A comparative analysis of CAD modeling approaches for design solution space exploration

Design solution space (DSS) exploration is a pivotal process for comprehending design challenges and identifying diverse solution alternatives based on varying requirements. Computer-aided design (CAD) approaches, such as parametric design, knowledge-based design, and generative design, have proven successful in DSS exploration. However, a comparative study evaluating their performance is lacking in the technical literature. This paper addresses this gap by conducting a comparative analysis of these approaches regarding their performance in exploring DSS. The research begins by providing an overview of parametric design, knowledge-based design, and generative design, establishing the foundation for the study. Six evaluation criteria are identified based on the DSS exploration process. A qualitative analysis is then conducted, considering these criteria, to objectively assess the performance of each modeling approach. The results highlight the strengths and weaknesses of each approach, revealing that DSS exploration success is directly tied to the quantity of implemented knowledge. The results also emphasize the complementarity of those approaches, as their strengths and weaknesses are based on different problem-solving logics, demonstrating the synergy that can be achieved through strategic combinations of them. Additionally, the paper discusses open issues related to DSS exploration, contributing valuable insights for future developments in this field.


Introduction
In the realm of design, the exploration of the Design Solution Space (DSS) stands as a pivotal process, involving the thorough examination and discovery of diverse design alternatives or a spectrum of potential design candidates before settling on a specific solution.The objective is not to prematurely commit to a single optimal solution, but rather to actively pursue multiple parallel alternatives, defining requirements using value ranges instead of fixed values. 1 As proposed by Kang et al., 2 this mechanism aims to uncover new ideas and validate existing ones.During evaluation, alternatives that significantly violate requirements are excluded, while the remaining options are refined and re-evaluated at subsequent decision gates.
The fundamental purpose of DSS exploration is to cultivate a comprehensive understanding of the design problem by exploring a diverse range of solution alternatives. 3Two key characteristics contribute to this endeavor: firstly, the unique characteristics of the design problem are revealed through solution alternatives, allowing designers to identify promising solutions and expand the boundaries of the DSS. 4 Secondly, comparison plays a crucial role in connecting customer requirements to the selection of the optimal solution, facilitating informed decision-making. 5Once a feasible solution addressing variable design requirements is determined, appropriate decisions can be made for further implementation. 6In this context, DSS exploration is recognized as a significant success factor in product development.
Advancements in computer technologies, particularly computer-aided design (CAD) modeling approaches, have revolutionized DSS exploration.][9] However, the varying nature of design tasks necessitates different size requirements for a DSS, leading to challenges in practical applications.Despite attempts to address this challenge by utilizing PD for routine and innovative design, KBD for routine and innovative design, and GD for innovative and creative design, a surprising lack of comparative studies exists.This lack of research impedes the ability to draw conclusive results regarding their effectiveness in DSS exploration.
Motivated by this gap, this paper presents a comparative analysis of three widely used CAD modeling approaches (PD, KBD, and GD).The analysis explores their operationalization, implementation and limitations within the context of DSS exploration.Rather than determining superiority, the focus is on identifying the strengths and weaknesses of each modeling approach, with an emphasis on potential complementary interactions among them.
The remainder of this paper unfolds as follows: Section 2 provides an extensive review of current research and key issues related to DSS exploration, forming the foundational framework for this study.Section 3 conducts a rigorous comparative analysis of three modeling approaches, utilizing six criteria derived from the DSS exploration process to assess their strengths and weaknesses.Section 4 offers a detailed summary of the findings and issues uncovered through the analysis.Finally, the paper concludes by presenting key insights and avenues for future research in the realm of DSS within CAD modeling.

CAD modeling approaches and DSS exploration
The CAD modeling approach for solution generation and exploration is not novel and has been extensively explored across various design domains.To contextualize this research within the existing literature, this section introduces key works that have delved into CAD modeling approaches and DSS exploration.

