Neural heuristics for mixed-integer configuration optimization
Keywords: Engineering.
Aeronautics and Astronautics.

In design and optimization, engineers commonly rely on computational tools to assist in determining and specifying the necessary features and parameters that comprise the solution to the design problem. In general, however, certain predicate assumptions are made outside the scope of the formal design process. Configuration selection - determining major, non-parameterized design features - is frequently and significantly often accomplished by brainstorming or eschewed altogether in favor of simply updating a pre-existing configuration with new features that fit inside its pre-established envelope. For example, a new generation of an airplane or an automobile may incorporate a new engine. Still, the placement of that engine under the wing as opposed to over it or within the engine bay ahead of the passenger compartment as opposed to behind it are configuration choices that are unlikely to be re-considered in most design problems. Like engine placement, fuel type, or structural material selection, configuration choices are those whose implications are far-reaching in the design of other system elements. Changing any of them results in a need to fully re-assess the performance of a proposed solution using different analysis methods. The multiplicity of possible solutions to design problems often outstrips designers' ability to assess the performance of different possible configurations comprehensively. As such, informal brainstorming or updating from prior design points serve as "heuristics" for searching the design space. They produce viable answers but do not follow formally specified rules that can be analyzed and improved upon. Several formal methods or algorithms for configuration design are extant in the literature - notably evolutionary optimizers, simulated annealing methods, and conventional mixed-integer optimizers. These approaches either rely on designer foreknowledge of the structure and trade-offs within the design space or provide little to provide an understanding of such structure and trade-offs in the way the informal methods do. This work develops several advancements that enable the application of artificial intelligence to the problem of engineering design. In particular, it develops the theory and methods necessary to deploy generative neural networks as optimization heuristics in an architecture labeled GEMINI for "Generative Evolutionary Mixed-Integer Network Interpreter." GEMINI can provide both recommendations for solutions to the design problems and, as a result of its training procedure, a structured distribution over all possible designs indicating their likely performance. This work covers several theoretical points behind both configuration optimization and artificial intelligence via machine learning: Conceptual-level design problems germane to aerospace applications are covered in detail, and an approach is developed to formalize the relationship between possible configurations of design solutions and mixed-integer optimization problems. Artificial intelligence is approached as a matter of epistemology, formalized via probability theory and actualized by a paradigm of Data, Model, and Loss to reflect the actual machinery involved and how it is variously applied across fields of engineering and science. Shortcomings in state-of-the-art methods in both configuration design and artificial intelligence are identified. These include the difficulty of obtaining enough valuable data about design spaces to enable the use of artificial intelligence, the lack of a coherent probabilistic interpretation of configuration design problems, and limits to global optimizers' ability to generalize across the many possible solutions to a design problem. To address these, this work presents distinct contributions: High-performance computing applications of hardware acceleration, modern automatic differentiation, and functionalization of conceptual design analyses that can reduce the time necessary for the evaluation by several orders of magnitude. An adaptation of cladistic methods for phylogeny to establish an interpretable, invertible, parsimonious correspondence between configuration design and mixed-integer optimization. An architecture for developing a probabilistic distribution over all possible configurations for a system and incorporating that knowledge into evolutionary optimization processes to accelerate their progress.