A Generative Design Exploration Methodology for Integration of Structural,Environmental,and User Agencies in an Early Design Stage

Abstract

This article presents a generative design exploration methodology utilized to assist designers in problem structuring and decision-making in a multi-disciplinary setting. This novel design exploration methodology is based on the hybridization of a genetic algorithm (GA) and the Theory of Innovative Problem Solving (TRIZ). This methodology allows investigation of unexpected solutions, application of innovative ideas for resolving contradictory design objectives, and continuous interaction between designers and the search engine. In this study, the design case of a mid-rise apartment complex is used to examine the capacity of the proposed multi-agent design exploration method. Accordingly, both quality and numeric performance-based values of the design alternatives, including the visual appearance of the complex and apartments’ shadows over one another, structural and energy efficiency, and life-cycle impact of the building’s structural system, are investigated to demonstrate the usability and benefits of the developed method.

Keywords

Conceptual design design exploration TRIZ genetic algorithm multi-objective design Cross-Laminated Timber (CLT) plates informed decision-making life-cycle assessment

Introduction

Several studies have demonstrated the importance of utilization of an appropriate design exploration methodology as well as decisions made during the conceptual phase of design^1-3 in which the designers uncover the design problem and solutions simultaneously^4-6 through an iterative process.⁷ In the past decade, many computational design exploration methodologies have been developed to assist designers in generating and evaluating diverse solutions and making appropriate decisions. However, very few developed design exploration methodologies assist designers in defining or re-structuring the design problem, the parametric model, and the search process.^4,8 Hence, a design exploration process may yield solutions for an ill-defined problem or offer solutions around a design parameter not initially included in the parametric model. For example, the design alternatives of a multi-family housing complex may be studied to find solutions that have low heating energy demand and bright interior space. The building is modeled parametrically such that all the generated building masses have greater heights on the south side versus the north side. Thus, many apartment units will be shadowed, and the exploration process has been inevitably directed toward units with larger window areas that compromise the energy efficiency goal. In this case, designers have to either create another parametric model, re-run all the simulations, and re-do the design exploration from the beginning or remain restricted to the generated solutions provided by the ill-defined parametric model. This study aims to introduce a novel multi-objective design exploration methodology to support the simultaneous evolution of the design problem and design solutions in the conceptual phase of design. This design methodology, called the GA+TRIZ method, helps the designer to define and re-structure the design problem as needed, build a suitable parametric model in which pertinent and dominant variables are included, and investigate unexpected solutions.

Moreover, within the field of architecture, a quantitatively optimal solution is not always the best solution. A multi-disciplinary design team usually needs to evaluate the quality of generated solutions as well as the performance-based quantitative values and adjust their preferences during the design process.^9-11 Qualitative evaluation of solutions requires dynamic and continuous interaction between designers and search engines.¹² The proposed GA+TRIZ method aims to support continuous interaction, investigation of quantitatively optimal and qualitatively desirable solutions, and dynamic adjustment of search criteria throughout the design exploration procedure.

Furthermore, when a set of contradictory design objectives exist, the existing design exploration methodologies usually provide designers with a Pareto set and prompt making a trade-off .^12,13 Although a Pareto set can help designers in decision-making, it constrains designers’ creativity in resolving the contradictions among design objectives and making innovative design decisions. The novel GA+TRIZ method is based on a combination of a Non-Destructive Dynamic Population Genetic Algorithm (NDDP-GA)¹⁴ and the Theory of Inventive Problem Solving (TRIZ)^15-17 that will be discussed in further details in the following sections. This combination supports the investigation of unexpected solutions and gives further room to designers’ creativity to make innovative decisions when contradictory design objectives exist. In addition to providing designers with Pareto optimal solutions, the application of TRIZ Inventive Principles intends to provide implicit search goals to make an appropriate final decision.

In this research, the novel GA+TRIZ methodology is utilized, examined, and calibrated through the design exploration of a mid-rise apartment complex in Montreal, Canada. This paper begins with an overview of state-of-the-art GA-based design exploration methodologies and the application of TRIZ principles in architectural design. Then, the paper continues to demonstrate the proper application of the GA+TRIZ methodology and analyze the integration of automation techniques, GA-based search engines, and TRIZ tools in advancing a multi-disciplinary design practice.

