Sequential second-order cone programming relaxation for distributionally robust truss optimization using Gaussian kernel

Abstract

This paper addresses truss topology optimization under an uncertain external load. We formulate a bi-objective optimization problem for the worst-case expected value and the worst-case conditional value-at-risk (CVaR) of the compliance within a distributionally robust optimization framework based on kernel density estimation with a Gaussian kernel. We solve the resulting convex optimization problem by a sequential second-order cone programming method, using supporting hyperplanes of the feasible set. Furthermore, we utilize a constraint pruning strategy for numerical stability and scalability. The numerical experiments on a challenging instance demonstrate the convergence histories of the proposed method with and without the pruning strategy.