  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.
