Multi-objective optimization framework based on review of form-finding of architectural parametric forms

Abstract

Parametric architecture has played a vital role in architectural design in recent times. Research on early form-finding of architectural forms represents a notable area of study. Despite the significance of energy performance, digital fabrication, and aesthetics as design objectives, there is a lack of a comprehensive framework that integrates them in the form-finding process. To address this gap, this research conducts a systematic review of previous studies on form-finding and optimization of architectural forms, focusing on the three aforementioned objectives. Then, based on the analysis of the selected studies, the research proposes a multi-objective optimization framework for form-finding of architectural parametric forms, considering energy performance, digital fabrication, and aesthetics. The framework comprises five phases: form generation, multi-objective optimization, aesthetic evaluation, geometry rationalization, and digital fabrication of a prototype. This framework is usable by any architect, regardless of their programming knowledge, and is applicable to any new architectural design.

Keywords

Aesthetics computer-aided design digital fabrication energy performance form-finding geometry rationalization grasshopper multi-objective optimization parametric design

Introduction

The introduction of new digital tools to the architectural design process has always affected the architectural practice.¹ This development of digital tools has shifted the design paradigm from being a traditional representational process to being a contemporary complex generative digital process based on simulation and evaluation.² It also caused the emergence of one of the most recent approaches in architectural design, which is parametric design. Parametric design generates architectural parametric buildings whose designs correspond to the rules or algorithms given at the beginning of the design process.³

Various approaches are used in research on architectural parametric buildings, as shown in Figure 1. One such approach is to conduct research on the form-finding of the building’s form which is a result of the building’s geometry in plan and in 3D together and does not include any other details or design components. This was found in⁴ where the building’s form was optimized to minimize external thermal load using genetic algorithm, and in⁵ where the building’s form was optimized for energy performance based on hierarchical geometry relation, also in,⁶ and many other works. Another approach is to conduct research on the form-finding of the building’s envelope which includes all the exterior design components shaping the facades of the building. For example, this was found in both^7,8 where the building’s envelope characteristics were the focus of the study and optimization. A third approach involves the form-finding of a specific building’s interior or exterior design component, such as: openings, structure, roofs, etc. For instance, this can be found in⁹ where the openings characteristics were optimized for two performance objectives.

Of all the previous approaches, the building’s form impacts how a building responds to external conditions¹⁰ and thus has a great effect of its energy performance. It also greatly influences the determination of a fabrication method used for implementing the building. In addition, the aesthetic appeal of a building strongly depends on its form.¹¹ Therefore, optimizing a building’s form in the early form-finding process can be the key to a design’s success in many aspects. Adding to that, decisions made at the early design stage of form-finding have greater impacts on the overall building’s performance,¹² while changes at the late design stages are very limited, hard to implement and expensive.¹³ This indicates the huge importance of considering the optimization of the important aspects of a design in the early stages of form-finding to avoid going through time and cost consuming design modifications in the later phases of design. Accordingly, the research focuses on the building’s form approach.

Parametric form-finding process

In parametric architecture, architects no longer have to create forms by pen on paper, or by mouse in computer-aided design program.¹⁴ They define parameters and control procedures, collaborating with computers in terms of finding the appropriate form for a given design case through parametric design, which is called “form-finding”. Form-finding is a design method where generation of form is based on rules or algorithms, often deriving from computational tools.¹⁵ Many researchers described the form-finding process, where each of them used different terms and methods according to the context and the scope of their research. In general, it can be divided into four main phases as shown in Figure 2. These phases are described in the following parts.

Phase one: Form generation

This phase involves creating the main idea or setting the design approach. Then, gathering general design information that acts as the constraints of the process, such as: the design environment, requirements, etc.¹⁵ After that, it is important to decide the design objective/objectives used for optimization¹⁶ and define the different parameters that control the design and establish the relationships between them.¹⁷ Finally, setting the rules or algorithms that control the different parameters. The result of that phase is generating an initial design result.¹⁸

Phase two: Optimization

It is an iterative phase¹⁹ that involves testing the initial design through simulation and analysis, then collecting feedback. After collecting the feedback, the design results are tested for whether they achieved the design objectives or not. If they do not achieve the objectives, the process will go back to the form generation phase to modify the design again through this feedback loop until the design objectives are met.¹⁹ On the other hand, if the results have managed to achieve the objectives, the process would proceed to the next phases without the need for any iterations.

Phase three: Design output

This phase revolves around obtaining the final design result. Here, if the design had a single objective in the optimization phase, then there will only be one final result. While if the design had multi-objectives in the optimization phase, then there will be more than one result.²⁰ In this case, the architect will need to filter and evaluate these results to select a final one.²¹ This evaluation can be done by different means or criteria decided by the architect according to what they see suits the design case.

Phase four: Pre-implementation

In this phase, the model of the final design may have to undergo some modifications to be able to be fabricated and constructed in real life.^15,18 These modifications usually depend on the rationality and complexity of the design model.

As we can find from the previous phases of the parametric form-finding, architects can now use parametric modelling tools combined with performance analysis software to influence the architectural form in the early form-finding phase.^22,23 Although the parametric design has facilitated that process, there is still a challenge for architects in setting the appropriate form-finding objectives in such an early phase of form-finding in order to reduce design modifications in later design phases. They need to make careful decisions regarding which design objectives to include.

Objectives of form-finding

There exists a various range of design objectives for a design in general. The research only focuses on the objectives which are relevant during the early stage of form-finding and are applicable on any design case regardless of their nature. These design objectives are energy performance, digital fabrication, and aesthetics. Other design objectives, such as structural, acoustic, visual performance, etc. which are attributed to special types of buildings or specific design cases are not addressed in this research. The following sections discuss each of the three objectives in scope.

Energy performance

In the light of the increase of the global population, there is a major increase in energy use in buildings worldwide.^6,10 Today, buildings are responsible for about 40% of the global energy consumption.²⁴ In the future, this percentage is expected to increase due to population growth and the higher levels of mechanization in buildings. Therefore, more attention should be given to improving buildings’ energy performance.

