Collective Intelligence is the Architect

Automatized Space Layout Planning from Preceding Typologies Martin Stacey Ruales

This dissertation is submitted in partial fulfilment of the requirements for the degree: Master of Science in Architectural Computation Bartlett School of Graduate Studies, UCL | September 2017 1

I, Martin Stacey confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis.

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Is it feasible for an algorithm to comprehend the complexity of zone allocation in architectural design? Is it possible to quantify and use traits of existing designs to create new ones? The following thesis explores how existing floorplans can be used to define qualities of spaces and design; as well as how these qualities can help generate future typologies. The objective is to develop a space layout algorithm that understands qualities of spaces such as proportion, area, connectivity, adjacency etc. from existing designs to later apply that knowledge into automatized floorplan generation. This would be achieved by analysing a database of floorplan designs of a particular socioeconomic, cultural, and historic background and then use that knowledge to identify consistent traits which are replicated in automatized generated floorplans. While the majority of previous attempts in computational space layout design have focused on hardcoding rules and qualities defined by a programmer, and then optimize these qualities by a generative algorithm this attempt aims to discover which qualities are consistent in existing floorplans by examining room traits in existing typologies and later on use this information to generate new designs. A method of automatized design that is founded on previous designs may be useful because it can depict many subtle qualities which would be inefficient or impossible to identify manually by a programmer, and furthermore understand more in debt the traits that are intrinsic in a design of a specific context. The results obtained suggest that the designs generated by the algorithm resemble the designs from the databases. Nevertheless, more work could be done to obtain more unique databases.

Keywords:

Computational Floorplan, Knowledge Transfer, Style Transfer, Design Automation, Generative Design, Generative Floorplan, Space Layout Algorithms, Customizing Mass Housing Word Count: 10479

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Declaration ...........................................................................................................................................................................................................2 Abstract ................................................................................................................................................................................................................. 3 Contents................................................................................................................................................................................................................ 4 Illustrations .......................................................................................................................................................................................................... 6 Acknowledgements...................................................................................................................................................................................... 9 Introduction....................................................................................................................................................................................................... 10 The architect and the floorplan ................................................................................................................................................... 10 Proposed change of focus ............................................................................................................................................................... 11 Background ....................................................................................................................................................................................................... 12 Antecedents of Space Layout Planning................................................................................................................................ 12 More complex layout planning techniques: ....................................................................................................................... 13 Report on a System for General Planning (Eastman) ............................................................................................... 14 Graph Theoretic Representation of Architectural Arrangement (Steadman) ......................................... 15 Synthesis and Optimization of small rectangular floorplans (Mitchells) .....................................................17 Shape grammars (Mitchells) ......................................................................................................................................................... 19 Constraint Based Systems (Li) .................................................................................................................................................. 20 Expert Systems (Flemming) .......................................................................................................................................................... 21 Classification of Algorithms and Current Applications: ........................................................................................... 21 Methodology ................................................................................................................................................................................................... 24 Simplified version of the plan: ..................................................................................................................................................... 24 Defining a Design:.................................................................................................................................................................................. 24 Example of House Definition ........................................................................................................................................................ 25 The universe of solutions ................................................................................................................................................................ 26 Method for defining the “optimal� ............................................................................................................................................ 27 Variables and Criteria taken into account .......................................................................................................................... 27 Determining how to measure Consistence ....................................................................................................................... 29 The GA .......................................................................................................................................................................................................... 32

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Results ................................................................................................................................................................................................................. 34 First Step: (Hardcode Fitness) ..................................................................................................................................................... 34 Extracting Criteria from Existing Typologies: ................................................................................................................... 37 Database 1: Random Floorplan Selection (Google Search) ................................................................................. 38 DATABASE 2: Collective Housing in Mexico ................................................................................................................... 45 Comparison ................................................................................................................................................................................................ 51 Conclusion ........................................................................................................................................................................................................ 55 References........................................................................................................................................................................................................ 57

