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A variable neighborhood search (VNS) algorithm has been developed to solve the multiple objective redundancy allocation problems (MORAP). The single objective RAP is to select the proper combination and redundancy levels of components to meet system level constraints, and to optimize the specified objective function. In practice, the need to consider two or more conflicting objectives simultaneously increases nowadays in order to assure managers or designers’ demand. Amongst all system level objectives, maximizing system reliability is the most studied and important one, while system weight or system cost minimization are two other popular objectives to consider. According to the authors’ experience, VNS has successfully solved the single objective RAP (Liang and Chen, Reliab. Eng. Syst. Saf. 92:323–331, 2007; Liang et al., IMA J. Manag. Math. 18:135–155, 2007). Therefore, this study aims at …