A method and device for reliability evaluation of a multi-state flow network of a state-heterogeneous component

Abstract

The present application relates to a kind of state heterogeneous component's multi-state flow network reliability evaluation method and device.The method includes: obtaining the multi-state flow network of state heterogeneous component and its component state probability distribution, using implicit enumeration method according to the constraint condition of demand level to obtain the candidate state vector set of minimum cut vector.According to candidate state vector set, the state combination of component in the minimum cut vector corresponding to the candidate state vector that satisfies the first constraint condition of pre-set is generated, and the minimum cut state combination comparison method is used to generate candidate multi-state minimum cut vector set with the second constraint condition of pre-set.According to candidate multi-state minimum cut vector set, it is judged that each candidate multi-state minimum cut vector and the size of all derivative vectors of candidate multi-state minimum cut vector, according to the result of judging, obtain the real multi-state minimum cut vector set.Using this method can effectively improve the search efficiency of minimum cut vector in the multi-state flow network of state heterogeneous component.

Description

TECHNICAL FIELD

[0001] The application relates to the field of vector search technology for reliability evaluation of a multi-state flow network, and particularly relates to a method and device for reliability evaluation of a multi-state flow network of state-heterogeneous components. BACKGROUND

[0002] As a more realistic 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 binary network, such as communication networks, distribution networks, power networks, road traffic networks and unmanned aerial vehicle cluster networks. The multi-state network considers that the system and its nodes or components will be in multiple states due to design factors or performance degradation, and has network flow characteristics, and is also called a multi-state flow network (MFN). Reliability, as an important attribute and indicator of the safe operation of a complex system, is focused on by designers and managers, and the MFN reliability refers to the ability of the MFN to complete the transmission of a specified physical quantity within a specified time and under specified conditions. The probability R d+1 that a d+1 unit demand flow is transported from a source point s to a sink point t is a key performance indicator for the search of MFN reliability. Searching for the exact solution of MFN reliability is an NP-hard problem, and the reliability exact solution algorithm based on the minimum cut set vector (d-MC) is an effective method. However, the existing d-MC search method can only obtain d-MC in the network in which the state space of the component is a set of integers that are sequentially increased from 0, and if there is one or more state-heterogeneous components (SHC), the existing d-MC search algorithm cannot be directly used. Therefore, it is of great significance to propose an accurate and efficient algorithm for searching for all d-MC* in the MFN containing SHC.

[0003] The ultimate purpose of searching for d-MC or d-MC* is to obtain the MFN reliability of the MFN at the d demand level. For the d-MC search problem, the algorithm proposed in “Niu Y F, Xu X Z. A new solution algorithm for the multistate minimal cut problem[J]. IEEE Transactions on Reliability, 2019, 69(3): 1064-1076” has the highest solution efficiency, and by supplementing the missing states between two adjacent integer states of the network component and setting the corresponding probability value to 0 in the state probability distribution, the algorithm is used to solve all d-MC, and the correct network reliability can also be obtained.

[0004] The object of the existing minimum cut set vector d-MC search method mainly focuses on the multi-state flow network (MFN) without state heterogeneous components (SHC), most of which do not directly use the performance value of the component in actual situation as its state. Taking a communication network system as an example, it is assumed that the maximum transmission rate of the data flow transmission link connecting the user or network node (router or switch) can be in the following mapping with the state of the component of the MFN: state 0: 0Gbps, state 1: 2Gbps, state 2: 4Gbps, state 3: 6Gbps (performance level increases proportionally). At this time, if the maximum transmission rate demand d = 3 (6Gbps) between the source user s and the sink user t in the communication network with two components in parallel, there are two combinations of link states corresponding to the rate combination that meet the demand, i.e. d = 0 + 3 = 3 (0Gbps + 6Gbps = 6Gbps), d = 1 + 2 = 3 (2Gbps + 4Gbps = 6Gbps). But 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, only one combination meets the demand, i.e. d = 0 + 3 = (0Gbps + 6Gbps = 6Gbps), the other combination d = 1 + 2 = 3 (2Gbps + 5Gbps ≠ 6Gbps) does not meet. This shows that if the actual performance level of the component in the MFN is not proportional to the increase, they cannot be mapped to the state set {0, 1, 2,..., W}, but only their own state set as the state set of the component, for example {0, 2, 5, 6}, such components are defined as SHC. Therefore, in the MFN containing SHC, the existing various d-MC search methods cannot be directly used. SUMMARY

[0005] Therefore, it is necessary to provide a state heterogeneous component multi-state flow network reliability evaluation method and device capable of correctly and efficiently searching a state heterogeneous component multi-state flow network containing state heterogeneous components in view of the above technical problems.

