SHCs), and most of them do not directly use the performance values ​​of the components in actual situations as their states. Taking the communication network system as an example, it is assumed that the maximum transmission rate of the data flow transmission link connecting users or network nodes (routers or switches) may be mapped to the component states of the MFN as follows: state 0: 0Gbps, state 1: 2Gbps, state 2: 4Gbps, state 3: 6Gbps (performance levels increase proportionally). At this time, if the maximum transmission rate requirement d=3 (6Gbps) between the source user s and the sink user t in the communication network with two components in parallel is d, then there are two rate combinations corresponding to the link state combinations that meet this requirement, namely d=0+3=3 (0Gbps+6Gbps=6Gbps) and d=1+2=3 (2Gbps+4Gbps=6Gbps). However, if the maximum transmission rate of the link and its state mapping are state 0: 0Gbps, state 1: 2Gbps, state 2: 5Gbps, state 3: 6Gbps, then only one combination meets the requirement, that is, d = 0 + 3 = (0Gbps + 6Gbps = 6Gbps), and the other combination d = 1 + 2 = 3 (2Gbps + 5Gbps ≠ 6Gbps) does not meet the requirement. This means that if the actual performance levels of the components in the MFN do not increase in proportion, they cannot be mapped to the state set {0, 1, 2, ..., W}, and can only be used as the state set of the component itself, such as {0, 2, 5, 6}, and such components are defined as SHC. Therefore, in MFNs containing SHC, various existing d-MC search methods cannot be used directly. Summary of the invention

[0005] Based on this, it is necessary to provide a multi-state flow network reliability assessment method and device that can correctly and efficiently search for a state-heterogeneous component containing state-heterogeneous components in response to the above technical problems.

[0006] A reliability assessment method for a multi-state flow network of state-heterogeneous components, the method comprising:

[0007] Obtain multi-state flow networks with state-heterogeneous components, minimal cut sets of multi-state flow networks, component state distributions, and demand levels.

[0008] The minimum capacity bound of each component is calculated based on the demand level, and the associated value of the state vector of each minimum cut vector in the minimum cut set.

[0009] The number of candidate vectors of the minimum cut vector is set to 1, and the implicit enumeration method is used to obtain the candidate state vector set of the minimum cut vector according to the constraint conditions of the required level.

[0010] A state combination of components in a minimum cut vector corresponding to a candidate state vector that satisfies a preset first constraint condition is generated according to a candidate state vector set, and a candidate multi-state minimum cut vector set is generated using a state combination comparison method and a preset second constraint condition.

[0011] According to the candidate multi-state minimum cut vector set, the size of each candidate multi-state minimum cut vector and all derived vectors of the candidate multi-state minimum cut vector is judged. If the judgment result is negative, the index set of duplicate values ​​is returned by sorting method, and the duplicate multi-state minimum cut vectors corresponding to the index in the candidate multi-state minimum cut vector set are deleted to obtain the real multi-state minimum cut vector set. If the judgment results are all positive, a candidate search is performed on each candidate minimum cut state vector in the candidate state vector set according to the minimum capacity bound to obtain the search result, and the real multi-state minimum cut vector set is obtained according to the search result.

[0012] A reliability assessment device for a multi-state flow network of state-heterogeneous components, the device comprising:

[0013] An input module is used to obtain a multi-state flow network containing state-heterogeneous components, a minimum cut set of the multi-state flow network, component state distribution, and demand level.

[0014] The real set initialization module is used to calculate the minimum capacity bound of each component according to the demand level, as well as the associated value of the state vector of each minimum cut vector in the minimum cut set.

[0015] The candidate state vector set acquisition module is used to set the number of candidate vectors of the minimum cut vector to 1, and adopt an implicit enumeration method to acquire the candidate state vector set of the minimum cut vector according to the constraint conditions of the required level.

[0016] The candidate multi-state minimum cut vector set generation module is used to generate the state combination of components in the minimum cut vector corresponding to the candidate state vector that meets the preset first constraint condition according to the candidate state vector set, and use the state combination comparison method and the preset second constraint condition to generate the candidate multi-state minimum cut vector set.

[0017] The minimum cut vector search module is used to judge the size of each candidate multi-state minimum cut vector and all derived vectors of the candidate multi-state minimum cut vector according to the candidate multi-state minimum cut vector set. If the judgment result is negative, the index set of duplicate values ​​is returned by sorting method, and the multi-state minimum cut vector duplicates corresponding to the index in the candidate multi-state minimum cut vector set are deleted to obtain the real multi-state minimum cut vector set. If the judgment results are all positive, a candidate search is performed on each candidate minimum cut state vector in the candidate state vector set according to the minimum capacity bound to obtain the search result, and the real multi-state minimum cut vector set is obtained according to the search result.

[0018] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the following steps are implemented:

[0019] Obtain multi-state flow networks with state-heterogeneous components, minimal cut sets of multi-state flow networks, component state distributions, and demand levels.

[0020] The minimum capacity bound of each component is calculated based on the demand level, and the associated value of the state vector of each minimum cut vector in the minimum cut set.

[0021] The number of candidate vectors of the minimum cut vector is set to 1, and the implicit enumeration method is used to obtain the candidate state vector set of the minimum cut vector according to the constraint conditions of the required level.

