BAT-based algorithm for finding all Pareto solutions of the series-parallel redundancy allocation problem with mixed components

•Propose the first algorithm to find all Pareto solutions for RAP.•Propose the first BAT-algorithm for RAP.•Propose the first BAT-based algorithm to find all Pareto solutions for RAP.•Propose the first algorithm to combine SSO and BAT for the RAP.•Find all Pareto solutions for Fyffe RAP and Coit RAP. The active strategy series-parallel redundancy allocation problem (RAP) with mixed components involves setting reliable objectives for components or subsystems to meet the resource consumption constraint, for example the total cost. RAP has been actively researched for the past four decades. NP-hard problems confronted by RAP include maintaining feasibility with respect to two constraints: cost and weight. To provide all Pareto solutions to RAPs, e.g., the Fyffe RAP and Coit RAP, a novel algorithm is proposed, which is called the bound-rule-BAT (BRB). The BRB is based on the binary-addition-tree algorithm (BAT), the dominance rule, and dynamic bounds. The BRB is tested on three experiments to demonstrate its efficiency in solving the Fyffe RAP and its ability in finding all Pareto solutions of the Coit RAP.