The computational tool ARLE GPS "geometric planning solver of floor plan layout", converts the spatial planning of a house, conceptualized as a "wicked" problem, into a "well-defined" problem; and thus, helps the architect to solve it in a rational, innovative, and creative way, using a physical-biological meta-model. The physical model simulates solutions of the candidate FPL repetitively, in real time, and evaluates the geometric qualification of the FPL, representative of the quality of the solution, in an analogy with the physical functional performance of the house. The biological model makes it possible to build and explore design spaces, with the goal of retrieving information about inheritance and genetic transmission of high-performance solutions, to transcribe them into the development of innovative and creative designs. Thus, ARLE GPS evaluates creative design against the social value of the house, represented by its utility/functionality, and the quantitative innovation established by the fulfillment of the home purpose, by the user. Through geometric qualification (QQL) and optimization, in relation to the defining qualification of the house's required performance. (QQA). Associated with the evaluation of the house's performance over its useful life, represented by its usability. Computed by the ARLE GPS robust design model, through the geometric cost of losses (AN) variable, induced by the FPL design solution, as in the case of confined rooms, which persist during the house's lifetime.
Research Article
ARLE GPS: A computational tool to aid solve the creative design of a house. Case study.
https://doi.org/10.21203/rs.3.rs-1518854/v1
This work is licensed under a CC BY 4.0 License
Version 1
posted
You are reading this latest preprint version
floor plan layout (FPL)
simulation
evaluation
optimization
creative design
design studio
The case study presents the application of the ARLE GPS tool acting as an assistant to the architecture student, in the habitational design process. Helping him to convert the "wicked" spatial planning problem of a floor plan layout (FPL) into a "well defined" problem (Buchanan 1992). Since, this is a critical issue of the process, especially for the student who is beginning his contact with the complex problem of design (Lawson 2005 p.31). Design is a social process of creating artifacts, which aims to conceive and make available new and better situations for humanity. (Gero 1990; Schaathun 2022). Designers play a vital role in this effort to make the planet a better world. However, one of the challenging factors in achieving this goal is the fact that most design problems are characterized as being "ill-defined" or "wicked" (Casakin and Wodehouse 2021). According to Sosa (Cascini et al. 2022), in an ill-defined problem, the requirements, constraints, and evaluation criteria, are unclear. This lack of clarity/explicitness of the problem particularly in the conceptual phase of design, induces a vastness of solution possibilities; the formulation of varied strategies to attack and overcome the problem, and that results in different implications and difficulties for solving the problem (Wortmann 2018), such as: meeting the multiplicity of objectives, requirements, constraints, viewpoints and tastes (Sönmez 2018); refining the solutions without compromising the problem objectives (Bao et al. 2013); finding the best solution to the problem (Weise et al. 2009); quantifying the quality of the solution (Dino 2016); objectively judging the solution (Archer et al. 2005). In case the problem is clear, such as getting a cup of coffee, its solution follows a rite of possibilities, strategies, and solutions previously available, and in the domain of the solving agent/individual. However, in the case where the problem is ill-defined, and, without a consensus on what a good solution is, it requires greater understanding, exploration, skill, effort, intuition, and creativity to solve it, such as the case of an architectural design (Ball and Christensen 2019). In this case, the data initially available, are not sufficient and clear for students to solve the problem simply by transforming, reducing, optimizing, or overlaying the information provided (Archer 1979). And, therefore, they problems cannot be completely solved using routine problem-solving processes applying pre-established strategies and rules, either by manual or computational mode (Casakin and Wodehouse 2021). Due to the lack of an established and precise method for solving them (Medjdoub and Yannou 2000). Thus, the student is compelled to use his knowledge and experience and apply his ability/faculty of intuition and creativity to solve this type of problem (Doulgerakis 2007). Attributes and abilities that in most cases he does not have yet. Intuition plays a significant role in decision making, as it allows the designer to idealize relationships of elements and concepts, and make decisions instantaneously, following recognized patterns based on their experience and ability (Taura and Nagai 2017). Creativity in turn constitutes an important topic related to solving these design