Support Vector Machine-Assisted Importance Sampling for Optimal Reliability Design

A population-based optimization algorithm combining the support vector machine (SVM) and importance sampling (IS) is proposed to achieve a global solution to optimal reliability design. The proposed approach is a greedy algorithm that starts with an initial population. At each iteration, the population is divided into feasible/infeasible individuals by the given constraints. After that, feasible individuals are classified as superior/inferior individuals in terms of their fitness. Then, SVM is utilized to construct the classifier dividing feasible/infeasible domains and that separating superior/inferior individuals, respectively. A quasi-optimal IS distribution is constructed by leveraging the established classifiers, on which a new population is generated to update the optimal solution. The iteration is repeatedly executed until the preset stopping condition is satisfied. The merits of the proposed approach are that the utilization of SVM avoids repeatedly invoking the reliability function (objective) and constraint functions. When the actual function is very complicated, this can significantly reduce the computational burden. In addition, IS fully excavates the feasible domain so that the produced offspring cover almost the entire feasible domain, and thus perfectly escapes local optima. The presented examples showcase the promise of the proposed algorithm.