Redundancy optimization problem is extremely popular as redundancy is a useful technique to improve the reliability of system. In this paper, the progresses of this problem during the past two decades are reviewed. Firstly, a framework is proposed with decomposition into four main modules consist of component characteristic, redundancy strategy, reliability modeling of system, and optimization algorithm. Next, the existing literatures are classified into common and extended studies through this framework to identify the details and methods associated with each module thoroughly. The conclusions demonstrate that the framework is indeed general to contain all the existing studies. Further, the widely used benchmarks are collected and divided for ease of referring. Finally, the future studies are pointed out based on the gaps and extensions between the current studies and framework, including absent studies concerning different combinations of elements, the expansions of component characteristics, more general redundancy structures, exploitation of knowledge-inspired optimization algorithm, integration with other techniques improving reliability and focus on real system in engineering.
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