In the early form-finding phase, buildings’ forms are crucial for energy performance as they impact how a building responds to external conditions.¹⁰ Thus, optimization of buildings’ forms through making cautious modifications to their design variables is key to future reduction in their energy consumption.²⁵ This is why in the recent years, significant efforts have been already made to optimize energy performance in buildings,²⁶ and attempts of researchers in that field are increasing.²⁷

Digital fabrication

Most of the parametric buildings we see nowadays involve complex or free-form double-curved skins and structures.²⁸ With NURBS modeling becoming more available in architecture, modelling of these free-forms is well understood. However, their actual fabrication represents a great challenge.²⁹ Surfaces no longer have the repeating details that could be drawn once and multiplied over a whole building.³⁰ Complexity has made it curvy and non-regular, where every part has a slightly different geometry than the other.³¹ This is why these forms require the use of the various techniques provided by digital fabrication in their implementation.^32,33 Accordingly, it is important to no longer consider digital fabrication as a tool, but as an integrated objective in the form-finding³⁰ as it can greatly influence the initial design phase and inform the form.³⁴ However, in a typical form-finding process, fabrication is rarely embedded into the initial design.³¹ Forms designed by the architect are shaped at the concept stage, while the fabrication information is usually provided later by a specialist.³⁵ This failure to acknowledge fabrication constraints within the early stages of design can result in a need to edit designs for fabrication at a later stage, leading to delays and errors.³⁶

In addition to that, free-form designs usually cannot be built as planned due to the limitations of the different machines and fabrication processes. Thus, they require a long process of simplification and adaptation, which is the process of rationalization.³² Geometry rationalization is the process of making a complex design feasible (physically realizable) and affordable (comparing to a non-rationalized design) by manipulating its geometry.³⁷ It is the key to be able to transfer complex forms from intentions in the virtual space into buildable forms in the physical reality.^38,39 Therefore, geometry rationalization for the different fabrication constraints and objectives should be defined as a main part in the early form-finding process.

Aesthetics

Although aesthetics is a subjective feature in judging an architectural design.⁴⁰ It has a huge significance for in measuring the success of buildings’ designs. This is why some buildings are appreciated worldwide, while others are criticized or neglected.¹¹ However, the aesthetic criterion is not usually considered in the form-finding process as opposed to the other buildings’ quantitative performance criteria that are thoroughly considered.⁴¹ The problem here is that rating design options according to only performance does not usually produce aesthetically pleasing forms.⁴² In this regard, aesthetics should be considered in the form-finding process, especially for the recent non-standard free-form designs. This can be done through considering an aesthetic evaluation when looking for design options of these free-forms.⁴³

Main research gap

Through the initial screening of some of the previous studies concerning the three objectives mentioned in previous section, it was found that most of the existing form-finding or optimization frameworks/workflows have only considered the objective of energy performance, as found in: 4–6,12,21,44–52. Others went further from that and included aesthetics together with energy performance, as found in: 53–56. Other studies have focused on digital fabrication objectives and constraints through geometry rationalization, as found in: 57–62.

Furthermore, previous reviews have always focused on one of these predefined objectives. For instance,^37,39,63 highlight the increasing use of geometry rationalization to adapt architectural designs for fabrication constraints. Also,^{20,25,26,64–66} reviewed different aspects of buildings optimization for different performance related objectives. Nevertheless, no reviews integrating the three predefined objectives or even two of them were found.

Despite the huge importance of each of energy performance, digital fabrication, and aesthetics and their potential influence on the early stage of form-finding, we can see that there exists a main research gap which is the lack of integration between the studies addressing them.

Since an architectural form that is optimized for a specific design objective might not be good or acceptable in terms of other important design objectives, the form-finding of architectural forms needs to integrate different design objectives. This can be possibly done through parametric design and its various tools. Therefore, more research should be done on the methods, possibilities, and implications of a multi-objective form-finding process.

In respond to this gap, the research’s main objective is to define the best practices and the gaps in previous research on the design objectives: energy performance, digital fabrication, and aesthetics, and find a method for their integration in order to construct and propose a multi-objective optimization framework for form-finding of architectural parametric forms that considers these crucial objectives and can be applied to most design cases.

The research is organized as follows: First, the objective and the entire methodology of the research are presented, including details of the systematic literature review. Next, an analysis of selected previous studies is provided, divided into the three main categories of the predefined objectives: energy performance, digital fabrication, and aesthetics, along with the observed practices and main conclusions in each category. Following this, the proposed multi-objective optimization framework for the form-finding of architectural parametric forms is explained in detail. This is followed by a discussion on the significance of the proposed framework. Finally, conclusions of the research and recommendations for future work are given.

Objective and methodology

Objective

As mentioned before, the main objective of this research is to propose a general multi-objective optimization framework for form-finding of architectural parametric forms, which can be achieved through the following goals:

• Understanding the phases of the basic parametric form-finding process.

• Defining the most important design objectives in the early form-finding phase.

• Extracting the best practices and conclusions found in previous related studies.

• Find a method for the integration of the defined design objectives in the form-finding process.

Methodology

The research follows a combined methodology of theoretical and analytical approaches as shown in Figure 3. It starts by following a theoretical approach, where a general overview of the topic is done to understand the phases of the general form-finding process, the main objectives of form-finding, obtain the main research gap, and develop the main objective of the research. This was all presented in the previous section.

After that, the research follows an analytical approach, where a systematic review of existing studies on architectural buildings’ forms form-finding or optimization in the early stages of design is conducted. The Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) method was used to conduct the review as shown in Figure 4. Six consecutive steps are followed to conduct this systematic review.

First, the research selects the scientific databases used in the review. The ‘SCOPUS’ and the ‘Google Scholar’ databases, whose data are highly regarded for correctness and widely used by researchers, are both used as search engines in current research.

Second, the research sets up a search strategy to be used in searching and identifying studies in these databases. The study query is composed of the following keywords: (“form-finding” OR “optimization” OR “early-stage”) AND “architecture” AND “buildings” AND “forms”, which were searched within the Article Title, Abstract, and Keywords. Furthermore, the study will focus on the publication period from 2009 to 2024, written in English, and limit the subject area research to Engineering, Arts and Humanities, Environmental Sciences, and Energy. Following this search strategy, a total of 9247 documents were initially identified in the review.

