Multi-state network irregular minimum cut set vector identification and prevention method

Abstract

The invention discloses a multi-state network irregular minimum cut set vector identification and prevention method, which comprises the following steps: constructing a multi-state network according to an actual network system, and obtaining all minimum cut sets MC and demand levels d; whether repeated d-MC exists or not is judged according to the relation between the demand level and the minimum value of the state parameters, and therefore the state upper limit of the edge under the minimum cut set is calculated in a self-adaptive mode; calculating a state lower limit of each edge in the multi-state network; based on a preset repetition-free d-MC search rule, searching for all candidate d-MCs; and carrying out authenticity verification on all the candidate d-MCs, rejecting unreal candidate d-MCs, and taking the remaining candidate d-MCs as real d-MCs. The method is applied to the field of reliability evaluation of the multi-state network, can eliminate the need of deleting a single step of repeating the d-MC, eliminates redundant conditions of non-real d-MC verification, and obviously improves the identification efficiency of the d-MC.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-state network reliability assessment, and in particular to a method for identifying and preventing non-compliant minimum cut set vectors of a multi-state network. Background Art

[0002] Traditional network reliability research assumes that the network and its components (nodes and edges) have only two states: intact and failed. This type of network reliability model is called a binary state network. However, in real life, network systems perform given tasks under specific conditions. Due to the influence of their own or external uncertainties, the system and its components generally exhibit different performance levels, that is, they usually experience many intermediate states from normal operation to complete failure. This type of network system is called a multi-state network system, or simply a multi-state network or multi-state system.

[0003] At present, in the field of scientific research, polymorphic network reliability models have been widely used in real network systems, such as logistics supply chain networks, communication and information networks, oil and gas transportation and distribution networks, power transportation networks, and traffic networks. Compared with binary networks, polymorphic networks can more accurately describe and characterize the complex behaviors of network systems.

[0004] Reliability is an important indicator for evaluating network performance. d -MP / d -MC) is the main method for calculating the reliability of multi-state networks. d -MP / d -MC search is an NP-hard problem, so improving the multi-state network d -MP / d -The search efficiency of MC is of great significance.

[0005] In the literature reported so far, based on d -MP / d The reliability calculation method of -MC is widely used because of its two-step process: (1) searching all possible d -MP / d -MC; (2) According to the search results d -MP / d -MC to calculate the reliability of polymorphic networks However, looking for all possible d -MP / d -MC is still an NP-hard problem. d -MP represents the lower bound point, the minimum cut set d-MC as demand level The upper bound of provides important information about the failure mechanism. d -MC research can effectively support system performance evaluation and maintenance strategy selection.

[0006] Previous studies have introduced a mathematical model with three constraints to search for d -MC candidate, that is, if X is a candidate with multiple unsaturated edges (unsaturated edges are edges whose actual flow is less than their maximum state) d -MC, then there is at least one MC that satisfies the following conditions: ; ; ; in, For the multi-state network Strip edge The maximum state, ) is a state vector consisting of the maximum capacity states of each edge in the network. For edge A capacity state, Represents a state vector consisting of the capacity states of each edge. Structure function Represents the network in the state vector The maximum flow rate under . Represents the state lower limit of each edge, which is calculated as follows: ; in, Represents the network in the state vector The maximum flow rate under , Represents edge The maximum state.

[0007] Subsequently, many studies have extended this model and pointed out that the verification of non-compliance d -MC is an important factor affecting the efficiency of the algorithm. d -MC includes two categories: (1) Non-real d -MC, candidates in this category d -MC, there is at least one edge whose flow increases while the maximum flow of the system remains unchanged; (2) Repeat d -MC, that is, there are at least two identical candidates d -MC.

[0008] For non-real d-MC, verification methods can be divided into three categories: definition method, pairwise comparison method and residual network method. d -MC is the most direct method, and the residual network method is widely recognized for its low time complexity. Recently, some scholars have proposed a method to compare candidate d -MC different cut set capacity method to verify d -MC, but there is room for further improvement.

