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Review

A Systematic Mapping Study and a Review of the Optimization Methods of Structures in Architectural Design

by
Bunji Izumi
1,*,
Marcin Luczkowski
2,
Nathalie Labonnote
3,
Bendik Manum
1 and
Anders Rønnquist
2
1
Department of Architecture and Technology, Norwegian University of Science and Technology, 7491 Trondheim, Norway
2
Department of Structural Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway
3
SINTEF Community, 7465 Trondheim, Norway
*
Author to whom correspondence should be addressed.
Buildings 2024, 14(11), 3511; https://doi.org/10.3390/buildings14113511
Submission received: 17 September 2024 / Revised: 28 October 2024 / Accepted: 29 October 2024 / Published: 2 November 2024
(This article belongs to the Section Building Structures)
Browse Figures
Versions Notes

Abstract

:
Structural optimization has gained popularity in modern structural design, helping to reduce material consumption while maintaining the structural performance of buildings. This process also significantly influences the architectural appearance, affecting various aspects such as cross-section sizing, structural forms, and the layout of structural members. Beyond minimizing materials or costs, structural optimization can serve as a powerful tool for making architecture more visually appealing. However, with the wide variety of structural optimization methods proposed, gaining a comprehensive overview has become challenging. To address this, a systematic mapping study has been conducted, focusing on methods introduced over the past decade. The relevant journal articles are categorized based on several factors, including types of optimization, materials used, structural typologies, areas of application, and optimization objectives. The results of this study provide both a broad overview of recent developments in structural optimization and valuable insights into research-rich and under-explored areas. Moreover, the paper discusses which types of structural optimization are more relevant when applied as part of the architectural design process. It is suggested that future research should focus on identifying gaps and challenges in effectively applying structural optimization to architectural design, thus enhancing both efficiency and aesthetic potential.

1. Introduction

The structural performances of a building are determined by combining material selection, structural system selection, structural member layout, building shape, and cross-section size of each structural member. It has been common practice for structural engineers, together with architects, to make a series of decisions about the structural planning of the building. Structural optimization helps this process increase structural performances while maintaining material consumption, or reduce material consumption while maintaining structural performances. Structural optimization in the modern sense, employing a finite element program and an optimization engine, began in earnest in the 1960s by Schmit [1], according to Vanderplatts [2]. Since then, many structural optimization methods have been proposed at different levels. Bendsøe et al. [3] categorized the methods into three levels, which are topology, shape, and size. Furthermore, the number and type of structural optimizations have increased significantly. As shown in Figure 1, the number of academic articles published annually in two journals directly related to the field of structural optimization has risen, particularly in the last decade [4,5]. Despite this growth, previous research by the authors [6] using web scraping techniques revealed that the application of topology optimization in architecture remains limited. To gather preliminary data that could serve as a basis for developing a new type of optimization tool for architectural and structural design, the authors have focused on topology optimization methods proposed in the last decade. This focus leads to the following research questions (RQs).
  • What topology optimization methods have been proposed in the last decade?
  • Are there any changes in trends observed during the period?

