Approximate optimization of systems with high-dimensional uncertainties and multiple reliability constraints

A novel approach is proposed to solve reliability-based optimization (RBO) problems where the uncertainty dimension can be large and where there may be many reliability constraints. The basic idea is to transform all reliability constraints in the target RBO problem into non-probabilistic ordinary ones by a pilot analysis. It will be shown that such a pilot analysis only requires a single run of the modified subset simulation (called the parallel subset simulation) regardless the number of the reliability constraints. Once the reliability constraints are approximated by the ordinary ones, the RBO problem can be solved as if it is an ordinary optimization problem. The resulting optimal solution should be approximately feasible, and the corresponding objective function value is minimized under the approximate constraints. Three numerical examples are investigated to verify the proposed novel approach. The results show that the approach may be capable of finding approximate solutions that are usually close to the actual solution of the target RBO problem.