[0009] For repetition d -MC, researchers have also proposed three solutions. The first is the paired comparison method, which converts the vector d -MC is converted into a one-dimensional value, and duplicates are identified by numerical comparison instead of vector comparison. The second is the network structure method, which proposes a method to verify the duplication of series-parallel and parallel-series networks. d -MC has some useful properties. The third method is related to the unsaturated edge, using d -MCs structure and special features of minimum cuts to eliminate duplication d -MC. However, the above are all post-processing methods, that is, these algorithms generate repeated d -MC, and then performs additional post-hoc steps to detect and eliminate duplicates d -MC.

[0010] In summary, the current impact d -MC search algorithm efficiency is mainly due to non-compliance d -MC (including non-real d -MC and repetition d -MC) identification and removal. And as the scale and complexity of the network increase, the d -MC candidates increase exponentially, occupying a lot of space and time, which seriously affects the efficiency of the algorithm. It is urgent to propose a more efficient d -MC search algorithm. Summary of the invention

[0011] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for identifying and preventing non-compliant minimum cut set vectors in a multi-state network, which can more effectively verify non-authentic d -MC, and prevent duplication d -The creation of MC.

[0012] To achieve the above object, the present invention provides a method for identifying and preventing non-compliant minimum cut set vectors in a multi-state network, comprising the following steps: Step 1: Build a multi-state network based on the actual network system and obtain all the minimum cut sets of the multi-state network. , , , , and the maximum state vector and demand level ,in, , For the multi-state network Strip edge The maximum state, Value taken from , is the number of cut sets, is the number of edges in the multi-state network; Step 2: Get the second minimum value of the maximum state of the network edge in the multi-state network , and judge Is it established: If so, it indicates that d - During the MC search process, no duplicate d -MC, for each minimal cut set , , , Perform the operation of step 5; Otherwise, proceed to step 3; Step 3: Calculate the capacity of each minimum cut set , if exists and satisfy , then the minimum cut set , Put them in the same group and sort all the combinations of minimum cut sets in descending order of capacity, which is: ,in, is the number of combinations of the minimum cut set; Step 4: For any minimum cut set combination , , determine the minimum cut set combination Is the number of minimum cut sets contained in 1? If so, for the minimum cut set combination Perform step 5 on the minimum cut set in; Otherwise, for the minimum cut set combination Perform step 6 on the minimum cut set in; Step 5: Based on each edge in the multi-state network The lower limit of the state , search all candidates for the corresponding minimum cut set d -MC, proceed to step 7; Step 6: Based on each edge in the multi-state network The lower limit of the state and the upper capacity limit on each minimal cut set , based on preset no-repeat d -MC search rule, search all candidates for the corresponding minimum cut set d -MC; Step 7: Verify all candidates in step 5 or step 6 according to the preset authenticity verification rules. d -MC conducts authenticity verification and eliminates non-authentic candidates d -MC, and the remaining candidates d -MC as a real d -MC; Step 8, based on real d -MC evaluates the reliability of the network system.

[0013] In one embodiment, when Not true, and the minimum cut set The minimum cut set combination When the number of minimum cut sets contained in is not 1, the edges in the multi-state network In the minimum cut set The upper limit of the state is: ; in, To be included in the minimum cut set In but not included in the minimum cut set The set of edges in .

[0014] In one embodiment, in step 6, the non-repetitive d -MC search rules are as follows: is a non-repeating polymorphic minimal cut set containing multiple unsaturated edges, then there exists at least one minimal cut set The following conditions are met: ; ; ; ; in, For edge The current status.

