Robust Optimization and Sensitivity Analysis with Multi-Objective Genetic Algorithms: Single- and Multi-Disciplinary Applications.

摘要

Uncertainty is inevitable in engineering design optimization and can significantly degrade the performance of an optimized design solution and/or even change a feasible solution to infeasible. The problem with uncertainty can be exacerbated in multi-disciplinary optimization whereby the models for several disciplines are coupled and the propagation of uncertainty has to be accounted for within and across disciplines. It is important to determine which ranges of parameter uncertainty are most important or how to best allocate investments to partially or fully reduce uncertainty under a limited budget. This dissertation concentrates on a new robust optimization approach and a new sensitivity analysis approach for multi-objective and multi-disciplinary design optimization problems that have parameters with interval uncertainty. The dissertation presents models and approaches under four research thrusts. In the first, an approach is presented to obtain robustly optimal solutions which are as best as possible, in a multi-objective sense, and at the same time their sensitivity of objective and/or constraint functions is within an acceptable range. In the second the robust optimization approach in the first thrust is extended to design optimization problems which are decomposed into multiple subproblems, each with multiple objectives and constraints. In the third, a new approach for multi-objective sensitivity analysis and uncertainty reduction is presented. And in the final research thrust, a metamodel embedded Multi-Objective Genetic Algorithm (MOGA) for solution of design optimization problems is presented. The new MOGA requires a significantly fewer number of simulation calls, when used to solve multi-objective design optimization problems, compared to previously developed MOGA methods while obtaining comparable solutions.