A novel minimal cut-based algorithm to find all minimal capacity vectors for multi-state flow networks

Huang, Ding; Huang, Chung-Ming; Lin, Yi

doi:10.1016/j.ejor.2019.10.030

Cited by 17 publications

(5 citation statements)

References 36 publications

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“…The capacities, lead times, and transmission costs of the arcs in both cases-Arpanet and the randomly generated test problems-were assigned random integer values within the intervals [5,20], [3,10], and [5,15], respectively. It is essential to note that with sufficiently large time and budget limits, any SSV can be a solution, rendering the algorithms redundant.…”

Section: Resultsmentioning

confidence: 99%

“…While deterministic (non-stochastic) flow networks have undeniably been instrumental in understanding and optimizing various systems, the practical reality is that many real-world systems exhibit dynamic characteristics, necessitating the adoption of a more nuanced approach. Multistate (stochastic) flow networks (MFNs) have gained prominence as a result of their ability to model complex systems in which fluctuations, failures, maintenance, and other dynamic factors play a significant role [14][15][16][17][18][19][20]. Within an MFN, arcs and nodes can exist in various potential states that are influenced by traffic conditions, maintenance activities, failures, or other underlying causes.…”

Section: Introductionmentioning

confidence: 99%

“…It is the probability of transmitting at least a given demand for d units of flow/data/commodity from node one (source) to node n (destination). Numerous exact and approximative algorithms have been proposed in the literature to compute this indicator [8,10,15,20,[22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

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Using a Node–Child Matrix to Address the Quickest Path Problem in Multistate Flow Networks under Transmission Cost Constraints

Forghani-elahabad,

Alsalami

2023

Mathematics

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The quickest path problem in multistate flow networks, which is also known as the quickest path reliability problem (QPRP), aims at calculating the probability of successfully sending a minimum of d flow units/data/commodity from a source node to a destination node via one minimal path (MP) within a specified time frame of T units. Several exact and approximative algorithms have been proposed in the literature to address this problem. Most of the exact algorithms in the literature need prior knowledge of all of the network’s minimal paths (MPs), which is considered a weak point. In addition to the time, the budget is always limited in real-world systems, making it an essential consideration in the analysis of systems’ performance. Hence, this study considers the QPRP under cost constraints and provides an efficient approach based on a node–child matrix to address the problem without knowing the MPs. We show the correctness of the algorithm, compute the complexity results, illustrate it through a benchmark example, and describe our extensive experimental results on one thousand randomly generated test problems and well-established benchmarks to showcase its practical superiority over the available algorithms in the literature.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Using a Node–Child Matrix to Address the Quickest Path Problem in Multistate Flow Networks under Transmission Cost Constraints

Forghani-elahabad,

Alsalami

2023

Mathematics

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“…Consider a multi-state delivery network (MSDN) with multiple suppliers, in which a vertex denotes a supplier, a transfer station or a market, while a branch denotes a carrier providing the delivery service for a pair of vertices [1][2][3][4][5]. The capacity that is available for a specific customer of the carrier responsible for the delivery on a branch is treated as a multi-state variable, since this capacity is shared among several customers including the one under consideration.…”

Section: Introductionmentioning

confidence: 99%

Symbolic Derivation of a Probability-Ready Expression for the Reliability Analysis of a Multi-State Delivery Network

Rushdi

Amashah

2021

JAMCS

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This paper deals with the reliability of a multi-state delivery network (MSDN) with multiple suppliers, transfer stations and markets (depicted as vertices), connected by branches of multi-state capacities, delivering a certain commodity or service between their end vertices. We utilize a symbolic logic expression of the network success to satisfy the market demand within budget and production capacity limitations even when subject to deterioration. This system success is a two-valued function expressed in terms of multi-valued component successes, and it has been obtained in the literature in minimal form as the disjunction of prime implicants or minimal paths of the pertinent network. The main contribution of this paper is to provide a systematic procedure for converting this minimal expression into a probability-ready expression (PRE). We successfully extrapolate the PRE concept from the two-valued logical domain to the multi-valued logical domain. This concept is of paramount importance since it allows a direct transformation of a random logical expression, on a one-to-one one, to its statistical expectation form, simply by replacing all logic variables by their statistical expectations, and also substituting arithmetic multiplication and addition for their logical counterparts (ANDing and ORing). The statistical expectation of the expression is its probability of being equal to 1, and is simply called network reliability. The proposed method is illustrated with a detailed symbolic example of a real-case study, and it produces a more precise version of the same numerical value that was obtained earlier by an alternative means. This paper is a part of an ongoing activity to develop pedagogical material for various candidate techniques for assessing multi-state reliability.

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“…Huang [14] proposed an algorithm to obtain minimal capacity vectors for evaluating the system reliability that the multi-state distribution network can meet all retailers' demand under stocks. As the MSN reliability can be computed in terms of all minimal capacity vectors meeting the demand requirements, Huang et al [16] proposed a group approach with both the concepts of minimal cut and minimal path (MP) in order to narrow the search range of feasible capacity vectors.…”

Section: Introductionmentioning

confidence: 99%

Optimal Transmission Line Assignment Considering Reliabilities and Assignment Cost in the Multi-State Network

Yang

Zhang

2020

IEEE Access

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As the improvement of the network reliability can be achieved by the components assignments, the optimal transmission line assignment with maximal reliabilities and minimal cost (OTLAMRMC) problem under the transmission time constraints is investigated. The OTLAMRMC problem contains two sub-problems: the reliabilities and assignment cost evaluation under the transmission time constraint (RACETTC) and the multi-objective transmission line assignment optimization problem. First, the RACETTC algorithm is proposed to evaluate reliabilities and assignment cost under the transmission time constraints for a certain transmission line configuration. Then, the Non-dominated Sorting Genetic Algorithm III (NSGA-III) is adopted to search the optimal transmission line assignment based on the results obtained by the RACETTC algorithm. Therefore, combining the RACETTC algorithm and the NSGA-III together, the RACETTC-NSGA-III algorithm is proposed to solve the OTLAMRMC problem. Finally, example simulations are given to illustrate the proposed algorithm. The example results show that the RACETTC-NSGA-III algorithm can provide efficient solutions in a reasonable time.

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A novel minimal cut-based algorithm to find all minimal capacity vectors for multi-state flow networks

Cited by 17 publications

References 36 publications

Using a Node–Child Matrix to Address the Quickest Path Problem in Multistate Flow Networks under Transmission Cost Constraints

Using a Node–Child Matrix to Address the Quickest Path Problem in Multistate Flow Networks under Transmission Cost Constraints

Symbolic Derivation of a Probability-Ready Expression for the Reliability Analysis of a Multi-State Delivery Network

Optimal Transmission Line Assignment Considering Reliabilities and Assignment Cost in the Multi-State Network

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