State of the art

GA-based design exploration methodologies in architectural design

The suitability of a design exploration methodology highly depends on the design problem and goals. When multiple design goals should be explored for a population of diverse design alternatives, using parametric modeling tools and an evolutionary search algorithm will be appropriate. Among various evolutionary algorithms, genetic algorithms (GAs) are commonly used in architectural design explorations because of their robustness, relatively simple implementation,¹⁸ and the capacity to incorporate a set of multi-disciplinary objectives. Accordingly, the scope of this study is limited to the development and application of a novel GA-based design exploration methodology.

In all variations of a GA, the variables of the parametric model are analogous to genes on chromosomes,¹⁹ and the search process begins with generating a population of solutions. Then, the search process continues through evaluating and selecting a pair of parents, generating the new offspring by using mechanisms such as recombination and mutation. Usually, the generated solutions are stored and ranked in a database.²⁰ The fitness of generated solutions is usually evaluated using an objective function, called the fitness function, derived from the design objectives and constraints.²¹ Any design process includes four main steps: problem structuring, solution generation, evaluation, and decision-making.⁷ The iterative process of a GA-based design exploration encompasses the same four main steps described in Figure 1.

Figure 1.

Mapping the steps of a GA-based design exploration on a typical iterative design process.²²

Much of the literature on the development and implementation of a GA in design exploration methodologies highlights the adaptation of the Non-Dominated Sorting Genetic Algorithm (NSGA-II),²³ the Non-Destructive Dynamic Population Genetic Algorithm (NDDP-GA),²⁴ and the Strength Pareto Evolutionary Algorithm 2 (SPEA-2)²⁵ in the field of architecture. Most of the developed design exploration methodologies, using any of these two GAs, allow some extent of visual inspection of generated solutions as well as robust assessment of multiple performance-based numeric values such as energy use, structural performance, life cycle impact, and cost. However, some aspects of these computational design exploration methodologies have remained understudied and need to be improved for better integration of architectural and engineering design. First, most of the design exploration methodologies established so far allow designers’ interaction at either the first step of problem structuring (priori mode, e.g.^26-28) or the last step of selecting the final suitable solution (posteriori, e.g.^29-33). However, the design problem and design solutions usually evolve simultaneously, and a multi-disciplinary team of designers needs to adjust the design problem regarding design context and qualitative goals and obtain an almost realistic expectation of final solutions. Thus, a continuous and dynamic interaction is necessary to let the design team specify subjective goals, such as the suitability of the visual appearance, and adjust their preferences after each iteration. However, very few design exploration methodologies, namely ParaGen^14,24,34,35 and Design Space Exploration (DSE),^36,37 let the design team interact with the search engine continuously. Moreover, a limited number of design exploration methodologies allow problem re-structuring.^4,8,22,38 In most cases, iteration happens between the two steps of form generation and evaluation (steps two and three). This shortcoming might be due to the assumption of unnecessary or unrealistic design restrictions or the inconvenience of pausing the automated design exploration procedure.

The other deficiency relates to the limited decision-making mediums with which a design exploration methodology can provide a designer. The common mediums include sorting and ranking the performance-based values of the generated solutions or using a Pareto set to make a trade-off between two conflicting design objectives. Although a Pareto front (see an example of a Pareto front in Figures 8 and 9) presents a series of non-dominated and suitable solutions, the designer still needs to sacrifice one objective to improve another and make an informed final decision. Unlike architectural design exploration projects, several engineering design explorations rely on a supplemental search method, such as weighting, data mining, or clustering and classification algorithms, to select a quantitatively optimal solution.^13,39,40 However, applying these methods requires designers’ broader knowledge of computer science and constrains their creativity in resolving contradictory goals. Hence, the designer’s final decision is usually minimized to Pareto optimal solutions and an inevitable performance-based trade-off. Table 1 presents a list of prominent GA-based design exploration methodologies employed in architectural design and compares their features regarding their structure, interaction mode, and capacity to include both qualitative and quantitative design goals.

Table 1.

Review of features of prominent GA-based design exploration methodologies in architectural design.

