In modular design, one of the most important roles of designers is to select appropriate combination of the functional parts. To support part selection, this paper proposes hu - man-computer interaction system. We firstly propose a classifier to estimate the functional relationship between the design requirement and the modularized functional parts based on data of parts usage in actual products. Simulations revealed the effectiveness of the pro - posed classifier. As another proposal, we also propose the parts recommendation system to suggest good combination of the parts to designers in order to find less cost combination of the parts within limited time. Simulations revealed the effectiveness of the proposed algorithm. Introduction Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat. Duis autem vel eum iriure dolor in hendrerit in vulputate velit esse molestie consequat, vel illum dolore eu feugiat nulla facilisis at vero eros et accumsan et iusto odio dignissim qui blandit prae - sent luptatum zzril delenit augue duis dolore te feugait nulla facilisi. Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat. Duis autem vel eum iriure dolor in hendrerit in vul - putate velit esse molestie consequat, vel illum dolore eu feugiat nulla facilisis at vero eros et accumsan et iusto odio dignissim qui blandit praesent luptatum zzril delenit augue duis dolore te feugait nulla facilisi. Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat. Duis autem vel eum iriure dolor in hendrerit in vulputate velit esse molestie consequat, vel illum dolore eu feugiat nulla facilisis at vero eros et accumsan et iusto odio dignissim qui blandit praesent luptatum zzril delenit augue duis dolore te feugait nulla facilisi. Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat. Submitted 4 November 2014 Accepted 30 November 2014 Published 13 January 2015 Corresponding author Kamen P. Simeonov kamen.simeonov@gmail.com Published by Cambridge University Press under the Creative Commons Attribution licence (http://creativecommons.org/ licenses/by/3.0/ ) © The Author(s) 13 January 2015 Des. Sci. journals.cambridge.org/dsj DOI 10.1234/abcdef 1/7 Human–computer interaction for part selection in product design Kamen P . Simeonov 1,3 and Daniel S. Himmelstein 2,3 1 Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA 2 Biological & Medical Informatics, University of California, San Francisco, CA, USA 3 Department of Mechanical Science and Engineering, Graduate School of Engineering, Nagoya University Abstract In modular design, one of the most important roles of designers is to select appropriate combination of the functional parts. To support part selection, this paper proposes hu - man-computer interaction system. We firstly propose a classifier to estimate the functional relationship between the design requirement and the modularized functional parts based on data of parts usage in actual products. Simulations revealed the effectiveness of the pro - posed classifier. As another proposal, we also propose the parts recommendation system to suggest good combination of the parts to designers in order to find less cost combination of the parts within limited time. Simulations revealed the effectiveness of the proposed algorithm. Introduction Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat. Duis autem vel eum iriure dolor in hendrerit in vulputate velit esse molestie consequat, vel illum dolore eu feugiat nulla facilisis at vero eros et accumsan et iusto odio dignissim qui blandit prae - sent luptatum zzril delenit augue duis dolore te feugait nulla facilisi. Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat. Duis autem vel eum iriure dolor in hendrerit in vul - putate velit esse molestie consequat, vel illum dolore eu feugiat nulla facilisis at vero eros et accumsan et iusto odio dignissim qui blandit praesent luptatum zzril delenit augue duis dolore te feugait nulla facilisi. Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat. Duis autem vel eum iriure dolor in hendrerit in vulputate velit esse molestie consequat, vel illum dolore eu feugiat nulla facilisis at vero eros et accumsan et iusto odio dignissim qui blandit praesent luptatum zzril delenit augue duis dolore te feugait nulla facilisi. Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat. Submitted 4 November 2014 Accepted 30 November 2014 Published 13 January 2015 Corresponding author Kamen P. Simeonov kamen.simeonov@gmail.com Published by Cambridge University Press under the Creative Commons Attribution licence (http://creativecommons.org/ licenses/by/3.0/ ) © The Author(s) 13 January 2015 Des. Sci. journals.cambridge.org/dsj DOI 10.1234/abcdef Design Science KABOOM: An Agent-Based Model for Simulating Cognitive Style in Team Problem Solving Samuel Lapp1, Kathryn Jablokow2, and Christopher McComb1 1College of Engineering, The Pennsylvania State University, University Park, PA, USA 2Penn State Great Valley, Malvern, PA, USA Abstract The performance of a design team is inﬂuenced by each team member’s unique cognitive style - i.e., their preferred manner of managing structure as they solve problems, make decisions, and seek to bring about change. Cognitive style plays an important role in how teams of engineers design and collaborate, but the interactions of cognitive style with team organization and processes have not been well studied. The limitations of small- scale behavioral experiments have led researchers to develop computational models for simulating teamwork; however, none have modeled the e ects of individuals’ cognitive styles. This