[0022] A state combination of components in a minimum cut vector corresponding to a candidate state vector that satisfies a preset first constraint condition is generated according to a candidate state vector set, and a candidate multi-state minimum cut vector set is generated using a state combination comparison method and a preset second constraint condition.

[0023] According to the candidate multi-state minimum cut vector set, the size of each candidate multi-state minimum cut vector and all derived vectors of the candidate multi-state minimum cut vector is judged. If the judgment result is negative, the index set of duplicate values ​​is returned by sorting method, and the duplicate multi-state minimum cut vectors corresponding to the index in the candidate multi-state minimum cut vector set are deleted to obtain the real multi-state minimum cut vector set. If the judgment results are all positive, a candidate search is performed on each candidate minimum cut state vector in the candidate state vector set according to the minimum capacity bound to obtain the search result, and the real multi-state minimum cut vector set is obtained according to the search result.

[0024] The above-mentioned multi-state flow network reliability assessment method and device of state heterogeneous components, through implicit enumeration method and state combination comparison method, combined with preset constraints, efficiently screens the minimum cut vector set that meets the demand level. First, obtain the information of the multi-state flow network, including state heterogeneous components, minimum cut set, component state distribution and demand level (d). Then, calculate the minimum capacity bound of each component according to the demand level to provide a basis for screening the candidate state vector set. Using the implicit enumeration method, according to the constraint of the demand level, preliminarily screen out the candidate minimum cut state vector set. Subsequently, generate the state combination of the components in the minimum cut vector corresponding to the candidate state vector that meets the preset first constraint condition, and further screen out the candidate multi-state minimum cut vector set through the state combination comparison method and the second constraint condition. When judging the size of the candidate multi-state minimum cut vector and all the derived vectors of the candidate multi-state minimum cut vector, if the two are consistent, use the sorting method to return the duplicate value index, delete the duplicate items in the candidate set, and obtain the real multi-state minimum cut vector set; if the two are inconsistent, the number of candidate multi-state minimum cut vectors is small or too many, then search each candidate state vector according to the minimum capacity bound, and finally obtain the real multi-state minimum cut vector set. When the number of state-heterogeneous components increases, the discreteness of component states increases, and the demand level increases, the state differences and demand constraints are used to reduce the search space and improve the reliability search efficiency. Therefore, in multi-state flow networks, by optimizing reliability search and screening techniques, the time complexity is effectively reduced and the search efficiency is improved, especially when the component states are diversified and the demand level is high, showing higher computational efficiency and reliability search effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 An application scenario diagram of a multi-state flow network reliability assessment method for state-heterogeneous components in one embodiment;

[0026] Figure 2 A schematic diagram of a flow chart of a d-MC* search step in one embodiment;

[0027] Figure 3 A schematic diagram of an ARPA network framework in an embodiment;

[0028] Figure 4 A diagram showing a medium-scale multi-state flow network structure in one embodiment;

[0029] Figure 5 A time ratio comparison diagram of three methods on a medium-sized network in one embodiment;

[0030] Figure 6 A diagram showing a large-scale multi-state flow network structure in one embodiment;

[0031] Figure 7A comparison chart of the results of three algorithms on a large network in one embodiment;

[0032] Figure 8 A structural block diagram of a multi-state flow network reliability assessment device for a state-heterogeneous component in one embodiment;

[0033] Fig. 9 FIG. 4 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0035] In one embodiment, Figure 1 As shown, a reliability assessment method for a multi-state flow network with state heterogeneous components is provided, comprising the following steps:

[0036] Step 102, obtaining a multi-state flow network including state-heterogeneous components, a minimum cut set of the multi-state flow network, component state distribution, and demand level.

[0037] Step 104 , calculating the minimum capacity bound of each component and the associated value of the state vector of each minimum cut vector in the minimum cut set according to the demand level.

[0038] Step 106, setting the number of candidate vectors of the minimum cut vector to 1, and using implicit enumeration method to obtain a set of candidate state vectors of the minimum cut vector according to the constraint conditions of the demand level.

[0039] Step 108, generating a state combination of components in a minimum cut vector corresponding to a candidate state vector that satisfies a preset first constraint condition according to the candidate state vector set, and generating a candidate multi-state minimum cut vector set using a state combination comparison method and a preset second constraint condition.

[0040] Step 110, judging the size of each candidate multi-state minimum cut vector and all derived vectors of the candidate multi-state minimum cut vector according to the candidate multi-state minimum cut vector set, if the judgment result is negative, returning the index set of duplicate values ​​by a sorting method, deleting the duplicate multi-state minimum cut vectors corresponding to the index in the candidate multi-state minimum cut vector set, and obtaining a true multi-state minimum cut vector set; if the judgment results are all positive, performing a candidate search for each candidate minimum cut state vector in the candidate state vector set according to the minimum capacity bound, obtaining a search result, and obtaining a true multi-state minimum cut vector set according to the search result.