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Figure 1 Facility Allocation Problem (Eastman, 1972)..................................................................................................... 12 Figure 2 Flow Matrix. (Garcia-Diaz & MacGregor, n.d.) ............................................................................................... 13 Figure 3 Craft Method (Jensen, 2004)....................................................................................................................................... 13 Figure 4 Eastman set of Operations Formula ....................................................................................................................... 14 Figure 5 Eastman State Generation Formula ........................................................................................................................ 14 Figure 6 Steadman Representation of Space (Eastman, 1972) .............................................................................. 15 Figure 8 spanning subgraph (Steadman, June 1973)................................................................................. 16 Figure 7 Possible arrangements for adjacency graph (Steadman, June 1973)........................................... 16 Figure 9 Plan graph (Steadman, June 1973) Figure 10 Dual graph relationship (Steadman, June 1973) ...................................................................................................................................................................................................................... 16 Figure 11 Possible Floorplan Configuration on Adjacency Graphs up to 4 rooms (Steadman, June 1973) ...................................................................................................................................................................................................................... 16 Figure 12 No of Possible Graphs.......................................................................................................................................................17 Figure 13 No of Possible Rectangular Arrangements .......................................................................................................17 Figure 14 Topological Shape and Matrix Figure 15 Topological Floor Plan

Figure

16 Dimension Representation .............................................................................................................................................................17 Figure 17 Possible dissections for n subdivision in terms of n-1 subdivision

Figure

18 Spiral Configuration ............................................................................................................................................................................ 18 Figure 19 Possibilities of Graphs ...................................................................................................................................................... 18 Figure 20 Dimension Assignment .................................................................................................................................................. 19 Figure 21 Tree Diagram for Dimension Assignment (Mitchell, Steadman, & Ligget, 1976) .............. 19 Figure 22 Constraint System Layout........................................................................................................................................... 20 Figure 23 Adjacency Function ........................................................................................................................................................... 21 Figure 24 Expert System Overview ............................................................................................................................................... 21 Figure 25 Desired Algorithm Structure...................................................................................................................................... 24 Figure 26 Binary Tree to Represent Floorplans .................................................................................................................. 25 Figure 27 Sample Tree ........................................................................................................................................................................... 25 Figure 28 Sample Floorplan .............................................................................................................................................................. 26 Figure 29 Sample Room ....................................................................................................................................................................... 26 Figure 30 Catalan Number (Stanley, 2013)........................................................................................................................... 26 Figure 31 Possible combinations .................................................................................................................................................... 26 Figure 32 Example 1 for Room Criteria ....................................................................................................................................30 Figure 33 Example 2 for Room Criteria ....................................................................................................................................30 Figure 34 Multidimensional Representation of Designs................................................................................................ 31 6

Figure 35 Gene Type 1 Diagram ..................................................................................................................................................... 32 Figure 36 Gene Type 2 Diagram .................................................................................................................................................... 33 Figure 37 Gene Type 4 Diagram .................................................................................................................................................... 33 Figure 38 Gene Type 4 Diagram .................................................................................................................................................... 33 Figure 39 Input for Hardcoded Designs .................................................................................................................................... 34 Figure 40 Results Hard Coded Designs .................................................................................................................................... 35 Figure 41 Hardcoded Result 1 in Interface ............................................................................................................................... 36 Figure 42 Hardcoded Result 2 in Interface ............................................................................................................................. 36 Figure 43 Processing Program for Area Selection ........................................................................................................... 37 Figure 44 Floorplan Trait Extraction ............................................................................................................................................ 37 Figure 45 Database 1 Summary from Google Search................................................................................................... 38 Figure 46 Room’s Short Side Dimensions for DB1 ........................................................................................................... 39 Figure 47 Room’s Long Side Dimensions for DB1............................................................................................................. 39 Figure 48 Room's Area for DB1 .......................................................................................................................................................40 Figure 49 Rooms Area/ Total House Area for DB1..........................................................................................................40 Figure 50 Room’s Proportions for DB1 ....................................................................................................................................... 41 Figure 51 Adjacencies Matrix and Graph................................................................................................................................... 41 Figure 52 Inserted Fitness Parameters for floorplan Generation ......................................................................... 42 Figure 53 Unevolved Population .................................................................................................................................................... 42 Figure 54 Generated Example 1 using DB1 ............................................................................................................................ 43 Figure 55 Generated Example 2 using DB1 ........................................................................................................................... 43 Figure 56 Generated Example 3 using Db1 ........................................................................................................................... 43 Figure 57 Evolved Examples using Db1..................................................................................................................................... 44 Figure 58 Evolved Example 2 using DB1.................................................................................................................................. 44 Figure 59 Database 2 Summary from Google Search ................................................................................................. 45 Figure 60 Rooms Short Side Dimension for DB2 ............................................................................................................. 46 Figure 61 Rooms Long Side Dimension for DB2 ................................................................................................................ 46 Figure 62 Room's Areas for DB2 ................................................................................................................................................... 47 Figure 63 Rooms Area / Total House Area for DB2 ....................................................................................................... 47 Figure 64 Room's Proportion for DB2 ........................................................................................................................................ 48 Figure 65 Rooms Adjacencies for DB2 ..................................................................................................................................... 48 Figure 66 Unevolved Population DB2 ........................................................................................................................................ 49 Figure 67 Evolved Example DB2 ....................................................................................................................................................50 Figure 68 Evolved Example DB2 ..................................................................................................................................................50 Figure 69 Evolved Example DB2....................................................................................................................................................50 7