[0015] In one embodiment, in step 7, the d -MC's authenticity verification process is as follows: If and only if ,as well as When the state vector It is the minimum cut set Generated reality d-MC; Specifically: ; ; ; in, To exclude and The minimum cut set subscript set after , is the subscript of the minimum cut set containing unsaturated edges in X, is the subscript of the minimum cut set in which there is no intersection with the unsaturated edge in the state vector X, is the value of the minimum cut set flow and the value of the generated The flow of the minimum cut set exceeds d The subscript of the minimum cut set of for The flow and under the state vector X, is the minimum cut set generated under the state vector X, and the flow under the state vector X.

[0016] In one embodiment, step 7 further includes, for each edge in the multi-state network , calculate its lower capacity limit With the corresponding , and in Time judgment For real d -MC, where For edge The state of is 0, and the states of all other edges are the state vectors corresponding to their maximum states, that is, , is the state vector The maximum network flow under .

[0017] Compared with the prior art, the present invention has the following beneficial technical effects: 1. The present invention is repeated d -MC generation mechanism, proposed to prevent duplication d -MC generation method, able to search for candidate d -MC directly avoids repetition d -MC, not only improves the candidate d -MC search efficiency, also omits deleting duplicates d -MC This operation step can seamlessly integrate search d - Identification of MC candidates and duplications; 2. The present invention analyzes the redundant conditions of the existing Kozyra algorithm and eliminates unnecessary constraints, thus effectively improvingd -MC candidate authenticity verification efficiency, thereby improving d -MC recognition efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.

[0019] Figure 1 It is a flow chart of a method for identifying and preventing non-compliant minimum cut set vectors in a multi-state network according to an embodiment of the present invention; Figure 2 This is an example diagram of a small multi-state network in an embodiment of the present invention; Figure 3 This is an example diagram of a medium-scale benchmark network in an embodiment of the present invention; Figure 4 This is an example diagram of a large-scale benchmark network in an embodiment of the present invention; Figure 5 is an example diagram of a large-scale benchmark network with various maximum state vectors in an embodiment of the present invention; Figure 6 Schematic diagram of CPU time ratio of three methods in embodiments of the present invention.

[0020] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0021] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0022] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0023] like Figure 1 The figure shows a non-compliant minimum cut set vector ( d-MC) identification and prevention methods, which mainly include the following steps: Step 1: Build a multi-state network based on the actual network system and obtain all the minimum cut sets of the multi-state network. , , , , and the maximum state vector and demand level , , For the multi-state network Strip edge The maximum state, Value taken from , is the number of cut sets, is the number of edges of the multi-state network, wherein the actual network system may be a logistics supply chain network, a communication and information network, an oil and gas transportation and distribution network, an electric power transportation network or a traffic network, etc. As for the process of constructing the actual network system into a multi-state network, it is a relatively conventional technical solution in the art, so it will not be described in detail in this embodiment; Step 2: Get the second minimum value of the maximum state of the network edge in the multi-state network , and judge Is it established: If so, it indicates that d -No duplication will occur during MC search d -MC, for each minimal cut set , , , Perform the operation of step 5; Otherwise, proceed to step 3; Step 3: Calculate the capacity of each minimum cut set , if exists and satisfy , then the minimum cut set , Put them in the same group and sort all the combinations of minimum cut sets in descending order of capacity, which is: ,in, is the number of combinations of the minimum cut set; Step 4: For any minimum cut set combination , , determine the minimum cut set combination Is the number of minimum cut sets contained in 1? If so, for the minimum cut set combination Perform step 5 on the minimum cut set in; Otherwise, for the minimum cut set combination Perform step 6 on the minimum cut set in; Step 5: Based on each edge in the multi-state network The lower capacity limit , search all candidates for the corresponding minimum cut set d -MC, that is, using a conventional mathematical model with three constraints to search d -MC candidate items, which will not be described in detail in this embodiment; Step 6: Based on each edge in the multi-state network The lower capacity limit and the upper capacity limit on each minimal cut set , based on preset no-repeat d -MC search rule, search all candidates for the corresponding minimum cut set d -MC, where the preset no-repeat d -MC search rules are as follows: is a non-repeating d -MC, then there is at least one minimal cut set The following conditions are met: ; ; ; ; in, For edge status, To be included in the minimum cut set In but not included in the minimum cut set The set of edges in , for The number of elements in ; Step 7: Verify all candidates in step 5 or step 6 according to the preset authenticity verification rules. d -MC conducts authenticity verification and eliminates non-authentic candidates d -MC, and the remaining candidates d -MC as a real d -MC, where the process of authenticity verification is: If and only if ,as well as When the state vector It is the minimum cut set Generated reality d -MC; Specifically: ; ; ; in, To exclude and The minimum cut index set after , is the subscript of the minimum cut containing the unsaturated edges in X, is the subscript of the minimum cut in the minimum cut set that does not intersect with the unsaturated edges in the state vector X, is the value of the minimum cut set flow and the value of the generated The flow of the minimum cut set exceeds d The subscript of the minimum cut set of for The flow and under the state vector X, Under the state vector X, generate the minimum cut of X, and the flow and flow of the state vector X;