Third, determination of the research selection criteria for the previous studies during the screening phase of the review. One criterion is the scope of the research, where the study must focus on the building’s form (shape of a building in plan or/and in 3D), and it must include either energy performance, digital fabrication, or aesthetics as a design objective. The other criterion is the accessibility of the research, where the online text of the study must be available. After the screening phase of the identified research studies, the review’s final dataset contained 71 documents.

Fourth, the research defines an analysis strategy for the selected research studies. They are mainly divided into three categories: studies concerning energy performance, studies concerning digital fabrication, and studies concerning aesthetics. Then, aspects of data extraction and analysis for each category are determined as shown in Figure 5.

Fifth, the analysis of the selected research studies is performed, where an analysis table is presented for each of the three categories. These tables will be shown in the next section.

Sixth, the extraction of the research conclusions for each of the three categories based on the review analysis, which also will be shown in the next section.

Finally, based on the conclusions from the review analysis of the existing research, the research proposes a multi-objective optimization framework for form-finding of architectural parametric forms, considering the three objectives: energy performance, digital fabrication, and aesthetics. The framework involves the utilization of parametric tools, namely McNeel Rhinoceros (Rhino) and Grasshopper (GH), along with specific GH plug-ins, such as: Ladybug, Wallacei, Kangaroo, Human UI, and OpenNest. It focuses on the free-form designs of buildings, as discussed in detail later in the paper.

Analysis of the three categories of the selected previous research studies

In this section, the selected research studies are analyzed according to the predefined analysis strategy in Figure 5. The 71 selected studies are divided into three categories, where each category represents a design objective, namely energy performance, digital fabrication, and aesthetics. Analysis of these categories is shown in the following parts.

Energy performance

According to the predefined search and analysis strategies, 39 studies concerning the energy performance objective are found and analyzed in terms of the form’s degree of complexity, performance objective, and pattern of optimizing forms as shown in Table 1.

Table 1.

Analysis of form-finding studies concerning energy performance.

Ref.	Form’s degree of complexity	Performance objectives	Pattern of optimizing forms
⁴⁷	Simple forms: Rectangular, square, courtyard, L, T, U, ellipse, and circle shape.	Reduce cooling load.	Shapes comparison
⁶⁷	Simple forms: T-shape	Optimize thermal properties. Enhance daylighting.	Optimization of a predefined shape
⁶⁸	Compound forms: Formed by a shape grammar-based parametric design system.	Optimize the energy demand (energy for heating and cooling)	Optimization of a predefined shaping strategy
⁶⁹	Simple forms: Basic building shape.	Minimize operational cost. Minimize carbon emissions.	Optimization of a predefined shape
⁷⁰	Simple forms: Rectangular shaped and circular shaped layouts	Optimize solar heat gain and operative temperature	Shapes comparison
⁷¹	Simple forms: Single dense form, central courtyard buildings, U form and linear form.	Minimize the annual energy consumption.	Shapes comparison
⁴²	Compound forms: An enclosed trussed arch, a ‘PI’ structure that contains two columns and a spanning truss with cantilever, and a ‘x-brace’ that contains a three-hinged arch supporting cantilever roof beams.	Optimize energy of the structure. Optimize annual operational energy.	Multi-shapes optimization
²¹	Simple forms: A simple orthogonal box. Compound forms: Orthogonal shapes of moderate complexity. Complex forms: Geometrically complex shapes.	Spatial programing compliance (meeting of project defined requirements by a generated design). Optimize energy performance and financial performance.	Multi-shapes optimization
¹²	Simple forms: Rectangle, L-shaped, H-shaped, U-shaped, cross, T-shaped, and trapezoidal.	Minimize the total energy consumption.	Shapes comparison
⁴⁸	Simple forms: Cubic buildings.	Reduce building energy cost Increase PV capacity.	Optimization of a predefined shape
⁴⁹	Simple forms: Rectangle, L, T, cross, U, H, and trapezoid.	Minimize energy use.	Shapes comparison
⁵¹	Simple forms: Trapezoid with a courtyard.	Optimize cooling energy consumption and daylighting.	Optimization of a predefined shape
⁷²	Simple forms: Rectangle, H-shape, L-shaped, rectangle minus corner, triangle, T-shape and U-shape.	Minimize the total energy consumption.	Shapes comparison
⁷³	Compound forms: Existing building extension.	Maximize annual solar radiation availability.	Optimization of a predefined shape
⁴	Complex forms: A free-form shape which has a polygonal footprint at the bottom and top surfaces.	Optimize the thermal load (the heat gain and loss).	Optimization of a predefined shape
⁵	Complex forms: Free-forms generated by defining hierarchical relationship between geometry points.	Minimize heat flow (surface heat flow, heat gain and loss). Minimize energy use.	Optimization of a predefined shape
⁴⁴	Compound forms: The building is defined by an aspect ratio (height: width), a total floor area, and number of floors. Then, two multipliers (a and b) are used to generate more complex shapes with an increasing number of exterior corners while maintaining the original floor area.	Optimize the performance of daylighting, solar control, and natural ventilation.	Optimization of a predefined shaping strategy
⁵²	Complex forms: A minimal surface form that can transform into curvilinear forms and thus create various spatial configurations during optimization.	Reduce solar radiation. Increase daylight. Increase floor surface area.	Optimization of a predefined shape
⁵⁰	Compound forms: A design with eight facades, where a node-based description is applied. Internal nodes are fixed, while external nodes are moved by genetic algorithm operators during evolution.	Minimize the annual total energy demand.	Optimization of a predefined shaping strategy
⁴⁵	Compound forms: The building plane is determined by four radius circles of 10 meters and their tangent arcs. The center of the circle moves in the range of 0-20m and 0-40m at both ends of the axis.	Reduce annual energy use. Reduce solar radiation during April to September. Increase natural ventilation during April to October.	Optimization of a predefined shape
⁴⁶	Complex forms: A free-form shape consisting of two curves, one upper and one lower.	Maximize solar radiation gain.	Optimization of a predefined shape
⁷⁴	Compound forms: A 3D cellspace grammar implemented in NetLogo program, mainly consisting of 3 × 3 built cells and surrounding connectors.	Minimize heating demand.	Optimization of a predefined shaping strategy
⁷⁵	Simple forms: three rectangular shapes with sides’ ratio of 1:1, 1:1.5 and 1:2, ‘L’, ‘T’ and ‘U’ shapes.	Reduce thermal loads (heating and cooling loads).	Shapes comparison
⁶	Complex forms: The building is defined as a 3D rectangular prism of length L, width W and height H. Then, a total of 2(L + W)(H + 1) 3D data points are generated and their coordinates saved. In each iteration step, the building envelope is deformed, and the coordinate values are updated.	Reduce incident solar radiation.	Optimization of a predefined shaping strategy
⁷⁶	Simple forms: Square, rectangle elongated on east-west, rectangle elongated on north-south, H-shape, and cross form	Reduce total annual energy use.	Shapes comparison
⁷⁷	Simple forms: Rectangular, L shaped, C shaped, H shaped, cylindrical, polygonal, etc.	Optimize daylighting and cooling and heating demand.	Shapes comparison
⁷⁸	Simple forms: Square, rectangle, L shaped, U shapes, C shaped	Optimize heating energy consumption	Shapes comparison
⁷⁹	Simple forms: Rectangular shape dimensions variations	Optimize thermal performance.	Optimization of a predefined shape
⁸⁰	Complex forms: Different parametrization strategies and equations produced different forms	Minimize energy consumption due to solar radiation	Multi-shapes optimization
⁸¹	Compound forms: Square, rectangle, polygon, circle, ellipse plan shapes with different roof configurations.	Increase solar potential for PV.	Multi-shapes optimization
⁸²	Simple forms: Hexagonal, pyramid, prism, incomplete prism, rectangular, cube, hemisphere, cylinder, cylinder-rectangular	Optimize the absorption of solar energy (thermal performance).	Shapes comparison
⁸³	Complex forms: Twisting building morphologies	Optimize wind performance for thermal comfort.	Optimization of a predefined shape
⁸⁴	Simple forms: Squares and rectangles with different ratios	Minimize heating, cooling and lighting energy demand.	Shapes comparison
⁸⁵	Complex forms: The shape is based on a closed planar curve formed by attractor points derived from wind direction.	Optimize wind performance for environmental benefits.	Optimization of a predefined shape
⁸⁶	Complex forms: A rectangular form whose four upper corners can move freely	Optimize daylighting and cost of used glass.	Optimization of a predefined shape
⁸⁷	Complex forms: One half of an ellipsoid shaped building with some variable parameters	Minimize the annual energy consumption.	Optimization of a predefined shape
⁸⁸	Simple forms: Rectangular shape, L-shape, T-shape, Cross-shape, H-shape, U-shape and Cut-shape shape.	Reduce the total annual energy use.	Shapes comparison
⁸⁹	Compound forms: A rectangular shaped building that has one curved façade with varying parameters	Minimize energy consumption and improve daylighting.	Optimization of a predefined shape
⁹⁰	Simple forms: Six rectangular models with aspect ratios ranging from 1:1 to 4:1	Minimize the energy consumption.	Optimization of a predefined shape

