Algorithm optimization of architectural form through sequential landscape evaluation

Abstract

Designing architectural and urban spaces based on continuous human spatial experience throughout a sequence may lead to architectural and urban forms not bound to conventional concepts. These forms would be made possible through the combination of a quantitative sequential landscape evaluation and morphological optimization utilizing algorithmic processes. In this study, we introduce a method for evaluating sequential landscapes, in which the configuration of buildings, trees, etc., in view changes as pedestrians move along a particular path, using a genetic algorithm optimization of architectural forms to bring them closer to the designer’s ideals. The method’s validity was tested using two case studies, assuming the design of a sequential landscape in an actual city and park. The results present a more efficient, objective, and reproducible method for designing sequences in buildings, cities, and landscapes, compared to traditional methods.

Keywords

Sequencing landscape evaluation algorithmic design optimization architectural design design methods

Introduction

It is essential for designers to consider how buildings and urban spaces are perceived from multiple, continuous sequential perspectives as people move about. Even if the building or urban space appears aesthetically pleasing when viewed from a certain point, the sequential experience as people move through the interior and exterior spaces is rarely addressed or explored, often resulting in poor architectural quality. When designing an urban fabric, the designer must not only design the overall shape, but also anticipate the movements of people visiting the site and decide upon the continuity of space, and the position and form, of the various elements that enter people’s field of view. Therefore, sequential landscapes with changing compositions are indispensable in architectural and urban design.

There have been attempts to analyze and apply sequential landscape as a design method in architecture, urban, and landscape design. Lynch emphasized cities’ legibility, and tried to analyze urban images by identifying types of forms: paths, landmarks, edges, nodes, and districts.¹ Thiel proposed a notation to describe surrounding visual elements and human motion along a sequence.²

Miyauji et al. applied this method of notation to real-world cases, attempting to analyze the structures of architectural sequences in Japan, such as shopping malls, art museums, temples, shrines, and teahouse gardens.^3,4 Suzuki et al. endeavored to quantitatively analyze changes along such sequences. Following a survey of tourist roads in Japan, Suzuki et al. recorded the changes in topography, trees, landmarks and other features of the landscape as they drove along, using special photographic equipment, and attempted to describe the spatial changes along the sequence, similar to Thiel et al.⁵

These studies are significant because they attempted to evaluate the sequence of specific architectural and urban spaces, and more proactively utilize them in design. However, recent developments in advanced computation have facilitated studies in 3D space, to effectively evaluate the diverse, vast, and complex information of the spaces and landscapes that people interact with. Visual analyses of space and landscape using advanced computation include the use of an eye tracker, that records eye movements of subjects in actual architectural and urban spaces, to analyze how buildings and landscapes are perceived,⁶ and the use of machine learning algorithms to evaluate images of walking spaces.⁷ According to a visual spatial analysis developed by Benedikt et al., known as the isovist field,⁸ some studies reproduced the architecture or urban space to be analyzed or designed using a 3D model, and quantitatively evaluated visibility from a particular viewpoint.⁹ On the matter of evaluating continuous sequential perspectives generated through motion, Dalton et al. examine how Omni Vista, a Mac application that generates isovists, can be used as a means of analyzing changes along a path of movement on a two-dimensional architectural plane.¹⁰

Furthermore, Yasufuku et al., utilizing the walk-through function of the 3D model, attempted to quantitatively describe the visual spatial changes that occur when a pedestrian moves through the sequence of an architectural space.¹¹ Giovanni Betti et al. also conduct simulations to examine how various indicators such as visibility and daylight change as people move through the interiors of office buildings.¹²

Among proposals to determine architectural and urban forms based on visual information, some optimize urban forms which vary depending on variables in 3D space, by evaluating the visual characteristics from multiple observation points.¹³

However, these studies provide reference information for improving architectural and urban spaces, and have made it possible to determine architectural form and urban space based on information from a single viewpoint or multiple discrete viewpoints, and as yet have not proposed reproducible methods based on quantitative evaluation, such as using information from the evaluation and analysis of sequences with continuous viewpoints to improve the sequences themselves, or to determine the forms that constitute the landscape for design.