paper presents KABOOM (KAI Agent-Based Organizational Optimization Model), the ﬁrst agent-based model of teamwork to incorporate cognitive style. In KABOOM, heterogeneous agents imitate the diverse problem-solving styles described by Kirton’s Adaption-Innovation construct, which places each individual somewhere along the spectrum of cognitive style preference. Using the model, we investigate the interacting e ects of a team’s communication patterns, specialization, and cognitive style composition on design performance. By simulating cognitive style in the context of team problem solving, KABOOM lays the groundwork for the development of team simulations that reﬂect humans’ diverse problem-solving styles. Introduction Current design research frequently draws conclusions based on small scale behavioral experiments. Though valuable, these studies are severely limited in scope, and the results are di cult to generalize. The future of design cognition analysis will increasingly need to leverage computational methods for modeling and analyzing both individual and team behavior to enable larger scale studies. In addition, design cognition research must continue its trend toward more rigorous modeling of individual cognitive di erences among designers to support more accurate simulations; cognitive style, or one’s preference for managing structure in solving problems, is one key example. In general, cognitive style describes patterns in problem-solving behavior and social interactions that result from an individual’s unique cognitive processes. For example, one measure of cognitive style di erentiates verbal and visual learners [Riding, 1997], while another distinguishes more adaptive and more innovative thinkers [Kirton, 2003]. Cognitive style varies widely across engineers and designers, and di erences in cognitive style can have positive or negative e ects on the problem-solving performance of an individual or team [Kirton, 2003, Jablokow, 2008, Jablokow et al., 2015a, Sonalkar et al., 2017]. While researchers are beginning to develop simulation approaches for studying team problem solving, current methods do 1/34 Design Science not yet attempt to model the inﬂuence of cognitive style on individual and team activities. To address this gap, we present in this paper an agent-based model for assessing how individuals’ cognitive styles impact an engineering team’s problem-solving performance, thereby linking cognition, behavior, and design activity. Cognitive style is assessed using psychometric instruments such as the Kirton Adaption-Innovation (KAI) inventory [Kirton, 1976]. While there are many ways to measure cognitive di erences between people, KAI has been broadly studied and shown to have wide-reaching e ects on problem solving behavior [Kirton, 2003, 1976, Sonalkar et al., 2017, Jablokow and Booth, 2006, Jablokow et al., 2015b,a]. Therefore, although it is only one construct for explaining cognitive di erences, KAI o ers great potential for this vein of research. The KAI inventory measures an individual’s relative preference for structure along a bipolar continuum between two equally valued extremes (highly adaptive and highly innovative, respectively). More adaptive individuals prefer more structure in their problem solving (with more of it consensually agreed) and therefore tend to make incremental improvements within the current system to improve and enhance it. In contrast, more innovative individuals prefer less structure, with less concern about consensus, and tend to make radical changes that may ignore rules in an attempt to make the current system work “di erently”; their e orts may or may not lead to improvements in that system. Kirton’s A-I cognitive style inﬂuences both individual problem-solving characteristics and team interactions, and its e ects have been studied in observations of engineering teams [Sonalkar et al., 2017, Jablokow and Booth, 2006, Jablokow et al., 2015b,a]. However, it is unclear how cognitive style as measured by KAI could be used to inform the formation of engineering teams. In fast moving projects, team formation is a critical task that managers must perform using their best guesses about optimal team composition and structure [Levitt, 2012]. As engineering teams become more interdisciplinary and develop increasingly complex structures, selecting the right members for a team is becoming more di cult as well [Crowder et al., 2012]. However, research on optimal team formation strategies is limited. Research on collaboration in team performance is often based on qualitative descriptions and small studies [Bergner et al., 2016]. In vivo studies of design teams over long periods of time are expensive, and the results are often applicable only in a speciﬁc context [Perisic et al., 2016]. In light of these issues, agent-based models of team problem solving can serve as a powerful tool for design cognition analysis, because they can quickly compare many di erent team compositions, structures, and processes [Crowder et al., 2012]. Also, simulation can be useful for isolating independent variables in studies of cognition or social interaction [Singh et al., 2013, e.g.], which is dicult in a human subjects study. Current methods in design cognition analysis can simulate team problem solving involving agent communication [Fan and Yen, 2004, Perisic et al., 2016, e.g.], sometimes with learning mechanisms [Hulse et al., 2017, McComb et al., 2015, e.g.] and social interaction [Tsvetovat and Carley, 2004, Singh et al., 2013], and for some real-world design problems [Zurita et al., 2017, Levitt, 2012, e.g.]