[0041] In the above-mentioned reliability assessment method of a multi-state flow network with state heterogeneous components, the implicit enumeration method and the state combination comparison method are combined with preset constraints to efficiently screen the minimum cut vector set that meets the demand level. First, the information of the multi-state flow network is obtained, including state heterogeneous components, minimum cut sets, component state distribution and demand level (d). Then, the minimum capacity bound of each component is calculated according to the demand level to provide a basis for the screening of the candidate state vector set. The implicit enumeration method is used to preliminarily screen the candidate minimum cut state vector set according to the constraint of the demand level. Subsequently, the state combination of the components in the minimum cut vector corresponding to the candidate state vector that meets the preset first constraint is generated, and the candidate multi-state minimum cut vector set is further screened by the state combination comparison method and the second constraint. When judging the size of the candidate multi-state minimum cut vector and all the derived vectors of the candidate multi-state minimum cut vector, if the two are consistent, the sorting method is used to return the duplicate value index, delete the duplicate items in the candidate set, and obtain the real multi-state minimum cut vector set; if the two are inconsistent, the number of candidate multi-state minimum cut vectors is small or too many, then each candidate state vector is searched according to the minimum capacity bound, and finally the real multi-state minimum cut vector set is obtained. When the number of state-heterogeneous components increases, the discreteness of component states increases, and the demand level increases, the state differences and demand constraints are used to reduce the search space and improve the reliability search efficiency. Therefore, in multi-state flow networks, by optimizing reliability search and screening techniques, the time complexity is effectively reduced and the search efficiency is improved, especially when the component states are diversified and the demand level is high, showing higher computational efficiency and reliability search effect.

[0042] In one embodiment, if the demand level is not less than the maximum flow of each component under the maximum capacity vector in the multi-state flow network, the minimum capacity bound of each component is calculated:

[0043] L(e i )=max{b ij |b ij ≤dM(W(0 i )),b ij ∈b i}

[0044] Among them, e i For components, b ij is the state vector of the component, d is the demand level, M(W(0 i )) is the maximum flow of the component under the maximum capacity vector, b i is the state vector set of the component, L(e i ) is the minimum capacity bound of the component. And the associated value of the state vector of each minimum cut vector in the minimum cut set:

[0045]

[0046] Among them, AV(x) is the associated value of the state vector of the minimum cut vector, x is the state vector of the minimum cut vector, and e i-1 , m is the maximum flow of the i-th component under the maximum capacity vector.

[0047] In one of the embodiments, the number of candidate vectors j of the minimum cut vector is set to 1, and an implicit enumeration method is used to obtain a set of candidate state vectors of the minimum cut vector according to a constraint condition that the demand level is not less than a set of state vectors corresponding to each component.

[0048] In one embodiment, the preset first constraint condition is:

[0049] 0≤x(e i )≤min{W(e i ),max{b ij |b ij ≤d,b ij ∈b i}},e i ∈C i

[0050] L(e i )≤x(e i )≤min{W(e i ),max{b ij |b ij ≤d,b ij ∈b i}},e i ∈C j And M(W(0 i ))≤d

[0051] 0≤x(e i )≤min{W(e i ),max{b ij |b ij ≤d,b ij ∈b i}},e i ∈C j And M(W(0 i ))>d

[0052] Among them, x(e i ) is the minimum cut state vector of the component, L(e i ) is the minimum capacity bound of the component, W(e i ) is the maximum capacity vector of the component, b ij is the state vector of the component, d is the demand level, C i is the minimum cut set, C j is the candidate state vector set, bi is the state vector set of the component, M(W(0 i )) is the maximum flow of the component under the maximum capacity vector. The second preset constraint is:

[0053] And x(e i )∈b i

[0054] Among them, x(e i ) is the minimum cut state vector of the component, C j is the candidate state vector set, d is the demand level, b i is the state vector set of the component.

[0055] In one embodiment, the state combination of the components in the minimum cut vector corresponding to the candidate state vector that satisfies the preset first constraint condition is generated according to the candidate state vector set, and the state combination comparison method is used to determine the current state combination Comb k Comb with states other than the current state combination l If the current state combination Comb k Not greater than the state combination Comb except the current state combination l , then delete the current state combination Comb k , get the candidate state combination; otherwise, delete the state combination Comb except the current state combination l , and obtain a candidate state combination. The candidate state combination generates a candidate multi-state minimum cut vector set according to the preset second constraint condition.

[0056] In one of the embodiments, the size of each candidate multi-state minimum cut vector and all derived vectors of the candidate multi-state minimum cut vector is determined based on the candidate multi-state minimum cut vector set. If the current candidate multi-state minimum cut vector and the number of all derived vectors of the candidate multi-state minimum cut vector are equal and 1, the judgment result is negative, and a sorting method is used to return an index set of duplicate values, and the duplicate multi-state minimum cut vectors corresponding to the index in the candidate multi-state minimum cut vector set are deleted to obtain a true multi-state minimum cut vector set.

[0057] In one embodiment, if the current candidate multi-state minimum cut vector is not equal to the number of all derived vectors of the candidate multi-state minimum cut vector, or the two are equal and the value is not 1, the judgment result is positive, and a candidate search is performed on each candidate minimum cut state vector in the candidate state vector set according to the minimum capacity boundary. If the set of the maximum capacity vectors of the component is equal to the demand level, the current candidate state vector set is a true multi-state minimum cut vector set, and the numerical size of the number of candidate minimum cut state vectors and the number of minimum cut vectors in the current candidate state vector set is determined. If the number of candidate minimum cut state vectors in the current candidate state vector set is less than the number of minimum cut vectors, a candidate search is performed on each candidate minimum cut state vector in the next candidate state vector set. If the number of candidate minimum cut state vectors in the current candidate state vector set is not less than the number of minimum cut vectors, a sorting method is used to return an index set of duplicate values, and duplicates of candidate minimum cut state vectors corresponding to the index in the candidate state vector set are deleted to obtain a true multi-state minimum cut vector set. If the set of maximum capacity vectors of the component is not equal to the demand level, the candidate minimum cut state vectors of the candidate state vector set are filtered according to the current candidate state vector, the maximum flow corresponding to the current candidate state vector and the demand level to obtain the true multi-state minimum cut vector set.

