— The multi-objective components assignment problem (MOCAP) for multi-source multi-sink flow networks when each component has an assignment cost is never discussed. The main objective of MOCAP is to search the optimal components that maximize network reliability of multi-source multi-sink flow networks and minimized the total assignment cost. An approach based random weighted genetic algorithm (RWGA) is proposed to solve the MOCAP. The Optimal Components Assignment Problem (OCAP) has a solution that is produced by RWGA. The results demonstrated that using the suggested method, optimal component assignment yields the greatest reliability, lowest assignment cost, and shortest total lead-time. The proposed algorithm has been applied to various networks to assert its efficiency in comparison with other approaches based on single genetic algorithm. We applied it to different types of network models, including two-source two-sink networks and three-source two-sink networks, with varying numbers of available components. Also, the obtained results show that the proposed RWGA approach works well and find optimal solutions for all studied cases.

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Multi-objective components assignment problem for multi-source multi-sink flow networks

: Robust design for a flow network is considered an NP-hard problem. It is defined as finding the best capacities for components so that the network survives even when nodes fail. MMSFNs (multi-source multi-sink flow networks are utilized across numerous real-world systems, including logistics, computing, transportation, and telecommunication systems. In this paper, the robust design for multi-commodity MMSFNs with node failures been investigated and solved using GA-based approach. Because despite many studies in this area, no study is given in this section. The solution approach to this problem is divided into two parts, outer GA and internal GA. The outer GA searches for the optimal capacity of nodes into the minimum-sum network. The internal GA searches for the best vector with maximum system reliability. This study was applied to three networks to ensure their effectiveness and success in achieving the desired objective of the study.

Solving the Robust Design Problem for MMSFNs Considering Node Failure

System reliability optimization problem of multi-source multi-sink flow network is defined by searching the optimal components that maximize the reliability and minimize the total assignment cost. Therefore, a genetic-based approach is proposed to solve the components assignment problem under budget constraint. The mathematical model of the optimization problem is presented and solved by the proposed genetic-based approach. The proposed approach is based on determining the optimal set of lower boundary points that maximize the system reliability such that the total assignment cost does not exceed the specified budget. Finally, to evaluate our approach, we applied it to various network examples with different numbers of available components; two-source two-sink network and three-source two-sink network. 

Components Assignment Problem for Multi-Source Multi-Sink Flow Networks with Reliability and Budget Constraints

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Components Assignment Problem for Multi-Source Multi-Sink Flow Networks with Reliability and Budget Constraints