. However, none of these methods address the role of cognitive style in problem solving and team performance explicitly. This paper presents the KAI Agent-Based Organizational Optimization 2/34 Design Science Model (KABOOM), the ﬁrst agent-based modeling framework for studying the problem-solving performance of teams of individuals with diverse cognitive styles. In KABOOM, individual agents exploring a solution space in order to maximize an objective are used to model human problem solving. Each agent has a unique cognitive style to reﬂect the range of styles measured by the Kirton Adaption-Innovation inventory (KAI). An agent’s cognitive style inﬂuences its exploration and evaluation of the solution space. The interaction and collaboration between agents also depends on the agents’ respective cognitive styles. The goals of this research are: (1) to construct an agent-based model with agents that reﬂect the diverse cognitive styles of humans across the Adaption-Innovation spectrum; (2) using the model, analyze the performance of individual agents and teams solving a design problem; and (3) investigate how cognitive style impacts the e ects of team specialization and communication on performance. As with any model, the assumptions made here limit the extent to which the model reﬂects real-world scenarios. Rather than predicting a speciﬁc team’s performance on a real-world problem, the end goal of this model is to investigate and understand the relationships between cognitive style and various aspects of team process (such as communication) and structure (such as specialization). Two outcomes of this research are: (1) hypotheses about cognitive style that can be investigated in human subjects studies; and (2) heuristics related to cognitive style and team work that can support e ective team management. After reviewing related work in Adaption-Innovation theory and agent-based modeling, this paper describes the development of KABOOM and discusses the results of several computational experiments on team specialization, communication, and cognitive style composition. Background The Kirton Adaption-Innovation inventory The Kirton Adaption-Innovation inventory (KAI) is a psychometric instrument designed to measure a person’s cognitive style on a continuous spectrum that ranges from “highly adaptive” to “highly innovative” [Kirton, 2003]. In general terms, more adaptive problem solvers aim to do things better by using incremental changes to continuously improve a system or solution. In contrast, more innovative problem solvers prefer to do things di erently, pursuing radically di erent solutions with more regard for originality than quality. Innovators tend to challenge the existing structures and constraints of a problem, while adaptors tend to support and stay within preexisting structures and bounds. No cognitive style is universally better than another. However, one cognitive style is sometimes advantageous over others for a speciﬁc design problem. For example, problems that require adherence to a given structure, meticulous attention to detail, and conformance to speciﬁc rules or standards (e.g., repairing an antique grandfather clock, tuning a nuclear reactor) will tend to favor a more adaptive approach, although more innovative methods will still yield some kind of solution. In contrast, problems that require spanning multiple disciplines, taking a systems view, and challenging current practice (e.g., creating a disruptive product, “breaking” a patent) will tend to favor a more innovative approach, although more adaptive methods will still lead to some kind of progress. The KAI has 32 items, each answered on a 5-point scale [Kirton, 1976]. 3/34 Design Science In addition to an overall KAI score, the instrument provides three sub-scores: Suciency of Originality (SO), E ciency (E), and Rule /Group Conformity (RG) [Kirton, 1976] that are related to di erent aspects of cognitive style. The Su ciency of Originality sub-score relates to the quantity and paradigm- relatedness of the solutions a person generates. More adaptive individuals tend to generate fewer ideas (based on cognitive preference, not ability); these ideas tend to be paradigm-preserving and are easier to integrate into existing systems. More innovative individuals tend to generate a higher number of solutions (again, based on preference, not capacity); these ideas tend to be more paradigm-breaking and can be di cult or even harmful to integrate into the existing system [Kirton, 1976]. The E ciency sub-score describes an individual’s attention to detail and methodological approach. More adaptive individuals prefer incremental changes to a solution that are sure to improve quality. In contrast, more innovative individuals may alter a solution in riskier, less well-deﬁned ways, with less regard for the resulting quality [Kirton, 1976]. The Rule /Group Conformity sub- score describes an individual’s preference for adhering to constraints and norms, as well as their cohesion with a group (i.e., social structure). More adaptive individuals prefer to leverage the prevailing rules, guidelines, and norms in their problem solving; they also tend to promote group cohesion and continuity. More innovative individuals, however, are more likely to disregard the prevailing rules and norms, and are less concerned about conforming to a group; they may actively move away from group consensus and can cause disruption or discord in a team [Kirton, 1976]. The methods section describes how each of these sub- factors