IPSO-based hybrid approaches for reliability-redundancy allocation problems

The problem of maximizing system reliability through component reliability choices and component redundancy is called reli-ability-redundancy allocation problem (RAP), and it is a difficult but realistic nonlinear mixed-integer optimization problem. For the RAP, we pay attention to an improved particle swarm optimization (IPSO), and introduce four hybrid approaches for combining the IPSO with other conventional search techniques, such as harmony search (HS) and LXPM (a real coded GA). The basic structure of the hybrid approaches includes two phases. After devising an initial solution by the HS or LXPM technique in the first phase, the IPSO performs an optimal search in the next phase. In addition, a new procedure by using golden search, named GS, is developed for further improving the solutions obtained by IPSO. Consequently, four ISPO-based hybrid approaches are proposed including HS-IPSO, LXPM-IPSO, HS-IPSO-GS, and LXPM-IPSO-GS. In order to validate the per-formance of proposed approaches, five nonlinear mixed-integer RAPs are investigated where both the number of redundancy components and the corresponding component reliability in each subsystem are to be decided simultaneously. As shown, the proposed approaches are all superior in terms of both optimal solutions and robustness to those by IPSO. Especially, the pro-posed LXPM-IPSO-GS has shown more excellent performance than other typical approaches in the literature.