CAD modeling approaches
The CAD modeling approach addresses design challenges by capturing and representing product information through CAD systems. 10Typically, this process yields CAD models that closely approximate real-world objects, thereby reducing the occurrence of engineering errors and enhancing solution visualization. 11The subsequent sections provide a concise overview of three widely adopted modeling approaches currently in use.
Parametric design.Parametric design (PD) entails utilizing a CAD system to automatically adjust a design as parameter values change, resulting in corresponding modifications to the CAD model throughout the design process. 12A fundamental characteristic of the PD approach is the distinct separation of geometry elements and their associated parameters within the CAD model. 8As the design process unfolds, parameters are introduced to define the dimensions of an object and potentially specify its physical properties for subsequent construction.In the context of a given design problem, the specified requirements are translated into a set of parameters, and their interdependencies are represented through a hierarchical network of mathematical or logical relations.This hierarchical structure captures the behaviors and structures of the product. 13Parameter values can be influenced either through direct data input or by employing equations.The introduction of geometric variations is achieved by adjusting parameter values or modifying constraints within and between the models. 14In order to facilitate the parameter combination handling process, different approaches have been discussed, such as statistical sampling and sensitivity analysis.Besides, efficiently managing these combinations often involves the use of specialized tools, for example, DOE software, optimization software (such as genetic algorithms or gradient-based optimization algorithms), statistical analysis tools (program-based statistical packages).As illustrated in Figure 1, the value combinations of different design parameters lead to a large DSS.
Various research works have been reported, attempting to accommodate different issues in product development.Turrin et al. 15 underscored that the Parametric Design (PD) approach holds significant promise in supporting product development during the conceptual design stage.This is because it enables designers to automatically generate a diverse range of potential solution alternatives.Fuchkina et al. 16 introduced a solution exploration framework that integrates the PD approach into the design process, enhancing the flexibility of solution generation and facilitating the identification of potentially optimal solutions.Costa et al. 17 put forth an exploration modeler based on the PD approach, aimed at delineating an expansive solution space for mass customization.This empowers nondesigners, such as end-users, to customize their designs with greater flexibility.
Knowledge-based design.Knowledge-based design (KBD) is a focal area of research in CAD model generation that encompasses intricate and iterative processes involving the capture and reuse of engineering knowledge. 18The primary aim of KBD is to expedite the product development process while curbing costs by automating repetitive, non-creative design tasks and facilitating multidisciplinary design optimization across all phases of design. 19Once engineering knowledge related to the problem is amassed and stored in the form of a generic knowledge-based CAD model (e.g., a template), designers can swiftly and effortlessly generate and assess various design variations.This can be achieved through adjustments to input specifications or modifications to the model itself. 20Consequently, both domain knowledge and control knowledge play pivotal roles during the design process.The former structures feasible design solutions, typically through a set of constraints or design templates, while the latter dictates problem-solving methodologies, such as rule-based or case-based reasoning techniques. 1 A standard architecture of a KBD model comprises three core components: a knowledge base, an inference engine, and a user interface, as depicted in Figure 2. Additionally, certain KBD models may incorporate auxiliary elements, such as a knowledge acquisition module that acts as an interface between developers and the knowledge base for the storage and retrieval of additional knowledge, and an explanation module for querying the inference engine and accessing case-specific databases to gain insights into the reasoning processes. 21he implementation of KBD has found application across various design domains.Chong et al. 22 developed a framework that organizes knowledge-enriched objects and their interrelationships, providing guidance to designers in the exploration of design solutions.During the configuration design phase, Saxena and Karsai 23 introduced an abstract DSS exploration framework, which was integrated into exploration solvers.This innovation paved the way for the creation of customized design configurations.Subsequently, Wyatt et al. 24 put forward a DSS exploration approach aimed at aiding topological configurations through formal computational methodologies, treating the design task  as a numerical optimization problem.More recently, Wang et al. 25 proposed a template-based ontological method for systematic DSS exploration.This method empowers designers to identify suitable configurations that meet various goals and requirements within a given process chain.
Generative design.Generative design (GD) represents an iterative approach where the exploration of new designs is viewed as a sequence of transformations, starting from initial data and progressing towards the generation of a multitude of design possibilities. 26GD harnesses production rules derived from existing engineering knowledge to autonomously generate a vast array of solution alternatives that align with specific requirements and constraints, such as target weight and stress. 27The GD design process typically commences with the representation of design concepts through a set of algorithmic rules.Subsequently, generative mechanisms enable the computer to automatically generate design solutions and present these as visual outputs for evaluation by designers. 28In this process chain, the solution alternatives are no longer directly generated by designers but by a programmed algorithm. 29In essence, GD supplants a single-end design approach with a multitude of solution alternatives and automates the generation process.
Given the versatility of GD for various applications, numerous methods have been developed in the past two decades, offering a versatile framework adaptable to different design scenarios. 30Among these methods, the most commonly employed for CAD model creation are graph grammar and spatial grammar due to their capacity to produce products directly usable in a CAD environment. 31Graph grammar employs a vocabulary of graphs and a set of rules to construct a CAD model by interconnecting these graphs within a network.The rules in use offer mechanisms for identifying and modifying predefined structures within this graph network.When a rule is applied, the structure of the graph network is first examined and subsequently replaced by a predefined structure. 32Spatial grammar follows a similar approach but employs a 3D geometric representation instead of a graph network.In this case, the vocabulary comprises geometric primitives. 33Figure 3 illustrates a walker robot design using the GD approach from production rules to final concepts. 34enerative Design (GD) also possesses the capability to simulate the design process, capture compositional conventions, and provide guidelines for constructing designs.Consequently, numerous research efforts have been dedicated to integrating GD into DSS exploration.McCormack and Cagan 35 introduced a GD framework, grounded in shape grammar, serving as a design tool for generating both standard and innovative designs facilitated by early-stage design rules.Kunkhet et al. 36 developed a GD approach based on graph grammar, enabling the generation of a substantial number of conceptual designs for black-box systems.Their method involves the generation and evaluation of feasible design solutions, followed by the application of optimization techniques to select the best design.Strobbe et al. 37 proposed a shape grammar-based GD approach that enables the visual and interactive exploration of .GD approach of a walker robot design. 34iverse solution alternatives.In a similar vein, Khan and Awan 38 presented a generative design technique aimed at producing variant design alternatives, ensuring a cohesive approach to DSS exploration.

