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

Sahbi Boubaker (), Noha Hamdy Radwan, Moatamad Refaat Hassan, Faisal S. Alsubaei, Ahmed Younes and Hameda A. Sennary
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Sahbi Boubaker: Department of Computer & Network Engineering, College of Computer Science and Engineering, University of Jeddah, Jeddah 21959, Saudi Arabia
Noha Hamdy Radwan: Department of Mathematics and Computer Science, Faculty of Science, Aswan University, Aswan 81528, Egypt
Moatamad Refaat Hassan: Department of Mathematics and Computer Science, Faculty of Science, Aswan University, Aswan 81528, Egypt
Faisal S. Alsubaei: Department of Cybersecurity, College of Computer Science and Engineering, University of Jeddah, Jeddah 23218, Saudi Arabia
Ahmed Younes: Department of Computer Science, College of Applied Studies and Community Service, Imam Abdulrahman bin Faisal University, Dammam 34212, Saudi Arabia
Hameda A. Sennary: Department of Mathematics and Computer Science, Faculty of Science, Aswan University, Aswan 81528, Egypt

Mathematics, 2023, vol. 11, issue 18, 1-16

Abstract: 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.

Keywords: flow network; robust design; MMSFNs; reliability optimization; genetic algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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