Figure 70 Examples Db1 vs Db2 ...................................................................................................................................................... 51 Figure 71 Short Side Dimension Comparison ........................................................................................................................ 51 Figure 72 Examples Db1 vs Db2 ..................................................................................................................................................... 52 Figure 73 Long Dimension Comparison ................................................................................................................................... 52 Figure 74 Area Comparison ............................................................................................................................................................... 52 Figure 75 Examples Db1 vs Db2 ..................................................................................................................................................... 53 Figure 76 Proportion Comparison ................................................................................................................................................. 53 Figure 77 Area / Total Area Comparison ................................................................................................................................ 53 Figure 78 Examples Db1 vs Db2 ..................................................................................................................................................... 54 Figure 79 Comparison in Radar Graph...................................................................................................................................... 54

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I would like to thank all of the people who helped me in the development of this thesis, starting with my tutors Martin Zaltz Austwick and Tasos Varoudis for their support during the process of putting together the thesis.

Also, I would like to thank Sean Hanna, Christopher Leung and Martha Tsigkari, Khaled Elashry for their impressive wisdom as teachers of the course, and also my colleagues that were really supportive during the whole semester. They were so supportive that they gave me an incredible bike to go around London.

I would also like to thank Mohamed Naeim who was a great help with his time and dedication in answering my multiple questions on his experience. His altruistic help gave me hope for people.

I would also like to thank Azul who was a great inspiration during this whole year and a constant auditor of all my excitement for what I was learning.

Finally, my family who have been supportive for all my life and in all my crazy adventures and ideals.

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The architect and the floorplan Floorplan layout is key in defining architectural design. The field of automation in floorplan layout focuses on how computers can aid in this process. This field of research has been studied for around fifty years, with various techniques and degrees of success, but with great mistrust from the architect profession.

One may argue that this mistrust has emerged from an apparent incompatibility between the rigid structure of algorithms and the ill-structured of architectural design problems. Algorithms typically deal with well-structured problems “which the initial state, goal state, and constraints are clearly defined” (Marisel, 2011) vs. the ill structured nature of architectural problems “Ill-structured problems have no initial clear or spelled out goals, set of operations, end states, or constraints.”

(Marisel, 2011).

Also, optimization is not always the desired output as a designer. An architect/client may be more inclined for a particular design over another even though the objective qualities of a given design may be inferior to its counterpart. Not all decisions made in design are intrinsically logical, not all of our spaces are intrinsically functionally. Even though the modern movement was inspired by claims such as “form follows function” (Sullivan) contemporary buildings as OMA’s China Central Television Headquarters show that seeking for optimal space qualities is not always the main driving force in design.

Another reason of this mistrust is the neglect of social aspects of space planning which are many times embedded in the floorplan design logic, but which are many times taken for granted. This social layer is widely studied through space syntax by Hillier and Hanson in books such as The Social Logic of Space and Decoding Homes and Houses. As described by Hillier “society enters into the very nature and form of buildings, through the ways in which buildings, individually and collectively create and order space we are able to recognise society” (Hillier & Hanson, 1984) Hillier also implies that this social relation is implicit in its spatial configuration (connectivity between spaces).

Finally, algorithms tend to work as black boxes with little disturbance from the user. There is little understanding on how an algorithm comes up with a design, and how can their output be altered. Architect Peter Eisenman has blamed algorithms (computing) for creating a culture of “passivity”. A culture in which “instant” response from the computer numbs critical thinking.