Design solution space exploration
As discussed, the successful development of a product hinges on effective DSS exploration which involves the exploration of a substantial number of solution alternatives.It is widely recognized that the greater the exploration of solution alternatives, the higher the performance of the final solution is likely to be. 5 Within the exploration process, two primary challenges must be addressed.Firstly, the formulation of the requirement space necessitates the identification and representation of requirements and their associated constraints. 39Secondly, DSS exploration within the requirement space should be executed in a controlled manner.Often, the requirement space can be seen as a metaphorical domain encompassing designers' interpretation of all development goals and essential product characteristics directly linked to the given design task. 40DSS exploration, in response to the requirement space, entails activities where designers generate solutions by adopting suitable modeling approaches in conjunction with existing design choices during the design process.These choices may include alternatives derived from previous solutions, design catalogs, advanced features, solution elements, or combinations thereof (Figure 4). 41s stated by Li and Lachmayer, 42 the identification of a feasible solution to a design task is based on a proper exploration of DSS.However, it is impossible to explore all solution alternatives in the DSS because their number is ''astronomically vast.'' 5Thus, a systematic exploration procedure is an essential element for successful product development.Drawing the basic work from Ponn, 3 Gembarski 40 introduced a conventional DSS exploration process through synthesisanalysis loops, as depicted in Figure 3. Synthesis and analysis are on the forward path of the exploration process.Synthesis is a creative activity that addresses the problem or requirements and thus develops a set of solution concepts based on previous knowledge and expertise. 43The objective of synthesis is to produce a set of solution alternatives aiming at achieving an optimal solution capable of satisfying the stated requirements.Analysis is a crucial evaluative process where the properties of the intended product are systematically compared with those of the generated solutions.This assessment relies on the examination of their physical representations and inherent characteristics. 12The purpose of analysis is not only to result in a conclusion whether the solution fulfills the specific requirements or not but also in a comparison of its performance with other solution alternatives.Since the development of the best possible product means evaluating as many solution alternatives as possible, these two stages are intertwined with iterations moving back and forth until a satisfactory design is achieved. 42y thoroughly exploring the DSS, engineers and designers can identify the most promising solutions, leading to more innovative and efficient products.This process plays a pivotal role in achieving successful outcomes lies in its ability to enhance decision-making processes and optimize design solutions.On the one hand, DSS exploration facilitates a systematic evaluation of various design alternatives, allowing decisionmakers to make informed choices based on comprehensive analyses.This optimization process helps in selecting solutions that align with project goals, resource constraints, and customer requirements, several practical applications can be found in automotive design optimization in order to make informed decisions on aspects like body shape, material selection, and component placement to achieve an optimal balance between performance and efficiency.On the other hand, understanding the DSS enables the identification and mitigation of potential risks early in the development process.By exploring various scenarios and considering possible outcomes, teams can proactively address challenges and uncertainties, reducing the likelihood of costly errors and design flaws, especially in aerospace engineering for mitigating risks associated with complex systems by simulating various flight conditions and scenarios.Finally, DSS exploration encourages creativity and innovation by encouraging the consideration of a broad range of design possibilities.This approach fosters out-of-the-box thinking and may lead to breakthrough solutions that may not be apparent through more conventional approaches.

Comparative analysis of CAD modeling approaches
Concerning the DSS exploration process, a modeling approach should be able to explore the DSS by generating a set of CAD models and each model can be varied in terms of the inputs instead of one model that contains all design variations.As mentioned in section 1, there are so far no commonly scoring criteria available for comparing those CAD modeling approaches.Thus, a qualitative analysis is conducted in the following parts that evaluate those modeling approaches in terms of the criteria derived from the synthesis-analysis exploration process.