problems (Casakin and Wodehouse 2021). It has the potential to induce the designer in the systematic search to satisfactorily solve an intended function, satisfy specific performance criteria, generating and selecting creative design alternatives (Cross 1997; Clevenger and Haymaker 2011; Bradner et al. 2014). One of the issues concerning the topic of creativity focuses on the investigation of distinguishing creative design from the act of design. With the goal of establishing when and how a designer is being creative while he designs (Gero 2020). The act of design involves exploration, that is, defining which variables are appropriate for the solution of the problem, and formulating the strategy to be used for this purpose. The exploration process, on the other hand, involves finding the variables and attributes that allow setting the goals, as well as making and implementing the decisions (Gero 1990). Regarding the process of creativity, the first step is to extract and analyze the customer's needs (Fidler 2021). Once the design needs/brief are defined and frozen, creativity happens within the space of that briefing (Verganti et al. 2020). Creativity is conceptualized from various approaches: artistic expression, technological innovation, cognitive phenomena; as well as it is described considering various criteria to categorize a solution as creative (Davis and Gristwood 2016a; Cascini et al. 2022). One of the most employed is as a function of the degree to which the artifact is useful or novel, or both. Utility represents the social value of artifacts, which is established by their actual use, while novelty is defined, in terms of an artifact, by one that does not resemble another previously designed or known (Shah and Vargas-Hernandez 2003; Sarkar and Chakrabarti 2011). The activity of the designer's creativity is crucial to the design solution, and production of innovative artifacts. It represents the changes introduced in society by science and technology, from the perspective of design solution, according to the quantitative or qualitative innovation model. From the quantitative innovation perspective, the design is generated to fulfill a pre-assigned purpose or objective of an existing artifact. As in the case of the commissioned design of a house/apartment. Thus, the contracting/ requester provides the required specifications of the artifact based on their needs. In contrast, from the qualitative innovation perspective, the purpose (specifications) of a product become clear as its design process progresses. In this case, the products that are being designed do not exist, yet they carry with them the expectation of bringing new lifestyles to society (Taura and Nagai 2017). Now, it can be exemplified by the changes that will come to society, regarding design, manufacturing, and use of products, software’s, services/activities, which will be introduced with the advent of the metaverse. Which aims to create a collective, shared virtual world and replicate reality through digital devices, using "virtual reality", "augmented reality", and "internet" technologies. While there is a vast amount of literature related to creativity, there is a limited amount aimed at assisting architecture design students in the context of creative design developed in a studio (Casakin and Wodehouse 2021). To contribute to this issue and share a successful experience in the teaching learning process of architectural design in a design studio, particularly in relation to the process of generation and exploring the design solution, and its interface with the action-decision field of design resources, and with innovation and creativity, the case study is presented: ARLE GPS – A computational tool to aid solve the creative design of a house. The tool acts on the housing design process through an action-decision model, and the robust design, in solving open and significant questions for design research, particularly in relation to the evaluation of design quality. Which according to Goldschmidt and Matthews (2022), to be considered as a acting with good performance, it must solve mainly the following questions: resolve an important open question, which models the design process, in a robust way, and with effective metrics; present a new perspective for the solution of the question, through the generation of new hypotheses, and a new resolution procedure, shedding new light on design phenomena, and opening new lines of investigation; show what are the keys to successful decision making for resolving the open question; improve the practice of design problem solving; fill a gap in the existing literature, and expand the state of the art; meets the fundamental principles of ethical research through data transparency. These issues must be complemented, according to Boujut (Papalambros 2015), in relation to the domain of the process, through a methodological tool that allows to be shared, evaluated, discussed and with easily reproducible and verified results. Which are fully met in the case study presented and can be evaluated through the application of the ARLE GPS tool, and the results achieved.
