Network systems are commonly used in various fields, such as power grids, Internet of Things, and gas networks. The reliability redundancy allocation problem is a well-known reliability design tool that needs to be developed when the system is extended from a series-parallel structure to a more general network structure. Therefore, this study proposes a novel reliability redundancy allocation problem, referred to as the general reliability redundancy allocation problem, to be applied in network systems. Because the general reliability redundancy allocation problem is NP-hard, a new algorithm referred to as binary-addition simplified swarm optimization is proposed in this study. Binary-addition simplified swarm optimization combines the accuracy of the Binary Addition Tree Algorithm with the efficiency of Simplified Swarm Optimization, which can effectively reduce the solution space and speed up the time required to find high-quality solutions. The experimental results show that binary-addition simplified swarm optimization outperforms three well-known algorithms: the Genetic Algorithm, Particle Swarm Optimization, and Simplified Swarm Optimization in high-quality solutions and high stability on six network benchmarks.