A glance at Table 1 clarifies the scarcity of computational design exploration methodologies that allow designers’ continuous interaction with the search engine. The table also shows that most design exploration methodologies do not facilitate problem-restructuring through their iterative search process. Moreover, merely a few of the GA-based design exploration methodologies offer diverse decision-making mediums that support the assessment of qualitative design goals.

Application of TRIZ in architectural design

In the 1960s, Genrich Altshuller and his colleagues examined over 2.5 million inventions and recognized that a series of common principles and concepts were being used to solve a series of common technical problems. They developed an inventory of those common general problems and solutions and devised the Theory of Innovative Problem Solving to let the future inventors learn from past successes and change the technical problem-solving procedures from trial and error to a systematic practice^15-17. Altshuller and his fellows described the TRIZ problem-solving Prism in four consecutive steps.⁷⁵ First, the problem-solving process begins with identifying the specific technical problem and then re-stating the specific problem more generically. Third, it continues by referring to the treasury of past inventions, finding one or more generic solutions for the generic problem, and fourth, interpreting the generic solution to a specific solution for the initial specific problem (Figure 2).

Figure 2.

The plot displays the distribution of solutions regarding their total floor area (m²) and GWP (tonCO2eq).

TRIZ tools have been developed and used in different engineering disciplines as well as design science. The literature review shows that TRIZ principles have also been employed in developing architectural design concepts. Architectural design is rather an interdisciplinary practice, and the design team is to address multiple design objectives related to geometrical, material, structural, and mechanical systems as well as some super-systems such as a neighborhood, region, and city. Thus, applying TRIZ analytical and organized knowledge system in problem-solving and decision-making seems valid. Moreover, TRIZ tools are formulaic and can be compounded by computational design exploration systems. To date, several studies examined the application of TRIZ concepts and tools in architectural design that can be reviewed in three groups. The first group explains the TRIZ concepts and discusses the related epistemology.^76,77 The second group of studies investigates the feasibility and impediments of TRIZ application in architecture.^78-83 The third group demonstrates the combination of TRIZ principles and tools with other design-aid toolkits, among which there are very few studies that examined the hybridization of TRIZ tools with evolutionary design exploration methodologies. Table 2 summarizes the scope and outcome of the studies that contributed to the development of a design exploration methodology using a GA and TRIZ principles. In brief, most of the previous studies have been initiated from the perspective of computer programmers and data scientists. There is a paucity of literature on the application of developed algorithms and designers’ interaction with the computational search components. Moreover, the very few pieces of literature that explain the application of such methodologies have focused on the optimization of relatively small products and not multi-objective design exploration of an architectural design case whose performance impacts the stakeholders and environment on a different scale. An overview of the literature shows that very few developed methodologies allow a suitable visualization method and provide a user-friendly interface for establishing a design problem through an iterative process.

Table 2.

Studies that contributed to the development of a design exploration methodology using a GA and TRIZ principles.

Research scope	Research outcome	References
Algorithm development	A dialogue-based software application using a combination of ARIZ (algorithm for inventive problem solving) with some OTSM-TRIZ (general theory of powerful thinking)	⁸⁴
Developing an idea-generation tool	Combination of TRIZ and nonlinear static pushover analysis	⁸⁵
Developing a design exploration methodology	A new systematic approach by combining quality function deployment (QFD), TRIZ, and a refined Kano’s model	⁸⁶
Geometric optimization	An optimization methodology by combining a GA and TRIZ and Java programming for automation	⁸⁷
Theory development	A multi-agent system called Agents-based DEsign activity Analysis (ADEA) for design activity reasoning	⁸⁸
Developing a problem-solving methodology	Developing a “dialectical negation algorithm” (DNA) composed of an evolutionary algorithm and TRIZ	⁸⁹
Developing a design exploration methodology	Design an export packing system by combining a GA and TRIZ	⁹⁰
Developing a CAD tool	Developing AEGIS (accelerated evolutionary Graphic interface system) by combining TRIZ and a GA is being developed and applied to graphic design.	⁹¹
Developing a design exploration methodology * the fitness function and interaction mode should improve to make the design process efficient	Developing automated generation of innovative alternatives (MAGIA) methodology using TRIZ tools and text mining techniques for specific applications in the building construction industry	⁹²

The GA+TRIZ design exploration methodology

In this section, the theoretical foundation and the rationale for establishing the GA+TRIZ methodology are explained and the specification of the GA and the TRIZ component of this methodology are described. This section is followed by the case study section, where the use and benefits of the methodology’s specifications are demonstrated through explicit examples.