(Olcayto, 2008)

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Proposed change of focus Many floor plan automations have focused in optimization through enumerating all of its ideal qualities and this has led to criticism. In this thesis, the idea explored is that computers can have an active role in understanding and defining ideal qualities of a design through analysing previous examples which are relevant to the new design. By analysing previous examples of a desired author/period/place, the computer would recognize patterns that are consistent in all/most of its designs and try to replicate them in a new design.

The method tries to learn from previous designs, and what traits are consistent through collections of designs. If a certain connection, adjacency, proportion is repeated constantly in a database, it can be inferred that this trait is typical of this database, and in order to create a new design that resembles the database it is important to take it into account. If a trait is less consistent then the new design can be more flexible towards this trait.

By creating a method that uses existing knowledge to solve new scenarios the collective knowledge gathered becomes the architect.

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Antecedents of Space Layout Planning In its 50 years of history there has been multiple proposals for addressing space layout automation. Since the first examples which dealt with dimensionless locations to the more complex expert systems, space layout planning has been addressed through industrial engineers, architects and computer scientists. The first attempts to conceptualize the problem of layout planning were worked in three main fields: industrial planning in problems of plant production, electrical engineering in the layout of electronic circuits and architectural planning in complex building facilities. Nevertheless, the first industry to embrace systematic layout planning was industrial planning. Given the more structured nature of industrial floor plans there was a bigger incentive to develop procedures that would objectively satisfy a set of constrains many times imposed by the logic of the production process. (Liggett, 2000) An interesting example in space layout planning is Weber’s approach to locate industries according to the location of its market and suppliers. The weber problem, named after the economist and theoretician Alfred Weber, became one of the most famous problems in location theory and was one of the first primitive attempts for defining location in terms of transportation cost. Weber problem uses the geometric median of a set of points. To be able to prioritize certain connections to others a weight is added to each of the connections, making it similar to an attraction-repulsion problem. (Weber, 1957).

Following Weber’s concepts facility layout planning would focus on developing tools to evaluate industrial layout design. Methods as the operation sequence analysis would help industrial floorplans calculate the weighted total distance from each of the plan elements. In systematic facility layout planning a first attempt to evaluate the spatial configuration and not only the space dimensions was explored. (Garcia-Diaz & MacGregor, n.d.)

The general purpose of facility location planning is to minimize the following equation, were plan element’s (i-j) distance (d) times weight (w) is minimized. �

đ?‘›

đ?‘šđ?‘–đ?‘› ∑ ∑ đ?‘‘đ?‘–đ?‘— đ?‘¤đ?‘–đ?‘—

đ?‘¤â„Žđ?‘’đ?‘&#x;đ?‘’âˆś đ?‘‘đ?‘–đ?‘—=((đ?‘‹đ?‘– −đ?‘‹đ?‘— )2 + ((đ?‘Œâˆ’đ?‘Œđ?‘— )2

đ?‘–=1 đ?‘—=0

Figure 1 Facility Allocation Problem (Eastman, 1972)

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The flow matrix is then developed to make the facility allocation problem more graphic.

The flow matrix, as the facility allocation problem, calculates the total weighted flow of material between departments and then layouts are compared in terms of efficiency. The flow matrix and adjacency graph illustrate each layout.

A B C D E F

A -

B 15 -

C 30 12 -

D 0 40 20 -

E 15 10 8 30 -

F 6 8 8 6 10 -

AA

FA

CA

EA

DA

BA

Non-adjacent pair loads AB: 15 x 2 = 30 AD: 0 x 2 = 0 FB: 8 x 2 = 16 FD: 6 x 2 = 12 58

Figure 2 Flow Matrix. (Garcia-Diaz & MacGregor, n.d.)

The methods described before would only evaluate created layouts. Craft method would later use this information to generate new layouts. Craft was studied by Armour and Buffa in 1964.

It is used to improve existing layouts by swapping departments and comparing their total flow cost. The method first selects two departments with same size or that are adjacent in the layout.