[0058] In one embodiment, if the sequence number of the current candidate state vector is less than the number of state combinations, the candidate minimum cut state vector of the candidate state vector set is screened according to the next candidate state vector, the maximum flow corresponding to the next candidate state vector, and the demand level. Otherwise, it is determined whether the number of candidate minimum cut state vectors in the current candidate state vector set is less than the number of minimum cut vectors.

[0059] In one embodiment, if Figure 2 As shown, a d-MC* search step is provided, which specifically includes the following contents:

[0060] Input: Multi-state flow network G(V,E,W), known network minimum cut set C{C1,C2,…,C p}, component status distribution and demand level d.

[0061] Output: The set Ω containing all real and non-repeating d-MC*.

[0062] Step 1: Set up the real d-MC* set The associated value set for each element Use the maximum flow algorithm to calculate M(W) = D. For each component e i , if M(W(0 i ))≤d, calculate its minimum capacity bound L(e i )=max{b ij |bij ≤dM(W(0 i )),b ij ∈b i}. And, each d-MC* candidate x=(W(e1),…,L(e i ),…,W(e m ))No verification is required, it can be directly included in the set Ω, and the associated value AV(x) of each x is calculated according to the following formula and then incorporated into the set Δ.

[0063]

[0064] Step 2: Let j=1.

[0065] Step 3: For the minimum cut C j , use implicit enumeration to obtain the d-MC* candidate x that satisfies the following four constraints. If no d-MC* candidate is found, go to step 6. Otherwise, during the solution process, generate the minimum cut C that satisfies (1)(2)(3) according to the order of constraints. j Comb k , where C9 = {e8, e9}. Using the state combination comparison method, if Comb k ≤Comb l ,l=1,2,…,σ j And l≠k, then delete Comb k , otherwise delete Comb l Then, according to the remaining state combinations combined with constraint (4), at most σ j d-MC* candidates, namely

[0066] 0≤x(e i )≤min{W(e i ),max{b ij b ij ≤d,b ij ∈b i}}For e i ∈C j (1)

[0067] L(e i )≤x(e i )≤min{W(e i ),max{b ij b ij ≤d,b ij ∈b i}}For e i ∈C j And M(W(0 i ))≤d(2)

[0068] 0≤x(e i )≤min{W(e i ),max{b ij |b ij ≤d,b ij ∈b i}}For e i ∈C j And M(W(0 i ))>d(3)

[0069] And x(e i )∈b i (4)

[0070] x(e i )=W(e i )for

[0071] Step 4: If j=p=1, go to step 8.

[0072] Step 5: Based on the definition verification method, perform σ according to the following steps j Verification of d-MC* candidates:

[0073] Step 5.2: If but are all real d-MC*, let At the same time, calculate the associated value AV(x) of each d-MC*, let Go to step 6.

[0074] Step 5.2: Let k=1.

[0075] Step 5.3: For a d-MC* candidate x jk =(x jk (e1),…,x jk (e i )=b il ,…,x jk (e m )), b il For component e i The l-th state of , according to the definition, verifies whether it is a true d-MC*. If the maximum flow M(x jk )≤d and all e i ∈U(x jk ) All satisfy the maximum flow Then x jk is a real d-MC*, let Ω=Ω∪x jk , calculate AV(x jk ), let Δ=Δ∪AV(xjk )。Otherwise, x jk is not a true d-MC*.

[0076] Step 5.4: If k < σ j , let k = k + 1, and jump back to Step 5.3.

[0077] Step 6: If j < p, let j = j + 1, and jump back to Step 3.

[0078] Step 7: Since the elements in the true d-MC* set Ω are in one-to-one correspondence with the elements in the associated value set Δ, use a sorting method for the latter to return the index set Index of duplicate values, and delete all d-MC* duplicates corresponding to the indices in Ω.

[0079] Step 8: Finally, obtain the set Ω of non-duplicate true d-MC*. The program stops.

[0080] In one of the embodiments, an ARPA network as shown in Figure 3 and the component state distribution in Table 1 are used to verify this method step by step. In the ARPA network, W = (8, 6, 3, 4, 3, 6, 3, 6, 8), which contains p = 9 minimum cuts, as shown in Table 1. Assume d = 9, then the steps to search for all 9-MC* are as follows:

[0081] Table 1 All minimum cuts in the ARPA network

[0082]

[0083] Step 1: Set Calculate M(W) = 13 using the maximum flow algorithm. Since M(W(01)) = 6 < d = 9, so L(e1) = max{b 1j |b 1j ≤ 9 - 6 = 3, b 1j ∈ [0, 3, 4, 8]} = 3, and the corresponding (3, 6, 3, 4, 3, 6, 3, 6, 8) is a true 9-MC*. L(e2) = 0, L(e4) = 0, L(e6) = 0, L(e8) = 0, L(e9) = 3, and the corresponding (8, 0, 3, 4, 3, 6, 3, 6, 8), (8, 6, 3, 0, 3, 6, 3, 6, 8), (8, 6, 3, 4, 3, 0, 3, 6, 8), (8, 6, 3, 4, 3, 6, 3, 0, 8), (8, 6, 3, 4, 3, 6, 3, 6, 3) are all true 9-MC*, and all are incorporated into Ω. Add the associated values 32813.842, 32802.532, 32738.499, 31928.363, 26239.043, and 17914.052 corresponding to the above 6 9-MC* to Δ.