From the previous table we can find that three degrees of form complexity were used in the analyzed studies. Some studies used simple geometric forms in their form-finding, such as: rectangle, L-shape, T-shape, U shape, box, etc. Utilizing these simple forms helped to simplify the design problem for the purpose of demonstrating the main idea of design optimization. However, these simple basic geometric forms are not suitable for the current architectural design which is shifted to using more complex forms. Other studies went to a higher level of complexity using compound forms, which are derived from simple forms with some adjustments added to them, such as: extruded and filleted parts or inclined surfaces. They are just an extension to simple forms with a moderate degree of complexity. While some studies found an approach to use complex forms in their form-finding. Complex forms can be organic, twisted, or deconstruction forms, also known as “free-forms”.

Although the move towards complex forms is the main focus of contemporary architecture, form-finding and optimization studies conducted on them are still limited,²⁵ where only 9 studies out of the 39 analyzed studies have addressed them. That might be due to the difficulty in representing complex building forms as straightforward parameters.²⁰ Therefore, more studies need to be done regarding generating complex forms that are suitable for optimization.

Regarding the performance objectives, various energy performance objectives were used in the analyzed studies. Optimizing thermal performance of the form and minimizing energy consumption, especially from cooling and heating are the most mentioned objectives. Some studies also addressed reducing incident solar radiation on a form or optimizing the form for the maximum utilization of solar radiation. All these previous objectives are affected by the amount of solar radiation lying on the form of the building.⁹¹ The amount of incident solar radiation that is received by the form of the building affects the space cooling and heating demands, thus affect the energy efficiency.⁹¹ Thus, one way to enhance the energy performance of a building is to minimize the solar radiation on its form in summer and maximize it in winter. In addition to that, some other performance objectives were used in the analyzed studies, such as: optimizing wind performance, minimizing operational cost, and minimizing lighting energy. However, these objectives were mentioned in studies that usually included fenestration in their design variables, which is not suitable for the early design stages of the buildings’ forms.

We can clearly understand that the impact of solar radiation is a key factor in a building’s energy performance and that there is a strong relation between solar radiation as an energy performance objective and buildings’ forms. Therefore, the underlying principle for optimizing energy performance in early form-finding stages usually remains the same for most climates and locations, maximizing the amount of incident solar radiation in winter and minimizing it in summer.