Qualitative analysis of CAD modeling approaches
To effectively explore the design solution space (DSS), a robust approach should address two main aspects.First, it must handle defining requirements and creating solution alternatives by representing the design problem in CAD models with constraints.Second, the generated alternatives should undergo evaluation to ensure alignment with engineering requirements.When selecting a modeling approach, it's crucial to consider these dual challenges.Additionally, while modeling approaches facilitate DSS exploration, the size and scope of the final DSS may vary. 42Therefore, a comparative analysis of CAD modeling approaches can be conducted based on three key aspects: solution generation, solution evaluation, and properties of the explored DSS.
Solution generation.Given the existence of multiple viable pathways to a practical design solution, modeling approaches should provide effective means to comprehensively grasp the problem and generate a design solution. 8Although these approaches can all generate design solutions, the level of effort required can vary significantly.Therefore, it is crucial to compare the effort needed to quickly identify a solution concept and translate it into a CAD model.Considering the potentially infinite number of viable solutions to a design task, the modeling approach's ability to explore diverse solution alternatives becomes pivotal for successful DSS exploration.Consequently, it is essential to discuss the three modeling approaches in terms of their capacity to minimize the modeling effort for solution creation and their ability to uncover a wide range of solution alternatives.
Modeling effort for solution creation.The PD approach enables designers to create a well-defined plan with parameters and constraints for modeling a product's transition from the functional to the physical domain.Designers translate requirements into parameters, each representing a dimension in the solution space, and their interrelationships throughout the design process.This leads to a parametric CAD model embodying the required functions and behaviors.The primary effort in solution creation with PD involves identifying suitable parameter sets and establishing their interdependencies, a task efficiently handled by leveraging designer intuition and expertise.In summary, PD offers a straightforward and efficient approach to address varying requirements and performative issues in solution creation, excelling in this aspect compared to other modeling approaches (Figure 5).
KBD generates solutions by extracting relevant knowledge from a knowledge base (Figure 6).The primary effort in solution creation lies in establishing this knowledge base, which requires structuring and documenting knowledge for ready access.Formulating knowledge is challenging for human designers, especially capturing tacit knowledge like cognitive understanding, problem-solving strategies, and representation of uncertain information.This complexity prompts designers to conduct abstraction analysis to identify the most relevant knowledge for describing required functionalities.The KBD approach also demands collaboration among designers from different engineering domains, as the  formalized knowledge base dictates and limits solution creation.The negotiation between designers increases modeling effort, resulting in a considerable effort for creating a solution and a lower rating compared to the PD approach.
GD approach autonomously creates geometric solutions using predefined production rules and an initial vocabulary.Instead of focusing on geometric features, design requirements and constraints are transformed into a sequence of production rules during the design process (see Figure 7).The effort for solution creation in GD is closely linked to defining these production rules.However, formulating these rules may not always be straightforward, making it crucial to identify adequate design knowledge for rule definition to avoid incorrect representations and infeasible solutions.While adapting production rule sets to domain and process knowledge may require substantial effort, it is generally less complex than establishing a comprehensive knowledge base.Therefore, the generative design approach is rated lower than PD but superior to KBD in terms of solution creation effort.
Capacity for finding solution alternatives.PD approach allows designers to define a parametric model with potential solutions, and alterations can be made manually by manipulating the model's parameters or features.A change in parameter value or the constraints between parameters triggers a simultaneous modification of the parametric model, generating different solution alternatives while maintaining model consistency.However, only initially expressed constraints and parameter interrelations are explicitly used for finding alternatives.The modeling logic is sometimes visible but often remains difficult to decipher. 44This implies that designers may struggle to generate alternatives without a clear understanding of the design rationale, limiting the range of solutions.Consequently, the PD approach is considered to have a restricted capacity for discovering diverse alternatives, leading to a lower rating in this aspect.
Once a KBD model (e.g., a template) is established, designers can efficiently generate diverse design variations by modifying input specifications.The generic KBD model allows for the rapid production of solution alternatives in an associative and automatic manner.While it holds the potential for generating alternatives, it is crucial to recognize that these solutions are constrained within a predictable region.This limitation arises from the boundaries set by the engineering knowledge embedded in the knowledge base during the design process. 45Extracting engineering knowledge from KBD models and inference engines presents a significant challenge, hindering ready accessibility for designers and making knowledge reuse labor-intensive.The task-oriented, black-box nature of the knowledge base further complicates matters, leading to an effortintensive process in generating solution alternatives. 46n summary, the KBD approach's capacity to discover solution alternatives is intricately tied to the quality of the knowledge base, resulting in an intermediate assessment that reflects both its support and limitations in solution generation.
GD approach is typically perceived as an iterative method that shifts the design process from focusing on a single physical object to generating numerous variations within predefined production rules automatically.Given the recursive nature of these rules, it is not surprising that an infinite number of solution alternatives can emerge.Despite using the same rule sets, the GD production system can yield diverse variations, presenting both opportunities and challenges.While it generates a large number of alternatives, ensuring their feasibility is challenging as some solutions are beyond the designer's control.Consequently, the GD approach excels in generating solution alternatives, surpassing KBD but requires additional effort to identify real feasible solutions, making it a better-rated option with some limitations.
Solution evaluation.Once the solution alternatives are generated, a tradeoff among them should be maintained to determine if they fulfill all properties as expected and obtain an accurate estimate of them. 47his activity may be driven manually, with the designers choosing sets of parameters based upon their intuition or observations from previous projects and then recording the performance afforded by the new parameters.However, enumerating them one by one is time and cost-intensive and also not guaranteed to be necessarily the optimal one.Thus, the modeling approaches should provide methods or mechanisms for evaluating all solution alternatives so that it is possible to find the optimal solution with minimum effort. 48In terms of this assumption, two aspects have to be considered: how much effort should be investigated for solution assessment and what are the limitation resulting from the applied modeling approach for solution evaluation.Related to these two aspects, the performance of those modeling approaches is compared and analyzed.
Effort for solution evaluation.PD approach transforms design requirements into parameters, creating a controlled environment for solution evaluation.The performance of solutions is determined by varying parameter combinations and their constraints, with the optimal solution identified through the best parameter combination (see Figure 8).Designers, relying on experience and expertise, evaluate these combinations, considering decisive parameters and managing conflicts between interacting parameters.However, the exploration process demands manual variation of parameters, relying on intuition and observations from previous projects.Achieving the optimal solution with PD requires significant effort, and knowledge limitations may lead to nonoptimal outcomes.Consequently, the PD approach receives a lower rating for solution evaluation effort.
KBD approach facilitates evaluation through reasoning mechanisms, employing various inference engines with control knowledge.These engines automatically seek optimal solutions based on the knowledge base information (see Figure 9).The gained knowledge refines design parameters for further analysis or identifies the best-met design solution.This characteristic stems from the ability of inference engines to be repeatedly triggered with changed inputs, allowing the KBD approach to evaluate numerous design variations swiftly.Consequently, KBD offers efficient support for solution evaluation with lower effort compared to the PD approach.
Solution evaluation with GD approach involves an auxiliary optimization algorithm that varies production system rules, encompassing vocabulary and rules defining required properties and boundary conditions (see Figure 10).This evaluation is primarily a designeroriented task, with crucial interactions between designers and optimization algorithms during the search process.Since a small change in production system rules can lead to a significant alteration in the CAD model, designers invest considerable effort in identifying optimal rule sets for each design case based on requirements.Consequently, the effort for solution evaluation is closely tied to the decision-making process for rule set identification.While the GD approach is better estimated than the PD approach due to its semiautomatic evaluation, it is not superior to the KBD approach, as managing interactions and determining production rule sets requires additional effort.
Limitation for solution evaluation.While designers' expertise allows them to assess various design solutions, the evaluation process in the PD approach is  constrained by their cognitive limitations and understanding of the design problem.As product complexity increases, the number of design parameters grows exponentially, particularly when dealing with tasks involving multiple objectives.Balancing these objectives requires a nuanced understanding of tradeoffs, referencing performance requirements.In this context, designers tend to evaluate solutions within their comfort zone, relying on their experiences and cognitive abilities from past projects.Consequently, this limitation results in a narrow assessment range, hindering a comprehensive analysis of all possible solutions during the evaluation process.
Regarding KBD approach, the main limitation in solution evaluation is closely tied to the size of the knowledge base, where problem-solving strategies and related knowledge are documented.This knowledge guides designers and offers recommendations for evaluating solutions, which are generated in a predefined manner.Consequently, solution evaluation is performed based on given specifications before the solutions are generated, rendering them predictable and validated.However, the KBD approach lacks a mechanism to conclusively identify the optimal solution, as all alternatives are considered equally for the task.This places a burden on designers to decide which alternative to implement.Nevertheless, despite this challenge, the KBD approach experiences minimal limitations in solution evaluation because the knowledgebacked solutions ensure their correctness.
GD approach lacks inherent support for solution evaluation, necessitating reliance on designers and auxiliary optimization algorithms.Generating different variations with the same rule sets poses a challenge for evaluation, as success within the explored DSS is not guaranteed, and failure is not certain outside of it.Designers must specify actions at each derivation step clearly.As product complexity increases, identifying production rule sets becomes challenging due to a growing number of design variables.Therefore, the GD approach plays a crucial role in solution evaluation.
Properties of explored DSS.Design tasks vary across engineering disciplines, and effective exploration of the DSS is crucial for finding optimal solutions.Different modeling approaches can be applied to explore the DSS, each with distinct mechanisms, leading to variations in the properties of the explored DSS.Gero 49 highlights the dynamic nature of DSS size requirements, emphasizing the need for adaptability to variable solution demands.The primary property of an explored DSS is its size, denoting the variety of solution alternatives it encompasses. 50A broader range of solutions results in a larger explored DSS.Further, designers often face changing requirements during exploration, necessitating adjustments to the DSS. 51his raises concerns about the DSS's ability to meet new requirements, potentially leading to a lack of feasible solutions.To address this, the second key property of the explored DSS is its expandability, indicating the flexibility to adapt to evolving design requirements.Analyzing and comparing modeling approaches in terms of the size and expandability of the explored DSS provides valuable insights for effective design exploration.
Size of the explored DSS.While implementing PD approach for DSS exploration, the final size of the DSS is heavily influenced by the designer's existing knowledge of the problem domain and potential solutions.Designers often prioritize creating solutions within their comfort zone rather than exploring a diverse range of possibilities.Consequently, significant portions of the DSS may remain unexplored, as handling greater variety introduces complexity that may exceed their capacity.Despite the relative ease of application, the PD approach limits designers to exploring a small range of variety due to knowledge constraints, resulting in a comparatively small explored DSS.
KBD approach provides design automation capability for exploring solutions by leveraging a knowledge base, generating diverse solution alternatives to meet various requirements.However, heavy reliance on the knowledge base diminishes the role of creativity.During the exploration process, all solution alternatives can only be generated in a predefined region due to limitations in the engineering knowledge within the base, restricting the variety of solutions.Despite this constraint, KBD achieves a relatively broader range by drawing from knowledge contributed by multiple experts from different disciplines, distinguishing it from the more individual-focused PD approach.Hence, while the KBD approach is rated higher than PD, its overall rating is tempered by the perceived decrease in design creativity.
GD approach operates iteratively across various domains, facilitating the generation of diverse design alternatives.This empowers designers to explore layouts or topologies that differ significantly, producing solutions beyond the typical imagination of human designers.This characteristic offers twofold advantages: it greatly enhances solution variety through large structural and topological differences, and it serves as a source of unimagined design solutions for creative inspiration.Consequently, the GD approach excels in providing a wide range of distinct and innovative solutions, making it highly favorable in this aspect from an academic perspective.
Expandability of the explored DSS.The expansion of the explored DSS through PD approach is challenging due to the unavailability of dependencies and parameters to respond to design changes.In face of the design changes, the explored DSS becomes unreliable as the parametric model struggles to accommodate such alterations.Expanding the DSS may require a complete repetition of the exploration process, involving the addition of new design variables and the removal or replacement of current parameter sets.Thus, expanding the DSS involves redefining new parameter sets and their relationships, often leading designers to restart the whole development process.For this reason, PD approach provides little ability for DSS expansion.
As the design process progressed, the knowledge base of KBD approach is subject to dynamic editing.In case the initial knowledge base cannot generate a feasible solution regarding the changed requirements, the appropriate knowledge will be gathered and documented.In this context, expanding the explored DSS involves updating and managing the knowledge base to meet specific demands.As long as the knowledge was captured and stored in the knowledge base, the DSS will be expanded by defining proper solutions automatically.However, the effort associated with formulating and implementing new knowledge is considerable.As the design process advances, designers can accumulate additional information and knowledge, systematically incorporating pertinent knowledge to augment the DSS.Thus, KBD approach provides more support for DSS expansion compared to PD approach.
Owning to the automated generation process, GD approach facilitates the iterative creation of a variety of solution alternatives, reducing the effort for expanding the DSS.However, the same production system poses challenges in decision-making and achieving the optimal solution, necessitating additional tools for solution evaluation after each iteration.While the GD approach excels in generating solutions amid changing requirements, the subsequent individual analysis of each solution poses a significant challenge for evaluation.In this regard, GD approach proves superior to the KBD approach for DSS expansion, but not entirely, as it requires additional effort for thorough solution evaluation.

