If a solvable problem is currently unsolved, then something important to a solution is most likely being overlooked. From this simple observation we derive the obscure features hypothesis: every innovative solution is built upon at least one commonly overlooked or new (i.e., obscure) feature of the problem. By using a new definition of a feature as an effect of an interaction, we are able to accomplish five things. First, we are able to determine where features come from and how to search for new ones. Second, we are able to construct mathematical arguments that the set of features of an object is not computably enumerable. Third, we are able to characterize innovative problem solving as looking for a series of interactions that produce the desired effects (i.e., the goal). Fourth, we are able to construct a precise problem-solving grammar that is both human and machine friendly. Fifth, we are able to devise a visual and verbal problem-solving representation that both humans and computers can contribute to as they help counteract each other's problem-solving weaknesses. We show how computers can counter some of the known cognitive obstacles to innovation that humans have. We also briefly discuss ways in which humans can return the favor. We conclude that a promising process for innovative problem solving is a human–computer collaboration in which each partner assists the other in unearthing the obscure features of a problem.

This paper introduces the special issue “Advances in Implemented Shape Grammars: Solutions and Applications” and frames the topic of computer implementations of shape grammars, both with a theoretical and an applied focus. This special issue focuses on the current state of the art regarding computer implementations of shape grammars and brings a discussion about how those systems can evolve in the coming years so that they can be used in real life design scenarios. This paper presents a brief state of the art of shape grammars implementation and an overview of the papers included in the current special issue categorized under technical design, interpreters and interface design, and uses cases. The paper ends with a comprehensive outlook into the future of shape grammars implementations.

Embedding emergent parts in shape grammars is computationally challenging. The first challenge is the representation of shapes, which needs to enable reinterpretation of parts regardless of the creation history of the shapes. The second challenge is the relevant part searching algorithm that provides an extensive exploration of the design space–time efficiently. In this work, we propose a novel method to solve both problems; we treat shapes as they are and use a parallel particle swarm optimization-based algorithm to compute emergent parts. The execution time of the proposed method is improved substantially by dividing the search space into small parts and carrying out searches in each part concurrently using a graphics processing unit. The experiments show that the proposed implementation detects emergent parts accurately and time efficiently.

This paper presents a computational design method to analyze and synthesize representation mechanisms in structural design. The role of shape grammar schemas in analyzing parametric and grammatical structural analysis is discussed, and a set of schema to generate novel structural topology is provided.

The aim of this paper is to investigate the challenges associated with the industrial implementation of generative design systems. Though many studies have been aimed at validating either the technical feasibility or the usefulness of generative design systems, there is, however, a lack of research on the practical implementation and adaptation in industry. To that end, this paper presents two case studies conducted while developing design systems for industrial uses. The first case study focuses on an engineering design application and the other on an industrial design application. In both cases, the focus is on detail-oriented performance-driven generative design systems based on currently available computer-assisted design tools. The development time and communications with the companies were analyzed to identify challenges in the two projects. Overall, the results show that the challenges are not related to whether the design tools are intended for artistic or technical problems, but rather in how to make the design process systematic. The challenges include aspects such as how to fully utilize the potential of generative design tools in a traditional product development process, how to enable designers not familiar with programming to provide design generation logic, and what should be automated and what is better left as a manual task. The paper suggests several strategies for dealing with the identified challenges.

The goal of this paper is to examine meaning as a component of creativity. We take a demand-based approach for conceptualizing meaning, and propose that it emerges from user needs instead of emerging from already existing creative solutions. Meaning is proposed as a third component of creativity, alongside novelty and usefulness. We test this proposition in a pre-study, and two empirical studies. In the pre-study, designers define creativity and provide examples of solutions that they deem creative. The results of the pre-study yield a 24-item scale for assessing creativity. Then, we conduct two empirical studies, in which we utilize the created scale for measuring creativity, and for examining the components arising thereof. In the first study, we ask creators (design engineering students) to generate ideas for one of two design briefs. Afterwards, creators were asked to rate their own creations, on the 24-item creativity scale. Here, we find a four-factor solution for creative outcomes, consisting of the dimensions novelty, usefulness, cleverness, and meaning. In the second study, we ask independent evaluators (individuals with related and relevant degrees) to assess the creators’ work on the creativity scale. Here, we find a three-factor solution for creative outcomes, consisting of the dimensions novelty, usefulness, and meaning. In both studies, meaning emerged as a separate component of creativity. Additionally, in both studies, it accounted for variance that was unaccounted for by novelty and usefulness, thereby increasing the overall explanatory power of creative solutions. These findings strongly speak of meaning as a third component of creativity.