For the pattern of optimizing forms, four main patterns were found in the analyzed work. The first one is shapes comparison, where several shapes of buildings’ forms are tested for their effect on specified performance objectives and then compared to find the optimum one between them in terms of these objectives. However, an optimum building form for a specific climate may not be optimum for another climate. The second pattern is multi-shapes optimization, where the optimization is conducted on different shapes separately. Studies using that pattern usually had a hypothesis to prove, so they attempted to prove it on more than one shape to validate their work and be able to extract a variety of general recommendations from the different shapes for that specific hypothesis. The third pattern is optimization of a predefined shape. The optimization is performed on a specific shape of the building’s form that is decided at the beginning of the design process. Several variable parameters of that predefined form are usually specified and manipulated for optimization. The fourth pattern is optimization of a predefined shaping strategy, such as,⁶⁸: who used shape grammars to generate variety of forms.,⁴⁴ who used a component that takes two multipliers (a and b) and uses them to automatically generate more complex shape boundaries. Also,⁵⁰ used an edge-based encoding method, where a node-based description of edges was applied.⁶ defined the initial rectangular building form as a mesh of variable triangular panels, allowing it to be transformed into free shapes.⁷⁴ used a 3D cell space grammar implemented in NetLogo consisting of built cells and connectors to shape the form.

From all the previous patterns, we can find that optimization of a predefined shape is the approach used in many of the analyzed studies and also in most of the real design projects, where the shape of the building is usually predetermined in the very beginning of the design process. Then, only the variable parameters are modified to optimize that shape in terms of the specified objectives.

In general, the analyzed research studies confirmed that optimization of a building during the form-finding process can significantly improve its energy performance. However, performance-based design of buildings results in buildings that are sustainable in their energy consumption but not in their other architectural aspects.²² The focus on optimizing building’s energy performance usually leads to neglecting other important architectural qualities in a design.⁶⁸ This is why it is very important to address optimization for the other aspects of buildings’ forms.

Digital fabrication

Geometry rationalization of the building’s form for fabrication constraints and objectives can play an effective role in enhancing the fabrication process. Therefore, this section focuses on the studies addressing buildings’ forms geometry rationalization for accommodating constraints related to digital fabrication in the form-finding of a design. According to the predefined search and analysis strategies, 18 studies concerning this objective are found and analyzed in terms of the type of rationalization, rationalization method, and fabrication objective as shown in Table 2.

Table 2.

Analysis of form-finding studies concerning digital fabrication.

Ref.	Type of rationalization	Rationalization method	Fabrication objectives
⁹²	Co-rationalization	Geometry adaptation (adjusting geometric designs to capabilities and dimensions of machinery)	Cost-effective fabrication. Reducing material consumption. Reducing machining time.
⁹³	Co-rationalization	Optimum surface discretization (sub-division of meshes)	Reducing material consumption.
⁹⁴	Post-rationalization	Optimum surface discretization	Cost-effective fabrication. High quality fabrication.
⁵⁸	Co-rationalization	Shape approximation by Elastica curves	High speed fabrication.
⁹⁵	Post-rationalization	Surface discretization	Simplifying fabrication of complex shapes.
⁵⁹	Co-rationalization	Geometry adaptation (adjusting geometric parameters of the form to be applicable for fabrication)	Cost-effective fabrication Reducing material consumption. Reducing machining time.
⁹⁶	Co-rationalization	Optimum surface discretization	Simplifying fabrication. Cost-effective fabrication.
⁹⁷	Post-rationalization	Optimum surface discretization	Simplifying fabrication. Cost-effective fabrication
⁶²	Pre-rationalization	Optimum surface discretization	Simplifying fabrication of beams and panels. Cost-effective fabrication.
⁶¹	Post-rationalization	Shape approximation by ruled surfaces	Cost-effective fabrication.
²⁸	Post-rationalization	Optimum surface discretization	Simplifying fabrication. Cost-effective fabrication.
⁶⁰	Post-rationalization	Optimum surface discretization	Cost-effective fabrication.
⁹⁸	Post-rationalization	Optimum surface discretization	Cost-effective fabrication.
⁹⁹	Post-rationalization	Shape approximation by sweeps	Cost-effective fabrication.
¹⁰⁰	Post-rationalization	Optimum surface discretization (reducing the number of different faces)	High quality fabrication. Cost-effective fabrication.
¹⁰¹	Pre-rationalization	Shape approximation by “canal surfaces”	Efficient fabrication.
¹⁰²	Post-rationalization	Optimum surface discretization (reducing the number of different panels)	Cost-effective fabrication.
¹⁰³	Post-rationalization	Geometry adaptation for two-axis CNC	Simplifying fabrication. Reducing fabrication cost.

From the previous table we can find that the rationalization type varied in the analyzed studies between pre-rationalization, post-rationalization, and co-rationalization. In pre-rationalization, the geometry is predetermined according to fabrication constraints, limiting the design to a set of geometries which are buildable.³⁷ Post-rationalization postpones fabrication related decisions to the construction detailing stage and it can significantly alter the appearance of the design.⁶² While co-rationalization is a hybrid type that uses both pre-rationalized design considerations and post-rationalized design modifications allowing for an optimized process.³⁷ It embeds the constraints of fabrication within the iterative cycle of generative design.¹⁰⁴ In order to avoid degradation of a design during construction, introducing fabrication constraints and objectives should be during all the process of design. Therefore, co-rationalization should be applied in form-finding processes.³⁷

Regarding the rationalization methods, three methods were found in the analyzed studies: optimum surface discretization, shape approximation, and geometry adaptation. Optimum surface discretization is done by decomposing a surface by a set of panels in the best possible way so that they can be manufactured using a specific technology at a reasonable cost, also known as: Panelization/paneling,^29,63 sub-division surfaces,¹⁰⁵ or surface discretization.⁹⁷ Shape approximation is done by replacing a complex surface by a surface which has a simple geometric nature in order to be suitable for fabrication.⁶³ However, it is difficult to stay close to the original geometry in this method. Geometry adaptation is adjusting the geometry to be applicable with the targeted fabrication technique in terms of capabilities and dimensions of machinery, and the targeted fabrication material in terms of the material properties and dimensions.

We can see that the most common method of rationalization in the analyzed studies is the optimum surface discretization. This method can be the best for a multi-objective form-finding as it provides flexibility in the issue of staying close to the original geometry in contrast to the shape approximation method. Adding to that, geometry adaptation method is very crucial for ensuring buildability, reducing waste materials, and cost effectiveness of the fabrication.³⁷ Consequently, it should be incorporated in any rationalization process.