2. Method

The systematic mapping method originated in software science in the 2000s proposed by Petersen et al. [7] and has been applied here to the field of structural optimization in architectural applications. The systematic mapping applied in this research has been made with the following procedure.
Regarding the databases, Scopus and Engineering Village (Compendex and Inspec) were chosen. Journal articles published between 2014 and 2023 and written in English were chosen as a parent set. Table 1 summarizes the keywords used for the search query. The search key was carefully designed according to the ’CIMO-logic’ proposed by Denyer et al. [8]. Elements within a column were combined with the Boolean operator ’OR’ and the columns were connected by the Boolean operator ’AND.’ In addition, the authors found at the initial attempts that the search key caused to include papers from irrelevant fields (such as medical, industrial, chemical, or food). Therefore, the search terms shown in the far right column in Table 1 were added to efficiently exclude irrelevant papers from these fields by the Boolean operator ‘AND NOT’. After identifying potentially relevant articles from the two databases, the overlapped articles were eliminated.
Here, in order to select articles based on a consistent standard while minimizing subjectivity, we established Inclusion and Exclusion rules. These are listed below in bullet points. From the database search results, we first efficiently selected articles that could potentially be relevant according to the inclusion rules, and then further refined the selection using exclusion rules to determine the articles for the population in the systematic mapping. In the inclusion rules, articles that met all the criteria were retained for subsequent processes, while in the exclusion rules, any article that met even one criterion was excluded.
(Inclusion rules)
  • (I1) Journal articles published between 2014–2023 written in English
  • (I2) Description of structure in the title
  • (I3) The description of optimization in the title, abstract or keywords
  • (I4) The term “Optim*” appears to be associated with its structure in the title, abstract or keywords
(Exclusion rules)
  • (E1) Not a design of new construction (ex. “diagnosis”, “inspection”, or “retrofit”)
  • (E2) The term “Optim*” is used without referring to particular methods (ex. “optimal shape”, “optimal solution” with no supporting information on methods)
  • (E3) Review articles
  • (E4) Found not to be a structural optimization after reading the body text.
Lastly, the remaining articles were examined from different classifications (C1 to C7), as shown in Table 2. This information was searched and classified, including the text itself. One paper can be associated with multiple items in the same classification category. For C1, the classification by Bendsøe et al. [3] is followed, and items that do not fit into this classification are categorized as Others. Material (C2) was observed for the main part that is being studied in each investigation. The objectives (C3) are classified as follows: Stiffness includes compliance, deformation, and displacement. Cost encompasses both Initial Cost and Operational Cost. Carbon and GHG emissions, which vary in terminology across studies and fields, include reductions in carbon, CO2, and other specific emissions. Vibration includes performance related to structural vibrations, such as response acceleration, natural periods, and floor vibrations. C4 refers to the number of objectives to optimize. Concerning C5, spatial refers to the structural system that supports large internal spaces with few or no columns, regardless of scale. The classification focuses on the typology of parts that are subject to optimization. The C6 Tool is aimed at tool development and generalizing the methodologies proposed. Case studies include past architectural projects and their contexts. Studies that do not incorporate the architectural context, such as form alone, are excluded. Prototyping involves the creation and validation of actual structures based on research content. Used case includes designs applied to actual projects, including those that are not completed. For C7, individual elements such as beams and exterior mullions are categorized as Building Component, parts composed of multiple types of Building Component (for example, lateral resistance elements like building-wide braces) are categorized as Part of Building, and those contributing to the entire building’s vertical support system are categorized as Entire Building.

3. Results

3.1. Systematic Search

Figure 2 shows the actual procedure with corresponding number of the remaining articles after each step. The search took place on 25 February 2024 on both databases. The search included the conditions presented in Table 1, and the actual search queries in both databases are shown in Figure 3. One inclusion rule set up for the later phase, (I1) “Journal articles published between 2014–2023 written in English”, was actually able to be included in both databases’ search queries. The search results from both databases accumulated 1236 results with 378 duplication of identical articles. After removing the overlap, 858 articles proceeded in the manual screening process to exclude irrelevant papers. Then, by the Inclusion rules (I2–I4), 239 articles were collected, from where by Exclusion rules, 152 article remained. Other than the rules set up in the Section 2, there were 20 articles for which access was found not granted by NTNU and could not be observed, and they were therefore excluded in the later process. There was one non-English article found in this subset of the database, and it was also excluded. The 152 articles [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160] are the population further analyzed in the next step.

3.2. Result by Classifications

The results according to the classifications are visualized in Figure 4. Figure 4a shows the most frequent category of structural optimization is the sizing optimization, followed by the topology and shape optimization. Among those in the category of “others”, the most popular type of optimization is that of devices (such as those of base isolation systems or dampers) against seismic or wind load, where the properties of the devices are design variables [9,10,11,12,13,14,15,16,17,18,19,20,21,90]. From the material point of view (Figure 4b), concrete is the most frequent material, followed by steel. Compared to these two materials, the small proportion of timber structures is noticeable. Among others, plastic types [22,87], masonry [91], fiber reinforced polymer [23], aluminum [24,25,26] were found. When it comes to the objectives, Figure 4c suggests that Stiffness, Weight/Mass and Cost are the three major objectives. It is worth mentioning that Emissions ( n = 16 ) and energy, which are not directly associated with structural performance, follow the top three objectives. There were 27 articles that had other types of objectives. Among these articles, the most frequent objective as a category was the damper device parameters as objectives [9,12,15,16,18,19,90]. In addition to those, Mangal et al. [27] uses the number of rebar clashes in the concrete cross sections; ref. [92] uses the proximity to the target shape; Steinar et al. [28] uses the number of freestanding columns in the architectural space; Wonoto and Blouin [29] uses the twist angle of a tower, Preisinger and Heimrath [24] use the angles between adjoining elements as objectives. Regarding the number of single-objective optimization (SOO) and multi-objective optimization MOO), the majority of articles used SOO, while about 20% of the articles handled MOO Figure 4d. Building typologies Figure 4e reveal that application to multi-story buildings is dominant with 125 cases, followed by spatial structures with 17 cases. Among others, there were single-story structures [24,30,87], bridges [31,32], as well as a tree-shaped structure [33], stairs [34] and the brick support bracket of the facade [35]. In terms of types of research (Figure 4f), methods articles are the largest population, followed by case studies. Finally, in terms of the area of application, the application to the entire building is the largest in number (Figure 4g), followed by the building components and part of the building.