The establishment of an analogy model marks the initial action of structuring the ARLE GPS computational tool. The model is defined by collecting, quantifying, and qualifying the geometric planning variables of the FPL (floor plan layout), in an analogy with the functional and usability performance of the house, here represented by a verticalized house, i.e., an apartment (Martins 1999). These variables shape the horizontal plane and quantify and qualify its spatiality and configuration, which represent the two main geometric conversions of the FPL solution (Hillier 1998). The capture, quantification and qualification of the configuration and spatiality of FPLs is achieved through the relationship between the vertical and horizontal planes. Defined by the quantification and qualification of the variables surface area (AU), perimeters: internal (PU) and external (PE). On the other hand, the internal perimeter variable, when allocated to confined rooms (PR), or circulation rooms (PC), is defined as a non-qualifier. The useful surface area (AU) has the function of providing the horizontal plane used for dimensional modeling of the rooms of the house (Medjdoub and Yannou 2000). It establishes the spaciousness of the house, which defines an indicative and overriding attribute of its performance. Its participation in the qualification of the FPL is computed by the spatiality index (IA). The internal perimeters act on the house's performance by establishing the function of a generating system for the house's vertical planes. These planes define the demarcation of the walls, which delineate the physical boundaries of the rooms, and reveal their spatial configuration (Peponis et al. 1997; Medjdoub and Yannou 2000; Sönmez 2015). Their share in qualifying this performance, is computed by the configuration index (IP). However, internal perimeters are computed as non-contributors to house performance when they are allocated to confined and circulation rooms (Nagy et al. 2017). Confined rooms are defined by the lack of a direct connection to the outside environment. The confinement is related to the problem of not allowing users direct access to sunlight, as well as hindering the exchange of air and heat with the outside environment, and not least, making it impossible for users to access the landscapes of the outside world. Its participation in this qualification computation is established by the confinement index (IR). The circulation room, on the other hand, does not have the function of a living room, and in this case, it is used as a passage and connection pathway, which configures a locomotion room (Bahrehmand et al. 2017). Its participation in this qualification computation is established by the circulation index (IC). The external perimeter has the function of establishing the shielding of the house in relation to external protection, climatic safety, and providing thermal and hygrometric comfort. It also establishes an access, exchange, and communication portal, at a physical, luminous, calorific, atmospheric, and visual level with the external environment of the house. In addition to providing aesthetic beauty to the house (Medjdoub and Yannou 2000). Its participation in the FPL qualification is calculated by the externalization index (IE). The condominium and symmetry perimeters define the section of the house's boundary perimeter located inside the building. These perimeters are not the exclusive property of the house, and do not appropriate the functions performed by the external perimeter (Hillier 2007). The differentiation between them, is that the condominium perimeter (PX) is shared with the collective area of the building, and the symmetry perimeter (PY) is shared with another house and establishes axes of symmetry between them. Therefore, in the analogy model, they are conceptualized as non-contributors to the FPL qualification and are not computed in the LEQC (Evaluation of geometric quality and layout cost) meta-model (Martins et al., 2021) DOI 10.13140/RG.2.2.21101.51681). However, they are contributors to the cost of converting the FPL into the house artifact and are computed for this purpose. The geometric variables quantified and qualified in the house performance analogy model represent the totality of the variables used for geometric planning of the FPL, and structure the LEQC meta-model which is converted into the computational tool named ARLE GPS (geometric planning solver), through spreadsheet editor software (Excel). The geometric variables of the FPL assembly are computed by the LEQC meta-model with the same degree of importance, i.e., the same weight. The LEQC meta-model aims to facilitate the tasks of students in the preliminary phase of FPL design, which are characterized by vagueness and uncertainty in decision making. It makes the design problem explicit/clear and assists the students in making decisions (Capilla et al. 2011). Defines a conceptual model of scientific modeling within a social context (Ritchey 2014). It is a simple mathematical representation of a complex high-fidelity simulator and explorer, which establishes a relationship between the performance of the artifact through the geometric parameters of the FPL design, outlines the paths to solution optimization, (Meckesheimer 2001), and evaluates them. Thus, enabling ARLE GPS to function as an assistant in the design process, especially in relation to the attributes of utility and quantitative innovation. (Taura and Nagai 2017).
