A Multi-fidelity Approach to Address Multi-objective Constrained Mixed-discrete Nonlinear Programming Problems with Application to Greener Aircraft Design
Engineering problems often involve solving constrained multi-objective Mixed-Discrete Nonlinear Programming (MDNLP) problems. These problems are inherently difficult to solve given the presence of multiple competing objectives, nonlinear objective and constraint functions, mixed-discrete type design variables, and expensive analysis tools. This work presents a multi-fidelity approach that addresses all these features together and exhibits its efficacy to solve constrained multi-objective MDNLP problems within a reasonable computational budget. The work addresses the high computational cost drawback associated with a previously developed "hybrid multi-objective optimization approach'' that combines a Genetic Algorithm (GA) with the gradient-based Sequential Quadratic Programming (SQP) algorithm. The multi-fidelity hybrid algorithm in this work employs surrogate models to provide low-fidelity approximations of the objective and constraint functions that are fast to evaluate. The gradient-based SQP algorithm uses these surrogate models in a goal attainment formulation. The combination of the GA with SQP then finds a diverse set of designs representing the best possible trade-off solutions for the multi-objective problem. For this thesis, the author initially pursues both Kriging and Radial Basis Function (RBF) surrogate modeling techniques, with their respective application to test problems (three-bar and ten-bar truss constrained, multi-objective, MDNLP problems) determining their feasibility of implementation in the multi-fidelity approach. The test problem results indicate that using RBF technique makes use of the hybrid approach more feasible as compared to using the Kriging technique. The results show a reduction of at least 98% in the "high-fidelity'' function evaluations with respect to the previously-developed hybrid approach, along with a reduction of at least 89% in the computational runtime. Subsequently, the multi-fidelity approach using RBF surrogate models is employed to solve a complex aerospace engineering problem used in previous studies - a 'greener' aircraft design problem - posed as a constrained multi-objective MDNLP problem. The resulting non-dominated design solutions are comparable to those obtained using the previously-developed hybrid approach. The result indicates a compromise that exists between the number of "high-fidelity'' evaluations performed and the ability of the multi-fidelity hybrid algorithm to find as diverse non-dominated designs as possible (indicating the spread of the Pareto frontier). This work also suggests a preliminary approach to choose the population size for the multi-objective multi-fidelity hybrid algorithm, so that the algorithm finds a satisfactory spread for the Pareto frontier at a reasonable computational cost.
Crossley, Purdue University.
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