The GA+TRIZ design exploration methodology is founded on Lawson’s model of an iterative design process⁷ and has two main components: a GA-based search engine and the TRIZ Inventive Principles. The design exploration process, demonstrated in Figure 1, is linked to the TRIZ prism, shown in Figure 2, at three stages (Figure 3):

1. The beginning of the design exploration process when the design objectives are defined.

2. When the fitness function is set for generating solutions systematically.

3. When the final decision is made, and the designer may improve the final design solution through post-processing.

Figure 3.

The plot displays the distribution of solutions regarding their total floor area (m²) and total heating energy from November to the end of March (MJ).

The GA-based search engine

The GA embedded in the GA+TRIZ methodology is a Non-Destructive Dynamic Population Genetic Algorithm (NDDP GA), which is originally implemented in the ParaGen framework.²⁴ Similar to other GA-based search processes, the ParaGen component begins the exploration by generating, evaluating, and storing an initial population of random solutions and continues through a systematic solution generation by defining and implementing a fitness function based on design objectives and constraints (Figure 3). The NDDP GA uses a half-uniform crossover (HUX)⁹³ to let the selected parents breed new offspring. This means that the newly created child solution may inherit some characteristics directly from parent 1, or directly from parent 2, or through a combination of the characteristics of the two parents. Unlike other conventional GAs, in which defective solutions are killed off and removed from the breeding population, the NDDP GA retains both well-performing and poor-performing solutions in the database. Storing all of the solutions in a database supports the re-definition of the design problem and modification of design objectives without the need to re-generate and re-evaluate a population of solutions because poor-performing solutions may become well-performing ones with a new set of design objectives.

The ParaGen component allows filtering and ranking based on any combination of geometry or performance-based parameters. In addition, the ParaGen interface improves the readability of the information by providing both images and key performance values associated with each solution. Designers can also use scatter point graphs to compare two performance values of the solutions and study Pareto sets²⁴ or Parallel Coordinate Plots (PCP)⁹⁰ to select a series of optimal solutions.

TRIZ matrix of contradiction and inventive principles

Among many problem-solving methods and several TRIZ tools, the matrix of contradiction and the 40 Inventive Principles (IP) are implemented in the GA+TRIZ method because they are formulable, compatible with algorithmic procedures, and intrinsically relevant for addressing contradictory goals in a design problem. Contradictory goals may be physical or technical. A physical contradiction appears when inconsistent benefits are desired. For example, increasing the thickness of a wall reduces heat loss but adversely affects the total weight of the building. TRIZ IPs suggest applying the concept of separation to resolve the contradiction. In this case, the wall thickness can be split into two parts: thermal insulation and structural component. Then, the thermal insulation can be thick enough to minimize heat transfer, and the thickness of the structural component can be safely reduced to minimize the total weight of the building. A technical contradiction appears when the improvement of specific attributes causes the deterioration of other attributes within a system. For example, increasing the gross floor area of a residential building is desirable, but a greater construction project contributes more to Global Warming Potentials (GWP). In case of a technical conflict, the TRIZ matrix of contradiction suggests generic solutions from the list of 40 IPs.

In the TRIZ literature, the design attributes that are desirable and should be improved are called Useful Functions (UF) and the design parameters that undesirably get worse are called Harmful Functions (HF). In the GA+TRIZ methodology, the designer should first study the design problem and highlight desirable (UF) and undesirable (HF) goals by constructing a “cause-and-effect” graph to uncover the conflicting goals and use the TRIZ component properly. In this study, the graph established by Khodadadi⁸ is employed to deconstruct the design parameters and identify the UFs and HFs. If any technical contradiction exists, the designer can refer to the matrix of contradiction in which the 39 desirable parameters to be improved (UF), and those which are getting worse (HF) are listed along the rows and columns, respectively (Figure 4). The solutions suggested in the matrix’s cells can help to resolve the technical contradiction. The suggested IPs rely on the inventory of solutions employed in over 2.5 million past inventions to resolve similar technical conflicts. The full list of 39 parameters and 40 IPs can be found in “TRIZ for Engineers” by Gadd.⁷⁵

Figure 4.