The ARLE GPS heuristic makes it possible to convert the FPL spatial planning problem, conceptualized as ill-defined, into an explicit problem, by allowing, establishing, and providing:
• facilities in meeting the demands and desires of users;
• clear problem requirements and constraints, already in the conceptual design phase;
• conceptual strategies for design assembly and modeling: top-down, bottom-up, and case study genetics;
• holistic response based on objective judgment;
• computer-friendly support, focused and centered on the decision maker, not the design;
• reveal the cost of design decisions.
Through systemization:
• prioritize geometry over topology;
• remove uncertainties in decision making;
• simulate and evaluate the geometric solution of the FPL;
• progressively refine the solution space exploration result;
• explore the state of the FPL geometric solution in real time;
• crossing the feasibility space with the acceptability domain, producing a performance space within which one or more optimal solutions can be found;
• quantify the quality of the FPL design solution that meets the required performance;
• determine the geometric and monetary cost, through the geometric variables of the FPL;
• calculate the losses in the use of the apartment, depending on the magnitude of the qualifying variables of the FPL, applying the robust design approach;
• encode, index, retrieve and adapt cases;
- build design spaces;
- configure and limit the FPL project's solution space and build a measure of its performance;
- explore the design space using original and accurate search tool through the FPL's genetic code;
- measure the similarity or relevance of problems and cases;
- use existing designs as a reference to guide solutions for similar architectural situations;
- indicate the space susceptible to improving the quality of FPL solution, since there is no single best solution to a design problem in architecture;
- scientify the spatial planning of the FPL, counterpointing the use of drawing methods;
- function as a tool that supports creative ideas.
The ARLE GPS tool introduces a biological view into the architectural design process, through the construction of a biological model, structured by encoding the FPL's digital signature (Shi and Gero 2000), as shown in table 04. The genetic code of the FPL design informs the formation, functionality, zoning, order of assembly of the rooms in the house, connection between the rooms, and quantifies the geometric variables used in the assembly of the design of the house. It uses for this purpose the genes Gform, Gfunction, Gtopology, and Gspace. The dimensional unit of geometric variables is centimeters (integer number). The AR(Archer) LE(LECQ) GPS(Simon) tool works according to the conceptualization shown above and demonstrated in the case study below. Structured to assist students in creative design solutions. Its mathematical structure is defined by the LEQC metamodel and is derived from the systematic model proposed by Archer (1968), coupled with the GPS "(General Problem Solver)" problem solving principle proposed by Simon (1973, 1996) for solving ill structured design problems. Archer intended that his model coupled with the use and aid of the computer would constitute a tool that would free the designer from the burdensome concerns of the quantitative and repetitive tasks of the design process, so that he could use more time and energy in managing the qualitative and creative issues of the design solution. At the International Conference on Computers in Architecture in 1972, Archer exposed that this tool was not being used at the time yet would be in the future. He was particularly optimistic about the emerging area of computer aided architectural design (CAAD) (Archer 1972). However, these first-generation design methods, developed in the 1960s, were judged to be too rigid and mechanistic. A situation that has generated controversy and prevented its use in practice. Renowned and influential architects, engineers, and designers of the time, such as Christopher Jones, Christopher Alexander, and John Chris Jones became staunch opponents to this considered mechanistic principle, going as far as Alexander's comment 'people who are playing with computers have obviously become interested in some kind of toy' (Margolin 2010; Davis and Gristwood 2016ª). This toy has evolved in such a way that today it is an integral and indispensable part not only in the lives of design professionals, but in the daily life of all humanity. The CAAD era has consolidated, and now the artificial intelligence (AI) era is consolidating, with vast possibilities and opportunities, to facilitate the lives of architects in the conception of creative designs, via automatic data collection and construction of big data systems; interactive designer-computer systems; AI assistance in the conceptual phase of design (co-creative AI); automation of the design process (Cascini et al. 2022). Regarding the ARLE GPS tool, its usage occurs essentially in assisting architecture design students. However, the tool can also assist professionals in the field of architecture, as well as contribute in the CAAD and (AI) area. Due to the tool's ability to support several types of activities inherent to the process of automated generation of architectural designs, such as: exploration of the design space, simulation, optimization, evaluation, establishment of the breakpoint of the automated generation process, classification, and selection of optimized solutions. With emphasis on the issues of the breakpoint, and quantitative evaluation, because the tools currently available do not support this type of activity.