For the fabrication objectives, most of the analyzed studies have included cost-effective fabrication as an objective. Fabrication cost has always been an important measure for the success of a design. Therefore, reducing fabrication costs should be considered as one of the main objectives.

It was also observed in the analyzed studies that geometry rationalization has always been considered for a specified fabrication technique, such as: subtractive, additive, etc. This technique usually varied according to the scope and field of the study.

Aesthetics

Many research studies have investigated the opportunities of integrating aesthetics in architectural design. This section focuses on the studies that used aesthetic evaluation in a form-finding context. According to the predefined search and analysis strategies, 14 studies concerning this objective are found and analyzed in terms of the tool used for the aesthetic evaluation, the position of the aesthetic evaluation in the form-finding process, and who performs the aesthetic evaluation as shown in Table 3.

Table 3.

Analysis of form-finding studies concerning aesthetics.

Ref.	Tool used for the aesthetic evaluation	Position of aesthetic evaluation in the form-finding process	Who performs the aesthetic evaluation
⁴³	A developed system called: “Archinder”.	Throughout the whole process The evolutionary algorithm generated images of design candidates and used their aesthetic score retrieved by the web platform as a fitness function for the next generation/population.	Users
¹⁰⁶	A developed interactive exploration tool called: “ParaGen”.	After obtaining design solutions (post optimization) Visual images of the results were accessed through a web site which included all solutions with their saved quantitative performance values, offering the potential of human interaction for aesthetics.	Designer
⁵⁶	A developed shape comparison algorithm.	Post the optimization process The shape comparison algorithm was implemented to decrease the number of the Pareto front solutions to a reasonable number of highly diverse optimal design solutions. Then, designers’ aesthetic judgment was accommodated to facilitate decision making.	Designer
⁵⁵	A developed shape comparison algorithm.	Throughout the whole process An aesthetically driven initial population was used as input to the evolutionary algorithm. A form diversity algorithm was used to eliminate similar solutions. After getting the final set of diverse solutions, the designer evaluated the results to make a final decision.	Designer
⁵⁴	The “Human UI” plug-in for Grasshopper.	Pre the optimization process Users’ preferences were received from the decision-making interface created by Human UI. Then, responses were analyzed to find numerical measurements for their aesthetical preferences. The last step was optimization through a multi-objective optimization algorithm.	Users
¹⁰⁷	A developed human-in-the-loop system together with artificial intelligence (human-computer interaction method).	Throughout the whole process The used design approach uses hybrid selection of solutions by designer and artificial intelligence. The model is trained to use the extracted aesthetic features from a sample input to from the design solutions.	Designer
⁵³	Genetic programming via Grasshopper, where two features were programed: Shape Comparison, and Online Classification	Throughout the whole process The used approach supported the designers in aesthetic decision making as part of the design process. Shape Comparison removed similar solutions. Online Classification captured users’ aesthetic preferences.	Users
¹⁰⁸	An especially developed multi-objective and interactive genetic algorithm for eco-performance, associated with a human machine interface for aesthetics.	During the optimization process The architect had the possibility to select one or more individuals during optimization and keep them available for manipulation. At any time during the process, the architect can export them or send them back inside the evolutionary loop to redirect the optimization into favoring these solutions.	Designer
¹⁰⁹	A developed technology of sketch-based image retrieval	In the stage of selecting a final design. Designers can directly find their most aesthetically preferred design alternative with respect to their hand-drawn design which was inputted at the beginning of the process.	Designer
¹¹⁰	Virtual reality, in particular, CAVE (Cave Automated Virtual Environment)	Throughout the whole process of design and planning Users could select between two main forms of the building, then contribute to the space organization of the building’s internal spaces	Users
¹¹¹	A mobile application “MAR” that uses augmented reality to superimpose real design alternatives on paper-based markers	Early design thinking stage Through the mobile application, users can contribute with their own design vision to provide ideas for the design taking place through AR.	Users
¹¹²	A supervised neural network system	After obtaining the design solutions The system was trained based on capturing user selection to create a predictive scoring model for design evaluation of solution options. Users’ selection patterns were decided according to neural networks.	Users
¹¹	A traditional survey/questionnaire	After obtaining the design solutions The survey was conducted among users to evaluate the aesthetic appeal of certain public buildings.	Users
¹¹³	A web based developed evolutive design tool	Throughout the whole process Model generation is done. Then, the system generates several variants for the defined design and displays them in an interactive 3D viewport for analysis and rating.	Designer

From the previous table we can find that all the tools used for aesthetic evaluation were specially developed or programmed for the specific project, except for the work of¹¹ who used a traditional questionnaire, and⁵⁴ who used Human UI, which is an available, free to use GH plugin that does not require any knowledge about programming. However, it lacks an embedded data collection method for the results. Therefore, more free tools for aesthetic evaluation should be developed, especially those that do not require any programming, and include methods for data collection. As a current alternative, Human UI can be used for aesthetic evaluation together with a method for results’ collection such as the questionnaire.

The position of implementing aesthetic evaluation in the design process varied. Some studies performed aesthetic evaluation throughout the whole process, others performed it before the optimization, and others performed it after obtaining results from the optimization process. However, in a multi-objective form-finding, aesthetic evaluation should be performed post the optimization process as an additional criterion for solutions selection.

Regarding who performs the aesthetic evaluation, a considerable number of studies targeted the designers themselves to perform the aesthetic evaluation, while the other studies incorporated the users’ aesthetic preferences. However, due to the overwhelming number of design solutions usually generated in a multi-objective form-finding, it would be difficult for architects to choose the most favorable solution¹¹⁴ and consider such a qualitative design aspect without users’ participation.¹¹⁰ Therefore, it is important to incorporate users’ aesthetic judgement in design decision making by developing methods, through which users can directly choose the most aesthetically preferred design solution.

In general, results of the analyzed studies prove that the problem of aesthetics is a possible criterion for searching for design solutions and that the combination of computer computational power with human perspective provides improved performance in such a qualitative design objective.¹¹⁵ Therefore, the aesthetic criterion should be included in the form-finding context as it can enhance the designs and overcome the criticism that a design accomplishes high performance but low aesthetic quality. In addition, Architects should interactively design buildings’ forms being more aware of the aesthetic features and their impact on the final impression of the building’s design.