In this study, we attempted to combine developments in advanced computation that make it possible to evaluate the sequences themselves more objectively and quantitatively, with a method of determining and optimizing architectural form based on visual characteristics from a given viewpoint, as in Schneider and Koenig,¹³ and apply this to sequence design. Specifically, we propose a method to evaluate changes in the percentage of the visual field occupied by an object seen from multiple consecutive viewpoints along some arbitrary sequence, and to optimize that form to be close to the designer’s ideal sequence, based on the information obtained from this evaluation. The development of such a method will facilitate objective design based on numeric sequence data in various architecture, urban spaces, and landscapes. Furthermore, it is possible to design spaces that not only consider the landscape from a specific viewpoint but value the spatial experience along the sequence itself. If existing architectural and urban spaces can be designed based on human spatial experience in the sequence, this may lead to architectural and urban forms not bound to conventional concepts. In this study, we use two case studies to examine the validity of the proposed method and discuss its significance and effectiveness.

Morphological optimization through evaluation of sequential landscapes

In a sequence, the percentage of visible objects within the field of view shifts as the viewpoint moves along the sequence path. Within an urban setting, the proportion of trees, building exteriors, etc., in the field of view changes. Similarly, when walking through the interior of a building, the proportions of walls, ceilings, windows, and furnishings within the field of view changes. In this study, we define “field of view occupancy” as the percentage of objects within the field of view. This change in the field of view occupancy along the path, or sequence, is path-specific and represents one aspect of the characteristics of spatial experience in architectural and urban spaces. To achieve the ideal sequence envisioned by architects and urban designers, a need exists to adjust the form and arrangement of visual objects, such as buildings and trees, along the path. While it is not particularly difficult to check and adjust the field of view occupancy from a single viewpoint with the naked eye according to the form and arrangement of the viewpoint, altering the sequence when the viewpoint moves along a path can be very complicated. This is because, after adjusting the field of view occupancy at one viewpoint according to the form and placement of the visual objects, similar adjustments at subsequent viewpoints would affect the evaluations at the preceding viewpoints. If the path itself is not a straight line but is staggered or curved, the degree to which the field of view occupancy adjustments at each viewpoint affect each other may grow even more complex. It is, therefore, extremely challenging to make adjustments that converge on the ideal sequence, based solely on a manual analysis of the visibility of a unique architectural or urban space. Although methods to quantitatively analyze visual characteristics from a given viewpoint exist, new methods are needed to adjust the sequence based on evaluations obtained from multiple consecutive viewpoints along the path.

As such, this study employs a genetic algorithm that can efficiently search for the optimal solution based on the relationship between multiple evaluative functions that serve as evaluation axes, and multiple variables that determine form. The landscape simulation and genetic algorithm are linked to evaluating the field of view occupancy, the architectural form around the route that affects the sequence is used as a design variable. The total difference between the ideal field of view occupancy change intended by the designer and the field of view occupancy change caused by the architectural form under evaluation, is used as the evaluative function to be optimized (Figure 1). The algorithmic setup for this study is as follows: (1) determine the target space and visible elements (sky, buildings, trees, etc.) that occupy the field of view to evaluate its occupancy; (2) set specific pathways within the target space, with evenly spaced observation points; (3) determine the ideal value of the change of the target element, in the field of view occupancy along the path, according to the design concept; (4) obtain the maximum field of view occupancy value of the landscape elements obtained at each observation point; (5) determine the architectural form and design variables that affect the change, in the field of view occupancy of the landscape elements, from each viewpoint on the path; and (6) sum the absolute value of the difference between the evaluated value at each observation point along the path, meaning the field of view occupancy of the elements constituting the field of view defined in (1) at each observation point, and the field of view occupancy at each viewpoint set in (3) for all observation points (hereinafter referred to as the total difference in field of view occupancy, Z) as the evaluation function, which is minimized using a genetic algorithm (Figure 2).

Figure 1.

Calculation method of the total difference in the field of view occupancy Z.

Figure 2.

Flow chart of the steps of this method.

