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Abstract A problem is a situation in which an agent seeks to attain a given goal without knowing how to achieve it. Human problem solving is typically studied as a search in a problem space composed of states (information about the environment) and operators (to move between states). A problem such as playing a game of chess haspossible states, and a traveling salesperson problem with as little as 82 cities already has more thandifferent tours (similar to chess). Biological neurons are slower than the digital switches in computers. An exhaustive search of the problem space exceeds the capacity of current computers for most interesting problems, and it is fairly clear that humans cannot in their lifetime exhaustively search even small fractions of these problem spaces. Yet, humans play chess and solve logistical problems of similar complexity on a daily basis. Even for simple problems humans do not typically engage in exploring even a small fraction of the problem space. This begs the question: How do humans solve problems on a daily basis in a fast and efficient way? Recent work suggests that humans build a problem representation and solve the represented problem—not the problem that is out there. The problem representation that is built and the process used to solve it are constrained by limits of cognitive capacity and a cost–benefit analysis discounting effort and reward. In this article, we argue that better understanding the way humans represent and solve problems using heuristics can help inform how simpler algorithms and representations can be used in artificial intelligence to lower computational complexity, reduce computation time, and facilitate real‐time computation in complex problem solving. 

Abstract Heuristics are essential for addressing the complexities of engineering design processes. The goodness of heuristics is context-dependent. Appropriately tailored heuristics can enable designers to find good solutions efficiently, and inappropriate heuristics can result in cognitive biases and inferior design outcomes. While there have been several efforts at understanding which heuristics are used by designers, there is a lack of normative understanding about when different heuristics are suitable. Towards addressing this gap, this paper presents a reinforcement learning-based approach to evaluate the goodness of heuristics for three sub-problems commonly faced by designers: (1) learning the map between the design space and the performance space, (2) acquiring sequential information, and (3) stopping the information acquisition process. Using a multi-armed bandit formulation and simulation studies, we learn the suitable heuristics for these individual sub-problems under different resource constraints and problem complexities. Additionally, we learn the optimal heuristics for the combined problem (i.e., the one composing all three sub-problems), and we compare them to ones learned at the sub-problem level. The results of our simulation study indicate that the proposed reinforcement learning-based approach can be effective for determining the quality of heuristics for different problems, and how the effectiveness of the heuristics changes as a function of the designer’s preference (e.g., performance versus cost), the complexity of the problem, and the resources available. 

Abstract Extracting an individual’s knowledge structure is a challenging task as it requires formalization of many concepts and their interrelationships. While there has been significant research on how to represent knowledge to support computational design tasks, there is limited understanding of the knowledge structures of human designers. This understanding is necessary for comprehension of cognitive tasks such as decision making and reasoning, and for improving educational programs. In this paper, we focus on quantifying theory-based causal knowledge, which is a specific type of knowledge held by human designers. We develop a probabilistic graph-based model for representing individuals’ concept-specific causal knowledge for a given theory. We propose a methodology based on probabilistic directed acyclic graphs (DAGs) that uses logistic likelihood function for calculating the probability of a correct response. The approach involves a set of questions for gathering responses from 205 engineering students, and a hierarchical Bayesian approach for inferring individuals’ DAGs from the observed responses. We compare the proposed model to a baseline three-parameter logistic (3PL) model from the item response theory. The results suggest that the graph-based logistic model can estimate individual students’ knowledge graphs. Comparisons with the 3PL model indicate that knowledge assessment is more accurate when quantifying knowledge at the level of causal relations than quantifying it using a scalar ability parameter. The proposed model allows identification of parts of the curriculum that a student struggles with and parts they have already mastered which is essential for remediation. 

Abstract In this study, we focus on crowdsourcing contests for engineering design problems where contestants search for design alternatives. Our stakeholder is a designer of such a contest who requires support to make decisions, such as whether to share opponent-specific information with the contestants. There is a significant gap in our understanding of how sharing opponent-specific information influences a contestant’s information acquisition decision such as whether to stop searching for design alternatives. Such decisions in turn affect the outcomes of a design contest. To address this gap, the objective of this study is to investigate how participants’ decision to stop searching for a design solution is influenced by the knowledge about their opponent’s past performance. The objective is achieved by conducting a protocol study where participants are interviewed at the end of a behavioral experiment. In the experiment, participants compete against opponents with strong (or poor) performance records. We find that individuals make decisions to stop acquiring information based on various thresholds such as a target design quality, the number of resources they want to spend, and the amount of design objective improvement they seek in sequential search. The threshold values for such stopping criteria are influenced by the contestant’s perception about the competitiveness of their opponent. Such insights can enable contest designers to make decisions about sharing opponent-specific information with participants, such as the resources utilized by the opponent towards purposefully improving the outcomes of an engineering design contest. 