[0084] Step 2: Let j = 1.

[0085] Step 3: For C1 = {e1, e2}, b1 = [0, 3, 4, 8], b2 = [0, 3, 4, 6], use the implicit enumeration method to generate the minimum cut component state combinations Comb1 = (4, 3), Comb2 = (4, 4) that satisfy the conditions. Then, execute the minimum cut component state combination comparison method. Since Comb1 < Comb2, delete Comb1. Thus, generate σ1 = 1 9-MC* candidate x 11 = (4, 4, 3, 4, 3, 6, 3, 6, 8).

[0086] Step 4: p ≠ 1.

[0087] Step 5: Verify x 11 according to the following steps:

[0088] Step 5.1: Since W(e1) + W(e2) = 14 > D = 13, it needs to be verified.

[0089] Step 5.2: Let k = 1.

[0090] Step 5.3: The maximum flow M(x 11 ) = 8 < d = 9 under x 11 . Its unsaturated component set U(x 11 ) = {e1, e2}. For e1, x 11 (e1) = b 13 = 4, b 14 = 8, and its corresponding satisfies the maximum flow For e2, x 11 (e2) = b 23 = 4, b 24 = 6, and its corresponding satisfies the maximum flow It can be concluded that x 11 is a true 9-MC*. Let Ω = Ω ∪ x 11 . Calculate Let Δ = Δ ∪ AV(x 11 ).

[0091] Step 5.4: k = 1 = σ1.

[0092] Step 6: Since j = 1 < p = 9, let j = 2 and jump back to Step 3.

[0093] Step 3: For MCC2 = {e2, e3, e4, e5}, b3 = [0, 3], b4 = [0, 3, 4], b5 = [0, 3], generate 7 C2 component state combinations Comb1 = (3, 0, 3, 0), Comb2 = (3, 0, 3, 3), Comb3 = (3, 3, 3, 0), Comb4 = (3, 0, 4, 0), Comb5 = (4, 0, 3, 0), Comb6 = (4, 0, 4, 0), Comb7 = (6, 0, 3, 0). After executing the minimum cut component state combination comparison method, the remaining combinations are Comb2, Comb3, Comb6 and Comb7, generating σ2 = 4 9-MC* candidate x 21 =(8,3,0,3,3,6,3,6,8),x 22 =(8,3,3,3,0,6,3,6,8),x 23 =(8,4,0,4,0,6,3,6,8) and x 24 =(8,6,0,3,0,6,3,6,8).

[0094] Step 4: p≠1.

[0095] Step 5: Verify the above 4 9-MC* candidates according to the following steps:

[0096] Step 5.1:

[0097] Step 5.2: k=1.

[0098] Step 5.3: x 21 The maximum flow M(x 21 )=d=9,U(x 21 )={e2,e3,e4}. For e2, x 21 (e2) = b 22 =3, b 23 =4, corresponding to have For e3, x 21 (e3) = b 31 =0, b 32 =3, have For e4, x 21 (e4) = b 42 =3, b 43 =4, have So, x 21 is a real 9-MC*, let Ω=Ω∪x 21 AV(x 21 )=32768.434, let Δ=Δ∪AV(x 21).

[0099] Step 5.4: Since k=1<σ2=4, set k=2 and jump back to step 5.3.

[0100] Step 5.3: It is verified that x 23 is the real 9-MC*, and x 22 and x 24 No. Let Ω=Ω∪x 23 ,AV(x 23 )=32627.443, let Δ=Δ∪AV(x 23 ).

[0101] Step 5.4: k = 4 = σ2.

[0102] Step 6: Since j=2<p=9, set j=3 and jump back to step 3.

[0103] …

[0104] Step 6: j=9=p.

[0105] Step 7: Repeat the above steps to obtain all true 9-MC*, which are stored in Ω, and the associated values ​​corresponding to d-MC* are in the Δ set. Since there are no repeated associated values ​​in Δ, the index set This indicates that there are no repeated 9-MC* in Ω.

[0106] Step 8: Finally, we get the non-repetitive 9-MC* set Ω as shown in Table 2, which contains 18 9-MC* in total. The search stops.

[0107] Table 2 ARPA network 9-MC* set Ω and its associated value set Δ

[0108]

[0109] In one embodiment, experiments are set under different network topologies, and the experimental result variables include: τ is the number of d-MC method candidates, L is the number of real d-MCs, ρ is the number of d-MC* basic method candidates, σ is the number of d-MC* method candidates in this solution, σ free is the number of d-MC* candidates that do not need to be verified, ρ-σ is the number of candidates reduced by the reduction technology, L * is the actual d-MC* number. In addition, T1, T2, and T3 are the running times of the d-MC method, the d-MC* basic method, and the d-MC* method proposed in this scheme, respectively. Example 1: Figure 4The medium-scale multi-state flow network shown in Figure 3 contains a medium-scale MFN with 13 nodes and 23 SHCs. The component state distribution is shown in Table 3. The source point s is 1 and the sink point t is 13. In order to comprehensively compare the efficiency of the methods, the integer requirement d∈[0,13). The experimental results are shown in Tables 4, 5 and Figure 5 shown.