In both the case studies, the field of view occupancy was set to a maximum where no architectural form was installed (in these cases, with all panels open), and the designer’s target field of view occupancy for the sequence was set to a range lower than those values.

Although there are countless possibilities for the initial conditions, we chose those that would most accurately express the method applied in this study (Figure 3).

Figure 3.

Initial conditions.

To reproduce human vision, a scope was created with reference to the work of Hatada et al.,¹⁴ as shown in Figure 4, with search lines randomly projected from the observation point into the scope. The number of search lines was set to 1,000, where the change in the value of Z (total difference in field of view occupancy) to optimize converges as the number of search lines increases. This field of view can be set arbitrarily, according to the application and purpose of the verification. This field of view can be set arbitrarily according to the application and purpose of the verification. Through these steps, we optimized architectural forms to achieve ideal changes in the field of view occupancy of the visual objects comprising the landscape along the sequence path according to the design concept. This study adopted the multi-objective genetic algorithm using the Wallacei software (V2.7), which is an evolutionary engine that employs the NSGA-II genetic algorithm developed by Deb et al.¹⁵

Figure 4.

Scope reproducing human vision.

A genetic algorithm abstracts selection mechanisms in the natural world and emulates them using a computer. Genetic-inspired processes, such as crossovers, mutations, and genetic transformations—expressed as variables in a program and with repeating heterogenesis—allow for optimal solutions to be derived following certain objectives.¹⁶

We examined two case studies in which the method was applied to changes in tree-view occupancy within urban and park sequences, to confirm the validity and effectiveness of this method.

Verification of the method and discussion

Case study 1: Tunnels in an urban space

As a simple example to illustrate this method, we considered a tunnel installed along a footpath in an urban space. In this example, this study aimed to optimize the sequence of existing buildings and city blocks, where the shapes of the buildings and city blocks are already determined, by setting up a new architectural form that can be changed depending on the variables between the viewpoint and the object to be viewed. In recent years, there has been a growing demand for urban development to enrich spatial experience, especially for pedestrians, such as walkable cities.¹⁷ Moreover, large cities worldwide, such as Tokyo, are expected to face an increasing risk of heat strokes due to climate change and the heat island effect.^18,19 Thus we chose a tunnel covered with plants as a conceptual model and the subject for a case study, to achieve the target sequence while reducing strong sunlight in an urban walking space. The objective was to provide both sun protection and landscaping while walking along footpaths, through a combination of opening and closing patterns of panels dividing the surface of the tunnel installed along the footpath. The visual targets for evaluating sequences were the trees lining the path, with the percentage of trees in the field of view from each viewpoint along the footpath (field of view occupancy) evaluated. The combination of panel openings and closings was used as a design variable, to establish a target sequence in which the percentage of trees in the field of vision increases linearly as one progresses along the footpath. Gradually increasing the percentage of visible trees was intended to increase pedestrians’ anticipation of trees as they walk along the route, and to change their walking experience (Figure 5).

Figure 5.

Adjustment of tree visibility by opening and closing panels on the tunnel surface.

Target space and observation points

The target space was a 40 m × 150 m urban block, while the landscape elements in the sequence were buildings and three types of trees of different sizes (tall trees: 16 m in height and 8 m in diameter, medium trees: 11 m in height and 6 m in diameter, and small trees: 6 m in height and 5 m in diameter). Path A was set in the center of a 6 m-wide path in the middle of the urban district; observation points were positioned at a height of 1.5 m at every 2.0 m, with a total of 25 observation points (Figure 6).

Figure 6.

The target urban block and tunnel.

Parameters

A tunnel that is 6 m high, 6 m wide, and 60 m long was installed along Path A. The roof and both sides of the tunnel consist of 90 4 m² panels each, that is, 270 panels in total. The combination of these 270 panels could be opened and closed (0: Open, 1: Closed), which was treated as the variable.

Figure 7.

Grasshopper definition for Case Study 1.

Design intent

The design concept was to set a target tree’s field of view occupancy value for each of the 25 observation points equally spaced along Path A, such that the sequence is one where “the field of view occupancy of trees gradually increases as the pedestrian progresses along Path A.”