of KAI inform the development of agents that have their own cognitive styles. Cognitive style diversity and design teams When individuals work together, their diverse cognitive characteristics can inﬂu- ence their collaborations in both positive and negative ways. Kirton uses the term cognitive gap to describe di erences in cognitive level (intelligence, experience, knowledge, etc.) and /or cognitive style that can appear between two individuals, an individual and a group, two groups, or between an individual /group and the problem at hand [Kirton, 2003, Jablokow and Booth, 2006]. In previous work related to KAI and teams, Kurtzberg Kurtzberg [2005] studied the creative ﬂuency of homogeneous teams and heterogeneous teams (as categorized by KAI cognitive gaps) and found that heterogeneous teams outperformed homogeneous teams in terms of creative output (i.e., number of ideas). Hammerschmidt [1996] studied team success and cognitive style diversity using KAI and found that teams had higher levels of success when tasks were coordinated with KAI (e.g., a more adaptive task aligned with a more adaptive sub-team). His work also revealed that when sub-teams had similar KAI scores (i.e., were homogeneous), overall team success increased as a result of enhanced inter-team communication, while diverse (i.e., heterogeneous) teams were more likely to fail as a result of unresolved cognitive gaps. Jablokow et al. [2015a] explored the e ects of cognitive gaps on dyad performance and interactions between design team members during concept generation. Their results suggest that as the cognitive gap between team members increases, the more adaptive team member tends to feel that they contributed less to team ideation, while the more innovative team 4/34 Design Science member tends to feel that they contributed more. In other previous work by Jablokow et al. [2015a], the results suggest that the presence of more innovative individuals on a team may be correlated with a greater occurrence of unique ideas in the team, where “unique” was deﬁned as “new to the current team discussion”. They also found that more innovative teams (determined by KAI mean) tended to exhibit team interactions with a higher degree of integration between topics. Mechanisms of agent-based modeling for design teams An Agent-Based Model (sometimes called a Multi-Agent System) is a software simulation method in which autonomous, heterogeneous agents interact with their environment and other agents [Garcia, 2005]. Each agent acts with a set of behavioral rules in order to accomplish an objective [Bonabeau, 2002]. Rather than deﬁning the macroscopic behavior of a system, an agent-based model only deﬁnes behavioral rules for individual agents and a structure for agent interactions [Bonabeau, 2002, Jennings, 2000]. Agents make run-time decisions based on limited knowledge of the environment and limited decision-making capabilities [Jennings, 2000, Tsvetovat and Carley, 2004]. In addition to these cognitive constraints, agents may be socially constrained with limited ability to connect and share information with other agents [Tsvetovat and Carley, 2004]. By simulating agent interactions, an agent-based model can capture emergent phenomena that are more than the sum of the individual agents’ actions [Bonabeau, 2002]. Some studies investigate the frequency of communication among agents throughout the course of the problem-solving period. In the context of design research, communication refers to the exchange of design solutions [Singh et al., 2013]. A solution is the outcome of a design e ort, which, when communicated to a teammate, may prove either beneﬁcial or detrimental in the form of false leads, failures, or ﬂawed concepts. Research on communication in design teams shows that more communication is not necessarily better; there is a trade-o between communication frequency and individual work [Patrashkova-V olzdoska et al., 2003, Patrashkova and McComb, 2004]. Some researchers have shown that intermittent communication can provide the beneﬁts of constant communication, as well as the beneﬁts of individual work [Bernstein et al., 2018]. There are even some cases where nocommunication is the best team process strategy [McComb et al., 2017a, McComb and Maier, 2018]. Engineering teams often divide the design of complex systems into multiple components that are then addressed or solved by specialized team members with corresponding expertise in a speciﬁc domain [Hulse et al., 2017, 2018]. This multi-component approach to complex systems design is analogous to coordination between multiple agents in a computational model: decisions are made with respect to separate components and later aggregated to form a global solution [Zurita et al., 2017]. An agent-based model can reﬂect the way engineering teams solve complex systems in a distributed manner by assigning agents to specialized sub-teams that each control a subset of all design variables for a global objective function [Hulse et al., 2018]. This approach makes it possible to use an agent-based model to rapidly investigate the e ects of team structure on a design team’s performance. Appropriate team composition is critical for high team performance [Mart ´ınez- Miranda and Pav ´on, 2012] and should consider not only the personal traits of 5/34 Design Science individuals, but also the nature of the problem being addressed by the team [Zhang et al., 2009]. Team composition can have a detrimental e ect on performance and social interactions if teams are not carefully constructed and managed [Mart ´ınez-Miranda and Pav ´on, 2012]. Although this paper examines team composition in terms of the cognitive styles of agents on a team, other factors of team composition exist and have been studied both in human subjects studies and through computational modeling. According to Singh et al. [2013], a team’s composition refers to its size, life-span (one project or several), location (collocated or geographically distributed), structure (ﬂat or hierarchical), and heterogeneity (homogeneous or heterogeneous). Not surprisingly, a team’s composition in terms of domain of expertise also plays a key part in product development success [Brown and Eisenhardt, 1995]. However, there is little evidence regarding how other personal cognitive qualities like cognitive style inﬂuence a team’s success. Mart ´ınez-Miranda and Pav ´on [2012] state that although some human resource departments use tests of personality and cognitive level: It could be even more useful for project managers to apply the results of cognitive and psychological tests to build virtual teams and simulate their possible behaviors in order to analyze what could happen when people with speciﬁc characteristics interact with each other and with their respective tasks over the entire duration of a project. [Mart´ ınez-Miranda and Pav´ on, 2012] Among the large number of psychological instruments used today, many have limited validation or scientiﬁc support. The Kirton Adaption-Innovation inventory (KAI), however, has been extensively validated and is regularly used for team management [Kirton, 2003]. This research, therefore, aims to ﬁll a gap at the intersection of cognitive style and agent-based modeling by incorporating Kirton’s Adaption-Innovation cognitive style characteristics into an agent-based model of engineering teamwork. State of the art In the 1990s, managers of the semiconductor manufacturer “Micro” were faced with the challenge of developing high-performance teams for complex and concurrent projects on an extremely rapid product life cycle [Levitt, 2012]. While the performance of their semiconductor chips could be modeled with computer simulations, managers still used guess-and-check methods for the design of their teams—but they began to ask for computational tools that could simulate team performance in the same way that software simulations could predict the performance of an engineering design [Levitt, 2012]. This led to the Virtual Design Team (VDT) project [Kunz et al., 1998, Levitt, 2012], an early e ort to create simulation tools that helped managers design software teams by simulating the assignment and completion of work items. The VDT simulation divides a problem into tasks and types of work, and then uses stochastic discrete-event simulation to model the time and number of errors incurred in completing each task. VDT models real and complex projects, and includes both errors in task completion and noise in communication [Levitt, 2012]. Since then, many researchers have developed models with the aim of reﬂecting some aspect of human behavior or teamwork [Fernandes et al., 2017, 6/34 Design Science Vermillion and Malak, 2015, 2018, e.g.] more accurately. These models vary in their purpose. Some, like VDT, are team management simulation tools that model team performance to avoid the associated costs of long and expensive human subjects studies [Perisic et al., 2016, e.g.]. Other models focus on studying the social aspects of communication and collaboration [Singh et al., 2013, Tsvetovat and Carley, 2004, e.g.]. For example, Tsvetovat and Carley [2004] develops a detailed model of complex social and technological systems by including learning, social network theory, and social psychology in an agent-based model. Recent research in systems engineering by Vermillion and Malak uses agent- based approaches to investigate the delegation of authority and use of incentives in design teams [Vermillion and Malak, 2015, 2018]. Fan and Yen [2004] presents an extensive review of agent-based models addressing communication and collaboration; some of the models reviewed include emotion and sentiment [Fan and Yen, 2004]. However, the authors are not aware of any models that incorporate individual cognitive style for heterogeneous agents. Recently, several agent-based models have attempted to focus on the person- alities, attitudes, and emotions of problem solvers, as well as their knowledge [Martinez-Miranda et al., 2006, Zhang et al., 2009, Dehkordi et al., 2012, e.g.]. For example, the TEAKS framework [Martinez-Miranda et al., 2006, Mart ´ınez-Miranda and Pav ´on, 2012] models the social and emotional aspects of team problem solving. Agent interactions are based on the PECS (physics, emotion, cognition, and social status) framework [Urban and Schmidt, 2001], and personality is described by drive, inﬂuence, steadiness, and compliance. Dehkordi et al. [2012] studies work-overload impact by modeling the e ects of stress and motivation on team performance, and Zhang et al. [2009] presents a model where human behavior, development process, and organizational structure all inﬂuence design outcomes. These models focus on emotions and sentiments to elicit human-like behaviors in computational agents. Finally, some models implement contextualized, real-world design problems that are solved by teams of agents in an agent-based model [Zurita et al., 2017, McComb et al., 2015, e.g.]