Then exchanges their positions, and then evaluates the distances between departments using the departments centroids (Jensen, 2004) 1 2 3 4 5 6 7 8 9 10 11

1 1 1 1 3 3 3 3 4 4 4 4

2 1 1 1 3 3 3 3 4 4 4 4

3 1 1 1 3 3 2 2 4 4 4 4

4 1 1 1 2 2 2 2 4 4 4 4

5 1 1 1 2 2 2 2 4 4 4 4

6 8 8 7 6 6 5 5 5 5 4 4

7 8 8 7 6 6 5 5 5 5 4 4

8 8 8 7 6 6 5 5 5 5 4 4

9 8 8 7 6 6 5 5 5 5 4 4

10 8 8 7 6 6 5 5 5 5 4 4

11 10 10 10 10 10 10 10 10 10 10 0

12 10 10 10 10 10 10 10 10 9 9 0

13 10 10 10 10 9 9 9 9 9 9 0

14 10 10 10 10 9 9 9 9 9 9 0

15 10 10 10 10 9 9 9 9 9 9 0

Figure 3 Craft Method (Jensen, 2004)

More complex layout planning techniques: Following the initial results of layout planning in industrial design, architecture began developing its own techniques for addressing floor plan design automation. Architecture’s more ill structured nature and social logic made automation results questionable, nevertheless a variety of approaches have been made.

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Report on a System for General Planning (Eastman) In architecture one of the pioneers in developing space planning algorithms was Charles M. Eastman. His work was summarized in a program called general space planner. His main critique towards craft was that it was limited to one criteria, weighted distance, and some relations were left behind. To list a few Eastman mentions “accessibility (as in being able to get to parts of a machine that must receive maintenance), direct adjacency (as in a room requiring a window and thus must be adjacent to an outside wall), sightlines (as from the control console of a computer), and specific distance constraints (as defined by cable lengths for computer memory boxes), plus others. “ (Eastman, 1972) In his study, Eastman examined architects working in space allocation problems. He would observe the process of design and would try to understand which aspects are taken into account.

Although architects do not claim to optimize criteria he focused on how certain protocols became constrains. This are then combined with secondary constrains, and if the solution is not feasible, constrains are relaxed, and solved through multiple iterations.

Eastman would define the following formulation for the evaluation and creation of his floorplans: 1)

a

: A Space

2) {b1, b2...,bm}

: A set of design unit (Rooms) to locate in that space

3) {c1, c2...,cn}

: A set of constraints delimiting acceptable solutions, plus possibly

.

1) {d1, d2...,dp} .

2) eâ °

evaluation functions to be optimized : A set of operations for manipulating the location or shape of design unit within space. : The initial design state, state is an arrangement of DUs.

With these parameters, the idea would be to obtain the following: A set of operations: 1) đ?‘’ đ?‘&#x;+1 â†? (đ?‘’ đ?‘&#x; , đ?‘? đ?‘&#x;+1 , đ?‘‘ đ?‘&#x;+1 ) Figure 4 Eastman set of Operations Formula

That would generate a state đ?‘’ đ?‘ that: 2) đ?‘’ đ?‘ ↔ {, đ?‘’ đ?‘&#x;+1 , đ?‘’ đ?‘&#x;+1 ) Figure 5 Eastman State Generation Formula

The equation would manipulate one or more design units until constrains are met.

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Eastman represented space through two - dimensional arrays. The array contained first the measurement of the space in the 0th place in x-x and y-y. Then every space was assigned a type according to a range of values either blank space, available space, dead space, solids or use space (Numbers 901,101,999 in Figure 5 Matrix).

5.0 3.6

0

1.6

5.5 4.0

3.0

0

1

2

3

4

1.5

3.5

5.0

0

1

3.0

901

901

901

999

2

4.0

101

901

101

999

3

5.5

101

101

101

999

4

0

999

999

999

999

Figure 6 Steadman Representation of Space (Eastman, 1972)

The output was then subjected to a series of constrained test (Booleans) and then it determined if the requirements were achieved. Constrains included adjacency, distance, sight and access. To transform the figure a series of operands were applied to the shapes, such as: translate, clean, clock or counter. These transformations were applied to shapes individually.

Graph Theoretic Representation of Architectural Arrangement (Steadman) In the following year (1973) a different approach was taken to deal with the same problem.

Philip Steadman focused on the topological relations between spaces instead of diving directly into the geometrical domains of floorplan design. In his approach Steadman utilized graph theory to recreate possible plan solutions for rectangular spaces. Since his research was focused in a particular domain (small housing plans) he ignored some complexities of systematic flow planning like flow and overall distance of facilities and focused on adjacency. (Steadman, June 1973) Steadman analysed adjacency graphs, spanning subgraphs plan graphs and dual graphs for layout creation.

