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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. 

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. 

Abstract The crowdsourcing literature has shown that domain experts are not always the best solvers for complex system design problems. Under certain conditions, novices and specialists in adjacent domains can provide novel solutions at lower costs. Additionally, the best types of solvers for different problems are dependent on the architecture of complex systems. The joint consideration of solver assignment and system decomposition, referred to as solver-aware system architecting (SASA), expands traditional system architecting practices by considering solver characteristics and contractual incentive mechanisms in the design process and aims to improve complex system design and innovation by leveraging the strengths of domain experts, crowds, and specialists for different parts of the problem. The joint consideration of problem decomposition and solver assignment decisions in SASA renders the design space exponentially more complex. Therefore, new computationally efficient and mathematically rigorous methods are needed to explore this high-dimensional space and extract reliable heuristics. To address this need, this paper presents a computational approach using a Markov decision process (MDP) formulation, Q-learning, and Gaussian mixture models. Together, these techniques explore the large space of possible solver–module assignments by modeling the sequential nature of solver assignment decisions, capturing these temporal dependencies, thereby enabling optimization for long-term expected rewards, and analyzing reward distributions. The approach identifies heuristics for solver assignment based on the designer’s preference for cost-performance trade-off through the parameterized reward function. The approach is demonstrated using a simple and idealized golf problem, which has characteristics similar to design problems, including how the problem is decomposed into interdependent modules and can be solved by different solvers with different strengths that interact with the module type. The results show that the proposed approach effectively elicits a rich set of heuristics applicable in various contexts for the golf problem and can be extended to more complex systems design problems.