3.3. Result by Interactions of Classifications

In the previous subsection, the results of the systematic mapping study according to the seven individual classifications were presented. In this subsection, the results were further analyzed by obtaining the interactions of the results from different classifications. Since there were seven classifications, the possible number of combinations of the two classifications is C ( 7 , 2 ) = 21 . However, only the combinations meaningful for understanding the landscape of structural optimizations in architectural design were chosen and presented here. The chosen combinations of the two classifications are summarized in Table 3.
Figure 5 and Figure 6 show the resulting frequencies of the articles by the interactions of the two classifications. In Figure 5a, it is observed that the Sizing problem with either Weight or Mass as the objective was the most frequent. It is also observed that Sizing optimization is more associated with the objectives Emissions and Weight/Mass whereas Topology optimization is more associated with the stiffness as objective. If we look at the interaction of Category(C1) and Number of objectives(C4), the share of the multi-objective optimization (59) in comparison to single objective optimization (14) in the Sizing optimization is found to be approximately proportionate to that found in Figure 4d (30 against 121), while that found for Topology optimization is significantly lower (5 against 46). Figure 5c shows that the most frequent kind of optimization is Sizing optimization applied for the Multistory building typology. When focusing on the category of Spatial, it can be observed that there are no significant differences in the frequencies of the categories Topology, Shape, and Size (n = 7, 8, 6 respectively). However, considering that Shape is the category with the lowest frequency among these three (n = 39), as shown in Figure 4a, it can be concluded that Shape optimization is more utilized within the Spatial category. Figure 5d shows that Single objective optimization is most frequent for Multistory buildings (n = 98), while the application of Multi-objective optimization in Spatial structures is significantly limited (n = 2).
Figure 6 is a continuation of Figure 5. Figure 6a shows the interaction between the optimization category and the Research Type. From this figure, it is clear that studies on Size are the most frequent for both Methodology and Case study. However, there are a sufficient number of cases in each of the three categories: Topology, Shape and Size. On the other hand, there are fewer studies on Tool, Prototyping, and Used case compared to the former two. Figure 6b shows the interaction between Building Typology and Research Type. It is evident that for Multistory Building Typology, the frequency of Methodology and Case study is remarkably high. Additionally, these items are less frequent for Spatial, which is not surprising as shown in Figure 4e. However, Figure 6b reveals that studies on Prototyping are more frequent for Spatial structures than for Multistory. Lastly, as the final figure in the interaction, Figure 6c. This figure shows which optimization categories are applied to which parts of the building. It is clear that the category of Size optimization is most frequently applied to the entire building.
Word clouds (Figure 7) were finally used to identify significant words by locating the most frequent words in larger letters toward the center of the graphic, and less significant words in the periphery and in smaller letters. The 100 most frequent words were collected and mapped in each graphic. Two word clouds were produced by the text data of the journal articles published in the period 2012–2014 and in the period 2019–2021, corresponding to the first and last three years of the entire period of this research. The difference in the location of each word can mean the trend difference in two periods. NVivo 14 was used to create those figures. By the software configuration, words with the same stem were grouped. By comparing the two figures, it is observed that the term “section(s)” has gained more weight, whereas the terms “topology” and “shape” have reduced their weights. Another finding is that the term “energy” has reduced its weight, while a couple of words in the peripheral fields, “carbon(ation)” and “emissions”, have emerged. This may indicate a greater awareness of more nuanced environmental performance in the field of structural optimization. It may also reflect the growing awareness and demands for environmental sustainability, such as the 17 Sustainable Development Goals adopted in 2015, aimed at achieving sustainable development by 2030.