[0006] A state heterogeneous component multi-state flow network reliability evaluation method, the method comprising:

[0007] Obtaining a multi-state flow network containing state heterogeneous components, a minimum cut set of the multi-state flow network, a component state distribution and a demand level.

[0008] 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.

[0009] Let the number of candidate vectors of the minimum cut vector be 1, and obtain the candidate state vector set of the minimum cut vector according to the constraint condition of the demand level by using the implicit enumeration method.

[0010] The state combination of the components in the minimum cut vector corresponding to the candidate state vector satisfying the preset first constraint condition is generated according to the candidate state vector set, and a state combination comparison method is used to generate the candidate multi-state minimum cut vector set together with the preset second constraint condition.

[0011] The size of each candidate multi-state minimum cut vector and all derivative 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, an ordering method is used to return the index set of repeated values, and the repeated items of the multi-state minimum cut vector 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 result is positive, candidate search is performed on each candidate minimum cut state vector in the candidate state vector set according to the minimum capacity bound, the search result is obtained, and the real multi-state minimum cut vector set is obtained according to the search result.

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

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

[0014] A real set initialization module for calculating the minimum capacity bound of each component and the correlation value of the state vector of each minimum cut vector in the minimum cut set according to the demand level.

[0015] A candidate state vector set acquisition module for setting the candidate vector number of the minimum cut vector to 1, and obtaining the candidate state vector set of the minimum cut vector according to the constraint condition of the demand level by using a hidden enumeration method.

[0016] A candidate multi-state minimum cut vector set generation module for generating the state combination of the components in the minimum cut vector corresponding to the candidate state vector satisfying the preset first constraint condition according to the candidate state vector set, and generating the candidate multi-state minimum cut vector set together with the preset second constraint condition by using a state combination comparison method.

[0017] A minimum cut vector search module for judging the size of each candidate multi-state minimum cut vector and all derivative 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, an ordering method is used to return the index set of repeated values, and the repeated items of the multi-state minimum cut vector 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 result is positive, candidate search is performed on each candidate minimum cut state vector in the candidate state vector set according to the minimum capacity bound, the search result is obtained, 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, the memory stores a computer program, and the processor implements the following steps when executing the computer program:

[0019] Obtaining a multi-state flow network comprising state heterogeneous components, a minimum cut set of the multi-state flow network, a component state distribution, and a demand level.

[0020] Calculating a minimum capacity bound of each component according to the demand level, and an associated value of a state vector of each minimum cut vector in the minimum cut set.

[0021] Let the number of candidate vectors of the minimum cut vector be 1, and obtain a candidate state vector set of the minimum cut vector according to the constraint condition of the demand level by using a hidden enumeration method.

[0022] Generating a state combination of a component in a minimum cut vector corresponding to a candidate state vector satisfying a preset first constraint condition according to the candidate state vector set, and generating a candidate multi-state minimum cut vector set by using a state combination comparison method and a preset second constraint condition.

[0023] 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 an index set of repeated values by using a sorting method, deleting the repeated items of the multi-state minimum cut vector corresponding to the index in the candidate multi-state minimum cut vector set, and obtaining a real multi-state minimum cut vector set. If the judgment result is positive, performing candidate search on each candidate minimum cut state vector in the candidate state vector set according to the minimum capacity bound, obtaining a search result, and obtaining the real multi-state minimum cut vector set according to the search result.