The TRIZ Prism.

Implementation of the methodological model

The ParaGen web interface and the developed TRIZ add-on, in which the matrix of contradiction and IPs are included, are used to implement the GA+TRIZ design exploration method. At the beginning of each design exploration cycle, when the designers synthesize the design objectives and identify conflicting goals, they can refer to the TRIZ add-on, choose the UF and HF from the respective dropdown lists, and find the corresponding generic solutions from the matrix of contradictions. At this step, the TRIZ component lets them build the parametric model with a better understanding of design parameters’ dependencies and include the pertinent design variables. When the fitness function is to be set during the form generation and evaluation, the TRIZ component can help better understand the connections among the parameters and the implicit search goals. Then, designers can set the breeding criteria within the GA by considering a wider range of relevant applicable parameters. During the final decision-making and post-processing step, designers can utilize all the visualization and post-processing tools, filter and sort performance values, and study the distribution of solutions regarding two selected parameters. In addition, the TRIZ component supports either a more convergent exploration around a specific performative output or the development of a suitable post-processing decision.

Case study

In this section, the design exploration of a mid-rise residential complex in Montreal, Canada, is carried out to examine the usability of the GA+TRIZ method in a multi-objective setting and its capacity to support user agencies. This case study aims to find a series of suitable solutions considering the visual appearance of the complex, the apartments’ shadows over one another, structural and energy efficiency, the life-cycle impact of the building’s structural system, and the cost of the structural shell.

Design exploration

Problem structuring, step 1

The first step of the GA+TRIZ design exploration method is synthesizing the design objectives, investigating conflicting goals, taking innovative preliminary actions when creating the parametric model, and setting up the database. This design project aims to have a minimum environmental impact, particularly regarding GWP. The cause-and-effect graph shown in Figure 5 demonstrates that minimizing the mass and thickness of structural panels seems desirable to decrease the GWP but acts against increasing the thermal mass for energy efficiency purposes. The TRIZ IPs suggest implementing the concept of separation to resolve this physical contradiction. Thus, separating the layers of the building shell for taking the different structural and thermal roles and defining two separate parameters in the computational model will be a good idea.

Figure 5.

The process of the GA+TRIZ design exploration method.

Moreover, the reduction of GWP conflicts with the desire to provide more apartment units and greater floor area (Technical contradiction). The matrix of contradiction suggests changing the physical or chemical properties of employed substance or employing composite materials (Table 3). This generic solution can be specified by choosing a building material with lower embodied carbon. This suggestion strengthens the intention of using wood materials such as Cross Laminated Timber (CLT) panels instead of reinforced concrete panels. Using CLT panels can additionally offset carbon emissions, as one of the main Canadian CLT suppliers is located in Montreal and the transportation-related carbon emission will be minimal.

Table 3.

The matrix of contradictions of the mid-rise residential complex.

Characteristics			Characteristic that is getting worse (HF)
			31	22	4	18
			Harmful side effects developed by an object	Waste of energy	Length of a stationary object (thickness of the building shell)	Brightness
Characteristic to be improved (UF)	26	Amount of substances	1- Local quality 35- Physical/chemical properties 40- Composite materials 39- Inert environment
	6	Area of aStationary object(Total floor area)		17-Moving to another dimension7-Nesting dolls30-Flexible films or membranes
	4	Length of a stationary object (thickness of the building shell)			AllorConcept of separation
	12	Shape				13- Other way round15- Dynamism32- Optical change

The cause-and-effect graph in Figure 5 also shows that energy efficiency conflicts with the desire to increase the total area of the residential complex. The matrix (Table 3) suggests Moving to another dimension that brings the idea of minimizing the volume of the interior space, which does not seem to be agreeable for this project. Application of the nesting doll principle can be specified as using thermal insulation in combination with CLT panels.

