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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. Extracting Design Process Heuristics: A Systematic Computational Approach

   https://doi.org/10.1115/DETC2025-168784  

   Gadi, Vikranth S; Szajnfarber, Zoe; Panchal, Jitesh H (August 2025, American Society of Mechanical Engineers)

   Abstract Engineering design relies heavily on heuristics, yet there is a lack of systematic methods for identifying and validating design heuristics. This paper introduces a computational approach to representing engineering design problems that involve decomposition and assignment decisions, facilitating systematic extraction of generalizable heuristics. We model design processes using a Markov Decision Process (MDP) framework, characterizing problems through attributes of the problem space, solver capabilities, and trade-offs embedded within preference functions. Reinforcement learning methods are employed to learn optimal policies, from which we extract inclusionary and exclusionary heuristics using Gaussian Mixture Models. The effectiveness of the approach is demonstrated through two case studies: solver-aware system architecting (SASA) for a robotic arm design and sequential information acquisition in parametric design optimization. The results highlight the context-dependent nature of learned heuristics, demonstrating how problem complexity, designer preferences, and solver characteristics influence their selection. 

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4. Developing Heuristics for Resource Allocation and Utilization in Systems Design: A Hierarchical Reinforcement Learning Approach

   https://doi.org/10.1115/1.4068449  

   Gadi, Vikranth S; Szajnfarber, Zoe; Panchal, Jitesh H (June 2025, Journal of Mechanical Design)

   Abstract Systems design involves decomposing a system into interconnected subsystems and allocating resources to teams responsible for designing each subsystem. The outcomes of the process depend on how well limited resources are allocated to different teams, and the strategy each team uses to design the subsystems. This article presents an approach based on hierarchical reinforcement learning (RL) to generate heuristics for solving complex design problems under resource constraints. The approach consists of formulating systems design problems as hierarchical multiarmed bandit (MAB) problems, where decisions are made at both the system level (allocating budget across subsystems) and the subsystem level (selecting heuristics for sequential information acquisition). The approach is demonstrated using an illustrative example of a race car optimization in The Open Racing Car Simulator (TORCS) environment. The results indicate that the RL agent can learn to allocate resources strategically, prioritize the subsystems with the greatest influence on overall performance, and identify effective information acquisition heuristics for each subsystem. For example, the RL agent learned to allocate a larger portion of the budget to the gearbox subsystem, which has a higher-dimensional design space compared to other subsystems. The results also indicate that the extracted heuristics lead to convergence to high-performing car configurations with greater efficiency when compared to using Bayesian optimization for design. 

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5. 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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