Applications of CAD modeling approaches in DSS exploration
As discussed in the introduction section, DSS exploration has been significantly enriched by the diverse applications of CAD modeling approaches.This section delves into the diverse applications of those approaches in order to provide a comprehensive understanding of their impact on pushing the boundaries of design possibilities within the DSS framework.
Table 1 summarized part of applications of PD in the last decade.The literature collectively highlights the importance of PD in influencing Decision Support Systems (DSS) across various industries.These industries span from automotive, aerospace, and mechanical engineering to architecture, furniture, and fashion design.These applications contribute to the understanding of how the DSS exploration through PD approach can enhance the efficiency, creativity, and functionality of designs in diverse domains.
A collection of KBD applications is summarized in Table 2.It is notable that KBD approaches has been already applied in a wide range of topics in the domain of DSS exploration.The collected literature demonstrates the pervasive influence of KBD in shaping and optimizing the DSS across diverse domains.From automotive to aerospace engineering, and from housing design to fashion, the integration of KBD systems consistently proves effective.The studies also underscore the adaptability of knowledge-based frameworks in addressing challenges such as multidisciplinary optimization, mass customization, and intelligent manufacturing.Overall, the collective findings affirm the versatility and effectiveness of KBD across a spectrum of applications, highlighting its pivotal role in navigating the complexities of DSS exploration.
Variable applications of GD published in recent years are presented in Table 3.The collected studies on  GD underscores its effectiveness in exploring DSS across diverse domains.From aerospace components to building architecture and robotic systems, the studies showcase how GD approaches contribute to innovative and optimized outcomes.The papers highlight the adaptability of GD approaches in addressing specific constraints, including shape variations, topology optimization, and user preferences.Furthermore, the exploration of GD potential in additive manufacturing and cultural contexts exemplifies its versatility.Overall, the collective findings reveal GD as a powerful tool for creative exploration and optimization in various design domains.