The initial concept of the residential complex is inspired by Habitat 67, Montreal, and relies on a stack of cubic modules in which a series of randomly selected units are removed to shape the roof gardens and private balconies. Units are expected to be constructed by structural panels, but columns and required structural supports are added to the model where the walls of the lower floors do not support units. The parametric model of the residential building is processed using Grasshopper,⁹⁴ and structural analysis is carried out in Karamba, a plugin for Grasshopper.⁹⁵ Thermal analysis of the building complex is narrowed down to the assessment of the Heating Ideal Zone Load between November 1^st to March 31^st, as the heating cost and maintaining a comfortable temperature during these 5 months are critical in Montreal. The sun path and thermal analysis are carried out using the Climate Studio⁹⁶ plugin for Grasshopper. The LCA assessment of the structural system is determined based on the Environmental Product Declarations (EPD) of the CLT panels provided by Nordic Structures Company in Montreal.⁹⁷ The geometrical properties of the residential complex and the expected structural and thermal loads are described in Table 4. Thermal properties, cost estimation, wall, floor assemblies, and the structural and environmental features of the panels are briefly presented in Table 5. The last activity in this step is to set up a database to store the input and output parameters of the solutions generated in the next steps.

Table 4.

The geometrical properties and structural and thermal loads of the residential complex.

	Geometrical properties
		Each residential unit includes two geometrical modules,Floor to floor height = 3.4 (11 ft)Geometrical dimension of each module = 5.8 × 5.8 m² (19 × 19 ft²)Maximum number of floors: 11
		Structural loads⁹⁸
		Load case 1 = self-weight + Roof load (promenade roof) of 2.8 kN/m² (58.5 psf)Load case 2 = self-weight + residential live load of 1.92 kN/m² (40 psf)
		Thermal load
		Load: 0.01 people/m² + 11 equipment w/m² + 7 lighting w/m2, 150 luxContinuous dimming, AllOn schedule ⁹⁹Conditioning: heating setpoint: 21C cooling setpoint 26 CVentilation: Air change per hour = 0.5 ACHHot water: On \| peak flow 0.03 m³/h/m² \| 65 C supply temperature \| all On

Table 5.

The environmental and structural properties of the CLT panels and cost estimation of the residential units.⁹⁷

Material and thermal properties
CLT plates density = 500 kg/m³ conductivity = 0.13 W/mK, specific heat 1600 J/kgK, thermal emittance = 0.9, Solar absorptance = 0.7 visible absorptance = 0.7 embodied energy = 10 MJ/kg embodied carbon = 0.71 kgCO2/kg
Material cost estimation
CLT structural system cost: Design + material supply +installation = 435-490 CAD/m² (40-45 CAD/ft²) ≈ 450 CAD/m²
Material properties
CLT plates: Spruce-Pine-Fir density = 400 kg/m³ (25 lb/ft³) thickness = 8–20 cm (3 1/8 – 7 7/8 in)Stress grade: E1 (L 1950Fb and T no. 3/Stud), number of layers: 3, 5, 7 and 9
Construction
Roof = 95 mm CLT + 80 mm rigid foam EPS 035 insulation + 95 mm CLT + 20 mm Gypsum fiber boardPartition = 20 mm Gypsum fiber board + 95 mm CLT + 20 mm Gypsum fiber boardCeiling = 95 mm CLT + 30 mm impact sound insulation + 95 mm CLT + 20 mm Gypsum fiber boardExternal floor = 95 mm CLT + 80 mm rigid foam EPS 035 insulation + 95 mm CLT + 30 mm pine woodFaçade = 30 mm pine wood + 80 mm rigid foam pur no coating insulation + 150 mm CLT + 20 mm Gypsum fiber board

Generation and assessment of the initial population of solutions, steps 2, 3, and 4

Design exploration continues by generating a population of solutions whose variables are defined by assigning random values from the acceptable intervals. These randomly generated solutions may perform well or poorly. Regardless, their performance values and images are all stored in the database. When designers find the number or diversity of the initial population of solutions satisfactory, they can move to the next step and get ready to explore the solution space systematically using the NDDP genetic algorithm.

