Abstract
In recent decades, the redundancy allocation problem (RAP) is becoming an increasingly important tool in the initial stages of planning, designing, and controlling of systems. Moreover, the multi-level redundancy allocation problem (MRAP) and multiple multi-level redundancy allocation problem (MMRAP) are extensions derived from the RAP for practical modeling of real-life problems. However, the two problems mentioned above still have restrictions that may be the best resolution in some special cases, but not in general. Therefore, this paper formulates a new kind of the MRAP called the general multi-level redundancy allocation problem (GMRAP) so as to break the restrictions and generalize previous problems. GMRAP designs are widespread in many critical systems, such as manufacturing systems, computing systems and software systems. GMRAP is not only NP-hard, but a nonlinear integer optimization problem with hierarchy. The complexity of GMRAP is much larger than the traditional RAP, MRAP and MMRAP. Furthermore, a novel algorithm called simplified swarm optimization with modular search (SSO-MS) is proposed to solve the GMRAP in this paper. To the best of our knowledge, this is the first attempt to use SSO for the hierarchal RAP instead of genetic algorithms. Finally, the result obtained by SSO-MS has been compared with those obtained from genetic algorithms and particle swarm optimization algorithms. Computational results show that the proposed SSO-MS is very competitive and demonstrate the effectiveness and the practical viability of this approach and model.