[0024] In the specific implementation process, step 7 also includes for each edge in the multi-state network , calculate its lower capacity limit With the corresponding , and in Time judgment For real d -MC, compare it with the true d -MC output together, where For edge The state of is 0, and the states of all other edges are the state vectors corresponding to their maximum states, that is, , is the state vector The maximum network flow under Step 8, based on real d -MC evaluates the reliability of the network system, for example, using the conventional inclusion-exclusion theorem method or the non-intersection-sum method.

[0025] In the specific implementation process, Not true, and the minimum cut set The minimum cut set combination When the number of minimum cut sets contained in is not 1, the edges in the multi-state network In the minimum cut set The upper capacity limit is: ; in, To be included in the minimum cut set In but not included in the minimum cut set The set of edges in , and Belong to the same minimal cut set combination , refers to contains only one element, namely: ; It is worth noting that in computing the edge In the minimum cut set combination When the capacity of the first minimum cut set in is upper bounded, its corresponding is an empty set. In addition, assume that the minimum cut set combination In Minimal Cut Set ,but Minimum cut set In the minimum cut set combination All Set, and when there is , then from Remove from the calculation, that is, only keep the subset. In the minimum cut set When the capacity limit is reached, For each subset in , a corresponding capacity upper limit result can be obtained.

[0026] For example, suppose : First, calculate the edge In the minimum cut set The capacity limit under is an empty set, then , then you can directly follow Use the default no-repeat d -MC search rules to search; Then, calculate the edge In the minimum cut set The capacity limit under , that is, according to and relationship and The value of can be obtained As a result, the subsequent Use the default no-repeat d -MC search rules to search.

[0027] Finally, calculate the edge In the minimum cut set The capacity limit under , at this time according to and relationship and The value of can be obtained As a result, according to and relationship and The value of can be obtained by another The results were followed up by two groups The results are respectively based on the preset non-repetitive d -MC search rules are used for searching. for A subset of from Remove it from the calculation of the edge In the minimum cut set The capacity limit under and relationship and The value of can be obtained result.

[0028] by Figure 2 As an example, in the multi-state network shown in The maximum state ,side The maximum state ,side The maximum state ,side The maximum state ,side The maximum state ,side The maximum state The multi-state network has 4 minimal cut sets , respectively: , , , .therefore, Figure 2 The maximum state vector of the multi-state network shown , It is the minimum cut set Generated candidate 10-MC.

[0029] According to Kozyra's method To verify, there are: ; ; ; ; in, is the state vector The set of unsaturated edges in is the minimum flow value of the minimum cut set containing unsaturated edges under the state vector X, For the exception The minimum flow value of all minimum cuts outside the state vector X; when Satisfy: a) and b) , then verify For Real d -MC. Among them, ,but is always greater than 10, which verifies condition b) for Kozyra's method Can be omitted. In addition, if , then verify condition b) for Can also be omitted.

[0030] It can be found that when the minimum cut set hour, Always greater than , the corresponding proof is given below: Lemma 1: Let is a real d -MC, if , then .