The design studio in the present case, covers the study sessions held in a classroom that provides logistical support to students, in the process of teaching-learning architectural design (Goldschmidt 2002). Applied in the assistance to fifth year students of the discipline “project” of the Civil Engineering course of the State University of Maringá. The discipline lasts one semester, with two weekly sessions. It is important to consider and mention that the exercise of the civil engineer profession allows them to act in the architectural design (Passos 2004). This prerogative of the professional activity of civil engineers, implies that the teaching of the process of architectural design in the Civil Engineering course, with respect to the curricular grid of the course, is composed of a minimum of disciplines in architectonic design. This context portrays as a challenge to be overcome the issue of equipping students with a sufficient level of knowledge, reflective practice, skills, and competencies that enable future engineers to solve problems related to the planning and design of housing FPLs, in their professional life. They are then, equipped with the ARLE GPS tool and supplied with a representative database of a design space (family seven, shown in Tables 01,02,03), and its value space. The studio represents an ideal environment for training of the students, as it serves among its purposes to replicate a place that aims to portray, an environment of imitation of the real 'life' of future professionals, and to institute a learning process where students conduct design tasks, under the guidance of the instructor teacher (Adiyanto 2017). In this space, individually, they exercise design assignments, which are planned and executed to solve real-life problems (Goldschmidt 2002). Problem-based learning (PBL- problem-based learning) constitutes a good methodology to break the vicious cycle of the general principles of traditional teaching and experience an innovative and instructive education (Cabodevilla-Artieda et al. 2018). It is up to the teacher, in this case, to provide students with a real-world problem that is relevant to the lives of future professionals, as well as to determine how the project will be evaluated, and, to define the formula for assigning a grade for the work done (Bridges 2007). On the other hand, this studio followed a current paradigm of unconventional design studios, namely that of a digital studio. It is characterized by the replacement of traditional design representations (freehand sketches), by a digital medium, by the incorporation of computational equipment and the digital tools Auto CAD and ARLE GPS (Ismail et al. 2012; Hettithanthri and Hansen 2021), in this studio. Computer simulation using ARLE GPS software, for its part, is defined as a process involving the use of the computer to structure and simulate the geometric planning of the FPL of an apartment. Computational processing has the potential to relieve students from repetitive, tedious, and error-prone tasks (Frankel and Racine 2010). It can perform enormous amounts of repetitive routines without fatigue or error (Rodrigues et al. 2013). Assists students to run simulations repetitively, in real time, and evaluate the geometric qualification of the FPL in an analogy to the performance of the house artifact; and refine the result of exploring the solution space progressively until they obtain the desired optimization (Machairas et al. 2014). Regarding the design studio, the main academic feature of the study sessions, is the individual “one-on-one” crits, in which student and teacher discuss the work in progress on a regular basis (Goldschmidt et al. 2010) throughout the study period (Dorta et al. 2016). The discussion about the task is coordinated by the instructor, during which questions are asked and answered, examples given, principles and precedents evoked, alternatives suggested, problem areas pointed out. The design sessions are apt for observation and documentation of the activities performed. However, in the present case the sessions were not documented. The students' final work is usually evaluated through a series of discussions and presentations. Through the results of the work performed, and presentation of the work, often publicly in an evaluation session, by a jury composed of invited professionals. (Dorta et al. 2016). Regarding the evaluation in this case, is processed mathematically, as a function of the degree of meeting the QQL qualification presented in the work, as discussed in section 10. In the present case, the students used for the solution of the problem the top-down assembly approach, and the genetic strategy of the case study.