4. Review—Topology Optimization

In the previous section, we clarified how research on applying structural optimization to architecture has been distributed over the past decade using the method of systematic mapping from various perspectives. Thus, in this section, we will conduct a review focusing particularly on topology optimization through an in-depth analysis of the relevant papers.
Zegard et al. [36] reported on the development of general tools by integrating three different topology optimization methods, the ground structure method, density-based and graphic statics, with existing numerical libraries and CAD environments such as Rhino and Grasshopper [161]. Those three methods were applied in different contexts, such as the layout of horizontal resistance elements in high-rise buildings and the conceptual design of single-story houses designed for 3D additive manufacturing. This is one of the few documented applications of topology optimization. These tools were designed with ease of use in mind for architects as an in-house development, distinguishing them from existing commercial tools. Beghini et al. [37] have proposed using structural optimization as a bridge between architectural design and structural engineering from the perspective of the practitioner. They highlighted the reciprocal relationship between architects and engineers, emphasizing the importance of integrated design in collaborative environments. Examples of topology optimization applied at the conceptual stage of several actual projects were shown, including horizontal resistance elements in skyscrapers and cantilevered structures in buildings such as bridges, where the optimized structural elements significantly shape the architectural form.
There were also many papers within a cluster that focused on lateral resistance elements of high-rise or super-high-rise buildings using topology optimization. For example, Angelucci et al. [85] reported a method to apply topology optimization based on the SIMP method (Solid Isotropic Material with Penalization method) initially proposed by Bendse and Kikuchi [162]. It is applied to the layout of horizontal resistance elements in multi-story buildings, similar to the Zegard ground structure method [36]. They proposed an optimization flow combining MathWorks [163] and Ansys [164], performing a parametric study with varying mesh sizes using shell elements to model floor slabs and exterior walls, and beam elements for columns and beams. Differences in topology between 2D and 3D models were discussed, recommending 3D modeling. Tsavdaridis et al. [38] provided an extensive review of two major topology optimization methods, the SIMP and ESO methods, considering structural efficiency and aesthetics. Their case studies proposed the application of SIMP algorithms to the exoskeleton of irregularly shaped skyscrapers and the topology of I-beam web openings, demonstrating the potential for broad-scale application. Lu et al. [39] also reported on the optimal placement of diagonal bracing within the vertical plane of high-rise buildings under different loading conditions using three types of bracing: Cross-bracing, Stromberg bracing, and Optimized bracing. Zhang and Mueller [40] described the presence or absence of shear walls in high-rise buildings using binary strings and proposed an evolutionary algorithm to optimize the placement of walls with structural weight as an objective function. This method is suitable for both the conceptual design stage and the identification of the shear positions of the wall after the architectural plan has been completed. Li et al. [41] examined the application of the BESO topology optimization method to real-world structural design, comparing engineer-designed layouts with those derived from topology optimization, accounting for static loads including seismic forces. This study emphasized the collaboration between architects and structural engineers and highlighted the need to consider loads not considered in topology optimization. Zhu et al. [42] proposed a method to determine the layout of the outriggers and diagonal bracing in skyscrapers using the SIMP method and the MMA (Method of Moving Asymptotes), considering dynamic loads such as seismic and wind pressures in different domains. Laccone et al. [43] combined parametric modeling and polygon partitioning to adjust polygon densities according to predefined structural schemes, such as outrigger systems, proposing a method for generating layouts of structural members on the periphery of skyscrapers.
Recent examples of horizontal resistance elements in buildings have also begun to include cases using machine learning. Lu et al. [44] utilized generative adversarial networks (GAN) to generate shear wall positions from the floor plans of skyscrapers. Their Physics-enhanced GAN generated multipoint models from the shear wall positions to calculate interstory displacements through dynamic analysis, showing the superiority of Physics-enhanced GAN over untrained GANs. Lou et al. [45] developed a method for the optimal placement of shear walls in skyscrapers using Support Vector Machine (SVM) and Tabu Search to avoid local optima and enable global optimization, minimizing structural weight while constraining story drift and period ratio.
Another cluster used a grammar-based approach. Boonstra et al. [46] proposed an efficient conversion of 3D domains into sets of rectangular regions using a grammar-based method, generating beam, truss, and slab elements within each region. Their case study proposed a multi-objective optimization for minimizing strain energy and structural volume. Steinar et al. [28] proposed an algorithm to minimize the number of independent columns within interior spaces by setting an initial structural grid from floor plans and inserting columns into structurally unstable areas, ensuring feasibility and minimizing the total length of beams. Tomei et al. [84] used shape grammar, a type of grammar-based approach, to apply structural layouts to high-rise and spatial structures, optimizing shapes with genetic algorithms to minimize structural weight.
Diverse notable papers also included Vantyghem et al. [35], who focused on optimizing brickwork support brackets with linear structural and thermal analyses using the MMA, and Lee et al. [26], who optimized the layout and sections of aluminum curtain wall supports for skyscraper exteriors using parametric modeling. Boonstra et al. [47] also proposed a co-evolutionary multidisciplinary optimization toolbox aiming at optimizing both structural and thermal performance by dividing cuboid-defined regions into structural and building physics models using grammar-based methods. He et al. [31] proposed combining BESO with genetic algorithms and stochastic approaches to efficiently explore variations in structural layouts, while Suau and Zegard [32] suggested dividing design domains into subdomains to optimize the layout of outriggers and bridge supports in high-rise buildings. Cousin et al. [75] presented a method to optimize the combination of existing branched materials using the Hungarian Matching Algorithm and FEA, reducing excessive deformation under loads and external forces.

