Keywords: reliability-based design optimization, asymptotic sampling, latin hypercube.

This paper is focused on multi-objective reliability-based design optimization. A weight of a structure and a probability of failure represented by a reliability index form two competing objectives. Since the probability of failure of realistic structures is low, e.g. 10^-4 - 10^-5 for ultimate limit states in the case of civil engineering structures, the required number of samples for crude Monte Carlo is overwhelming. Even the application of quasi Monte Carlo methods such as Latin Hypercube Sampling does not bring substantial reduction of the required computational time and therefore, an approximate method called asymptotic sampling for prediction of the probability of failure and/or the reliability index is used. Here, an application of multi-objective optimization to reliability-based design optimization is twofold: (i) single-objective optimization is usually not able to find all optima in a multimodal problem thus the multi-objective algorithm based on a non-dominated sorting genetic algorithm is employed to show the vicinity of the trade-off near the limit value of the prescribed reliability index and (ii) by inspecting the Pareto-front obtained, an estimation of the sensitivities of individual variables can be judged.

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