[0024] The method and device for reliability evaluation of a multi-state flow network with state-heterogeneous components can efficiently screen a minimum cut vector set meeting a demand level through a hidden enumeration method and a state combination comparison method in combination with preset constraint conditions. First, information of the multi-state flow network is acquired, including state-heterogeneous components, a minimum cut set, component state distribution, and a demand level (d). Then, the minimum capacity bound of each component is calculated according to the demand level, providing a basis for screening of a candidate state vector set. The hidden enumeration method is adopted to preliminarily screen a candidate minimum cut state vector set according to the constraint condition of the demand level. Subsequently, state combinations of components in a minimum cut vector corresponding to a candidate state vector meeting a preset first constraint condition are generated, and a candidate multi-state minimum cut vector set is further screened through a state combination comparison method and a second constraint condition. In the judgment of the size of a candidate multi-state minimum cut vector and all derivative vectors of the candidate multi-state minimum cut vector, if the two are consistent, a sorting method is used to return a repeated value index, and the repeated items in the candidate set are deleted to obtain a real multi-state minimum cut vector set; if the two are inconsistent, the number of candidate multi-state minimum cut vectors is less or excessive, and each candidate state vector is searched according to the minimum capacity bound, and finally the real multi-state minimum cut vector set is obtained. In the case of an increase in the number of state-heterogeneous components, an increase in the discrete degree of component states, and an increase in the demand level, the state difference and the demand constraint are used to reduce the search space and improve the reliability search efficiency. Therefore, in the multi-state flow network, the time complexity is effectively reduced and the search efficiency is improved through optimization of reliability search and screening technology, and especially in the case of component state diversification and high demand level, higher calculation efficiency and reliability search effect are shown. BRIEF DESCRIPTION OF DRAWINGS

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

[0026] Figure 2 A flowchart of a d-MC* search step in an embodiment;

[0027] Figure 3 An ARPA network framework diagram in an embodiment;

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

[0029] Figure 5 A comparison diagram of time ratios of three methods on a medium-scale network in an embodiment;

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

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

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

[0033] Figure 9 An internal structure diagram of a computer device in an embodiment. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application is further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0035] In an embodiment, as shown in Figure 1 a multi-state flow network reliability evaluation method of a state-heterogeneous component is provided, comprising the following steps:

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

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

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

[0039] Step 108, generating a state combination of the components in the minimum cut vector corresponding to the candidate state vector satisfying a preset first constraint condition according to the candidate state vector set, and generating a candidate multi-state minimum cut vector set by 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 an index set of repeated values by using a sorting method, deleting the repeated items of the multi-state minimum cut vector corresponding to the index in the candidate multi-state minimum cut vector set, and obtaining a real multi-state minimum cut vector set; if the judgment result is positive, performing candidate search on each candidate minimum cut state vector in the candidate state vector set according to the minimum capacity bound, obtaining a search result, and obtaining the real multi-state minimum cut vector set according to the search result.

[0041] In the aforementioned reliability assessment method for a multi-state flow network with state-heterogeneous components, an implicit enumeration method and a state combination comparison method, combined with preset constraints, efficiently screen a set of minimum cut vectors that meet the required level. First, information about the multi-state flow network is obtained, including state-heterogeneous components, minimum cut sets, component state distributions, and the required level (d). Next, a minimum capacity bound for each component is calculated based on the required level, providing a basis for screening a set of candidate state vectors. Using the implicit enumeration method, a preliminary set of candidate minimum cut state vectors is screened based on the required level constraints. Subsequently, state combinations of components in the minimum cut vector corresponding to candidate state vectors that meet the first preset constraint are generated. A state combination comparison method and a second constraint are used to further screen a set of candidate multi-state minimum cut vectors. When the size of the candidate multi-state minimum cut vector and all its derivatives are compared, if the two match, a sorting method is used to return the index of duplicate values, and duplicates are removed from the candidate set to obtain the true set of multi-state minimum cut vectors. If the two do not match, or the number of candidate multi-state minimum cut vectors is too small or too large, each candidate state vector is searched based on the minimum capacity bound, ultimately obtaining the true set of multi-state minimum cut vectors. As the number of state-heterogeneous components increases, component state dispersion increases, and demand levels rise, state differences and demand constraints are leveraged to reduce the search space and improve reliability search efficiency. Therefore, in multi-state flow networks, optimizing reliability search and screening techniques effectively reduces time complexity and improves search efficiency. This demonstrates higher computational efficiency and reliability search results, especially in situations with diverse component states and high demand levels.

[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] wherein 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, e i-1 is the maximum flow of the ith component at the maximum capacity vector.