[0110] Table 3. State space vectors of components in medium-scale networks

[0111]

[0112] Table 4 The number of products of the three methods on medium-sized networks

[0113]

[0114] Table 5 Computation time (seconds) and ratio of three methods on medium-sized networks

[0115]

[0116] As can be seen from Table 4, the number of d-MC* candidates σ generated by the proposed method is much smaller than that of the other two methods. In addition, as can be seen from Table 5, the proposed method is faster than the d-MC method when d ≥ 1, and more efficient than the d-MC* basic method when d ≥ 4. For intuitive comparison, Figure 5 As shown in the figure, the time ratio of different methods changes with d, and includes the ratio of the number of candidates. It can be seen that the change trend of the running time ratio is almost consistent with the change of the candidate number ratio, indicating that the number of candidates determines the efficiency of the method. The above results show that on medium-sized networks, the d-MC* method proposed in this scheme is more efficient than the d-MC method under most d, and the running speed is increased by more than 20 times. Compared with the d-MC* basic method, when the number of candidates increases with d to a certain number, the advantages of this scheme are prominent until d reaches the maximum, and the running time is reduced by more than 19,000 times.

[0117] Example 2: Figure 6 The large-scale multi-state flow network shown in the figure selects a large-scale MFN containing SHCs, where the number of nodes is 16, the number of components is 30, the source point s is 1, the sink point t is 16, and each component e i The state space vector b i The settings are as follows: let the odd-numbered components of non-prime numbers be (0,1,3), the even-numbered components be (0,2,3), and the prime-numbered components be (0,3). The demand level d is an integer from 0 to 8. The experimental results are shown in Tables 6 and 7:

[0118] Table 6 The number of products of three methods on large networks

[0119]

[0120] Table 7 Computation time (seconds) and ratio of three methods on large networks

[0121]

[0122] From the above table and Figure 7 As shown in the figure, in large networks, the relationship between the number of candidates generated by the three methods is: τ>ρ>σ. The d-MC* method proposed in this scheme has the least number of candidates. Compared with the d-MC* basic method, when d=8, the d-MC* method proposed in this scheme can avoid the generation of up to 148595 candidates, which makes the running speed of the method proposed in this scheme significantly improved compared with the d-MC method and the d-MC* basic method under most d, and the improvement effect is up to 41.871 times and 222.046 times. The experimental results in large networks also show that when searching for d-MC*, this scheme has a more obvious advantage than other methods.

[0123] It should be understood that although Figure 1-2 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, Figure 1-2 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0124] In one embodiment, Figure 8 As shown, a multi-state flow network reliability assessment device for state heterogeneous components is provided, comprising: an input module 802, a real set initialization module 804, a candidate state vector set acquisition module 806, a candidate multi-state minimum cut vector set generation module 808 and a minimum cut vector search module 810, wherein:

[0125] The input module 802 is used to obtain a multi-state flow network including state-heterogeneous components, a minimum cut set of the multi-state flow network, component state distribution, and demand level.

[0126] The real set initialization module 804 is used to calculate the minimum capacity bound of each component according to the demand level, and the associated value of the state vector of each minimum cut vector in the minimum cut set.

[0127] The candidate state vector set acquisition module 806 is used to set the number of candidate vectors of the minimum cut vector to 1, and adopt an implicit enumeration method to acquire a candidate state vector set of the minimum cut vector according to the constraint conditions of the demand level.

[0128] The candidate multi-state minimum cut vector set generation module 808 is used to generate the state combination of components in the minimum cut vector corresponding to the candidate state vector that meets the preset first constraint condition according to the candidate state vector set, and use the state combination comparison method and the preset second constraint condition to generate the candidate multi-state minimum cut vector set.

[0129] The minimum cut vector search module 810 is used to judge the size of each candidate multi-state minimum cut vector and all derived vectors of the candidate multi-state minimum cut vector according to the candidate multi-state minimum cut vector set. If the judgment result is negative, the index set of duplicate values ​​is returned by sorting method, and the multi-state minimum cut vector duplicates corresponding to the index in the candidate multi-state minimum cut vector set are deleted to obtain the real multi-state minimum cut vector set. If the judgment results are all positive, a candidate search is performed on each candidate minimum cut state vector in the candidate state vector set according to the minimum capacity bound to obtain the search result, and the real multi-state minimum cut vector set is obtained according to the search result.

[0130] For the specific definition of a multi-state flow network reliability assessment device for a state heterogeneous component, please refer to the definition of a multi-state flow network reliability assessment method for a state heterogeneous component mentioned above, which will not be repeated here. Each module in the above-mentioned multi-state flow network reliability assessment device for a state heterogeneous component can be implemented in whole or in part through software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0131] In one embodiment, a computer device is provided. The computer device may be a terminal, and its internal structure diagram may be as follows: Fig. 9As shown. The computer device includes a processor, a memory, a network interface, a display screen and an input device connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a multi-state flow network reliability assessment method for state heterogeneous components is implemented. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covered on the display screen, or a key, trackball or touchpad set on the computer device housing, or an external keyboard, touchpad or mouse, etc.

