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.