Computer-based shape grammar implementations aim to support creative design exploration by automating rule-application. This paper reviews existing shape grammar implementations in terms of their algorithmic complexity, extends the definition of shape grammars with sets of transformations for rule application, categorizes (parametric and non-parametric) sets of transformations, and analyses these categories in terms of the resulting algorithmic complexity. Specifically, it describes how different sets of transformations admit different numbers of targets (i.e., potential inputs) for rule application. In the non-parametric case, this number is quadratic or cubic, while in the parametric case, it can be non-polynomial, depending on the size of the target shape. The analysis thus yields lower bounds for the algorithmic complexity of shape grammar implementations that hold independently of the employed algorithm or data structure. Based on these bounds, we propose novel matching algorithms for non-parametric and parametric shape grammar implementation and analyze their complexity. The results provide guidance for future, general-purpose shape grammar implementations for design exploration.

In the product design realm, designers often use presentations to convey certain ideas about a product or a specific stage of the design process. The popular forms of presentation include verbal pitching, two-dimensional drawing, and prototyping. The clients, investigators, and other audiences rely on such presentations to evaluate an idea. Popular idea evaluation assessment tools, such as the consensual assessment technique, utilize such interactions. On the other hand, numerous pieces of literature state that the audiences are heavily influenced by the quality of presentation when evaluating the worth of the product being presented. In this study, we examine if the audience is able to discriminate between the quality of the presentation and the quality of the idea being presented. A total of 613 ideas were evaluated over a 4-year period during a specific product design class at different phases in the design process. The result shows that no matter the kind of presentation tool used, the presentation quality ratings and the idea value ratings had a very strong positive correlation despite the explicit instructions to reviewers to separate presentation quality from concept quality. Our additional analysis shows that such a pattern did not change during the different phases of the design process.

Freeform curves are commonly used in contemporary design practices, especially with digital modeling tools. We investigate facilitating shape subtraction and addition with two-dimensional (planar) non-uniform rational basis-spline (NURB) curves with the codes and conventions of modeling while preserving the visual continuity of curved shapes. Our proposed tool, developed in a common digital modeling environment, automates the adjustment of parameters for tangential continuity of curves in shape rule applications. When the user designates a curve range to subtract from an initial shape and provides a new curved shape to add to it, the tool splits the initial shape, scales and aligns the curve to be added to fit into this range, introduces additional control points at the joining ends of the new curve to preserve continuity and redraws the new curve. We present a sample set of design variations produced using this practical approach which can be utilized as a method or become part of an automated NURB curve manipulation tool for designers.

This paper reports on a study characterizing design processes and the potential of design spaces through measuring the information entropy of empirical data derived from protocol studies. The sequential segments in a protocol analysis can be related to each other by examining their semantic content producing a design session's linkograph, which defines the design space for a design session. From a linkograph, it is possible to compute the probabilities of the connectivity of each segment for its forelinks and its backlinks, together with the probabilities of distance among links. A linkograph's entropy is a measure of the information in the design session. It is claimed that the entropy of the linkograph measures the potential of the design space being generated as the design proceeds chronologically. We present an approach to the automated construction of linkographs by connecting segments using the lexical database WordNet and measure its entropy. A case study of two design sessions with different characteristics was conducted, one considered more productive and creative, the other more pragmatic. Those segments with high entropy and those associated with high rates of change of entropy are analyzed. The creative session has a higher linkograph entropy. This result indicates the potential of using entropy to characterize a design process.

