Keywords: parallelization, multi-objective optimization, reliability-based design optimization, meta-models, Monte Carlo, surrogates, radial basis functions, pairwise distances, Matlab.

Every structural design should satisfy several criteria; economic aspects as well as a reliability of the structural system belong to the most important ones. The reliabilitybased design optimization (RBDO) seeks such designs that comply both of the above criteria. As a most general case, we use a double-looped RBDO, in which the system reliability is assessed within the inner loop and a designing process is performed in the outer loop. A common approach expressed as a single-objective optimization is transformed into a multi-objective case providing results as an approximation of the Pareto front composed of the compromising solutions between cost and reliability. Despite the growing performance of computers, a reliability assessment is still computationally expensive especially for small failure probabilities despite the growing performance of computers. Therefore, researchers look for novel techniques for the computational cost reduction. In simulation techniques often used for the reliability assessment, the largest part of the computational time is devoted to a repeated evaluation of a performance function represented e.g. by a finite element model. However, the original model can be replaced by a surrogate model that has a similar response but it is faster to evaluate. Several samples still have to be evaluated with the original model; these samples are used for the surrogate model construction subsequently. The precision of the surrogate model grows particularly with a number of the construction samples. Interpolation surrogate models such as Kriging or Radial basis functions (RBF) are still computationally expensive since every construction sample increases a dimension of a linear system. The needed number of the construction samples grows with a number of dimensions of the design space as well as with its expansion. This paper focuses on a reduction of the computational effort spent on the RBDO using several implementation tricks and parallelization techniques. Note that no solution is optimal; the selection of the final version is dependent not only on the computational speed but also limitations imposed by available memory. Since the mentioned novel reliability assessment techniques can dramatically differ in obtained precision and computational demands, the pure Monte Carlo method is used to provide unified results for the application of surrogates. The profiling of the code shows two main bottlenecks: (i) enumeration of interpoint distances needed to compute values of radial basis functions and (ii) a solution of linear systems of equations to fit the surrogates. Several possible versions of the implementation of the first issue are proposed and tested on a classical RBDO example and parallelization efficiency and memory demands are presented.

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