[0031] Proof: Known ,in, is the minimum value of the network flow corresponding to all minimum cuts in the network. d -MC, exist , then for ,so .

[0032] Based on this, this embodiment uses Lemma 1 to d -MC verification process is improved to , , . If and only if as well as When both are true, the state vector Minimum Cut Set Generated reality d -MC.

[0033] For repetition d -MC generation mechanism, Figure 2 For example, search demand level For all candidates from 2 to 12 d -MC. Table 1 shows the repetition d-MC and its corresponding minimal cut set.

[0034] Table 1 Repeat d -MC and the corresponding minimal cut set

[0035] From Table 1, we can see that when No duplicates will be generated d -MC. In fact, when No duplicates will be generated. d -MC candidates, yes Sort the items in ascending order and define the second element as .For example, Figure 2 In The order is (2, 3, 4, 5, 5), then The corresponding proof is given below: Lemma 2: If If established, no duplication will occur d -MC candidate.

[0036] Proof: Assumption and are two different minimal cut sets, and They are respectively composed of the minimum cut sets and minimal cut sets Generated d -MC, and .because , then there is at least one edge belong , but not .because , then ,therefore, .In summary, ,and Contradiction. Lemma 2 is proved.

[0037] According to Table 1, there will be duplication d -MC's minimum cut set combinations are: , }、{ , }、{ , }. Table 2 discusses the causes of duplication d -MC minimum cut set, and the relationship between the minimum cut set and the demand level. In Table 2, express and The set of intersecting edges in Indicates belonging to But not The edge set of express The maximum state sum of the middle edge, such as .

[0038] Table 2 , , , and The relationship between

[0039] It can be seen from this that only when and Duplicates are generated only when d -MC. The corresponding proof is given below: Lemma 3: If and only if the following conditions are met, and Will generate duplicates d -MC: a) ; b) ; Proof: First, prove the sufficient condition. , Is Generated candidates d -MC, and satisfies .because ,so ,So It can also be Generate. Sufficient condition proved. Assumption It is And by Generated candidates d -MC, then Obviously, , . The necessity is proved.

[0040] According to Lemma 3, if Is Generated d -MC, is from Generated d -MC, then if and only if the following four conditions are met, : ; ; when ; when ; From this we can see that if ,and ,but Non-repeating d -MC. Therefore, as long as satisfy , you can avoid duplication d -MC generation.

[0041] Defining a Collection ,in ,Right now .by Figure 2 For example, .Will Incorporation , Therefore, when based on Generate no duplicates d -MC candidates only need to satisfy the following formula: when

[0042] The following are some examples: .based on Generate a list without duplicates d -MC candidate, Should meet: In addition, if ,but That is, these two conditions can be combined into , that is, if , then you can Remove .

[0043] In addition, if and ,but , which means The current state of is less than its maximum state. and , Therefore, this embodiment prevents duplication. d -Define edges when MC is generated In the minimum cut set The upper limit of the state is: ; Therefore, it can be determined that the non-repetitive d -MC search rule, that is, if is a non-repeatingd -MC, then there is at least one cut set The following conditions are met: ; ; ; ; Below Figure 2 The multi-state network is taken as an example to further illustrate the method for identifying and preventing non-compliant minimum cut set vectors in a multi-state network in this embodiment.

[0044] Get all minimal cut sets of a multi-state network , , , , and the maximum state vector and demand level ; ,show d -MC search process will generate duplicate d -MC. , calculated , .the remaining , , , Status upper limit ,therefore, , , , ; , , , , sort and group all cut sets , ; Calculate the capacity lower bound, , is a real 10-MC. Similarly, . 10-MC with only one unsaturated edge includes: , , , , ;

[0045] exist Search in group by Generated 10-MC candidates. Get candidate 10-MC: , , ; ; … Search by Generated candidate 10-MC: , , , , , , , ; verify , ,so It is 10-MC; verification , ,so is 10-MC; for , ,so is 10-MC; Again Verify and get is the real 10-MC, as shown in Table 3; Output all real 10-MCs.

