Solving the Robust Design Problem for a Two-Commodity Flow Network with Node Failure

Radwan, Noha Hamdy; Monsef, Hassan; Hussein, Mohamed Eid

doi:10.3844/ajeassp.2020.837.845

Cited by 1 publication

(2 citation statements)

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“…This network consists of 11 arcs as shown in Figure 3, it has 13 MPs; MP1,1,1 = {a1, a7}, MP1,1,2 = {a2, a5, a7}, MP1,2,1 = {a1, a8}, MP1,2,2 = {a2, a9}, MP1,2,3 = {a2, a5, a8}, MP1,3,1 = {a2, a10}, MP2,1,1 = {a3, a5, a7}, MP2,1,2 = {a4, a6, a5, a7}, MP2,2,1 = {a3, a9}, MP2,2,2 = {a4, a6, a9}, MP2,3,1 = {a3, a11}, MP2,3,2 = {a4, a6, a10}, and MP2,3,3 ={a4, a11}. Where nc = NG1 = 11, NF = NG2 = 26, Resources: R = (r1,1, r1,2, r2,1, r2,2) = (10,19,14,19). Demand: D = (d1,1, d1,2, d1,3, d2,1, d2,2, d2,3) = (3, 2, 2, 2, 3, 3).…”

Section: Case3: Network With Two Sources and Three Sinksmentioning

confidence: 99%

“…Hassan and Abdou [16] conducted a study to evaluate the MMSFNs' reliability under time constraints. The studies by [18,19] solved the robust design problem for single and two-commodity flow networks with node failure by using a genetic algorithm. Chen and Lin [20] proposed a solution to find feasible flows that meet flow requirements while minimizing the maximum occurring cost among all demand realizations.…”

Section: Introductionmentioning

confidence: 99%

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Robust Design Problem for Multi-Source Multi-Sink Flow Networks Based on Genetic Algorithm Approach

Boubaker,

Radwan,

Refaat Hassan

et al. 2023

Mathematics

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Robust design problems in flow networks involve determining the optimal capacity assignments that enable the network to operate effectively even in the case of events’ occurrence such as arcs or nodes’ failures. Multi-source multi-sink flow networks (MMSFNs) are frequent in many real-life systems such as computer and telecommunication, logistics and supply-chain, and urban traffic. Although numerous studies on the design of MMSFNs have been conducted, the robust design problem for multi-source multi-sink stochastic-flow networks (MMSFNs) remains unexplored. To contribute to this field, this study addresses the robust design problem for MMSFNs using an approach of two steps. First, the problem is mathematically formulated as an optimization problem and second, a sub-optimal solution is proposed based on a genetic algorithm (GA) involving two components. The first component, an outer genetic algorithm, is employed to search the optimal capacity assigned to the network components with minimum sum. The second component, an inner genetic algorithm, is used to find the optimal flow vectors that maximize the system’s reliability. Through extensive experimentation on three different networks with different topologies, the proposed solution has been found to be efficient.

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Section: Case3: Network With Two Sources and Three Sinksmentioning

confidence: 99%