The proposed multi-objective optimization framework for the form-finding of architectural parametric forms

The proposed framework, shown in Figure 6, concerns in particular the currently widespread free-form architectural designs. It is composed of five phases: form generation, multi-objective optimization, aesthetic evaluation, geometry rationalization, and digital fabrication of a prototype. Upon completion of each phase, the output seamlessly transitions as input to the subsequent phase. For instance, the result from the form generation phase serves as the starting point for the multi-objective optimization phase, and so on. This process is considered as finally done with the attainment of the final design and its fabricated prototype.

All phases of the framework are implemented within Rhino and its virtual programming environment, GH, owing to their versatility, accessibility, and widespread use in architectural modeling. Notably, the virtual programming capabilities of GH facilitate the integration of different design objectives in the optimization process and the visualization of the results. The following sections will discuss each of the five phases of the framework in detail.

Phase one – Form generation

The generation of initial form is the base of the whole design. Thus, we need to set the right constraints and parameters, paying attention to all the important aspects of the design. The output of this phase is an initial form that is ready for optimization (a parametric model). This phase uses the parametric modeling tool, Rhino especially its virtual programming environment, GH. Steps and procedures followed in that phase are:

• Setting the design approach.

Deciding the design approach/approaches¹¹⁶ to be used as a catalyst for generating the form. It is recommended here to consider fabrication between the approaches of the form generation.

• Defining constraints.

Understanding the constraints of the design to be used as guiding rules during the early process of modelling. For instance, site constraints, dimensions, functional requirements, etc.

• Geometric description of the design using parameters.

Providing the main parameters that shape the initial form of the building and incorporating several parameters with a specified interval of minimum and maximum bounds (specified range) in which parameters can vary.

• Forming relations between the parameters.

Writing all the equations and forming connections that consider the relations between the parameters in GH.

Phase two – multi-objective optimization

Multi-objective optimization is an iterative process that tries to find the best possible solution/solutions for a problem from a wide range of available solutions. It has become an efficient method to satisfy the several requirements of the recent buildings’ designs, especially through the Pareto front approach. Therefore, we will use it to search for optimum solutions that satisfy the quantitative predefined design objectives: energy performance, and digital fabrication. While the qualitative aesthetics objective will be addressed later in the next phase.

In that type of optimization, many solutions are produced, including the set of Pareto front solutions. The entire Pareto front set can be considered a final output of the multi-objective optimization. However, the number of these solutions is usually high. This is why these solutions should be filtered by the designer according to some criteria. Accordingly, the output of this phase is a filtered set of Pareto front solutions.

Ladybug plug-in, which allows to visualize and analyze weather data inside GH,¹¹⁷ is used as the simulation software. While Wallacei, the evolutionary multi-objective optimization engine,¹¹⁸ is used as the optimization software. It allows users to run evolutionary simulations in GH through utilizing highly detailed analytic tools and produces representations of the candidates together with diagrams. Steps and procedures followed in that phase are:

• Setting the main optimization objectives

Optimization is done for both energy performance and digital fabrication objectives. The energy performance objective here is minimizing the incident solar radiation in summer and maximizing it in winter, as concluded before from the analysis of previous related studies. Therefore, Ladybug is set to calculate the incident solar radiation on the form for a specified period in summer and winter seasons. While for the digital fabrication objective, cost-effective fabrication is mainly considered through minimizing the façade total surface area. Thus, an equation that calculates the façade total surface area is written on the GH canvas.

• Running the genetic algorithm

The initial design in addition to its predefined variable parameters and their specified ranges are provided to Wallacei. These variable parameters with their ranges are used as the genes for the optimization process. Number of generations, number of individuals in each generation, and the algorithm parameters (crossover and mutation probability, crossover and mutation distribution index, etc.) are also specified according to the nature of the design case and given to Wallacei.

• Filtering the final Pareto front solutions

The resulting set of Pareto front is known to give a representation of the best individuals. They make it easy for the designer to understand the trade-offs between the different objectives and make informed decisions. Post-optimization, the designer examines the Pareto front solutions. Since the number of Pareto front solutions in an optimization problem can vary up to a very high number, the designer will need to filter these solutions to find the ones that give the best trade-off (balances) between the objectives. After filtering the Pareto front set, the designer has the possibility to select a final design while relying on additional inputs, preferences,⁴² or any other subjective or performance criteria. This leads to the next phase of the framework, which is the final design selection criteria, the aesthetic evaluation.

Phase three – aesthetic evaluation

Aesthetic evaluation is measuring how aesthetically appealing an architectural form is. The framework considers aesthetics as possible criteria for design solution search by incorporating users’ aesthetic evaluation in choosing a final solution from the filtered set of design options. This phase ends by obtaining a final chosen solution that is the most aesthetically pleasing of all the other provided solutions for most of the users. Human UI plug-in, which is an interface paradigm for Grasshopper that creates professional looking custom user interfaces without writing any code,¹¹⁹ is used for the aesthetic evaluation. It is integrated with an online questionnaire on Google forms to be able to collect and receive answers from different users online and in real-time. Steps and procedures followed in that phase are:

• Evaluating the chosen Pareto front solutions in terms of aesthetics

A custom user interface for aesthetic evaluation is built with Human UI inside GH. Within the interface, there is a 3D view for the design options provided to allow the users to explore them and decide which one is their most aesthetically preferred. The 3D view shows each form separately with the ability to rotate around it and zoom in or out to see more or less details. Beside the 3D view, there is an online Google forms questionnaire which contains several questions to be answered by the users to allow the designer to rank the solutions according to the users’ aesthetic preferences and analyze their reasons of choosing a specific solution.

