The traditional (active) reliability redundancy allocation problem (RRAP) is used to maximize system reliability by determining the redundancy and reliability variables in each subsystem to satisfy the volume, cost, and weight constraints. The RRAP structure is very simple, that is, redundant components are parallel in each subsystem, and all subsystems are either connected in series or in a bridge network. Owing to its important and practical applications, a novel RRAP, called the general RRAP (GRRAP), is proposed to extend the series-parallel structure or bridge network to a more general network structure. To solve the proposed novel GRRAP, a new algorithm, called the BAT-SSOA3, used the simplified swarm optimization (SSO) to update solutions, the small-sampling tri-objective orthogonal array (SS3OA) to tune the parameters in the proposed algorithm, the binary-addition-tree algorithm (BAT) to calculate the fitness (i.e., reliability) of each solution, and the penalty function to force infeasible back to the feasible region. To validate the proposed algorithm, the BAT-SSOA3 is compared with state-of-the-art algorithms, such as, particle swarm optimization (PSO) and SSO, via designed experiments and computational studies.