. Work by Zurita et al. [2017] is an example of an agent-based model speciﬁcally created for a contextualized problem: designing a Formula SAE racing vehicle. Their model demonstrates that by using a cooperative evolutionary algorithm, an agent-based model can design a complex system. Like Hulse et al. [2018], members of the design team adopt specializations by breaking the problem into separate functional subsystems (e.g., engine, suspension, and brakes). The CISAT framework [McComb et al., 2015, 2017b,a] is another agent- based model that uses contextualized problems to study how problem charac- teristics a ect the optimal team process and team characteristics. The CISAT framework reﬂects eight characteristics of both team activity and individual cognition, namely: organic interaction timing, quality-informed solution sharing, quality bias reduction, self-bias, operational learning, breadth versus depth solution search, and satisﬁcing [McComb et al., 2015]. In McComb et al. [2017a], the CISAT model is used to ﬁnd optimal team characteristics based on properties of the problem being addressed. These two models provide much of the inspiration for KABOOM. 7/34 Design Science KABOOM Framework Problem Solving Simulated Annealing optimization gradually transitions from stochastic to downhill search. stochastic search downhill search Cognitive Style Agents’ unique Adaption-Innovation styles affect their exploration of the design space. Communication Agents share solutions with eachother. Large cognitive style gaps make communication less likely to succeed. Specialization Teams specialize to solve a problem concurrently by assigning decomposed parts of the problem to sub-teams.40 160 95 KAI sub-team 1 sub-team 2part 1 part 2incrementalconformimprove change radicaldisrupt team solution!? Figure 1. Outline of the KABOOM framework and its key features Methods KABOOM is the ﬁrst agent-based model to incorporate cognitive style of heterogeneous agents as a strategy to simulate the problem-solving behaviors of human teams. This section describes: (1) the agent-based model framework for KABOOM; (2) the implementation of Kirton’s Adaption-Innovation cognitive style for agents; (3) communication in the model through pairwise solution sharing and team meetings; and (4) creating a virtual population with KAI cognitive style traits. Figure 1 provides a high-level summary of the key components of the model. The KABOOM framework The KAI Agent-Based Organizational Optimization Model (KABOOM) is a multi-agent optimization scheme in which independent software agents explore a solution space by varying parameters and evaluating a cost function. KABOOM is based on a simulated-annealing [Kirkpatrick et al., 1983] optimization algo- rithm: the agents start with a high “temperature”, allowing them to explore widespread solutions non-greedily; the temperature gradually cools over the course of the simulation, leading to a local and more greedy search. The gradual transition from stochastic to downhill search in simulating annealing reﬂects the nature of human problem solving [Cagan and Kotovsky, 1997, Yu et al., 2016] and has been used in other human problem-solving simulations [McComb et al., 2015, e.g.]. Figure 2 illustrates an agent problem solving in a simulated annealing 8/34 Design Science start end solution path 0.0 0.1 0.2 0.3 0.4 0.50.00.10.20.30.40.5 x1x2 0.00.10.20.30.40.50.00.10.20.30.40.50.00.20.40.60.81.0score x1x2Objective Function Figure 2. Simulated annealing involves agents exploring a solution space (right) in order to maximize a deﬁned objective function (left). The path on the right shows a series of solutions starting at the circle and ending at the diamond. framework. The agent explores a 2-dimensional problem space with the goal of maximizing an objective function (left). The black line connects the sequence of solutions explored by the agent over the course of 100 iterations of the simulation, ending at the black diamond. The agent makes large changes to the solution early on, followed by smaller steps towards the end, in accordance with the simulated annealing scheme. In this paper, a solution is a set of parameters that deﬁne a position in the solution space, and the quality of a solution is the value of the objective function for those parameters. Team performance is taken to be the best solution any individual on a team has found. While this approach is the norm in the optimization and modeling literature, future work could consider more subtle measures of performance that include social integrity of the team, self- ecacy, consumption of resources such as money and time, or other measures of performance. Many computational models of team problem solving assume that agents can perfectly evaluate the objective function for solutions they create. This is due in part to agent-based models being grounded in the optimization literature. In contrast, KABOOM assumes agents can evaluate the quality of their solutions using the objective function, but their perception of solution quality is a ected by their respective cognitive styles. Each agent has an assigned cognitive style, which includes the three sub-score dimensions of Su ciency of Originality (SO), Eciency (E), and Rule /Group Conformity (RG), in addition to the total score (KAI). These parameters inﬂuence how the agent perceives solution quality and how it explores the solution space. The following sections describe how the total KAI score and each sub-score impact agent behavior. 