Identification of conflicts, adjustments of exploration goals and fitness function, steps 5, 6, and 7

Before setting the fitness function, the generated solutions and the database are studied to identify any conflicts and make any necessary adjustments to the design goals. Studying the captured sun path images of the solutions revealed several inappropriate generated solutions in which many apartments are shadowed. The solutions that have greater height at the south side versus the north side are expected to shadow the central courtyards and north apartment units (Figure 6). Reducing the height of the building complex on the south side and increasing the number of floors on the north side to maintain the same total floor area seems appropriate. This idea can be verified by using the TRIZ matrix of contradiction. It suggests creating the shape other way round to resolve the conflict between the shape and the brightness of the building (Table 3). Applying optical change might have worked if it was possible to change the direction of the building on the site. However, in this case study, the site’s dimensions do not allow for such modification. Thus, the fitness function is set to generate design alternatives with the appropriate geometrical feature that can yield brighter interior units. Furthermore, the fitness function is defined to systematically generate designer alternatives whose GWP and total heating energy from November to the end of March are less than 2,000 ton CO2 eq and 6500 MJ, respectively.

Figure 6.

A selected part of the TRIZ contradiction matrix.⁸ The parameters that may be improved (UF) are listed in the rows, and the parameters that may get worse (HF) are listed in the columns. The numbers listed in the matrix cells are associated with the list of 40 inventive principles.

Systematic exploration of the solution space, steps 8,9, and 10

The solution space is explored systematically to find a series of suitable solutions whose total floor area and brightness are maximum while their GWP and heating demand are minimal. At each cycle of systematic exploration, all the solutions, either generated randomly or systematically, are filtered to find design alternatives with a GWP of less than 2,000 ton CO2 eq and a total heating energy demand of 6500 MJ that can provide more than 450 total residential units (Figure 7). Designers can simultaneously interact with the search engine and use 2D graphs comparing solutions’ total floor area with GWP and total heating energy demand (Figures 8 and 9).

Figure 7.

A cause-and-effect graph to synthesize the design goals.

Figure 8.

South-East view of the solutions demonstrating the quality of shadows. Solutions 69 and 136 provide brighter units, while solutions 35 and 72 have more shadowed units.

Figure 9.

Display of solutions with a GWP less than 2,000 tonCO2eq and a total heating energy demand of 6500 MJ that can provide more than 450 total residential units.

Post-processing and exploration termination, steps 11, 12, and 13

Designers can continue the exploration process until they find suitable solutions by ranking and filtering the solutions, using 2D graphs and a Pareto front, or examining the captured images of solutions and qualitative diagrams associated with a solution’s performance. Even when they make their final decision about the most desirable solution, they can refer to the TRIZ component and see if any of the Inventive Principles can assist them in post-processing and improving the chosen solution. In this design case, comparing solutions’ total floor area versus GWP (Figure 8) and studying the associated Pareto set suggest solutions 158 and 124 as the best design alternatives. In a similar fashion, comparing solutions’ total floor area versus total heating energy demand (Figure 9) show that solutions 124, 25, 104, and 158 have the maximum total floor area. Evaluating other performance values, such as the structure’s total weight and maximum displacement of the roof structure (Figure 10), indicates that solutions 124 and 158 are lighter structures. Studying the visual representation and the quality of shadows of the buildings’ masses excludes solution 158 because it looks very dense and solid at its boundaries, does not have an outstanding appearance in the urban space, and will have fewer units with bright interior space. Therefore, solution number 124 is selected as the suitable solution regarding performance values, qualitative assessment of the complex brightness, and personal preferences. Table 6 represents the details of the key performance values of solution 124.

Figure 10.

The plot displays the distribution of solutions regarding their total structure weight (ton) and maximum displacement (cm).

Table 6.

The performance-based values of solution number 124.

Roof CLT thickness	10 cm	Max displacement roof	1.034533 cm
Floor CLT thickness	9 cm	Max displacement floor	0.909122 cm
Wall CLT thickness	9 cm	Structure weight	2744700 kg
Column Width	38 cm	Natural frequency	8.815827 Hz
Roof insulation thickness	3 cm	Model Mass natural frequency	149066.7297 kg
Floor insulation thickness	10 cm	Total cost	20378353.26 CAD
Façade insulation thickness	3 cm	Global warming impact	1887546.561 kgCO2 eq
Façade area	20351.04	Total heating energy	6414.3 MJ
Total floor area	18232.88 m²	November total heating energy	633.91 MJ
Roof area	8746.4 m²	December total heating energy	1485 MJ
Window area	2972.16 m²	January total heating energy	1780.3 MJ
Ground floor area	8746.4 m²	February total heating energy	1500.4 MJ
Total number of units	542	March total heating energy	1014.7 MJ
CLT volume	6363.3656 m³	—	—

