AbstractReliability-based design optimization (RBDO) is a well-known design strategy in engineering. However, RBDO usually requires uncertainties to be modeled by statistical distributions. This requires the availability of sufficient sample size so that these variables can be represented accurately by probabilistic distributions. In the design of new systems and structures, usually there is a lack of information about some uncertain variables or parameters and only a reduced set of samples might be available. This prevents their treatment as probability distributions. This type of uncertainty is called epistemic uncertainty. This paper proposes two effective multiobjective evolutionary algorithms to solve design problems under both types of uncertainty: aleatory and epistemic. Two objective functions, namely the cost of the structures and the probability of failure, are considered. The results are Pareto fronts with a trade-off between cost and reliability associated with a specified level of confidence. Pareto fronts show minimum achievable values for the probability of failure for a given cost. The effect of the epistemic uncertainty on the solution is also investigated. An analytical example and two structural examples are solved to show the applicability of the approach and how epistemic uncertainty may affect the results.