Multi-objective robust design optimization of planar steel frames using a Gaussian mixture model

摘要

We have presented an application of GMM to the RDO of planarsteel frames by letting the random input variables and thecorresponding structural response behave according to a jointPDF under the presence of uncertainty. The mean and variancevalues are approximated by Eqs. (10) and (11), respectively. Themulti-objective RDO problem is formulated for the steel frame tominimize three conflicting objective functions. Pareto-optimalsolutions of the optimization problem are found using NSGA-II.It is shown that the GMM-based RDO can effectively yieldoptimum solutions that well represent different levels of the tradeoffbetween the conflicting objective functions. Based on thesesolutions, structural engineers can further obtain their mostpreferred design.