Adjacency graphs describe all bordering rooms. Spanning subgraphs originate from adjacency graphs but only contain required connections. The plan graph shows the edges of rooms as points and the connections between them are the walls. The combination of plan graph and adjacency graph have a special relationship and therefore are called duals.

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Figure 8 spanning subgraph (Steadman, June 1973)

Figure 7 Possible arrangements for adjacency graph (Steadman, June 1973)

In a planar graph, the exterior is divided in four to denote solar orientation. Therefore, adjacencies can be either between rooms or between a room and an exterior faรงade.

Figure 9 Plan graph (Steadman, June 1973) Figure 10 Dual graph relationship (Steadman, June 1973)

The search space for solutions is then reduced to a more manageable size of exploration.

This way Steadman can enumerate possible topological arrangement of spaces (rectangular) to fit a particular adjacency criterion, below are examples for up to 4 rooms. (Steadman, June 1973) P=1

P=2

P=4

P=3

No dissection

q=1

P=5

No dissection

q=2

q=3

q=4

q=5

*

*

*

No dissection

q=6

Figure 11 Possible Floorplan Configuration on Adjacency Graphs up to 4 rooms (Steadman, June 1973)

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Using Polya enumeration theorem one may determine the total number of possible adjacency combinations given a number of rooms. But this number excludes graphs with no connected edges or non-planar graphs which have no use as architectural floorplans, and are harder to calculate. (Steadman, June 1973) Steadman then continues to develop tables to determine these amounts. The first table is made directly from Polya enumeration, but the second one is only an estimation made through extrapolation of graphs made from fewer rooms.

Steadman recommends exhaustive enumeration only for up to 6 leaves. (Steadman, June 1973)

Figure 12 No of Possible Graphs

Figure 13 No of Possible Rectangular Arrangements

Synthesis and Optimization of small rectangular floorplans (Mitchells) Mitchells worked on top of Steadman’s work to present a solution for exhaustive enumeration for rectangular floorplans up to eight rooms. As his predecessors Mitchell works first in topological arrangements to then insert dimension constrains. Mitchells uses a method developed in biology to express ‘similar’ forms using transformation grids and matrices to describe topological shapes. The example below shows his notation. (Mitchell, Steadman, & Ligget, 1976)

đ?‘Ž= [

1 0 1 ] 1 1 1

1 1 đ?‘… = [1 1 6 7

2 3 3 4 4 5] 7 7 5

đ?‘Ľ = [8,6,20,1,11] đ?‘Ś = [2,20,8]

Figure 14 Topological Shape and Matrix Figure 15 Topological Floor Plan

Figure 16 Dimension Representation

(Mitchell, Steadman, & Ligget, 1976)

(Mitchell, Steadman, & Ligget, 1976)

(Mitchell, Steadman, & Ligget, 1976)

To develop all possible arrangements for a given number of rooms. The n dissection has 4 possible solutions to correspond to the n -1 dissection. (Mitchell, Steadman, & Ligget, 1976)

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Figure 17 Possible dissections for n subdivision in terms of n-1 subdivision

Figure 18 Spiral Configuration

(Mitchell, Steadman, & Ligget, 1976)

(Mitchell, Steadman, & Ligget, 1976)

However, this method was discovered not to be exhaustive because it excludes spiral configurations. To include spiral configurations Mitchell added an algorithm developed by A. Sayed’s that includes these possible configurations. The total number of possibilities are displayed in the table below.

Figure 19 Possibilities of Graphs (Mitchell, Steadman, & Ligget, 1976)

As in Steadman’s technique adjacency graphs and external adjacency graphs (adjacency to exterior facades) are calculated for each floorplan, highlighting that some adjacency graphs may have none, one or more correspondent floor plans. Subsequently, matrixes to store adjacency requirements are made, these are simplified versions of the ones used in systematic facility layout planning that use -1, 0 1 to represent unwanted, indifferent, and wanted adjacencies respectively.