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

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

[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] wherein 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 a set of state vectors of the component, M(W(0 i )) is a maximum flow of the component at the maximum capacity vector. A preset second constraint condition:

[0053] and x(e i ) ∈ b i

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

[0055] In one embodiment, a state combination of the component in a minimum cut vector corresponding to a candidate state vector satisfying the preset first constraint condition is generated according to the set of candidate state vectors, and a state combination comparison method is used to judge a numerical value between the current state combination Comb k and a state combination Comb l other than the current state combination, if the current state combination Comb k is not greater than the state combination Comb l other than the current state combination, the current state combination Comb k is deleted, and a candidate state combination is obtained; otherwise, the state combination Comb l other than the current state combination is deleted, and the candidate state combination is obtained. The candidate state combination is used to generate a set of candidate multi-state minimum cut vectors according to the preset second constraint condition.

[0056] In one embodiment, the size of each candidate multi-state minimum cut vector and all derivative vectors of the candidate multi-state minimum cut vector is judged according to the set of candidate multi-state minimum cut vectors, if the current candidate multi-state minimum cut vector is equal to all derivative vectors of the candidate multi-state minimum cut vector and is 1, the judgment result is negative, a sorting method is used to return a set of index of repeated values, and a real multi-state minimum cut vector set is obtained by deleting the repeated items of the multi-state minimum cut vector corresponding to the index in the set of candidate multi-state minimum cut vectors.

[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 both are equal and the value is not 1, the judgment result is positive, and candidate search is performed on each candidate minimum cut state vector in the candidate state vector set according to the minimum capacity bound. If the maximum capacity vector set of the component is equal to the demand level, the current candidate state vector set is the real multi-state minimum cut vector set, and the value of the number of candidate minimum cut state vectors in the current candidate state vector set is compared with the number of minimum cut vectors. 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, 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, the sorting method is used to return the index set of repeated values, and the repeated items of the candidate minimum cut state vectors corresponding to the indexes in the candidate state vector set are deleted to obtain the real multi-state minimum cut vector set. If the maximum capacity vector set 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 the real multi-state minimum cut vector set.

[0058] In one embodiment, if the serial number of the current candidate state vector is less than the number of state combinations, the candidate minimum cut state vectors of the candidate state vector set are 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 judged 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, as shown in Figure 2 , 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 state distribution and demand level d.

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

[0062] Step 1: Set the real d-MC* set Each element corresponds to an associated value set Calculate M(W) = D using the maximum flow algorithm. For each component e i , if M(W(0 i )) ≤ d, calculate its minimum capacity bound L(e i ) = max{b ij |bij ≤ d - M(W(0 i )), b ij ∈ b i}. And each d-MC* candidate x = (W(e1),..., L(e i ),..., W(e m )) is directly included in set Ω without verification, and the associated value AV(x) of each x is calculated and included in set Δ according to the following formula.

[0063]

[0064] Step 2: Let j = 1.

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

[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 the verification of σ j d-MC* candidates according to the following steps:

[0073] Step 5.2: If then 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 is the lth state of component e i , according to the definition verification whether it is a real d-MC*. If the maximum flow M(x jk ) ≤ d and all e i ∈ U(x jk ) corresponding 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 real 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 real d-MC* set Ω are one-to-one corresponding to the elements in the associated value set Δ, the sorting method is used to return the index set Index of the repeated values for the latter, and all d-MC* repeated items in Ω corresponding to the index are deleted.

[0079] Step 8: Finally, the real d-MC* set Ω without repetition is obtained. The program stops.

[0080] In one of the embodiments, a method is provided as shown in Figure 3 The ARPA network and the component state distribution of Table 1 are used to verify the method step by step, and the W = (8, 6, 3, 4, 3, 6, 3, 6, 8) in the ARPA network contains p = 9 minimum cuts, as shown in Table 1. Assuming d = 9, the steps of searching all 9-MC* are as follows:

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

[0082]

[0083] Step 1: Set M(W) = 13 is calculated by using the maximum flow algorithm. Since M(W(01)) = 6 < d = 9, 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 real 9-MC*. L(e2) = 0, L(e4) = 0, L(e6) = 0, L(e8) = 0, L(e9) = 3, respectively, corresponding to (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 real 9-MC*, which are all incorporated into Ω. The associated values 32813.842, 32802.532, 32738.499, 31928.363, 26239.043 and 17914.052 corresponding to the above 6 9-MC* are added 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 implicit enumeration to generate the minimum cut component state combination Comb1 = (4, 3) and Comb2 = (4, 4) that meets the conditions. Then, perform the minimum cut component state combination comparison method. Since Comb1 <Comb2,删除Comb1,从而根据Comb2生成σ1=1个9-MC*候选x 11 =(4,4,3,4,3,6,3,6,8).