Results summary of the comparative analysis
The preceding qualitative analysis has examined the primary CAD modeling approaches, assessing their performance in DSS exploration through three distinct aspects.While these modeling approaches may appear quite distinct from one another, they share similar features for DSS exploration.However, it is evidently clear that the efficient harnessing of engineering knowledge emerges as the critical factor for a successful DSS exploration.The outcomes of this comparative analysis are succinctly summarized in Table 4. PD approach can quickly build a solution but also suffers from a distinct limitation for DSS exploration since the set of all solution alternatives is reduced to the ones that the parametric model is able to generate.This results in a small area of the final DSS.Another drawback of this approach is that there is a lack of sufficient capacity to capture and implement engineering knowledge for guiding solution evaluation, even with a clear parameter plan.Thus, the search for solution alternatives is limited to a small range because the designer's knowledge is restricted to a certain amount.This leads to the corresponding evaluation is confined to an even smaller range as well.Likewise, the explored DSS cannot keep up with the rapid changes of design interpretations by the designer in terms of the varied requirements, offering little flexibility in facing the frequent design changes in both requirements and design aspects.More specifically, decisions regarding the sequence of parameterization will dictate and constrain which aspects of the parametric model can be modified, as well as the extent to which these modifications can be made after the model has been constructed.The parametric model can only deal with changes when the changes have been anticipated in advance and represented with a proper modeling sequence.Otherwise, the model may not be sufficiently robust to accommodate such changes effectively.
KBD approach is considered to be equivalent to or better than others in all criteria, except the lower rating on solution creation because of the considerable effort required for explicit knowledge formulation and representation.An incomprehensive formulation of engineering knowledge about the given problem and related problem-solving strategies will eventually prevent designers from exploring the DSS.However, the high modeling effort is justified to deliver downstream benefits, that is, automation of the solution evaluation process.The knowledge enriched CAD model automates the evaluation process since all solutions are to be checked for correctness and consistency in terms of the performance requirements.Nevertheless, the main disadvantage of this approach is that all solutions are limited to a fixed scope.This can impose a significant burden on designers in certain cases, as they may need to reconstruct the knowledge base to facilitate the creation of a creative solution or to adapt to evolving design requirements.From there, a significant effort is expected to implement and represent the engineering knowledge successfully.
GD approach has a strong capacity for finding solution alternatives, leading to a wide solution variety, that is, a large breadth of the DSS.Regardless of the performance of these solutions, the wide variety can be viewed as an inspired source that increases designers' knowledge and awareness of the existing DSS.While the explored solutions may not always present fully developed concepts for design problems, they can act as prompts that aid in retrieving relevant knowledge, thereby facilitating the development of innovative solutions.This characteristic significantly enhances designers' creativity throughout the product development process.However, it's important to note that there is also a substantial burden placed on designers when it comes to solution evaluation and selection.In fact, since GD approach necessitates a designer-centric selection process during evaluation, conducting a systematic performance analysis of each solution alternative proves to be a challenging task for designers, given time constraints and other limitations.As the complexity of the product increases, the production system becomes progressively intricate.Designers are thus faced with the challenge of identifying production rule sets for generating solutions and evaluating the explored solutions for selection.

