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The reliability redundancy allocation problem (RRAP) is a well-known tool insystem design, development, and management. The RRAP is always modeled as anonlinear mixed-integer non-deterministic polynomial-time hardness (NP-hard)problem. To maximize the system reliability, the integer (component activeredundancy level) and real variables (component reliability) must be determinedto ensure that the cost limit and some nonlinear constraints are satisfied. Inthis study, a bi-objective RRAP is formulated by changing the cost constraintas a new goal, because it is necessary to balance the reliability and costimpact for the entire system in practical applications. To solve the proposedproblem, a new simplified swarm optimization (SSO) with a penalty function, areal one-type solution structure, a number-based self-adaptive new updatemechanism, a constrained nondominated-solution selection, and a new pBestreplacement policy is developed in terms of these structures selected fromfull-factorial design to find the Pareto solutions efficiently and effectively.The proposed SSO outperforms several metaheuristic state-of-the-art algorithms,e.g., nondominated sorting genetic algorithm II (NSGA-II) and multi-objectiveparticle swarm optimization (MOPSO), according to experimental results for fourbenchmark problems involving the bi-objective active RRAP.

Simplified Swarm Optimization for Bi-Objection Active Reliability Redundancy Allocation Problems