[0086] Step 4: p≠1.

[0087] Step 5: Follow the steps below to perform x 11 Verification:

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

[0089] Step 5.2: k=1.

[0090] Step 5.3: x 11 The maximum flow M(x 11 )=8<d=9, its unsaturated component set U(x 11 )={e1,e2}. For e1, x 11 (e1) = b 13 =4,b 14 =8, its corresponding Satisfy maximum flow For e2,x 11 (e2) = b 23 =4,b 24 =6, its corresponding Satisfy maximum flow It can be concluded that x 11 is a real 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, set 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], 7 C2 component state combinations are generated 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 performing the minimum cut component state combination comparison method, the remaining combinations are Comb2, Comb3, Comb6 and Comb7, generating σ2 = 4 9-MC* candidates 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 under 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, the corresponding has For e3, x 21 (e3) = b 31 = 0, b 32 = 3, has For e4, x 21 (e4) = b 42 = 3, b 43 = 4, has Therefore, 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, let k = 2, and jump back to Step 5.3.

[0100] Step 5.3: It is verified that x 23 is a real 9-MC*, while x 22 and x 24 are not. Let Ω = Ω U x 23 , AV(x 23 ) = 32627.443, and let Δ = Δ U AV(x 23 ).

[0101] Step 5.4: k = 4 = σ2.

[0102] Step 6: Since j = 2 < p = 9, let 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 real 9-MC*, which are stored in Ω, and the associated values corresponding to d-MC* in the Δ set. Since there are no duplicate associated values in Δ, the index set indicates that there are no duplicate 9-MC* in Ω.

[0106] Step 8: Finally, the set of non-duplicate 9-MC* Ω is obtained as shown in Table 2, which contains 18 9-MC*. The search stops.

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

[0108]

[0109] In one embodiment, experiments under different network topologies are set up, and the experimental results variables include: τ is the number of d-MC method candidates, L is the number of real d-MC, ρ is the number of d-MC* basic method candidates, σ is the number of d-MC* method candidates of the present scheme, σ free is the number of d-MC* candidates without verification, ρ-σ is the number of candidates reduced by the reduction technique, L * is the number of real d-MC*. In addition, T1, T2, T3 are the running times of the d-MC method, the d-MC* basic method, and the d-MC* method proposed in the present scheme, respectively. Example 1: As shown in Table 3, the experimental results of the d-MC method, the d-MC* basic method, and the d-MC* method proposed in the present scheme are compared. Figure 4The medium-scale multi-state flow network shown, a medium-scale MFN containing 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. For comprehensive comparison of method efficiency, the integer demand d is in [0, 13). The experimental results are shown in Table 4, Table 5 and Figure 5 as shown.

[0110] Table 3 Component state space vector in the medium-scale network

[0111]

[0112] Table 4 Product quantity of three methods on the medium-scale network

[0113]

[0114] Table 5 Calculation time (seconds) and ratio of three methods on the medium-scale network

[0115]

[0116] As can be seen from Table 4, the number of d-MC* candidates σ generated by the method proposed in the scheme is much smaller than that of the other two methods. In addition, as can be seen from Table 5, the speed of the scheme is faster than that of the d-MC method when d≥1, and the efficiency is higher than that of the d-MC* basic method when d≥4. For intuitive comparison, as shown in Figure 5 the trend of the time ratio of different methods with d, and the candidate quantity ratio is included. It can be seen that the change trend of the running time ratio is almost consistent with that of the candidate quantity ratio, which shows that the candidate quantity determines the efficiency of the method. The above results show that on the medium-scale network, the efficiency of the d-MC* method proposed in the scheme is higher than that of the d-MC method at most d, and the running speed is increased by more than 20 times. Compared with the d-MC* basic method, the advantage of the scheme is prominent when the candidate increases to a certain number, and the running time is reduced by more than 19000 times at most.

