An effective immune based two-phase approach for the optimal reliability–redundancy allocation problem

Highly reliable systems can reduce loss of money and time in practice. System reliability can be enhanced by: (i) increasing component reliabilities and/or (ii) providing redundancy at the component level. A trade-off between these two options is necessary for nonlinear-constrained reliability optimization. The problem of maximizing system reliability through component reliability choices and component redundancy is called as reliability–redundancy allocation problem, and it is a difficult but realistic nonlinear mixed-integer optimization problem. In this paper, under nonlinear constraints of weight, cost, and volume, we propose a new immune based two-phase approach to solve the reliability–redundancy allocation problem. In the first phase, an immune based algorithm (IA) is developed to solve the allocation problem, and in the second phase we present a new procedure to improve the solutions by IA. Numerical results of four benchmark problems are reported and compared. As shown, the solutions by the new proposed approach are all superior to those best solutions by typical approaches in the literature.