[0046] Table 3 10-MC containing multiple unsaturated edges

[0047] The following four groups of examples compare the method in this embodiment with the existing Niu method (i.e., dimensionality reduction method. The traditional method for identifying d-MC duplicates is to find duplicates by comparing d-MC vectors two by two. The Niu method converts d-MC vectors into numerical values ​​for comparison, so that n-dimensional vectors are converted into one-dimensional numerical comparisons, thereby improving efficiency) and the Kozyra method (i.e., MC split search method. Traditional d-MC is obtained based on MC search, while the Kozyra method splits MC into different edge combinations, and then searches for d-MC based on each edge combination, thereby avoiding the generation of duplicate d-MC). The specific average algorithm time is defined as In addition, the definition is the ratio of the running time of the Kozyra method to the CPU time of the method of this embodiment, is the CPU time ratio between the Niu method and the method of this embodiment.

[0048] In the first three examples, consider Figure 2 , Figure 3 and Figure 4The small, medium and large networks shown. Table 4 shows the experimental results, including “number of edges”, “number of nodes”, “number of minimum cuts”, “ d -MC number", and the CPU time consumed by the three methods and the time ratio. Figure 2 , Figure 3 , Figure 4 The number of minimum cut sets generated are 4, 140, and 396, and the maximum state vectors are , , , consistent with the Kozyra method example network.

[0049] Table 4 Figure 2 , Figure 3 , Figure 4 middle d -Computational efficiency of the MC solution algorithm

[0050] As can be seen from Table 4, the calculation time of the method in this embodiment is significantly shortened compared with the Kozyra method (average reduction of 2.597, 2.734 and 1.726) and the Niu method (average reduction of 1.917, 3.338 and 4.305). The above results clearly show that in searching for all demand levels d -MC aspect, the method of this embodiment is always better than the two existing methods. This result is easy to understand. d -The most time-consuming step in MC is identifying and removing duplicates d -MC. This embodiment method is repeated by studying d -MC generation mechanism, proposed a method to prevent duplication d -MC generation method. Although Kozyra's method also avoids duplication d -MC generation, but compared with the Kozyra method, the non-real d -The verification space of MC is significantly reduced.

[0051] The fourth example compares the efficiency of the three methods based on different maximum state vectors. Figure 5 The multi-state network shown contains 27 arcs, 21 nodes, and 222 minimum cuts to verify the impact of the maximum state vector.

[0052] Assume that the maximum state vectors are , , , 6. , The calculation results are shown in Table 5 below.

[0053] Table 5 Figure 5middle d -Computational efficiency of the MC solution algorithm

[0054] It can be observed that except for When , the method of this embodiment can obtain the maximum state vectors of all demand levels faster than the Niu method. d -MC. When The effectiveness of the method in this embodiment is lower than that of the Niu method. This is because the time consumed in searching for 1-MC is very short, and the time saved by the proposed algorithm is less than the time used for preprocessing.

[0055] The ratios of Niu's method to the method of this embodiment are 1.821, 2.488, 2.714, 3.005 and 3.646, respectively. Figure 6 The CPU time ratio variation trend of the three methods is shown. As the maximum state vector increases, the ratio of Niu's method to the method of this embodiment increases, indicating that the relative efficiency of the method of this embodiment is improved. And it can be seen from Table 5 that with the demand level and d - As the number of MCs increases, the relative efficiency of the method in this embodiment also increases. When the maximum state vectors are 3-7, the Kozyra method and the method in this embodiment search all d The CPU time ratios of -MC are 1.612, 1.592, 1.411, 1.276 and 1.315 respectively, and remain between 1.2 and 1.7. Although the ratios of the Kozyra method and the method of this embodiment do not change significantly with respect to the maximum state, the method of this embodiment still has an advantage over the Kozyra method.

