**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 *QQ**L*≥*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