Discussion
According to the analysis results, there was a high degree of agreement that each modeling approach has both strengths or weaknesses for DSS exploration.In this section, a critical discussion about the contributions and issues to be solved in the future related to DSS exploration is presented.

Contributions
DSS exploration is a knowledge-oriented activity: Referring to the analysis results, engineering knowledge plays a central role in DSS exploration whether automatic or manual.The activities of solution generation and evaluation can only be effectively conducted when there is a sufficient amount of knowledge available.In aerospace engineering, deep insights into aerodynamics and materials science facilitated the development of fuel-efficient aircraft.Biomedical engineers applied their understanding of biomechanics and materials to design prosthetics that closely mimic natural limb function.Civil engineers, drawing upon their knowledge of sustainability and community needs, explored a multitude of designs for eco-friendly and resilient infrastructure.In software engineering, a strong foundation in computer science guided the exploration of efficient algorithms, particularly in fields like artificial intelligence.Electrical engineers leveraged their expertise in electrical systems to design innovative renewable energy solutions.Finally, in mechanical engineering, knowledge of materials, structural mechanics, and crash dynamics played a pivotal role in optimizing automotive designs for safety.It follows that the size of DSS is directly proportional to the volume of engineering knowledge implemented.In essence, the effectiveness of DSS exploration is intricately tied to the quantity of engineering knowledge at hand.During the exploration practice, it requires not only a deep understanding of the problem to be handled as well as the engineering problem-solving knowledge but also a basic understanding of how the selected exploration approach operates, including what are the functions of the operators and how the mechanisms work.Clearly, knowledge implementation plays an integral role in the performance of DSS exploration, since the integrated knowledge is in charge of guiding the search into promising regions of the solution space.
Different application scenarios of modeling approaches: Due to its capacity to explicitly implement design knowledge by defining constraints between parameters, PD approach demonstrates high potential for adaptive and variant design tasks.Throughout the design process, the parametric model, serving as a representation of DSS can be manually manipulated by designers.This manipulation allows solutions to be achieved through either redefining parameter sets or modifying the relationships between them.KBD approach takes this a step further by streamlining the adaptation of solutions to new requirements and automating the routine generation process.This characteristic leads to a relatively extensive range of product variations that can effectively address high levels of heterogeneity to cater to diverse customer needs, such as mass customization.
However, the resulting solutions through PD and KBD approach tend to be less innovative because the solutions are generated in favor of reusing existing solutions.This decreases solution variety leading to PD and KBD approach might not be the most desirable approaches in the early design stages where exploration of DSS can make a significant difference and influence the further development of the design task.In contrast, although GD approach generates solutions with a set of production rules in a very definitive way, a wide variety of solution alternatives can be explored because many dissimilar solutions can be generated even with the same rule sets during the derivative process.Thus, the designers enlarge their creativity from the observation and inspiration of those solutions out of their imagination.For this reason, it is probably not surprising that GD is more suitable for creative design tasks, which right now only a little knowledge with the design solution is available.
Modeling approaches complement each other: Since the modeling approaches are based on different problem-solving logics, their strengths and weaknesses are located at different aspects (referred to Table 4).This implies the potentials of combinations of those approaches, in which they could be combined to improve their performance in exploring a DSS, as illustrated in Figure 11.
As discussed, PD and KBD approaches cannot deal very well with the solution variety but lower effort required for evaluation and conversely GD approach provides wide solution variety with little support in evaluation.Thus, it does make sense to take the union of them, thereby the explored solution alternatives from GD serve as an inspiration resource for PD and KBD approach and then achieve a wider variety of the DSS to a given problem with little effort for evaluation.Regarding the significant effort required for establishing a knowledge base, parametric models are one of the best knowledge carriers for knowledge implementation, which can be set up quickly.Thus, PD approach is among the most preferred tools for KBD approach regarding knowledge implementation.In addition, the knowledge derived from the knowledge base in turn provides strong support for determining the suitable combinations of parameters of PD approach and defining valuable production rules of GD approach respectively.It is confirmed that all three modeling approaches complement each other, enabling designers to maximize their strengths and minimize their weaknesses.

