In this study, we consider a bi-objective redundancy allocation problem on a series-parallel system with component level redundancy strategy. Our aim is to maximize the minimum subsystem reliability, while minimizing the overall system cost. The Pareto solutions of this problem are found by the augmented epsilon-constraint approach for small and moderate sized instances. After finding the Pareto solutions, we apply a well known sorting procedure, UTADIS, to categorize the solutions into preference ordered classes, such as A, B, and C. In this procedure, consecutive classes are separated by thresholds determined according to the utility function constructed from reference sets of classes. In redundancy allocation problems, reference sets may contain a small number of solutions (even a single solution). We propose the tau-neighborhood approach to increase the number of references. We perform experiments on some reliability optimization test problems and general test problems. (C) 2011 Elsevier Ltd. All rights reserved.