[0117] Example 2: As shown in Figure 6 a large-scale multi-state flow network, a large-scale MFN containing SHCs is selected, in which 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 the state space vector b i of each component e i is set as follows: let the odd-numbered components be (0, 1, 3), the even-numbered components be (0, 2, 3), and the prime-numbered components be (0, 3). The demand level d takes integer from 0 to 8. The experimental results are shown in Table 6 and Table 7:

[0118] Table 6 Product quantity of three methods on the large-scale network

[0119]

[0120] Table 7. The computation time (second) and the ratio of three methods on large network

[0121]

[0122] From the above table and Figure 7 , it is shown that the number of candidates generated by three methods in large network 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 148595 candidates at most, so that the method proposed in this scheme has a significant improvement in running speed relative to d-MC method and d-MC* basic method under most d, and the promotion effect is at most 41.871 times and 222.046 times. The experimental results in large network also show that the scheme has more obvious advantages than other methods in searching d-MC*.

[0123] It should be understood that, although Figures 1-2 the steps in the flowchart are shown in a sequential order following the arrows, the steps are not necessarily executed in the order indicated by the arrows. Unless otherwise explicitly stated herein, the execution of the steps is not strictly limited in order, and the steps can be executed in other orders. Moreover, Figures 1-2 at least part of the steps in may include multiple sub-steps or multiple stages, which are not necessarily executed at the same time, but can be executed at different times, and the execution order of the sub-steps or stages is not necessarily sequential, but can be alternately or alternately executed with other steps or at least part of the sub-steps or stages of other steps.

[0124] Figure 8 In one embodiment, as shown, a multi-state flow network reliability evaluation device of 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 acquire a multi-state flow network containing state heterogeneous components, a minimum cut set of the multi-state flow network, a component state distribution and a 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 correlation value of the state vector of each minimum cut vector in the minimum cut set.

[0127] The candidate state vector set obtaining module 806 is configured to set the number of candidate vectors of the minimum cut vector to 1, and obtain a candidate state vector set of the minimum cut vector according to the constraint condition of the demand level by using a hidden enumeration method.

[0128] The candidate multi-state minimum cut vector set generating module 808 is configured to generate a state combination of a component in a minimum cut vector corresponding to a candidate state vector set that satisfies a preset first constraint condition according to the candidate state vector set, and generate a candidate multi-state minimum cut vector set by using a state combination comparison method and a preset second constraint condition.

[0129] The minimum cut vector searching module 810 is configured to judge the size of each candidate multi-state minimum cut vector and all derivative 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, return an index set of repeated values by using a sorting method, delete the repeated items of the multi-state minimum cut vector corresponding to the index in the candidate multi-state minimum cut vector set, and obtain a real multi-state minimum cut vector set. If the judgment result is positive, perform candidate search on each candidate minimum cut state vector in the candidate state vector set according to a minimum capacity bound, obtain a search result, and obtain the real multi-state minimum cut vector set according to the search result.

[0130] The specific limitation of the state-heterogeneous component multi-state flow network reliability evaluation device can refer to the limitation of the state-heterogeneous component multi-state flow network reliability evaluation method in the foregoing, and will not be described here. Each module in the state-heterogeneous component multi-state flow network reliability evaluation device can be realized by software, hardware, and a combination thereof, in whole or in part. Each module 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 in the computer device in the form of software, so as to be called and executed by the processor to perform the operation corresponding to each module.

[0131] In one embodiment, a computer device is provided, which can be a terminal, and an internal structure diagram of the computer device can be as shown in FIG. 8. Figure 9The computer device includes a processor, a memory, a network interface, a display screen and an input device connected through a system bus. The processor of the computer device is configured 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 running the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is configured to communicate with an external terminal through a network connection. The computer program is executed by the processor to implement a method for evaluating reliability of a multi-state flow network of state-heterogeneous components. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen. The input device of the computer device can be a touch layer overlaid on the display screen, or a key, a trackball or a touchpad arranged on the shell of the computer device, or an external keyboard, a touchpad or a mouse, etc.

[0132] Those skilled in the art can understand that Figures 8-9 The structure shown in the figure is only a block diagram of part of the structure related to the scheme of the present application, and does not constitute a limitation on the computer device to which the scheme of the present application is applied. A specific computer device can 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. The memory stores a computer program, and the processor executes the computer program to implement the following steps:

[0134] Obtaining a multi-state flow network including state-heterogeneous components, a minimum cut set of the multi-state flow network, a component state distribution and a demand level.

[0135] Calculating a minimum capacity bound of each component according to the demand level, and an associated value of a state vector of each minimum cut vector in the minimum cut set.