Abstract Designers make information acquisition decisions, such as where to search and when to stop the search. Such decisions are typically made sequentially, such that at every search step designers gain information by learning about the design space. However, when designers begin acquiring information, their decisions are primarily based on their prior knowledge. Prior knowledge influences the initial set of assumptions that designers use to learn about the design space. These assumptions are collectively termed as inductive biases. Identifying such biases can help us better understand how designers use their prior knowledge to solve problems in the light of uncertainty. Thus, in this study, we identify inductive biases in humans in sequential information acquisition tasks. To do so, we analyze experimental data from a set of behavioral experiments conducted in the past [1–5]. All of these experiments were designed to study various factors that influence sequential information acquisition behaviors. Across these studies, we identify similar decision making behaviors in the participants in their very first decision to “choose x”. We find that their choices of “x” are not uniformly distributed in the design space. Since such experiments are abstractions of real design scenarios, it implies that further contextualization of such experiments would only increase the influence of these biases. Thus, we highlight the need to study the influence of such biases to better understand designer behaviors. We conclude that in the context of Bayesian modeling of designers’ behaviors, utilizing the identified inductive biases would enable us to better model designer’s priors for design search contexts as compared to using non-informative priors. 

Abstract The objective of this study is to investigate students’ decision-making during the information gathering activities of a design process. Existing literature in engineering education has shown that students face difficulties while gathering information in various activities of a design process such as brainstorming and CAD modeling. Decision-making is an important aspect of these activities. While gathering information, students make several decisions such as what information to acquire and how to acquire that information. There lies a research gap in understanding how students make decisions while gathering information in a product design process. To address this gap, we conduct semi-structured interviews and surveys in a product design course. We analyze the students’ decision-making activities from the lens of a sequential information acquisition and decision-making (SIADM) framework. We find that the students recognize the need to acquire information about the physics and dynamics of their design artifact during the CAD modeling activity of the product design process. However, they do not acquire such information from their CAD models primarily due to the lack of the project requirements, their ability, and the time to do so. Instead, they acquire such information from the prototyping activity as their physical prototype does not satisfy their design objectives. However, the students do not get the opportunity to iterate their prototype with the given cost and time constraints. Consequently, they rely on improvising during prototyping. Based on our observations, we discuss the need for designing course project activities such that it facilitates students’ product design decisions. 

Abstract Similarity assessment is a cognitive activity that pervades engineering design practice, research, and education. There has been a significant effort in understanding similarity in cognitive science, and some recent efforts on quantifying the similarity of design problems in the engineering design community. However, there is a lack of approaches for measuring similarity in engineering design that embody the characteristics identified in cognitive science, and accounts for the nature of design activities, particularly in the embodiment design phase where scientific knowledge plays a significant role. To address this gap, we present an approach for measuring the similarity among design problems. The approach consists of (i) modeling knowledge using probabilistic graphical models, (ii) modeling the functional mapping between design characteristics and the performance measures relevant in a particular context, and (iii) modeling the dissimilarity using KL-divergence in the performance space. We illustrate the approach using an example of a parametric shaft design for fatigue, which is typically a part of mechanical engineering design curricula, and test the validity of the approach using an experiment study involving 167 student subjects. The results indicate that the proposed approach can capture the well-documented characteristics of similarity, including directionality, context dependence, individual-specificity, and its dynamic nature. The approach is general enough that it can be extended further for assessing the similarity of design problems for analogical design, for assessing the similarity of experimental design tasks to real design settings, and for evaluating the similarity between design problems in educational settings. 

Abstract Existing literature on information sharing in contests has established that sharing contest-specific information influences contestant behaviors, and thereby, the outcomes of a contest. However, in the context of engineering design contests, there is a gap in knowledge about how contest-specific information such as competitors’ historical performance influences designers’ actions and the resulting design outcomes. To address this gap, the objective of this study is to quantify the influence of information about competitors’ past performance on designers’ belief about the outcomes of a contest, which influences their design decisions, and the resulting design outcomes. We focus on a single-stage design competition where an objective figure of merit is available to the contestants for assessing the performance of their design. Our approach includes (i) developing a behavioral model of sequential decision making that accounts for information about competitors’ historical performance and (ii) using the model in conjunction with a human-subject experiment where participants make design decisions given controlled strong or weak performance records of past competitors. Our results indicate that participants spend greater efforts when they know that the contest history reflects that past competitors had a strong performance record than when it reflects a weak performance record. Moreover, we quantify cognitive underpinnings of such informational influence via our model parameters. Based on the parametric inferences about participants’ cognition, we suggest that contest designers are better off not providing historical performance records if past contest outcomes do not match their expectations setup for a given design contest. 

Abstract Extracting an individual's scientific knowledge is essential for improving educational assessment and understanding cognitive tasks in engineering activities such as reasoning and decision making. However, knowledge extraction is an almost impossible endeavor if the domain of knowledge and the available observational data are unrestricted. The objective of this paper is to quantify individuals' theory-based causal knowledge from their responses to given questions. Our approach uses directed acyclic graphs (DAGs) to represent causal knowledge for a given theory and a graph-based logistic model that maps individuals' question-specific subgraphs to question responses. We follow a hierarchical Bayesian approach to estimate individuals' DAGs from observations.The method is illustrated using 205 engineering students' responses to questions on fatigue analysis in mechanical parts. In our results, we demonstrate how the developed methodology provides estimates of population-level DAG and DAGs for individual students. This dual representation is essential for remediation since it allows us to identify parts of a theory that a population or individual struggles with and parts they have already mastered. An addendum of the method is that it enables predictions about individuals' responses to new questions based on the inferred individual-specific DAGs. The latter has implications for the descriptive modeling of human problem-solving, a critical ingredient in sociotechnical systems modeling.