Optimization

The absolute difference value between the tree’s field of view occupancy, obtained at each observation point along Path A and the target tree’s field of view occupancy, was summed for all observation points (total difference in the field of view occupancy). Optimization using a genetic algorithm, that minimizes this total difference in the field of view occupancy, was performed by taking combinations of opening and closing each of the 270 panels across the tunnel surface as the variable. The height of the human eye-line was set at 1.5 m for each observation point, while calculating the field of view occupancy at each observation point. The genetic algorithm evolved 5000 solutions, comprising 100 generations with 50 individuals per generation. In this case, the following parameters can be set in Wallacei: crossover probability was set to 0.9, mutation probability to 1/n (where n, that is, the number of slider values), crossover distribution index and mutation distribution index to 10, and random seed to 1. Figure 7

Results

Optimization produced changes in the tree visibility rate, as shown in Figure 8. While the field of view occupancy of trees along Path A without the tunnel was relatively consistent and unchanged (the red line in Figure 8), installing the tunnel and optimization of the combination of opening and closing along the tunnel surface panels (Figure 9) resulted in a solution that was generally close to the target sequence, despite differences from the target value at some observation points. This suggests that it is possible to use this method to obtain an optimal solution for architectural form for adjustment, under conditions similar to those of this example, to achieve the target sequence.

Figure 8.

Optimization results (red line: maximum value, gray line: target value, blue line: post-optimization).

Figure 9.

The form yielded by the optimization.

Optimization lasted approximately 1 h using a PC with the following specifications: 11th Gen Intel (R) Core (TM) i9-11950H @ 2.60 GHz 2.61 GHz and 128 GB RAM.

Case study 2: A tunnel in a park

We next attempted to apply this method to landscape design. A tunnel that is 6 m high, 6 m wide, and 200 m long was installed along a park’s curved path, as shown in Figure 10. As in Case Study 1, the combination of opening and closing panels along the tunnel surface was varied to optimize the change in the field of view occupancy, along the sequence of two types of trees—red and green—in the park. We ensured that this method applied to more complex conditions than those of Case Study 1, such as cases with multiple targets for optimization of the field of view occupancy and with more complex paths, such as curves or circles. As mentioned, it is more difficult to intentionally introduce design changes in the composition of trees in a landscape design sequence, such as a park, than to design them for a field of view seen from a single viewpoint. If this method is able to effectively bring change in the field of view occupancy of multiple trees along a pathway in a particular landscape closer to the designer’s intended sequence, it would make the landscape design objective and repeatable, while facilitating efficient consideration of a variety of options. In this example, optimization of the change in the field of view occupancy of trees was signified with different red and green colors, as pedestrians move through the tunnel installed along a circumferential curved footpath, and was brought closer to the sequence intended by the designer. The designer’s intended sequence was to make the pedestrian experience more orderly and varied, by varying the field of view occupancy of green and red trees as they walk along the circumferential curved tunnel. When applied to Case Study 2, the flow of this method is as follows.

Space of interest and observation points

The target space was a 100 m × 100 m park. The landscape elements in the sequence were green and red trees planted in the park (tall trees: height 16 m, diameter 8 m; medium trees: height 11 m, diameter 6 m; small trees: height 6 m, diameter 5 m) (Figure 10). A curved path, Path B, was set up around the park, with 25 observation points equally spaced every 8 m along it (Figure 11).

Figure 10.

Target park and tunnel.

Figure 11.

Path and observation points.

Design variables

A tunnel 6 m high, 6 m wide and 200 m long, consisting of a roof and sides, each featuring 288 panels of approximately 4 m², for 864 panels, was installed along Path B, together with the green and red trees located between observation points that formed the elements of the landscape. Combinations of opening and closing the 864 panels (0: Open, 1: Closed) were set as the variable.

Design intent

The design concept was to set a target field of view occupancy for each of the 25 observation points evenly spaced along Path B, such that the change in the field of view occupancy of the two types of trees (green and red) along the sequence had a regular rhythm, with the field of view occupancy of green trees gradually decreasing and then increasing as the pedestrian walks along Path B, while the field of view occupancy of red trees gradually increases and then decreases.