Phase four – geometry rationalization

Generally, the hybrid, highly versatile type of rationalization, co-rationalization, is used in the framework as it considers fabrication objectives and constraints in every possible aspect. For instance, the approach for generating the initial form involves the consideration of fabrication. Geometry rationalization in this phase is used to determine the optimum paneling of the free-form surface in terms of reducing material consumption and simplifying fabrication, in addition to avoiding fabrication errors. Thus, obtaining a cost-effective fabrication. In the end of this phase, we obtain a final rationalized solution that is ready for fabrication. Kangaroo Physics plug-in (Kangaroo), which is a Live Physics engine for interactive simulation, form-finding, optimization and constraint solving,¹²⁰ is used for transforming the panels into specified goals with the use of given constraints. Steps and procedures followed in that phase are:

• Surface discretization of the free-form

The free-form surface is discretized into any geometrical shape including triangular, quadrilateral, hexagonal meshes, and hybrid meshes.

• Geometry adaptation for the panels of the free-form

The geometry is adjusted to be applicable with the targeted fabrication technique and material. It should be noted that panels of a free-form can be fabricated by many different methods, tools, and diverse materials. In this framework, we specifically focus on the subtractive fabrication technique due to its availability and suitability for fabricating objects with a low number of details, such as the façade panels.

According to that, geometry adaptation is done in two steps. The first one is considering the dimensions of the machinery and materials, where the dimensions of the panels of the geometry are adjusted to fit both the standard dimensions of the used materials and the dimension limit that the machinery can perform. The second step is considering the capabilities of the machinery and materials properties. In subtractive fabrication, normal laser or CNC machines are only able to fabricate planar panels, and also Medium-density fiberboard (MDF) sheets, which are commonly used for that type of fabrication, cannot be bent. Thus, all panels must be adjusted to be planar to be applicable for this method of fabrication, which is done with Kangaroo.

Phase five – digital fabrication of a prototype

Digital fabrication in such an early phase of form-finding refers to the digital fabrication of a prototype. That prototype can be a full scaled model, a part of a scaled model, or a small number of panels from the real scale model. It is also known as: rapid prototyping. Rapid prototyping closes the loop between design and production. It enables reflection over physical objects that can inform the design decisions.³⁰ Moreover, the limitation of a machine and capability of materials must be tested to move from digital to physical modelling.³⁴ Therefore, digital fabrication of a prototype is performed to evaluate the feasibility of the geometry as soon as it is designed, ensure the applicability of the design, and helps avoid fabrication errors and optimize the design towards specific fabrication goals before the final fabrication of the real building. The output of this phase is a fabricated prototype of the final rationalized form. The OpenNest plug-in is used to make 2D polyline packing for performing subtractive fabrication with a laser or CNC cutting machine.¹²¹ Steps and procedures followed in that phase are:

• Scaling the final rationalized 3D model to the desired scale of the prototype

After obtaining a rationalized solution, the designer scales the 3D model of that solution to the desired scale of the prototype. This step can be skipped if the designer chooses to fabricate a part of the real scale model.

• Preparing the scaled model for fabrication

The first step here is deciding which part of the scaled model is going to be fabricated. Then, panels of that part are transformed into 2D polylines and projected to the XY plane to be packed inside sheets for fabrication using OpenNest.

Discussion

This section mainly discusses the significance of the proposed framework. In summary, the proposed framework presents a shift from design methods that only deal with performance design objectives into optimization that also incorporates digital fabrication and aesthetic objectives. It expands the definition of the process of architectural parametric form-finding by integrating generation, optimization, evaluation, rationalization, and fabrication. Compared to the basic parametric form-finding process, the proposed framework introduces several potential improvements in the process, as shown in Figure 7.

The potential improvements in the form-finding process formed by the proposed framework can add significant value to the field of architecture through increasing the quality of the designed architectural forms. In addition to these potential improvements, the framework also realizes the following purposes:

• Ease of implementation: Simplifies the process through including all the phases within the same visual programming environment that requires no programming expertise.

• Comprehensive design criteria: Integrates both quantitative and qualitative criteria in design.

• Collaborative decision making: Supports collaborative decision making by engaging users in the design process.

• Flexible optimization: Optimizes different aspects of architectural buildings’ designs in the early form-finding stage, going further from just optimizing a building after its form has been defined.

• Synergy between human and machine: Builds a constructive relationship between rule-based computing and humans, through integrating human knowledge, expertise, creativity, intuition, and perception with machine-based accuracy, and computation power.

• Interactive and informed design: Enables architects to interactively design being more aware of different features and their impact on the final building’s design.

Overall, this framework has the potential to revolutionize the architectural design process, leading to buildings that are more sustainable, cost-effective, innovative, and finely tuned to both human and environmental needs. It represents a shift toward more adaptive, collaborative, and practical architecture, where designs are optimized early on and in a more informed, interactive manner.

Conclusions

Recently, architects have changed their role from making architectural forms that only depend on their creativity and intuition to controlling a complex generative process, where the result can depend on the design objectives desired at the beginning of the form-finding process. Furthermore, the integration and control of several objectives of a parametric architectural design in one form-finding process can have a great effect in terms of enhancing the quality of this design. In this regard, the paper presented the basic parametric form-finding process, and the main objectives of early form-finding. Following that, a systematic literature review for architectural buildings’ forms form-finding or optimization in the early stages of design was conducted. The review focused on the studies addressing the three objectives: energy performance, digital fabrication, and aesthetics. Then, based on the conclusions from the analysis of the selected studies, the paper proposed a multi-objective optimization framework for the form-finding of architectural parametric forms that considers energy performance, digital fabrication, and aesthetics. The framework consists of five phases: form generation, multi-objective optimization, aesthetic evaluation, geometry rationalization, and digital fabrication of a prototype.

The proposed framework in this paper posits the possibility of an expanded definition of architectural parametric design by embedding generation, optimization, evaluation, rationalization, and fabrication in the form-finding process. This holistic integration allows architects to seamlessly move from conceptualization to realization, ensuring that all the important aspects of the design are considered from the earliest stages. By doing so, the framework not only enhances the performance and aesthetics of architectural forms but also ensures the practicality of the final design, bridging the gap between creative design intent and practical implementation which adds great value to the field of architecture. It is recommended that this framework is applied on a case study building in future studies to showcase and validate its effectiveness in enhancing the design of the building in terms of the three mentioned design objectives. Also, more design objectives can be possibly considered in the framework depending on the nature of the design project.

Footnotes

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 iD

Lina A. Ramadan

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