5. Discussion

The systematic mapping of structural optimization methods reveals several key trends and developments in the past decade, which have important implications for both research and practice in architectural design. The analysis indicates that sizing optimization is the category most frequently studied, followed by topology and shape optimizations. This trend highlights a prevailing interest in optimizing material usage and structural performance by precisely adjusting the dimensions of structural elements. This is particularly relevant in contemporary design, where the efficient use of materials is paramount due to both economic and environmental considerations. Concrete and steel are the most commonly investigated materials in optimization studies, reflecting their ubiquitous use in the construction industry. However, there is a noticeable gap in the research that focuses on timber structures. This gap represents a significant opportunity for future exploration, especially given the increasing emphasis on sustainability and the potential of timber as a renewable building material. The development of timber optimization techniques could lead to innovations in sustainable architecture and a more widespread adoption of wood in large-scale construction projects.
Another gap is the limited application of optimization methods to spatial structures. These structures, which often feature complex geometries and require innovative design solutions, could benefit greatly from advanced optimization techniques. Future research should explore the potential of applying optimization methods to spatial structures to achieve both structural efficiency and aesthetic excellence.
It is also important to reiterate that most of the reviewed papers focused on methods for structural optimization and their validation through case studies. However, only a small number of articles reported on the development of tools (n = 2) and used cases (n = 6) that could facilitate the application of these methods in practical design. Several factors may contribute to this observation. First, sizing optimization has become so widely integrated into standard structural analysis software (e.g., Etabs [165], Rfem [166]) that it may no longer be deemed necessary to highlight it in academic papers. Similarly, shape optimization has reached a practical level of applicability due to the widespread use of tools such as Rhino, Grasshopper, and structural analysis plugins such as Karamba3D [24], which function within Grasshopper. Consequently, there may be less incentive to publish studies specifically focused on these tools. However, the tools that implement topology optimization remain limited. The only commercial tools identified by the authors are the Ameba [167], which is a Grasshopper plugin, and a feature within Karamba3D. One possible interpretation for the limited number of tools and used cases reported is that the scarcity of widely accessible tools for various optimization methodologies has resulted in fewer practical applications being documented. Although confirmation of the validity of this hypothesis will require further research, which should be addressed in future studies, the development and refinement of tools in this area is clearly needed.
The objectives of structural optimization have traditionally been to improve stiffness, reduce weight and mass, and reduce costs. These objectives are critical to improving the performance and cost-effectiveness of buildings. However, there has been a noticeable shift towards environmental sustainability, with an emerging focus on minimizing carbon and greenhouse gas emissions. This shift aligns with global sustainability goals, such as the 17 Sustainable Development Goals adopted by the United Nations. It reflects a growing awareness of the environmental impact of building structures and the need to develop more sustainable design practices. The results also show a dominant application of optimization methods to multi-story buildings, with less emphasis on spatial structures. Multistory buildings present more opportunities for optimization due to their complexity and scale, which can lead to significant material and cost savings. However, the relative lack of focus on spatial structures suggests that this area may benefit from further research and development. Spatial structures, which often involve complex geometries and require innovative design solutions, could greatly benefit from advanced optimization techniques.
Upon examining the use case examples in detail, three articles [36,37,41] applied topology optimization to architectural design in actual projects. The areas of application included lateral resistance elements arranged along the exterior walls of skyscrapers or diagrid structures integrated into the facade, the arrangement of bridge structure members connecting high-rise buildings, the placement of reinforcement ribs in monocoque pavilion structures, and the proposal of structural layouts after determining the shape of a mid-rise commercial facility. In the cases of skyscraper facades and the bridge structure, the design was treated as a member placement problem within a predefined design space after the shape was determined, creating a context that facilitated the application of topology optimization, and thus minimizing the need for adjustments with interior spaces. In the case of the mid-rise commercial facility, although the diagonal members proposed by topology optimization might interfere with the architectural space, the papers did not clarify whether such interference actually occurred. In any case, it is possible that the design space setting in topology optimization significantly influences the complexity of the design, which requires coordination among architectural planning, structure, and facilities. The pavilion employing a monocoque structure is one of the few examples where topology and overall shape were explored simultaneously, and its relatively small scale and adaptability to changes, along with its experimental nature, may have contributed to the project’s realization. In addition, the three articles were delivered by researchers involving two companies based in the United States and China, both of which have in-house architectural and structural engineering departments. Collaboration between architects and engineers may have been more effective within a single company than if structural engineers were external partners or subcontractors of the architects, but more research is needed to confirm this.
The integration of optimization methods into the architectural design process is identified as a critical area for further investigation. Structural optimization has the potential to influence not only the functional performance of buildings but also their aesthetic qualities. There is a growing recognition of the need for interdisciplinary collaboration between structural engineers and architects. This collaboration can ensure that optimization techniques are effectively integrated into the design process, leading to buildings that are structurally efficient and visually appealing.
Finally, we outline the limitations of this report. This study employed a systematic mapping approach to extract papers related to structural optimization published over the past decade, with a focus on a detailed review of papers specifically addressing topology optimization. While we conducted a thorough analysis of the terminology used in these papers to classify and review them, the accuracy of the content within each individual paper has not been independently verified. However, the purpose of this article is to provide an overview of the application of structural optimization techniques in architectural design, and we believe that the methods employed are appropriate for this objective.