9/34 Design Science 0.0 0.1 0.2 0.3 0.4 0.50.00.10.20.30.40.5 0.00.20.40.60.81.0 x1x2solution score more adaptive more innovativemid-range Figure 3. Agents with more adaptive styles (lower KAI scores) move in smaller steps on each iteration, while agents with more innovative styles (higher KAI scores) take larger steps in the solution space. Simulating cognitive style The agents’ exploration of the solution space depends on their total KAI score, as well as the three sub-factor scores of Su ciency of Originality (SO), E ciency (E), and Rule /Group Conformity (RG). People with higher KAI scores tend to make larger changes to a design in search of a di erent solution, while people with lower KAI scores tend to make smaller changes to reﬁne an existing solution. In the simulation, the distance an agent moves in the solution space on one turn (iteration) is positively correlated with the total KAI score. Figure 3 illustrates the di erences in step size for agents of adaptive, mid-range, and innovative styles in a 2-dimensional problem. When searching for new solutions, a more adaptive agent moves in smaller, incremental steps, tweaking the solution with marginal adjustments. In contrast, a more innovative agent moves in larger leaps, often generating ideas that are distant and very distinct from their current solution. Each agent has an individual speed parameter with an initial value dependent on their total KAI score. Speed determines how closely or distantly related an agent’s subsequent solutions are. Speed is roughly analogous to novelty of solutions in real-world problems, in that high speed will lead to a series of very distinct solutions, while low speed will lead to a series of very similar solutions. The speed decays geometrically throughout the course of the simulation. The distance, D, from the current solution to the next solution an agent generates is drawn from a chi ( ) distribution and scaled by the agent’s current speed, s: D=s (1) where is a random variable characterized by the chi probability density function with k=1:9 degrees of freedom. The minimum travel distance in one step is set to 10/34 Design Science one ten-thousandth of the entire space, and there is no upper bound. The agent’s start speed, s0, is calculated as s0=s+KAIs (2) where KAIis the standardized KAI score (re-scaled for a mean of 0 and a standard deviation of 1), sis the average starting speed for all agents, and s is the standard deviation of starting speed across all agents. Model parameters Parameters in the model are generally tuned to reﬂect observed human behavior. Except where noted, the parameters were held constant at the values listed in Table 1. An appendix contains a table listing all parameter values for each ﬁgure in the paper. Table 1. List of model parameters and their default values Parameter Symbol Value Description General Parameters Iterations 300 number of simulation steps in one simulation Team size 6 number of agents on the team Number of sub-teams 2 number of specialized teams Agents per sub-team 3 number of agents on each sub-team Average starting temperature T 1 Standard deviation of temperature T 0.8 Average starting speed s 0.01 Standard deviation of speed s 0.007 Objective Function Parameters Oscillation amplitude 0.1 Scaling parameter 1 Feasible solution space [-1, 1] each dimension is bounded by this range Communication Parameters Communication frequency c 0.2 probability an agent communicates on turn Meeting interval 50 number of iterations between team meetings Efﬁciency Eciency describes an individual’s preference for structure in their working methods, which range from applying highly detailed and incremental improve- ments to a solution (more adaptive) to dramatically or tangentially altering a solution, with less regard for detail and quality (more innovative). The temperature parameter in simulated annealing determines the probability of an agent accepting a candidate solution that does not improve the objective function relative to their own current solution. In a real-world design setting, temperature 11/34 Design Science corresponds to exploration. Early on in the design process, designers explore new solutions with little regard for quality in order to expand the known solution space. As the design process continues, solution quality becomes more important and exploration transitions to exploitation. In KABOOM, an agent’s starting temperature is correlated with the E sub- score. Temperature always decreases geometrically over the course of the simulation, but both the start temperature T0and the cooling rate are a function of E. An agent with a higher (more innovative) E sub-score starts with a higher temperature, and thus a higher probability of accepting solutions that do not improve the objective function. This can cause them to leave good solutions behind and miss high-quality nearby solutions, but it can also allow them to escape local minima to ﬁnd better solutions in a “rough” optimization topology. Agents with higher E ciency scores also cool down slower, meaning they might never reach a very low temperature or reﬁne a single local solution. In contrast, an agent with a lower (more adaptive) E sub-score starts with a lower temperature, and thus a lower probability of accepting solutions that do not improve the objective function. This can cause them to quickly achieve locally optimal results, but it can also lead them to become stuck in local minima. The resulting behavior of the agents overall is that the more adaptive agents choose a solution early on and polish it to perfection, while the more innovative agents spend most of their time exploring very diverse solutions without reﬁning them. The agent’s start temperature T0is calculated as T0=T+ET (3) where Eis the standardized