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1. Leveraging Design Heuristics for Multi-Objective Metamaterial Design Optimization

   Kumar, Roshan S; Srivasta, Srikar; Silberstein, Meredith N; Selva, Daniel (July 2021, IDETC/CIE2021)

   null (Ed.)

   Design optimization of metamaterials and other complex systems often relies on the use of computationally expensive models. This makes it challenging to use global multi-objective optimization approaches that require many function evaluations. Engineers often have heuristics or rules of thumb with potential to drastically reduce the number of function evaluations needed to achieve good convergence. Recent research has demonstrated that these design heuristics can be used explicitly in design optimization, indeed leading to accelerated convergence. However, these approaches have only been demonstrated on specific problems, the performance of different methods was diverse, and despite all heuristics being correct'', some heuristics were found to perform much better than others for various problems. In this paper, we describe a case study in design heuristics for a simple class of 2D constrained multiobjective optimization problems involving lattice-based metamaterial design. Design heuristics are strategically incorporated into the design search and the heuristics-enabled optimization framework is compared with the standard optimization framework not using the heuristics. Results indicate that leveraging design heuristics for design optimization can help in reaching the optimal designs faster. We also identify some guidelines to help designers choose design heuristics and methods to incorporate them for a given problem at hand. 

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2. Identifying and Leveraging Promising Design Heuristics for Multi-Objective Combinatorial Design Optimization

   https://doi.org/10.1115/1.4063238  

   Suresh Kumar, Roshan; Srivatsa, Srikar; Baker, Emilie; Silberstein, Meredith; Selva, Daniel (December 2023, Journal of Mechanical Design)

   Abstract Design heuristics are traditionally used as qualitative principles to guide the design process, but they have also been used to improve the efficiency of design optimization. Using design heuristics as soft constraints or search operators has been shown for some problems to reduce the number of function evaluations needed to achieve a certain level of convergence. However, in other cases, enforcing heuristics can reduce diversity and slow down convergence. This paper studies the question of when and how a given set of design heuristics represented in different forms (soft constraints, repair operators, and biased sampling) can be utilized in an automated way to improve efficiency for a given design problem. An approach is presented for identifying promising heuristics for a given problem by estimating the overall impact of a heuristic based on an exploratory screening study. Two impact indices are formulated: weighted influence index and hypervolume difference index. Using this approach, the promising heuristics for four design problems are identified and the efficacy of selectively enforcing only these promising heuristics over both enforcement of all available heuristics and not enforcing any heuristics is benchmarked. In all problems, it is found that enforcing only the promising heuristics as repair operators enables finding good designs faster than by enforcing all available heuristics or not enforcing any heuristics. Enforcing heuristics as soft constraints or biased sampling functions results in improvements in efficiency for some of the problems. Based on these results, guidelines for designers to leverage heuristics effectively in design optimization are presented. 

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3. Contact-Aware Controller Design for Complementarity Systems

   https://doi.org/10.1109/ICRA40945.2020.9197568  

   Aydinoglu, Alp; Preciado, Victor M.; Posa, Michael (May 2020, 2020 IEEE International Conference on Robotics and Automation (ICRA))

   While many robotic tasks, like manipulation and locomotion, are fundamentally based in making and breaking contact with the environment, state-of-the-art control policies struggle to deal with the hybrid nature of multi-contact motion. Such controllers often rely heavily upon heuristics or, due to the combinatoric structure in the dynamics, are unsuitable for real-time control. Principled deployment of tactile sensors offers a promising mechanism for stable and robust control, but modern approaches often use this data in an ad hoc manner, for instance to guide guarded moves. In this work, by exploiting the complementarity structure of contact dynamics, we propose a control framework which can close the loop on rich, tactile sensors. Critically, this framework is non-combinatoric, enabling optimization algorithms to automatically synthesize provably stable control policies. We demonstrate this approach on three different underactuated, multi-contact robotics problems. 

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4. Bayesian Network Structure Optimization for Improved Design Space Mapping for Design Exploration With Materials Design Applications

   https://doi.org/10.1115/DETC2017-67643  

   Sharpe, Conner; Morris, Clinton; Goldsberry, Benjamin; Seepersad, Carolyn Conner; Haberman, Michael R. (August 2017, Proceedings of the ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference)

   Modern design problems present both opportunities and challenges, including multifunctionality, high dimensionality, highly nonlinear multimodal responses, and multiple levels or scales. These factors are particularly important in materials design problems and make it difficult for traditional optimization algorithms to search the space effectively, and designer intuition is often insufficient in problems of this complexity. Efficient machine learning algorithms can map complex design spaces to help designers quickly identify promising regions of the design space. In particular, Bayesian network classifiers (BNCs) have been demonstrated as effective tools for top-down design of complex multilevel problems. The most common instantiations of BNCs assume that all design variables are independent. This assumption reduces computational cost, but can limit accuracy especially in engineering problems with interacting factors. The ability to learn representative network structures from data could provide accurate maps of the design space with limited computational expense. Population-based stochastic optimization techniques such as genetic algorithms (GAs) are ideal for optimizing networks because they accommodate discrete, combinatorial, and multimodal problems. Our approach utilizes GAs to identify optimal networks based on limited training sets so that future test points can be classified as accurately and efficiently as possible. This method is first tested on a common machine learning data set, and then demonstrated on a sample design problem of a composite material subjected to a planar sound wave. 

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5. Fast Inverse Design of 3D Nanophotonic Devices Using Boundary Integral Methods

   https://doi.org/10.1021/acsphotonics.2c01072  

   Garza, Emmanuel; Sideris, Constantine (October 2022, ACS Photonics)

   Recent developments in the computational automated design of electromagnetic devices, otherwise known as inverse design, have significantly enhanced the design process for nanophotonic systems. Inverse design can both reduce design time considerably and lead to high-performance, nonintuitive structures that would otherwise have been impossible to develop manually. Despite the successes enjoyed by structure optimization techniques, most approaches leverage electromagnetic solvers that require significant computational resources and suffer from slow convergence and numerical dispersion. Recently, a fast simulation and boundary-based inverse design approach based on boundary integral equations was demonstrated for two-dimensional nanophotonic problems. In this work, we introduce a new full-wave three-dimensional simulation and boundary-based optimization framework for nanophotonic devices also based on boundary integral methods, which achieves high accuracy even at coarse mesh discretizations while only requiring modest computational resources. The approach has been further accelerated by leveraging GPU computing, a sparse block-diagonal preconditioning strategy, and a matrix-free implementation of the discrete adjoint method. As a demonstration, we optimize three different devices: a 1:2 1550 nm power splitter and two nonadiabatic mode-preserving waveguide tapers. To the best of our knowledge, the tapers, which span 40 wavelengths in the silicon material, are the largest silicon photonic waveguiding devices to have been optimized using full-wave 3D solution of Maxwell’s equations. 

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