5.1 Top-down approach
The assembly of the FPL using the top-down approach is exemplified by the design of FPL 006 planned by student 06 (figure 01). Demarcated by structuring a geometric prototype of the FPL, using the ARLE GPS tool, to solve the following problem:
• FPL design of an apartment with required floor area AU=120.00±5.00 m²;
• functional configuration: three bedrooms (B,B1,B2);
• formation of two apartments per floor (Nf=2);
• functional program under the student's responsibility, through the components of the FPL structure, made available by the rooms: E1ULDOHT CFB1W1B2W2BP WKMGSB4W4E2 (table 01);
• FPL design requirement of a high-performance apartment (family 7 of design space): target area AA = 125.00m² and target performance QQA ≥19.50;
• building implementation on an existing physical site (provided: location, dimension, geographical positioning);
• obligation to comply with constructive public legislation.
Resources provided:
• ARLE GPS computer tool and auto CAD;
• systematic model of exploration and coevolution (figure 03);
• FPL database (design space - table 02);
• values space of design space (table 03);
• room dimensional values space (table 01);
• constructive public legislation that must be complied with.
Evaluation of the work
• requirement of meeting the minimum required performance QQL≥QQA;
• evaluation according to the performance established QQL;
• assignment of the grade of the work directly proportional to the performance QQL.
Family seven defines the design space and value space of FPLs in the high-performance region. The required performance required for the apartment, in the proposed problem, is established using the equation AU=0.0164(QQL)³ (envelope) (figure 02), considering the target area AA=AU=125.0 m², which results QQL = 19.64 (computed), and QQA = 19.50 (adopted).
Table 01 - FPLs room size value space - Family 7 design space
Table 02 - Database / Design Space family seven
Table 03 - FPLs qualification value space - Family 7 design space
The process begins with the student defining the program/briefing for the apartment. Exemplified by the program proposed by student 006, which is composed of the UOHT CB1W1B2W2BW KGB4W4 rooms, and defines the Gfunction gene. Initially she proceeded to assemble the geometric prototype using the minimum values of the surface areas of the rooms of the FPLs - Family 7 design space dimension values, (Table 01), which resulted in the value of AU = 93.23m², below the required value (120±5 m²) In this case, a second prototype is assembled, using the average values of the areas of the rooms, which resulted in the value of the AU area = 130.41 m², above the required value. Finally, the simulation is performed using the average areas for the CB1B2BW B4W4 UHT rooms, and the minimum areas for the O W1W2 KG rooms, resulting in a value of AU = 118.83 m², thus meeting the required value. Being considered for the assembly of this prototype, the condition of no confinement of the living rooms, for the positioning of the solution in the high-performance region of the value space. Once is defined the areas of the rooms; the respective perimeters are established as a function of the value space of the dimension of the FPL rooms (Table 01). Once the area and perimeter of the rooms are known, and their corresponding form factors (FF), the length: width relations are extracted, which make it possible to determine the dimensions of the rooms considering the shape of rectangular polygons (orthogonal geometry), through the equation makes it possible to establish the width (W) and the length (L) of the room. In this step of the simulation process, ARLE GPS computes the spaciousness, internal configuration, and circulation and confinement indexes. Missing to compose the geometric prototype, the form factor, number of vertices of the FPL polygon, and the exteriorization index. Are obtained the form factor FF, and the number of vertices LV using the statistical techniques of regression, established by response surface (RSM), according to the polynomials shown in figures 09 and 10. The computed values for these variables are equal to FF = 4.90, and LV = 19. These values allow the student to have a description of the format of the FPL polygon, and its respective numbers of sides, as well as making it possible to search for FPLs with similar FF in the design space of family seven. Portrayed by the FPLs 143, FF=4.94; 152, FF=4.89; 171, FF=4.92; as shown in Figure 04. Knowing the form factor FF, and the area of the FPL, and considering in this case the prototype as a sketch without walls, with AT=AU, the value of the boundary perimeter of the FPL polygon is obtained through the equation FF= PF/√AT (perimeter of the polygon, PF=53.41m).