Discussion

In this study, the design exploration of a mid-rise residential complex in Montreal has been considered to examine the usability of the GA+TRIZ methodology in architectural design. The goals of this design case were synthesized through a cause-and-effect graph to identify potential conflicts. As a result, the conflicts between the desire to maximize total floor areas and minimize the GWP and energy demand were revealed. The TRIZ IPs, along with the matrix of contradiction, prompted the selection of CLT panels to construct the structural system. In addition, the TRIZ design-aid component hinted at including two separate variables to define the thickness of the CLT panels and the thickness of thermal insulation in the parametric model. Moreover, the GA-based search component of the methodology allows for the investigation of unexpected solutions, the dynamic adjustment of the search process, the exploration of a great number of possible solutions, and the generation of a series of more suitable ones. Simultaneously, the TRIZ component assisted in setting the fitness functions and selecting the breeding criteria with a better understanding of connections among the parameters. Furthermore, TRIZ IPs can offer innovative ideas for post-processing the most desirable and optimal solution, improving performance-based values. This methodology is implemented within the ParaGen web interface, allowing continuous interaction between the designer and the search engine. The case study presented the instances that visual inspection of generated solutions adds further insights into assessing solutions’ performance values and the decision-making process.

Similar to other generative design exploration methods, the convenience of employing the GA+TRIZ methodology depends on the designers’ prior knowledge of generative design. In addition, specifying the generic solutions suggested by the TRIZ IPs requires the designer’s creativity. However, some helpful guidelines explain more details about each of the 40 IPs and their implications in the field of architecture.¹⁰⁰ Despite these potential challenges, the outcome of the GA+TRIZ methodology improves the design exploration process by facilitating the problem-(re)structuring, reducing the design cycles, and yielding more suitable design alternatives than those produced in a purely manual or a single approach generative methodology. What’s more, the implementation of the GA+TRIZ method is not limited to the ParaGen web interface and the developed TRIZ add-on. For example, a design exploration plugin in Grasshopper can be developed using the GA and TRIZ components of this methodology, or the TRIZ components of this methodology can be integrated with other existing GA-based search algorithms. The current implementation of the GA+TRIZ methodology allows the integration of different analytical tools and software systems. For example, environmental assessment can be carried out by Ladybug tools,¹⁰¹ LCA can be carried out by the One Click LCA Grasshopper plugin,¹⁰² or structural analysis can be done via STAAD pro.¹⁰³ In any case, a similar automation code can link different computational analytical tools with the GA, the TRIZ component, and the database developed in this methodology.

Conclusion

The generative design exploration in the conceptual architectural design should include both qualitative and quantitative goals, allow continuous and dynamic interaction with the search engine, and be flexible enough to evolve the design problem and solutions simultaneously through multiple cycles. The GA+TRIZ method addresses these three demands and allows the investigation of unexpected solutions and determination of the fitness function with a better understanding of the connections among the parameters when contradictory design objectives exist. This article demonstrates the usability of the novel GA+TRIZ method and the contribution of its two components, a GA and TRIZ Inventive Principles, to facilitate the problem-(re)structuring and make more informed decisions. The results of the design exploration case study confirm the capacity of the proposed method and the usability of the adopted computational tools and techniques. This methodology can be more broadly adopted by developing an associated plugin in Grasshopper integration of Rhino, which architects dominantly use for modeling and further performance-based assessments. Moreover, the usability of the GA+TRIZ methodology can be further examined through design exploration of diverse types of design projects, from a small-scale product design to architectural design cases in which multiple goals such as energy efficiency, costs, structural stability, durability, constructability, carbon footprint, circulation, and visual qualities are considered.

Footnotes

Acknowledgements

The author would like to acknowledge the Hydra Lab at the University of Michigan, Taubman College of Architecture and Urban Planning, where the servers used for ParaGen are hosted; Professor Peter von Buelow for sharing his insight throughout the research; Negin Zarnegar, who supported the author in the development of the TRIZ add-on.

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

Anahita Khodadadi

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