Data for the article "An Efficient Algorithm for the Reliability Evaluation of Multistate Flow Networks under Budget Constraints"
Many real-world systems can be modeled by multistate flow networks (MFNs) and their reliability evaluation features in designing and control of these systems. Considering the cost constraint makes the problem of reliability evaluation of an MFN more realistic.For a given demand valuedand a given cost limitc, the reliability of an MFN at level (d, c) is the probability of transmitting at leastdunits from the source node to the sink node through the network within the cost ofc. This article addresses the so-called (d, c)-MC problem, i.e., the problem of reliability evaluation of an MFN with cost constraints in terms of minimal cuts. It presents new results on which a new algorithm is based.This algorithm finds all (d, c)-MC candidates without duplicates and verifies them more efficiently than existing ones.The complexity results for this algorithm and an example of its use are provided. Finally, numerical experiments with R language implementations of the presented algorithm and other competitive algorithms are considered. Both the time complexity analysis and numerical experiments demonstrate the presented algorithm to be more efficient than the fastest competing algorithms in 81.41%–85.11% of cases.
The data set contains three ZIP folders: 'MCs lists', 'd_c_MCs lists', 'd_c_MCs lists2', an additional file Params_all_Ku.csv and the file 'Proof.zip' with the proof of Lemma 6 from the article.
Moreover, the dataset contains ZIP folder Codes with 5 R scripts:
The folder 'MCs lists' contains 7 files in the csv format. Each of these files contains the list of all minimal cuts for an appropriate multistate flow network (MFN) from figures 2-4. The arcs in networks 1,2,3,5,6,7 are ordered firstly according to the order of their beginning nodes and secondly on the order of their ending nodes. Only in the network Id 4 from Fig. 3 the order of the arcs is another, and this order is visible in Fig. 3.
The folder 'd_c_MCs lists' contains 126 files and the folder 'd_c_MCs lists2' contains 315 files in the csv format. Each of these files has the name of the form i_j_(d,c)-MCs, where i denotes the MFN ID, j - the number of the variant of the greatest state vector, d - demand level, and c- cost constraint. Each of these files contains all (d,c)-MCs determined for given MFN ID - i, and the greatest state vector of the number of the variant - j.
The file 'Params_all_Ku.csv' contains experimental results of numerical experiments conducted on a computer with Intel(R) Core(TM) i7-8750H CPU and 16 GB of RAM.
Column 1 'i' - MFN ID;
Column 2 'j' - the number of the variant of the greatest state vector;
Column 3 'd' - given level d of multistate minimal cuts;
Column 4 'c' - the total budget c;
Column 5 'n_Q1' - the number of elements of set Q_1 defined by (19) in Lemma 8 in the related article;
Column 6 'n_Q2' - the number of elements of set Q_2 defined by (20) in Lemma 8 in the related article;
Column 7 'n_dc'' - the number of all (d,c)-MCs;
Column 8 'T_aux' - the computational time of the introductory algorithm of the presented algorithm;
Column 9 'T_K' - expressed in nanoseconds the computational time of the main algorithm from the presented algorithm;
Column 10 'T_K_t' - expressed in nanoseconds the computational time of the presented algorithm;
Column 11 'T_F_K' - expressed in nanoseconds the computational time of the algorithm described in the article M. Forghani-elahabad, N. Kagan, Assessing Reliability of Multistate Flow Networks Under Cost Constraint in Terms of Minimal Cuts Int. J. Reliab. Qual. Saf. Eng.2019,26, 1950025;
Column 12 'T_Ku' - expressed in nanoseconds the computational time of the algorithm described in the article Kumari, S. and S. Namasudra (2021). System reliability evaluation using budget constrained real d-mc search. Computer Communications 171, 10–15;
Column 13 - the ratio T_K/T_F_K;
Column 14 - the ratio T_K_t/T_F_K;
Column 15 - the ratio T_K/T_Ku;
Column 16 - the ratio T_K_t/T_Ku;
Column 17 - the ratio T_F_K/T_Ku.
File Init_params.r contains the code downloading minimal cuts for all analyzed multistate flow networks and fixing all parameters of the networks.
Forghani.r contains the code with my implementation of the algorithm described in Forghani-elahabad, M. and N. Kagan (2019a). Assessing reliability of multistate flow networks under cost constraint in terms of minimal cuts. Int. J. Reliab. Qual. Saf. Eng. 26 (5), 1–18
Kumari.r contains my implementation of the algorithm described in Kumari, S. and S. Namasudra (2021). System reliability evaluation using budget constrained real d-mc search. Computer Communications 171, 10–15.
File kozyra_d_c_MCs.r contains my implementation of my algorithm
tests.r contains the code for the comparative analysis of my algorithm with competing algorithms.
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- MCs lists.zip (7.64 kB)
- d_c_MCs lists.zip (7.43 MB)
- d_c_MCs lists2.zip (10.66 MB)
- Params_all_Ku.csv (52.90 kB)
- Proof.zip (175.21 kB)
- Codes.zip (11.85 kB)
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