An extensible open-source deterministic global optimizer (EAGO) programmed entirely in the Julia language is presented. EAGO was developed to serve the need for supporting higher-complexity user-defined functions (e.g. functions defined implicitly via algorithms)
within optimization models. EAGO embeds a first-of-its-kind implementation of McCormick arithmetic in an Evaluator structure allowing for the construction of convex/concave relaxations using a combination of source code transformation, multiple dispatch,
and context-specific approaches. Utilities are included to parse userdefined functions into a directed acyclic graph representation and perform symbolic transformations enabling dramatically improved solution speed. EAGO is compatible with a wide variety of local optimizers, the most exhaustive library of transcendental functions, and allows for easy accessibility through the JuMP modelling language. Together with Julia’s minimalist syntax and competitive speed, these powerful features make EAGO a versatile research platform enabling easy construction of novel meta-solvers, incorporation and utilization
of new relaxations, and extension to advanced problem formulations encountered in engineering and operations research (e.g. multilevel problems, user-defined functions). The applicability and flexibility of this novel software is demonstrated on a diverse set of
examples. Lastly, EAGO is demonstrated to perform comparably to state-of-the-art commercial optimizers on a benchmarking test set.
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A Combinatorial Approach for Constructing Lattice Structures
Abstract Lattice structures exhibit unique properties including a large surface area and a highly distributed load-path. This makes them very effective in engineering applications where weight reduction, thermal dissipation, and energy absorption are critical. Furthermore, with the advent of additive manufacturing (AM), lattice structures are now easier to fabricate. However, due to inherent surface complexity, their geometric construction can pose significant challenges. A classic strategy for constructing lattice structures exploits analytic surface–surface intersection; this, however, lacks robustness and scalability. An alternate strategy is voxel mesh-based isosurface extraction. While this is robust and scalable, the surface quality is mesh-dependent, and the triangulation will require significant postdecimation. A third strategy relies on explicit geometric stitching where tessellated open cylinders are stitched together through a series of geometric operations. This was demonstrated to be efficient and scalable, requiring no postprocessing. However, it was limited to lattice structures with uniform beam radii. Furthermore, existing algorithms rely on explicit convex-hull construction which is known to be numerically unstable. In this paper, a combinatorial stitching strategy is proposed where tessellated open cylinders of arbitrary radii are stitched together using topological operations. The convex hull construction is handled through a simple and robust projection method, avoiding expensive exact-arithmetic calculations and improving the computational efficiency. This is demonstrated through several examples involving millions of triangles. On a typical eight-core desktop, the proposed algorithm can construct approximately up to a million cylinders per second.
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- Award ID(s):
- 1715970
- NSF-PAR ID:
- 10123706
- Date Published:
- Journal Name:
- Journal of Mechanical Design
- Volume:
- 142
- Issue:
- 4
- ISSN:
- 1050-0472
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4044521