An exterior adjacency graph is also made to denote adjacency requirements to either north south east west facades, or a general connection to the exterior. The next step would require assigning a function to each space. One more time, an exhaustive approach is used to determine all the possible assignments, nevertheless it is made only on the configurations in which the adjacencies requirements are possible. (Mitchell, Steadman, & Ligget, 1976) The final step would be to dimension the rooms. Constrains are set to the following criteria: length width proportion perimeter and area. Variables a-g are defined as following: a < length < b

c < width < d

e < proportion < f

g < perimeter < f

h < area < g

A wide variety of solutions exists to solve the dimensioning of rooms depending on the requirements they must fulfil, either through optimization, linear or nonlinear, or for integer or real numbers. An equation can be obtained for each proportion constrains needed in the floorplan.

Suppose that for a floorplan that has room 1 and 2 all rooms are needed to be squares, then this means that x1 = y1 and x2 = y2 and x1 + x2 = y2 since we are talking about proportion a random size is assigned to x1 as 1 and we obtain the plan displayed in figure 20. (Mitchell, Steadman, & Ligget, 1976) 18

x1

x2

1

y1

1

y2

2

1

Figure 20 Dimension Assignment

By adding additional constrain equations the process becomes more complex and may have none one or many solutions. For example, in figure 21, to achieve a 2:1 proportion in all rooms for floorplan 21.A A series of chain equations can relate all dimensions. Since there are two possible equations to maintain a proportion 2:1 (defining X as the shorter side or defining Y as the shorter side) This could be diagrammed through a binary decision tree. (Mitchell, Steadman, & Ligget, 1976)

Figure 21 Tree Diagram for Dimension Assignment (Mitchell, Steadman, & Ligget, 1976)

Shape grammars (Mitchells) Shape grammars propose a different approach towards solving the problem of automation. Instead of focusing in optimization the purpose of shape grammars is to generate designs through the execution of shape rules. A clear example can be seen in Mitchelâ&#x20AC;&#x2122;s book The 19

Logic of Architecture. In this book, there is a critique to previous strategies in floorplan generation.

Mitchel argues that “the trouble with algebras, as universes of design possibilities, is that they usually contain too much. They tend to contain vast numbers of possibilities that are meaningful but irrelevant or uninteresting. The state-action trees that they establish contain numerous branches that are not worth exploring.” (Mitchel, 1990) He later argues that “We need some way to curb promiscuous combination of shapes to tighten up the rules of the game” (Mitchel, 1990) Shape grammars try to solve this problem by introducing grammatical combination of parts. The aim is to “specify in the definition of an architectural vocabulary element that it is only instantiated in certain kinds of combinations with other elements. In other words, “we specify certain external decisions in the type definition.” (Mitchel, 1990) The best analogy is related to speech “not every string of English words is an English sentence: only strings that comply with the rules of English grammar count as sentence.” Following this technique some interesting results have been obtained. Stiny’s exploration in Palladian grammar is an example of this method to recreate Andrea Palladio’s villas. (Stiny & Mitchell, 1978) Duarte has also implemented a similar technique to recreate Alvaro Siza’s designs.

Constraint Based Systems (Li) Siu-Pan Li, John H. Frazer, and Ming-Xi Tang developed a method using a constraint based system. This method uses nonlinear programming to develop results that satisfy the greater possible amount of constraints of a given floorplan system. The method converts architectural constrains into mathematical models. Architectural constrains are divided into dimensional constrains which limit the size of each block or room and functional constrains that determine the placement of each room or block.

Figure 22 Constraint System Layout (Li, Frazer, & Tang, 2000)

By describing each room with distinct set of variables each constraint determines a function. As an example, the function that determines adjacencies is described in figure 23. It relates length, width and position of compared spaces. Additional to this function there are 20

functions to determine boundaries, overlapping and dimensional constrains. Then all constrains are converted into mathematical form and a commercial optimization tool is used called LINGO. As other nonlinear algorithms, a solution is not guaranteed. (Li, Frazer, & Tang, 2000) {