Optimization

Optimization was performed to minimize the sum of the absolute values of the differences between the trees’ field of view occupancy obtained at each observation point along Path B and the target trees’ field of view occupancy (the total view occupancy difference). The combination of the opening and closing of the 864 panels along the tunnel surface was taken as a variable. The genetic algorithm evolved 10,000 solutions including 200 generations, with 50 individuals per generation. In this case, the following parameters can be set in Wallacei: Crossover probability was set to 0.9, mutation probability to 1/n (where n, that is, the number of slider values), crossover distribution index and mutation distribution index to 10, and random seed to 1.

Results

Optimization yielded the change in the field of view occupancy for each of the two tree types, red and green, as shown in Figures 12 and 13. This method was able to converge toward the designer’s target sequence, even in this complex case where the path was a circumferential curve with two viewing targets. Optimization was performed for 200 generations of 50 individuals. It lasted approximately 5 h using a PC with the following specifications: 11th Gen Intel(R) Core(TM) i9-11950H @ 2.60 GHz 2.61 GHz and 128 GB RAM. Figure 13

Figure 12.

Results of optimization (red line: maximum value; gray line: target value; blue line: post-optimization).

Figure 13.

The form yielded by the optimization.

Turning to the specifics, the change in field of view occupancy of the two types of trees along Path B before the tunnel’s installation was generally consistent (the red line in Figure 12).

If we attempt to reproduce the change in visibility along the sequence, as shown in Figure 14, we can see that this is the same as the change in visual field occupancy for the green and red trees shown in Figure 12. However, following the installation of the tunnel and as a result of optimizing the combination of panels that were opened and closed along its surface, the field of view occupancy of green trees was made to gradually decrease and subsequently increase, while the field of view occupancy of red trees was made to increase progressively and then decrease, thereby converging toward the sequence intended by the designer. However, some locations, such as observation points 5,10 and 15 in the case of the change in green trees, and observation points 11, 15, and 18 in the case of the change in field of view occupancy of red trees, were not as fully optimized as others. This may be due to the interaction in the effects of tree placement, the original viewing target, and the evaluation of the field of view occupancy at the preceding and subsequent observation points, which may have resulted in the optimization of certain observation points falling short of the optimization of other observation points. If the target value is set too close to the maximum value, the relationship with the evaluation at other observation points and the scope for optimization itself may be reduced. In this validation, the target values were not set too close to the maximum and were set with a margin for error. In each case where this method was applied, it is necessary to set appropriate target maximum values. In future, it will be necessary to validate the method against general problems faced in architecture and urban design. Moreover, improving on insufficiently optimized areas may be possible by adjusting the architectural form individually after optimization.

Figure 14.

Reproduction of landscapes along the sequence.

Conclusion

In this study, we proposed a method to evaluate the field of view occupancy of visual objects composing a sequence. Further, we reflected it in the architectural form using a genetic algorithm. The process of applying the proposed method and its validity were demonstrated through two case studies, one in an urban environment, and the other in a park. In contrast to studies and methods utilizing conventional algorithms to evaluate the landscape from single or multiple viewpoints, we could reflect morphology based on visual information from a sequence while maintaining reproducibility. By utilizing this method in real architecture, cities, park and other landscapes, designers can make sequence designs more objective and reproducible, whereas in the past such designs have tended to rely on designers’ experience and sensibilities. Moreover, this study facilitates the efficient evaluation of multiple proposals for analyses using genetic algorithms.

When designing a continuous spatial experience, the designer’s experience, subjectivity, and preconceived notions of architecture may take precedence. Through these processes, the landscape that encompasses the architecture and the city may either blend into the background and environment or accentuate the continuous spatial experience itself. For example, entrance spaces with awnings or semi-outdoor spaces that involve the frequent entry and exit of people act as boundaries between the interior and exterior. These may be adjusted to be more gentle or striking. Alternatively, the form and arrangement of buildings, monuments, urban blocks, terrain, and vegetation in the continuous spatial experience of the city and landscape can be relatively interdependent and possess features that can only be perceived in the context of a continuous spatial experience. This will contribute to raising the value of sequences, together with other indicators, in the design of architectural and urban spaces.

