Network systems are commonly used in various fields, such as power grid, Internet of Things (IoT), and gas networks. Reliability redundancy allocation problem (RRAP) is a well-known reliability design tool, which needs to be developed when the system is extended from the series-parallel structure to a more general network structure. Therefore, this study proposes a novel RRAP called General RRAP (GRRAP) to be applied to network systems. The Binary Addition Tree Algorithm (BAT) is used to solve the network reliability. Since GRRAP is an NP-hard problem, a new algorithm called Binary-addition simplified swarm optimization (BSSO) is also proposed in this study. BSSO combines the accuracy of the BAT with the efficiency of SSO, which can effectively reduce the solution space and speed up the time to find high-quality solutions. The experimental results show that BSSO outperforms three well-known algorithms, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Swarm Optimization (SSO), on six network benchmarks.