To structure the prototype, the size of the external perimeter, the condominium, and the symmetry are not yet computed. For this purpose, is defined the exteriorization index using the data of the family seven, which can also be established by response surface. Since the FPLs of family seven are in the high-performance region of the design space, the values of the average indices of the FPL qualification indices, compose a space of solutions that meet the required performance required for the problem. And in this case, is adopted IE = 1.81. Computing the size of the external perimeter through the equation IE = PE/2√AT, and obtaining the value of 39.45 m. Thus, making it possible to complete the structure of the geometric prototype of the FPL with the value of the sum of the condominium perimeter and symmetry PX +PY = 53.41 - 39.45 = 13.96m (Martins et al. 2021). The student then completes the ARLE GPS prototype, with the input data provided (Nf, AA, QQA), with the type of finishes adopted for the floor/ceiling and walls of the rooms, and their cost, and ARLE GPS provides for the design modeling, the following information:
• FPL formation: two apartments per floor;
• connections to the external environment: two;
• number of functional environments: fifteen rooms;
• form factor (FF) of FPL: equal to 490 (FF multiplied by one hundred = integer);
• number of sides of the FPL polygon (equal number of vertices LV): nineteen;
• functionality of the apartment: social zone UOHT; intimate zone CB1W1B2W2BW; service zone KGB4W4;
• order of assembly of the FPL structure and connections between the rooms:
{[→U→(OHT)] ϵ [C→(B1W1B2→(W2)B→(W))] ϵ [K→(G→(B4W4))]};
according to the model:
Assembly parts - E1ULDOHTCFB1W1B2W2BPWKMGSB4W4E2
{ - start assembling the artifact
} -end assembling the artifact;
[-start the assembly of a block of the artifact;
]-end the assembly of a block of the artifact;
→ -process the connection;
( - process the multiple connections;
) - finish multiple connections;
ϵ - connect the next part with the "U" part of the artifact assembly;
• dimensions of the rooms (rectangular polygons): width and length.
And provides as evaluation values of the candidate case (geometric prototype) (table 04):
• floor area AU = 118.83m², meets the required floor area = 120±5m²;
• geometric qualification QQL = 19,90 >QQA;
• monetary cost of the FPL solution, VGL = 422.79 U$/m²;
• nominal area AN= 133.87m² > AU (geometric gain, according to the LEQC approach of robust design);
• monetary cost of geometric qualification VQL = 2524.92 U$/QQL;
• geometric cost of geometric qualification VAQ = 59719 cm²/QQL, (5.97 m²/QQL);
FPL genetic code:
• formation gene (Gform): 2 2 15 490 19;
• function gene (Gfunction): UOHT CB1W1B2W2BW KGB4W4;
• topology gene (Gtopology): {[→U→(OHT)] ϵ [C→(B1W1B2→(W2)B→(W))] ϵ [K→(G→(B4W4))]};
• space gene (Gspace): 1188300 1188300 0016730 0003945 0001396 0000000 0001060 0000000.
Table 04. Geometric planning/prototype of FPL 006