Reliability-based Hybrid Genetic Algorithm to address Mixed-Discrete Nonlinear Programming Problems under Uncertainty

Engineering design, when posed as an optimization problem, often involves mixed-discrete nonlinear programming problems under uncertainty. In addition to the mix of discrete and continuous variables, the use of high-fidelity, expensive black-box analyses, and complex probabilistic constraints, these problems typically deal with both aleatory and epistemic uncertainty. A hybrid optimization framework – with a genetic algorithm(GA) to handle the global search, the mixed-discrete variables and associated discontinuities, as well as the non-stationary behavior of the objective and constraints computed via sampling; combined with a gradient-based method to enforce constraints strictly and perform local search that meets local optimality conditions – with safety factors as part of the decisions variable vector in a reliability-based design optimization (RBDO) approach is presented to handle Uncertain mixed-discrete nonlinear programming (MDNLP) problems. The framework is assessed against well-characterized engineering design problems, such as the three-bar truss and ten-bar truss, under uncertainty.