An efficient simulation optimization method for the generalized redundancy allocation problem

The redundancy allocation problem (RAP) is concerned with the allocation of redundancy that maximizes the system reliability subject to constraints on system cost, or minimizes the system cost subject to constraints on the system reliability, has been an active research area in recent decades. In this paper, we consider the generalized redundancy allocation problem (GRAP), which extends traditional RAP to a more realistic situation where the system under consideration has a generalized (typically complex) network structure; for example, the components are connected with each other neither in series nor in parallel but in some logical relationship. Special attention is given to the case when the objective function, e.g., the system reliability, is not analytically available but has to be estimated through simulation. We propose a partitioning-based simulation optimization method to solve GRAP. Due to several specially-designed mechanisms, the proposed method is able to solve GRAP both effectively and efficiently. For efficacy, we prove that the proposed method can converge to the truly optimal solution with probability one (w.p.1). For efficiency, an extensive numerical experiment shows that the proposed method can find the optimal or nearly optimal solution of GRAP under a reasonable computational budget and outperforms the other existing methods on the created scenarios.