E ciency sub-score (re-scaled for a mean of 0 and a standard deviation of 1), Tis the average temperature for all agents, and Tis the standard deviation of temperature across all agents. The agent’s ratio of start temperature r0to ﬁnal temperature rfis r0 rf=1 exp (2 E)(4) which is bounded by 1010and 1. The geometric decay ratio for each time step is calculated based on start temperature, start-to-end ratio, and the number of steps in the simulation. Figure 4A shows the temperature over the course of a simulation for agents with more innovative (high E), mid-range (mid-range E), and more adaptive (low E) E ciency sub-scores. The agent’s speed decays with the same ratio as the temperature. In simulated annealing, the probability that an agent will accept or reject a solution that is inferior to its current solution depends on its temperature and the di erence in solution quality according to Equation 5 [Kirkpatrick et al., 1983]. At high temperatures, an agent will accept solutions regardless of quality, but at low temperatures, agents only accept solutions that improve the objective function, as shown below: Paccept =exp f(~xn)f(~x) kBT! ;f(~xn)<f(~x) (5) where Paccept is the probability that an agent with current solution ~xaccepts a 12/34 Design Science 0.0 0.2 0.4 0.6 0.8 1.00.0050.0100.0150.0200.025Memory Weight time of memoryearliest memories recent memories0 20 40 60 80 1000.00.20.40.60.81.01.21.4Temperature Simulation Time (iterations) (A) (B) Figure 4. (A) Cooling schedules for agents with di erent E ciency sub-scores (B) In calculating the perceived memory location, an agent’s past memories are weighted based on the serial position e ect reﬂected in this curve: the most recent memories and earliest memories are recalled more easily than intermediate memories. new solution ~xnthat does not improve the objective function fas a function of current temperature Tand a constant kB. We can absorb kBinto the calculation of temperature. Figure 5 illustrates the e ect of the E ciency style sub-factor on three agents’ exploration of the solution space. Compared to the mid-range agent (black), the more adaptive agent (blue) reﬁnes an early solution, while the more innovative agent (red) continuously explores without reﬁning a solution. Sufﬁciency of originality An agent’s desire to retain and modify known solutions or, conversely, to explore more unfamiliar ideas, is related to the Su ciency of Originality sub-score of KAI. When agents evaluate a candidate solution in KABOOM, more adaptive agents are more likely to accept a candidate solution that directs them towards their previous solutions and are less likely to accept a solution that leads them away from previous solutions. On the other hand, more innovative agents prefer to choose ideas that move them further from ideas they have explored in the past and to reject ideas that lead them towards their previous solutions. An agent’s perception of its previous solutions is represented by a single point in the solution space, which is a weighted mean (centroid) of all of their previous positions or “memories”. The weights on an agent’s memories are strongest for the most recent memories, weakest for middle memories, and intermediate strength for the earliest memories (Figure 4B). This reﬂects the serial position e ect [Colman, 2015], which describes how people tend to remember early memories (primacy e ect) and recent memories (recency e ect) more readily than intermediate memories. The direction of the weighted memory position from the current position is a weighted average of the directions to all previous solutions the agent has visited. 13/34 Design Science 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.1 0.2 0.3 0.4 0.50.00.10.20.30.40.5 solution score more adaptive more innovativemid-range x1x2 Figure 5. E ect of E sub-factor on solution space exploration We call~vmemthe perceived memory direction, where the weights are given by the primacy-recency bias function Q: ~vmem=NX n=1(~xMn)Q(n) (6) and where the memory Mis a list of N previous solutions (each memory being a vector of the same shape as the current solution ~x). The primacy-recency bias function for memory n of N total memories is: Q(n)=n3+0:4(Nn)3(7) which gives a U-shaped curve with stronger biases for the earliest and most recent memories, respectively, than for other memories (Figure 4B). The weights are calculated with this equation then normalized so that they sum to 1. The direction of the candidate solution from the current solution is the vector di erence between the candidate solution and the current solution, ~vn=~xn~x. The dot product of these two directions indicates whether the new solution is in the direction of the perceived memory or away from the perceived memory. We call this dot product the originality : =~vmem~vn (8) Then, the Su ciency of Originality preference PS Ois: PS O= S O*WS O (9) where S O* is the standardized SO score (re-scaled for a mean of 0 and a standard deviation of 1), and WS Ois a global scaling constant that determines the strength 14/34 Design Science 0.00.20.40.60.81.0 0.0 0.1 0.2 0.3 0.4 0.50.00.10.20.30.40.5 score x1x2 more adaptive more innovativemid-range Figure 6. E ect of SO sub-factor on solution space exploration of the SO preference. For this paper, we set WS Oto 2, which creates a range of behaviors for agents across the KAI cognitive style spectrum. When an agent evaluates the quality of a candidate solution, the SO preference PS Oand RG preference PRG(explained below) inﬂuence the perceived solution quality: the p