By using the method presented in this study, designers can not only evaluate a sequence themselves, but also efficiently obtain their intended sequence. Certain areas in the urban and park case studies verified in this study presented a target field of view occupancy that was not fully optimized at some observation points. To improve these areas, it may be necessary to consider the mutual influence of each successive viewpoint of the evaluation and the relationship between objects to be viewed, as well as the architectural form and design variables. In doing so, variables and their range may be chosen according to the target and evaluation, and evaluation items can be appropriately set in advance. By increasing the number of examples of its application, the possible range of these settings and targets may be systematized and generalized for different building and city types.

If the field of view occupancy was to be set exceeding the maximum value for a given observation point, obtaining a field of view occupancy in excess of the maximum value would not be possible even after optimization. In such cases, it may be necessary to suggest or modify existing conditions, such as the location of the object to be viewed, and identify limitations when optimizing the sequence only using variable architectural forms for fixed viewing objects and conditions. Regarding the scope for improvement of the method itself, since the total difference from the target value is minimized at all observation points, the same evaluation is made where the difference is particularly significant at a specific observation point, or where the difference is distributed across multiple observation points. Should the difference between the target value and field of view occupancy result at a particular observation point be unacceptable, a more balanced solution can be obtained by multi-objective optimization adopting a new evaluation axis that minimizes the difference from the target at that observation point.

Accordingly, this method can be considered better suited to obtaining the designer’s intended sequence when the viewing object is also a variable. Subsequently, there is a need to consider applying this method in the early stages of architectural and urban design and to situations where the position, form, and sequence path of the viewing object can vary.

This leads to more dynamic designs of the broader landscape, including urban planning, topography, and the distribution of vegetation, expanding beyond architecture and individual objects. In addition to the static elements of virtual spaces, recent advances have introduced the possibility of realistically reproducing a continuous experience that includes wind movements and changes in light.²⁰ Together with such virtual space technology, the methods proposed in this study will contribute to enhancing the sensitivity of architectural, urban, and other landscape designs to human experiences.

Although changes in the landscape composition were evaluated using the field of view occupancy in the case studies presented in this paper, future research should explore the application of the developed method to other spatial and environmental elements not addressed in this study, such as varying the lighting intensity while moving along the sequence, and variations accompanying changes in the size of the space.

Furthermore, this study primarily focused on visual perception as a basic examination for the creation of an optimal design method that takes sequence into account, but visual perception is only one of many human senses. In order to realize design optimization based on more comprehensive sequence evaluation, it is important to incorporate non-visual environments such as heat, wind, light, and sound environments as objective functions in the optimization. If quantified, this method could also be applied to evaluation indicators related to senses other than vision such as hearing and touch. Applying this approach to multiple evaluation indicators of the human spatial experience along specific paths may also contribute to the creation of buildings, cities, and other landscapes that offer richer spatial experiences.

Supplemental Material

Supplemental Material - Algorithm optimization of architectural form through sequential landscape evaluation

Supplemental Material for Algorithm optimization of architectural form through sequential landscape evaluation by Masaaki Matsuoka and Kunihiko Fujiwara in International Journal of Architectural Computing.

Supplemental Material

Supplemental Material - Algorithm optimization of architectural form through sequential landscape evaluation

Footnotes

Acknowledgments

We would like to thank Dr Mohammed Makki of the University of Technology, Sydney, the developer of the Wallacei optimization plug-in used in this study and an expert in analyses of optimization in architecture and urban space, for his advice and cooperation in the streamlining of the optimization process and verification method. We would also like to thank Ishin Matsumoto, an undergraduate student at Waseda University, and Harumitsu Kuribayashi, a graduate student at Waseda University, for their assistance in creating the analytic model used for verification. We would like to thank Editage () for English language editing.

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.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Masaaki Matsuoka

Kunihiko Fujiwara

Supplemental Material

Supplemental material for this article is available online.

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