[0132] Those skilled in the art will understand that Figure 8-9 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present invention, and does not constitute a limitation on the computer device to which the solution of the present invention is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0133] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the following steps are implemented:

[0134] Obtain multi-state flow networks with state-heterogeneous components, minimal cut sets of multi-state flow networks, component state distributions, and demand levels.

[0135] The minimum capacity bound of each component is calculated based on the demand level, and the associated value of the state vector of each minimum cut vector in the minimum cut set.

[0136] The number of candidate vectors of the minimum cut vector is set to 1, and the implicit enumeration method is used to obtain the candidate state vector set of the minimum cut vector according to the constraint conditions of the required level.

[0137] A state combination of components in a minimum cut vector corresponding to a candidate state vector that satisfies a preset first constraint condition is generated according to a candidate state vector set, and a candidate multi-state minimum cut vector set is generated using a state combination comparison method and a preset second constraint condition.

[0138] According to the candidate multi-state minimum cut vector set, the number of candidate vectors and the number of minimum cut vectors in the minimum cut set are judged. If the judgment result is positive, the index set of duplicate values ​​is returned by sorting method, and the duplicates of the candidate minimum cut state vectors corresponding to the index in the candidate state vector set are deleted to obtain the real minimum cut vector set. If the judgment result is negative, a candidate search is performed on each candidate minimum cut state vector in the candidate state vector set according to the minimum capacity bound to obtain the search result, and the real minimum cut vector set is obtained according to the search result.

[0139] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided by the present invention can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0140] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0141] The above-mentioned embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A reliability assessment method for multi-state flow networks with heterogeneous state components. It is characterized in that The method comprises: Obtaining a multi-state flow network including state-heterogeneous components, a minimum cut set of the multi-state flow network, component state distribution, and demand level; Calculating a minimum capacity bound for each component and an associated value of a state vector of each minimum cut vector in the minimum cut set according to the demand level; Assuming that the number of candidate vectors of the minimum cut vector is 1, an implicit enumeration method is used to obtain a set of candidate state vectors of the minimum cut vector according to the constraint conditions of the demand level; Generate a state combination of components in a minimum cut vector corresponding to a candidate state vector that satisfies a preset first constraint condition according to the candidate state vector set, and generate a candidate multi-state minimum cut vector set using a state combination comparison method and a preset second constraint condition; The size of each candidate multi-state minimum cut vector and all derived vectors of the candidate multi-state minimum cut vector is judged according to the candidate multi-state minimum cut vector set. If the judgment result is negative, a sorting method is used to return an index set of duplicate values, and duplicate multi-state minimum cut vectors corresponding to the index in the candidate multi-state minimum cut vector set are deleted to obtain a true multi-state minimum cut vector set; if the judgment results are all positive, a candidate search is performed on each candidate minimum cut state vector in the candidate state vector set according to the minimum capacity bound to obtain a search result, and a true multi-state minimum cut vector set is obtained according to the search result.

2. The method according to claim 1, It is characterized in that Calculating a minimum capacity bound of each component and an associated value of a state vector of each minimum cut vector in the minimum cut set according to the demand level includes: If the demand level is not less than the maximum flow of each component in the multi-state flow network under the maximum capacity vector, then the minimum capacity bound of each component is calculated: L(ei)=max{bij|bij≤dM(W(0i)),bij∈bi} Among them, e i For components, b ij is the state vector of the component, d is the demand level, M(W(0 i )) is the maximum flow of the component under the maximum capacity vector, bi is the state vector set of the component, L(e i ) is the minimum capacity bound of the component; And the associated value of the state vector of each minimum cut vector in the minimum cut set: Among them, AV(x) is the associated value of the state vector of the minimum cut vector, x is the state vector of the minimum cut vector, and m is the number of components in the network.

3. The method according to claim 1, It is characterized in that The number of candidate vectors of the minimum cut vector is set to 1, and an implicit enumeration method is used to obtain a set of candidate state vectors of the minimum cut vector according to the constraint conditions of the demand level, including: The number of candidate vectors j of the minimum cut vector is set to 1, and the candidate state vector set of the minimum cut vector is obtained by implicit enumeration according to the constraint condition that the demand level is not less than the state vector set corresponding to each component.

4. The method according to claims 1 to 3, It is characterized in that The first preset constraint is: 0≤x(ei)≤min{W(ei),max{bijbij≤d,bij∈bi}},ei∈Cj L(ei)≤x(ei)≤min{W(ei),max{bijbij≤d,bij∈bi}},ei∈Cj and M(W(0i))≤d 0≤x(ei)≤min{W(ei),max{bijbij≤d,bij∈bi}},ei∈Cj and M(W(0i))>d Among them, x(e i ) is the minimum cut state vector of the component, L(e i ) is the minimum capacity bound of the component, W(e i ) is the maximum capacity vector of the component, b ij is the state vector of the component, d is the demand level, C i is the minimum cut set, b i is the state space vector of the component, M(W(0 i )) is the maximum flow of the component under the maximum capacity vector; The second preset constraint is: Among them, x(e i ) is the component state, C j is the minimum cut set, d is the demand level, and bi is the state space vector of the component.