The ability to work with ambiguity and compute new designs based on both defined and emergent shapes are unique advantages of shape grammars. Realizing these benefits in design practice requires the implementation of general purpose shape grammar interpreters that support: (a) the detection of arbitrary subshapes in arbitrary shapes and (b) the application of shape rules that use these subshapes to create new shapes. The complexity of currently available interpreters results from their combination of shape computation (for subshape detection and the application of rules) with computational geometry (for the geometric operations need to generate new shapes). This paper proposes a shape grammar implementation method for three-dimensional circular arcs represented as rational quadratic Bézier curves based on lattice theory that reduces this complexity by separating steps in a shape computation process from the geometrical operations associated with specific grammars and shapes. The method is demonstrated through application to two well-known shape grammars: Stiny's triangles grammar and Jowers and Earl's trefoil grammar. A prototype computer implementation of an interpreter kernel has been built and its application to both grammars is presented. The use of Bézier curves in three dimensions opens the possibility to extend shape grammar implementations to cover the wider range of applications that are needed before practical implementations for use in real life product design and development processes become feasible.

It is well-known that creativity is crucial for sustaining a product against competition. Many factors have been proposed in the literature as indicators of creativity, among which outcome-characteristics-based factors are considered the most reliable; among these, the creativity of an outcome is often indicated by two major factors: novelty and usefulness. Only a few studies address as to how creativity assessment methods and their results can be used during the design process. To systematically address the issue of how to influence creativity of design solutions, the following questions have been framed. (1) Which factors should be used as indicators of creativity consistently across different phases of the engineering design process? (2) How can creativity be assessed in terms of these factors during the engineering design process? In this work, we consider novelty and usefulness as the necessary factors for creativity. It is found, however, that it is not possible to directly assess the usefulness of outcomes during the design process. Therefore, requirement satisfaction is used as a proxy for usefulness. We propose a creativity assessment method that uses novelty and requirement satisfaction as indicators for creativity; the method can be used for assessing not only complete products but also ideas or concepts, as they evolve through the phases of the design process. The application of the method in design is explained using a detailed example from a case study.

The hub location problems involve locating facilities and designing hub networks to minimize the total cost of transportation (as a function of distance) between hubs, establishing facilities and demand management. In this paper, we consider the capacitated cluster hub location problem because of its wide range of applications in real-world cases, especially in transportation and telecommunication networks. In this regard, a mathematical model is presented to address this problem under capacity constraints imposed on hubs and transportation lines. Then, a new hybrid algorithm based on simulated annealing and ant colony optimization is proposed to solve the presented problem. Finally, the computational experiments demonstrate that the proposed heuristic algorithm is both effective and efficient.

Shape grammars come in a variety of forms. Algebras of shapes have been defined for spatial elements of different kinds, as well as for shapes augmented with varying attributes, allowing for grammar forms to be expressed in terms of a direct product of basic algebras. This algebraic approach is extended here to the algebraic derivation of combinations of basic shape algebras with attribute algebras. This algebraic abstraction at the same time serves as a procedural abstraction, giving insights into the modular implementation of a general shape grammar interpreter for different grammar forms. In addition, we consider practical limitations on algebraic compositions of basic shape algebras with attribute algebras and identify a complication with respect to solving the matching problem for parallel and compound shape grammars, suggesting a way to address this complication.

This paper shows the way Leon Battista Alberti treatise De Re Aedificatoria column systematization shape grammar was built, and how the longitudinal elevation of the nave of the Sant'Andrea church was designed, evidencing some steps involved in the grammar construction process, its derivation, and the partial outputs gained from the grammar evaluation. The goal of this grammar is to infer Alberti's treatise rules through a computational approach evidencing its algorithmic nature, illustrating it, and understanding the De Re Aedificatoria rules that may be applied in the generation of some parts of buildings such as the Sant'Andrea church, showing a complementary method to archaeological, bibliographical, historical ones, among others, that have been used to understand the built environment. The rules provided by the grammar may be applied to an initial insertion point to produce a complete column and to a pre-existing plan or section element of a building generating its facade. It was proved, evaluating the grammar with a simple linear regression method, to what extent the treatise influenced the design of the facade in the study.