6. Conclusions

This systematic mapping study provides a comprehensive overview of the structural optimization methods developed over the past decade. It reveals that size optimization, which focuses on concrete and steel, and objectives related to stiffness, weight/mass, and cost dominate the field. The findings highlight an emerging focus on environmental sustainability, reflecting a shift in priorities toward reducing the carbon footprint and greenhouse gas emissions associated with building structures.
Structural optimization, particularly topology optimization, contributes to the efficient use of limited resources and enhances the appeal of architectural forms. Although studies on structural optimization methodologies have increased over the past decade, the number of topology optimization tools identified through systematic mapping remains limited, potentially hindering their application in architectural design. Future research should focus on developing methods that facilitate the seamless integration of optimization techniques into the design process, emphasizing the importance of incorporating structural optimization in the early stages of architectural design. This requires interdisciplinary collaboration between structural engineers and architects to ensure that optimization methods are technically sound and align with architectural goals and aesthetics. The development of tools may address these challenges and influence the reevaluation of collaborative relationships between architects and engineers.
In general, this study serves as a valuable resource for researchers and practitioners in the field of structural optimization. It provides information on current trends, highlights emerging areas of interest, and identifies opportunities for future research. By addressing identified gaps and fostering interdisciplinary collaboration, the field of structural optimization can continue to advance, leading to more efficient, sustainable, and aesthetically pleasing building designs.

Author Contributions

Conceptualization, B.I., B.M. and A.R.; methodology, B.I. and N.L.; formal analysis, B.I.; investigation, B.I.; writing—original draft preparation, B.I.; writing—review and editing, B.I. and M.L.; visualization, B.I.; supervision, B.M., A.R. and M.L. All authors have read and agreed to the published version of the manuscript.

Funding

The APC was funded by the Norwegian University of Science and Technology Publishing Fund.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The complete mapping and bibliography used in this study are openly available in GitHub at https://github.com/bunjii/Sysmap_2024 (accessed on 17 September 2024).