5. The method according to claim 4, It is characterized in that Generating a state combination of components in a minimum cut vector corresponding to a candidate state vector that satisfies a preset first constraint condition according to the candidate state vector set, and generating a candidate multi-state minimum cut vector set using a state combination comparison method and a preset second constraint condition, including: Generate the state combination of the components in the minimum cut vector corresponding to the candidate state vector that meets the preset first constraint condition according to the candidate state vector set, and use the state combination comparison method to determine the current state combination Comb k Comb with states other than the current state combination l If the current state combination Comb k Not greater than the state combination Comb except the current state combination l , then delete the current state combination Comb k , get the candidate state combination; otherwise, delete the state combination Comb except the current state combination l , get the candidate state combination; The candidate state combination generates a candidate multi-state minimum cut vector set according to a preset second constraint condition.

6. The method according to claim 5, It is characterized in that According to the candidate multi-state minimum cut vector set, the size of each candidate multi-state minimum cut vector and all derived vectors of the candidate multi-state minimum cut vector is judged. If the judgment result is negative, a sorting method is used to return an index set of duplicate values, and duplicate multi-state minimum cut vectors corresponding to the index in the candidate multi-state minimum cut vector set are deleted to obtain a true multi-state minimum cut vector set, including: According to the candidate multi-state minimum cut vector set, the size of each candidate multi-state minimum cut vector and all derived vectors of the candidate multi-state minimum cut vector is judged. If the current candidate multi-state minimum cut vector and the number of all derived vectors of the candidate multi-state minimum cut vector are equal and 1, the judgment result is negative, and the index set of duplicate values ​​is returned by sorting method. The duplicate multi-state minimum cut vectors corresponding to the index in the candidate multi-state minimum cut vector set are deleted to obtain the real multi-state minimum cut vector set.

7. The method according to claim 6, It is characterized in that If the judgment results are all positive, then a candidate search is performed on each candidate minimum cut state vector in the candidate state vector set according to the minimum capacity bound to obtain a search result, and a true multi-state minimum cut vector set is obtained according to the search result, including: If the current candidate multi-state minimum cut vector is not equal to the number of all derived vectors of the candidate multi-state minimum cut vector, or the two are equal and the value is not 1, the judgment results are all positive, and a candidate search is performed on each candidate minimum cut state vector in the candidate state vector set according to the minimum capacity boundary. If the set of maximum capacity vectors of the component is equal to the demand level, the current candidate state vector set is a true multi-state minimum cut vector set, and the numerical size of the number of candidate minimum cut state vectors in the current candidate state vector set and the number of minimum cut vectors is judged. If the number of candidate minimum cut state vectors in the current candidate state vector set is less than the number of minimum cut vectors, the next A candidate search is performed for each candidate minimum cut state vector in the candidate state vector set; if the number of candidate minimum cut state vectors in the current candidate state vector set is not less than the number of minimum cut vectors, a sorting method is used to return an index set of duplicate values, and duplicates of candidate minimum cut state vectors corresponding to the index in the candidate state vector set are deleted to obtain a true multi-state minimum cut vector set; if the set of maximum capacity vectors of the component is not equal to the demand level, the candidate minimum cut state vectors of the candidate state vector set are screened according to the current candidate state vector, the maximum flow corresponding to the current candidate state vector and the demand level to obtain a true multi-state minimum cut vector set.

8. The method according to claim 7, It is characterized in that After the step of screening the candidate minimum cut state vectors of the candidate state vector set according to the current candidate state vector, the maximum flow corresponding to the current candidate state vector and the demand level to obtain a true multi-state minimum cut vector set, the method further includes: If the sequence number of the current candidate state vector is less than the number of state combinations, the candidate minimum cut state vector of the candidate state vector set is filtered according to the next candidate state vector, the maximum flow corresponding to the next candidate state vector, and the demand level; otherwise, it is determined whether the number of candidate minimum cut state vectors in the current candidate state vector set is less than the number of minimum cut vectors.

9. A reliability assessment device for multi-state flow networks with heterogeneous state components, It is characterized in that The device comprises: An input module for obtaining a multi-state flow network including state-heterogeneous components, a minimum cut set of the multi-state flow network, component state distribution, and a demand level; a real set initialization module, for calculating the minimum capacity bound of each component according to the demand level, and an associated value of the state vector of each minimum cut vector in the minimum cut set; A candidate state vector set acquisition module, used to set the number of candidate vectors of the minimum cut vector to 1, and to acquire the candidate state vector set of the minimum cut vector according to the constraint condition of the demand level by using an implicit enumeration method; A candidate multi-state minimum cut vector set generation module, used to generate a state combination of components in a minimum cut vector corresponding to a candidate state vector that satisfies a preset first constraint condition according to the candidate state vector set, and to generate a candidate multi-state minimum cut vector set using a state combination comparison method and a preset second constraint condition; A minimum cut vector search module is used to judge the size of each candidate multi-state minimum cut vector and all derived vectors of the candidate multi-state minimum cut vector according to the candidate multi-state minimum cut vector set. If the judgment result is negative, a sorting method is used to return an index set of repeated values, and the multi-state minimum cut vector duplicates corresponding to the index in the candidate multi-state minimum cut vector set are deleted to obtain a true multi-state minimum cut vector set; if the judgment results are all positive, a candidate search is performed on each candidate minimum cut state vector in the candidate state vector set according to the minimum capacity bound to obtain a search result, and a true multi-state minimum cut vector set is obtained according to the search result.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program. It is characterized in that When the processor executes the computer program, the steps of the method according to any one of claims 1 to 8 are implemented.

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