A Mixed Integer Efficient Global Optimization Algorithm with Multiple Infill Strategy - Applied to a Wing Topology Optimization Problem

With the advancement in high performance computing and numerical optimization techniques, engineering design optimization problems are becoming more complex, larger scale, higher fidelity, and computationally more demanding, requiring longer run times than ever before. There exists methodologies and techniques that can address some of these challenges but very few can address all, and most are limited in the extent that these concerns can be addressed. With the goal of addressing such challenging engineering problems, we developed a new optimization algorithm, named AMIEGO, that combines concepts from surrogate-based optimization approaches, gradient-based numerical methods, Partial Least Squares, evolutionary algorithms, and Branch-and-Bound, providing newer capabilities that were not previously perceived. The effort here builds upon this previously developed optimization algorithm to include multiple infill sampling capability that combines the concept of generalized expected improvement function, unsupervised learning, and multi-objective evolutionary technique. To demonstrate, AMIEGO with the multiple infill capability (called AMIEGO-MIMOS) solves a series of increasingly difficult engineering design optimization problems. The results reveal the performance of the new approach is problem dependent. When applied to a ten-bar truss problem, the newly proposed multiple infill strategy consistently leads to a better design solutions when compared to the existing CPTV method (implemented with the context of the AMIEGO algorithm). On the other hand, when applied to a mixed-integer high fidelity wing topology optimization problem MIMOS, despite showing a steeper convergence at the start, eventually leads to an inferior solution as compared to CPTV approach. These results also reveal that a small number of starting points, in general, are sufficient to lead to a good overall solution.