[0136] Taking the number of candidate vectors of the minimum cut vector as 1, and obtaining a candidate state vector set of the minimum cut vector according to the constraint condition of the demand level by using a hidden enumeration method.

[0137] Generating a state combination of the components in the minimum cut vector corresponding to the candidate state vector according to the candidate state vector set, and generating a candidate multi-state minimum cut vector set by 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 determined. If the determination result is positive, the sorting method is used to return the index set of repeated values, and the repeated items of the candidate minimum cut state vectors corresponding to the indexes in the candidate state vector set are deleted to obtain the real minimum cut vector set. If the determination result is negative, the candidate search is performed on each candidate minimum cut state vector in the candidate state vector set according to the minimum capacity bound, and the search result is obtained. According to the search result, the real minimum cut vector set is obtained.

[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 a computer program instructing related hardware. 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 above-mentioned embodiments. Any reference to memory, storage, database or other medium used in the embodiments provided by the present application 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 but not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), 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) and the like.

[0140] The technical features of the above embodiments can be combined in any way. To make the description concise, not all possible combinations of the technical features in the above embodiments are described, but as long as the combinations of the technical features do not exist, they should be considered as the scope of the present application.

[0141] The above embodiments only express several embodiments of the present application, and the description is more specific and detailed, but it should not be understood as a limitation on the scope of the patent. It should be noted that for ordinary skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are within the scope of the present application. Therefore, the scope of the patent of the present application should be subject to the appended claims.

Claims

1. A reliability assessment method for a multi-state flow network with heterogeneous state components, 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 for each minimum cut vector in the minimum cut set based on the demand level; 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 calculate the minimum capacity bound of each component: in, For components, is the state vector of the component, is the demand level, is the maximum flow of the component under the maximum capacity vector, is the state vector set of the component, 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: in, is the associated value of the state vector of the minimum cut vector, is the state vector of the minimum cut vector, is the number of components in the network; Assuming 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 first preset constraint is: in, is the minimum cut state vector of the component, is the minimum capacity bound of the component, is the maximum capacity vector of the component, is the state vector of the component, is the demand level, is the minimum cut set, is the state space vector of the component, is the maximum flow of the component under the maximum capacity vector; The second preset constraint is: in, is the minimum cut set, is the demand level, is the state space vector of the component; 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; 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 the true multi-state minimum cut vector set is obtained according to the search result.

2. The method according to claim 1, characterized in that Assuming 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, including: Let the candidate vector number of the minimum cut vector be is 1, and an implicit enumeration method is used to obtain a candidate state vector set of the minimum cut vector according to the constraint condition that the demand level is not less than the state vector set corresponding to each component.

3. The method according to claim 2, 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 Combined with a state other than the current state combination If the current state combination Not greater than the state combination other than the current state combination , then delete the current state combination , get the candidate state combination; otherwise, delete the state combination except the current state combination , 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.

4. The method according to claim 3, characterized in that Determine the size of each candidate multi-state minimum cut vector and all derivative vectors of the candidate multi-state minimum cut vector according to the candidate multi-state minimum cut vector set. If the determination result is negative, use a sorting method to return an index set of duplicate values, delete duplicate multi-state minimum cut vectors corresponding to the index in the candidate multi-state minimum cut vector set, and 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 sorting method is used to return the 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 the real multi-state minimum cut vector set.

5. The method according to claim 4, 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, then 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 the maximum capacity vectors of the component is equal to the demand level, then 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, then 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 indexes 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 a true multi-state minimum cut vector set.

6. The method according to claim 5, 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.

7. A device for evaluating the reliability of a multi-state flow network with heterogeneous state components, characterized in that: For implementing the method according to any one of claims 1 to 6, 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 demand level; a real set initialization module for 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; a candidate state vector set acquisition module, configured to set the number of candidate vectors of the minimum cut vector to 1, and 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, configured to generate, based on the candidate state vector set, a state combination of components in the minimum cut vector corresponding to the candidate state vector that satisfies a preset first constraint condition, and to generate the 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 determine the size of each candidate multi-state minimum cut vector and all derived vectors of the candidate multi-state minimum cut vector based on the candidate multi-state minimum cut vector set. If the determination 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 determination results are all positive, a candidate search is performed on each candidate minimum cut state vector in the candidate state vector set based on the minimum capacity bound to obtain a search result, and the true multi-state minimum cut vector set is obtained based on the search result.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 6 are implemented.

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