[0056] The above description is only a preferred embodiment of the present invention, and does not limit the protection scope of the present invention. All equivalent structural changes made by using the contents of the present invention specification and drawings under the inventive concept of the present invention, or directly / indirectly applied in other related technical fields are included in the protection scope of the present invention.

Claims

1. A method for identifying and preventing non-compliant minimum cut set vectors in a multi-state network, characterized in that: The steps include: Step 1: Build a multi-state network based on the actual network system and obtain all the minimum cut sets of the multi-state network. , , , , and the maximum state vector and demand level ,in, , For the multi-state network Strip Edge The maximum state, Value taken from , is the number of cut sets, is the number of edges in the multi-state network; Step 2: Get the second minimum value of the maximum state of the network edge in the multi-state network , and judge Is it established: If so, it indicates that d - During the MC search process, no duplicate d -MC, for each minimal cut set , , , Perform the operation of step 5; Otherwise, proceed to step 3; Step 3: Calculate the capacity of each minimum cut set , if exists and satisfy , then the minimum cut set , Put them in the same group and sort all the combinations of minimum cut sets in descending order of capacity, which is: , ,…, ,in, is the number of combinations of the minimum cut set; Step 4: For any minimum cut set combination , , determine the minimum cut set combination Is the number of minimum cut sets contained in 1? If so, for the minimum cut set combination Perform step 5 on the minimum cut set in; Otherwise, for the minimum cut set combination Perform step 6 on the minimum cut set in; Step 5: Based on each edge in the multi-state network The lower capacity limit , search all candidates for the corresponding minimum cut set d -MC, proceed to step 7; Step 6: Based on each edge in the multi-state network The lower limit of the state and the upper limit of the state on each minimum cut set , based on preset no-repeat d -MC search rule, search all candidates for the corresponding minimum cut set d -MC; Step 7: Verify all candidates in step 5 or step 6 according to the preset authenticity verification rules. d -MC conducts authenticity verification and eliminates non-authentic candidates d -MC, and the remaining candidates d -MC as a real d -MC; Step 8, based on real d -MC evaluates the reliability of the network system.

2. The method for identifying and preventing non-compliant minimum cut set vectors in a multi-state network according to claim 1, characterized in that: when Not true, and the minimum cut set The minimum cut set combination When the number of minimum cut sets contained in is not 1, the edges in the multi-state network In the minimum cut set The upper limit of the state is: ； in, To be included in the minimum cut set In but not included in the minimum cut set The set of edges in , that is .

3. The method for identifying and preventing non-compliant minimum cut set vectors in a multi-state network according to claim 1 or 2, characterized in that: In step 6, the non-repetitive d -MC search rules are as follows: is a non-repeating d -MC, then there is at least one minimal cut set The following conditions are met: ； ； ； ； in, For edge The current status.

4. The method for identifying and preventing non-compliant minimum cut set vectors in a multi-state network according to claim 1 or 2, characterized in that: In step 7, the above-mentioned d -MC's authenticity verification process is as follows: If and only if ,as well as When the state vector It is the minimum cut set Generated reality d -MC; Specifically: ； ； ； in, To exclude and The minimum cut set subscript set after , is the subscript of the minimum cut set containing unsaturated edges in X, is the subscript of the minimum cut set in which there is no intersection with the unsaturated edge in the state vector X, is the value of the minimum cut set flow and the value of the generated The flow of the minimum cut set exceeds d The subscript of the minimum cut set of for The flow and under the state vector X, is the minimum cut set generated under the state vector X, and the flow under the state vector X.

5. The method for identifying and preventing non-compliant minimum cut set vectors in a multi-state network according to claim 1 or 2, characterized in that: Step 7 also includes, for each edge in the multi-state network , calculate its state lower limit With the corresponding , and in Time judgment For real d -MC, where For edge The state of is 0, and the states of all other edges are their maximum states, that is, , is the state vector The maximum network flow under .

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