Conflicts of Interest

Author Nathalie Labonnote was employed by the company SINTEF Community. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Figure 1. Number of scholarly outputs of optimization by the year, searched on Scopus on 26 March 2024.
Figure 1. Number of scholarly outputs of optimization by the year, searched on Scopus on 26 March 2024.
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Figure 2. Procedure of systematic search.
Figure 2. Procedure of systematic search.
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Figure 3. Search keys used, (Left): Engineering Village, (Right): Scopus.
Figure 3. Search keys used, (Left): Engineering Village, (Right): Scopus.
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Figure 4. Frequencies of the articles by classifications. (a) By Category of optimization (C1); (b) By Material (C2); (c) By Objective (C3); (d) By Number of Objectives (C4); (e) By Building Typology (C5); (f) By Research type (C6); (g) By Application area (C7).
Figure 4. Frequencies of the articles by classifications. (a) By Category of optimization (C1); (b) By Material (C2); (c) By Objective (C3); (d) By Number of Objectives (C4); (e) By Building Typology (C5); (f) By Research type (C6); (g) By Application area (C7).
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Figure 5. Interaction of two classifications (1/2). (a) By Category (C1) and Objective (C3); (b) By Category (C1) and Number of Objectives (C4); (c) By Category (C1) and Typology (C5); (d) By Number of Objectives (C4) and Typology (C5).
Figure 5. Interaction of two classifications (1/2). (a) By Category (C1) and Objective (C3); (b) By Category (C1) and Number of Objectives (C4); (c) By Category (C1) and Typology (C5); (d) By Number of Objectives (C4) and Typology (C5).
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Figure 6. Interaction of two classifications (2/2). (a) By Category (C1) and Research type (C6); (b) By Typology (C5) and Research type (C6); (c) By Category (C1) and Application area (C7).
Figure 6. Interaction of two classifications (2/2). (a) By Category (C1) and Research type (C6); (b) By Typology (C5) and Research type (C6); (c) By Category (C1) and Application area (C7).
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Figure 7. Word clouds, (left): period 2014–2016, (right): 2021–2023.
Figure 7. Word clouds, (left): period 2014–2016, (right): 2021–2023.
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Table 1. Keywords for the search query.
Table 1. Keywords for the search query.
ContextInterventionMechanismsOutcomeExclusion
“structural design”building“optimi*” & “structure”“architectural design”infrastructur*
“structural engineering” “machine learning”/“ML” chemi*
“civil engineering” “evolutionary algorithm” medic*
“genetic algorithm” food
“algorithm based”
Table 2. Investigated items.
Table 2. Investigated items.
(C1) Category of optimizationTopology, Shape, Size, Others
(C2) MaterialSteel, Timber, Concrete, Composite, Not secified, Others
(C3) ObjectiveStiffness, Stress, Strain energy, Weight/Mass, Cost, Carbon and GHG emissions, Vibration, Energy, Others
(C4) Num. of objectivesSingle objective optimization (SOO), Multi-objective optimization (MOO)
(C5) Building typologyMultistory, Spatial, Others
(C6) Research typeMethodology, Tool, Case study, Prototyping, Used case, Others
(C7) Application areaEntire building, Part of building, Building component, Material, Others
Table 3. Used interactions of two classifications. (X: used interaction, -: unused interaction).
Table 3. Used interactions of two classifications. (X: used interaction, -: unused interaction).
C1C2C3C4C5C6C7
C1
C2-
C3X-
C4X--
C5X--X
C6X---X
C7X-----
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Izumi, B.; Luczkowski, M.; Labonnote, N.; Manum, B.; Rønnquist, A. A Systematic Mapping Study and a Review of the Optimization Methods of Structures in Architectural Design. Buildings 2024, 14, 3511. https://doi.org/10.3390/buildings14113511

AMA Style

Izumi B, Luczkowski M, Labonnote N, Manum B, Rønnquist A. A Systematic Mapping Study and a Review of the Optimization Methods of Structures in Architectural Design. Buildings. 2024; 14(11):3511. https://doi.org/10.3390/buildings14113511

Chicago/Turabian Style

Izumi, Bunji, Marcin Luczkowski, Nathalie Labonnote, Bendik Manum, and Anders Rønnquist. 2024. "A Systematic Mapping Study and a Review of the Optimization Methods of Structures in Architectural Design" Buildings 14, no. 11: 3511. https://doi.org/10.3390/buildings14113511

APA Style

Izumi, B., Luczkowski, M., Labonnote, N., Manum, B., & Rønnquist, A. (2024). A Systematic Mapping Study and a Review of the Optimization Methods of Structures in Architectural Design. Buildings, 14(11), 3511. https://doi.org/10.3390/buildings14113511

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