Issues for future research
Developing analysis tool for quick solution evaluation: Generally, there was a strong consensus among designers that the availability of a robust analysis tool would significantly enhance the effectiveness of DSS exploration. 79Essentially, when a large amount of solution alternatives has been explored, the primary issue is how to get a more precise estimate of their performance. 98During the evaluation process, multiple objectives (e.g., stiffness, cost and weight) should be considered simultaneously, even though they are often in conflict.Consequently, optimal decisions must be made while considering trade-offs between various design variables. 99Since the tradeoff analysis takes a large amount of time, analysis tools should be developed which can give an approximate analysis of solutions in a fraction of time compared to accurate analysis. 100Such tools are very important for a quick comparison of design decisions and are becoming more important with the increasing complexity of designs.
Providing consistent knowledge representation method: Another special issue is that a consistent knowledge representation framework for the integration of engineering knowledge into design solutions is missing. 101Currently, engineering knowledge is normally represented in different levels of abstraction and the designer has to select the one as required for a particular task manually. 102Thus, different knowledge representations, such as statements, sketches, rules, constraints, grammar, and programmers, are needed to describe the various aspects of design concepts so as to reflect the engineering knowledge and imagination in an exploration process.From there, the necessity for developing a new method with flexible knowledge representations for DSS exploration, is identified and worthy to be further investigated.
Considering requirement uncertainties during the DSS exploration process: Many requirements remain ambiguous in the early exploration stage due to the lack of information and knowledge, which brings a large amount of requirements uncertainties and thus many design changes. 103,104Such changes lead to a big issue that a feasible solution in the DSS frequently becomes an infeasible one.Concerning this issue, a useful modeling strategy for accommodating such changes is to utilize the same representation for requirements and the initial solution response to the changes. 105In this sense, the exploration of high-quality or robust solutions requires the integration of such uncertainties throughout the DSS exploration process.However, the uncertainties of requirements in the early development phase remain in a large amount and thus the integration of them along with the exploration process is still a challenge during design.
Handling the increased complexity of a design task: Due to the integration of new and additional functionalities, the product to be developed becomes more and more complex, whereby the number of design variables is largely increased. 106Further, ongoing understanding and evolving design requirements address continuous modifications of designs.The transitions from requirements to design variables are also a highly dynamic process that makes the design task even more complex.Consequently, the DSS grows exponentially because the possible variable combinations far outweigh the dependent combinations.This means that designers are confronted with the challenge by making the right decision of variables in the early exploration stage. 107owever, there is only low detailed knowledge of the design problem available at that time.As a result, designers will attempt to explore the DSS using a partial understanding of the problem in the presence of an increasing number of design variables. 108Obviously, due to a large number of possible design alternatives along with different variable combinations, the DSS is too large to exploration that beyond designers' capacity.In this regard, a new modeling approach should be developed under the consideration of handling all requirements at the same time with reduced complexity.

Conclusions
As elaborated in the preceding sections, CAD modeling approaches play a crucial role in developing solutions for various design tasks.This paper conducted an indepth examination of three prominent CAD modeling approaches, assessing their performance in the realm of DSS exploration.Following a comprehensive introduction to each modeling approach and their respective implementations, the procedures for solution development associated with each approach were identified.Additionally, the working process of DSS exploration was discussed.To facilitate a comparative analysis, six evaluation criteria, divided into three categories related to the exploration process, were established.The evaluation results indicated that the PD approach requires less effort for solution generation but faces challenges in solution evaluation and exhibits limitations in the size of its explored DSS.Conversely, the KBD approach demands considerable effort for solution generation but offers advantages in downstream solution evaluation and DSS expansion.The GD approach follows a different path by generating solutions automatically, with manual evaluation by designers themselves.In summary, the six evaluation criteria developed in this research serve as the foundation for gaining a comprehensive understanding of how these modeling approaches perform in DSS exploration.Importantly, these criteria enable the identification of the strengths and limitations of each modeling approach in DSS exploration and suggest possible avenues for combining these approaches to achieve improved DSS exploration.
For future research, two primary directions are proposed.First, there is room for enhancing the analysis and implementation of DSS exploration.The evaluation criteria used in this study are derived from the exploration process, which excludes the influence of designers and engineers.It may be valuable to consider how the performance of these modeling approaches varies among different designers due to their expertise and engineering knowledge, which can significantly impact DSS exploration outcomes.Additionally, given the increased complexity of design tasks and the presence of numerous requirement uncertainties, DSS exploration can be viewed as a method to naturally integrate robustness into the design process, effectively addressing continuous design changes with minimal effort.Lastly, the exploration of combining different modeling approaches to solve design tasks holds potential for further development and warrants exploration in future research endeavors.

Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Figure 2 .
Figure2.Basic structure of a KBD design application.21

Figure 3
Figure3.GD approach of a walker robot design.34

Figure 5 .
Figure 5. Schematic description of PD approach for a feasible solution generation.

Figure 6 .
Figure 6.Schematic description of KBD approach for a feasible solution generation.

Figure 7 .
Figure 7. Schematic description of GD approach for a feasible solution generation.

Figure 8 .
Figure 8. Schematic description of PD approach for determining the optimal solution.

Figure 9 .
Figure 9. Schematic description of KBD approach for determining the optimal solution.

Figure 10 .
Figure 10.Schematic description of GD approach for determining the optimal solution.

Table 1 .
Applications of PD in DSS exploration.

Table 2 .
Applications of KBD in DSS exploration.

Table 3 .
Applications of GD in DSS exploration.

Table 4 .
Evaluation results of different modeling approaches.