In inspiration and fixation experiments, example designs are often provided along with the instructions for how participants should treat them. However, research has not reached a consensus about the influence of such instructions, leading to difficulties in understanding how the examples and the instructions each affect idea generation. We conducted an experiment in which 303 participants designed for the same design problem, while given different examples and instructions, which ranged from strongly encouraging copying the examples to strongly discouraging copying. Exposure to the examples affected the number and type of ideas generated, whereas exposure to the instructions did not. However, instructions did affect how participants incorporated features of the examples in their ideas. Encouraged groups incorporated many features of the examples, while also incorporating structural features more than conceptual ones. Surprisingly, the incorporation of features in discouraged groups was not different from that of groups given no instructions or even no stimulus. This indicates that concrete features may be easier to recognize and reproduce than abstract ones, and that encouraging instructions are more effective than discouraging ones, despite how strict or lenient those instructions are. The manipulation of different features also allowed us to observe how similar approaches to solving a design problem can compete for attention and how the calculation of feature repetition can be misleading depending on how common or obvious the features might be. These findings have implications for the interpretation of results from fixation studies, and for the development of design tools that present stimuli to assist idea generation.

Design problems are often presented as structured briefs with detailed constraints and requirements, suggesting a fixed definition. However, past studies have identified the importance of exploring design problems for creative design outcomes. Previous protocol studies of designers has shown that problems can “co-evolve” with the development of solutions during the design process. But to date, little evidence has been provided about how designers systematically explore presented problems to create better solutions. In this study, we conducted a qualitative analysis of 252 design problems collected from publically available sources, including award-winning product designs and open-source design competitions. This database offers an independent sample of presented problems, designers’ alternative problem descriptions, and innovative solutions. We report the results of this large-scale qualitative analysis aimed at characterizing changes to problems during the design process. Inductive coding was used to identify content patterns in “discovered” problem descriptions, with qualitative codes reliably scored by two independent coders. A total of 32 distinct patterns of problem exploration were identified across designers and presented problems. Each pattern is described in the form of a generalized strategy to guide designers as they explore problem spaces. The exploration patterns identified in this study are the first empirical evidence of problem exploration in independent design problems. Further, the presence of exploration patterns in discovered problems is associated with the selection of the corresponding solution as a challenge finalist. These empirically identified strategies for problem exploration may be useful for computational tools supporting designers.

The use of grammars in design and analysis has been set back by the lack of automated ways to induce them from arbitrarily structured datasets. Machine translation methods provide a construct for inducing grammars from coded data which have been extended to be used for design through pre-coded design data. This work introduces a four-step process for inducing grammars from un-coded structured datasets which can constitute a wide variety of data types, including many used in the design. The method includes: (1) extracting objects from the data, (2) forming structures from objects, (3) expanding structures into rules based on frequency, and (4) finding rule similarities that lead to consolidation or abstraction. To evaluate this method, grammars are induced from generated data, architectural layouts and three-dimensional design models to demonstrate that this method offers usable grammars automatically which are functionally similar to grammars produced by hand.

Product variant design, as one of the key enabling technologies of mass customization, is the transfer of variant information among mating parts from the perspective of informatics. A dimension constraint network (DCN) among mating parts carries on the task of transferring variant information. What are the information transfer characteristics of dimensions in a constraint network is a fundamental issue to plan the product variant design process reasonably. We begin by showing the natural dynamics of the DCN from two aspects: structure and uncertainty. The information efficiency of the DCN was proposed based on its simple path to specify the information transfer capability of the network. Based on this, the information centrality of the dimension was developed by measuring the efficiency loss of the DCN after the removal of a dimension from the network, which describes the information transfer capability of this dimension. Further, the information centrality of a part was derived. Using a spherical valve subassembly, we calculated the information centrality of the dimensions in a constraint network. We determined that the information centrality of dimension is highly correlated to its out-degree. An approach to plan the sequence of the part variant design according to its information centrality was proposed. We calculated the uncertainties of the DCN and its cumulative uncertainties under different sequences of the part variant design. Results indicate that part variant design under the descending information centrality of the parts minimizes the uncertainty of the DCN. This suggests a new method of planning the sequence of part variant design.