(đ??żđ?&#x2018;&#x2013; + đ??żđ?&#x2018;&#x2014; ) á 2 â&#x2C6;&#x2019; | đ?&#x2018;Ľđ?&#x2018;&#x2013; â&#x2C6;&#x2019; đ?&#x2018;Ľđ?&#x2018;&#x2014; | â&#x2030;Ľ đ?&#x2018;&#x192;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014; (đ?&#x2018;&#x160;đ?&#x2018;&#x2013; + đ?&#x2018;&#x160;đ?&#x2018;&#x2014; ) á 2 â&#x2C6;&#x2019; | đ?&#x2018;Śđ?&#x2018;&#x2013; â&#x2C6;&#x2019; đ?&#x2018;Śđ?&#x2018;&#x2014; | = 0

or

{

(đ??żđ?&#x2018;&#x2013; + đ??żđ?&#x2018;&#x2014; ) á 2 â&#x2C6;&#x2019; | đ?&#x2018;Ľđ?&#x2018;&#x2013; â&#x2C6;&#x2019; đ?&#x2018;Ľđ?&#x2018;&#x2014; | = 0 (đ?&#x2018;&#x160;đ?&#x2018;&#x2013; + đ?&#x2018;&#x160;đ?&#x2018;&#x2014; ) á 2 â&#x2C6;&#x2019; | đ?&#x2018;Śđ?&#x2018;&#x2013; â&#x2C6;&#x2019; đ?&#x2018;Śđ?&#x2018;&#x2014; | = đ?&#x2018;&#x192;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;

Figure 23 Adjacency Function

Expert Systems (Flemming) Expert systems were introduced to architectural floorplan systems in Flemmingâ&#x20AC;&#x2122;s: A Generative Expert System for the Design of Building Layouts. (Flemming, 1988) In this paper, the idea of systematic exploration to alternative solutions for a design problem was explored.

The system works in terms of alterations of a given design. The following diagram shows the overview of the system.

Pre-Processor

Generator

Control Strategy

Tester

Post-Processor Figure 24 Expert System Overview (Flemming, 1988)

This system has five major components which can be modified independently of other components. A generator, a tester, a control strategy, pre-processing and post processing. The generator receives a spatial configuration and tries to expand it in all possible ways. The tester accepts configurations and evaluate it in terms of a given criteria. The control strategy inspects results obtained from tester and selects a next state for expansion. The pre-processing generates an initial state to create alterations. Finally, the post processing: fine tunes the result and displays it to the user.

Classification of Algorithms and Current Applications: Given the immense variety of proposals for automatized space layout planning and its fifty-year-old history it would be useful to classify such proposal into big categories. Lobos and Donath suggest the following 4 major groups, expert systems (Flemmming, Coyne) shape

21

grammars (Stiny Mitchell and Duarte), Generative (Gero, Fraser) and constraint based system.

(Gross, Medjdoub and Yannou, Hsu) Currently, the most common use of floorplan automata explorations outside of academia is in the development of large complex buildings such as hospitals or office layouts. One example is Perkins and Willâ&#x20AC;&#x2122;s SPACE PLAN GENERATOR which is used in the aid of major healthcare facilities. Nevertheless, due to the vast amount of time it takes to define all of the aspects which make a better design proposal, this tool is used mainly in large scale complex buildings. Also a big disadvantage posed by this method is that it requires to enumerate every quality, adjacency, constrain to consider in a design. This often leads to forgetting some hidden aspects which are essential to floorplan design.

A clever method that allows more interaction with the architect and the program has been developed by the generative design team at Autodesk, in the Autodesk office building. Where multiple design solutions are classified using principle component analysis. So, the user gets to navigate through a series of possible solutions to decide on a given design. (Nagy, Lau, Lock, & Stoddart, 2017) Other software such as Acadgraph, Affinity and Onuma Planning also propose floor plan automation for architecture. Acadgraph, developed by a German company is a complete package for the creation of room layouts. This software uses neural networks to manage the relationships between spaces and constrains each room has. This program would create 100 possible solutions to then choose the optimal one, one of the great disadvantages of this program is that it requires all enumerations of qualities to be optimized. (Lobos & Donath, 2010) Affinity is a software developed to compare building specifications to architectural solutions it compiles a list of areas with requirements that are compared to a floorplan layout the program guides the architect by highlighting which requirements are not met in the floorplan. (Trelligence, 2017) Onuma Planning is a system that incorporates BIM technologies with big data analysis. It challenges the notion of project focused based creation to a greater focus of solutions that uses data from previous projects. Although Onumaâ&#x20AC;&#x2122;s main focus is not total space automation but rather a list of requirements for spaces it is an important precedent in the use of big data for design. Onuma is used specially for health care facilities. (Onuma, 2017) Although space plan automation has been widely explored there still needs to be some more research on making it more accessible, comprehensible and flexible to designers and users.

As seen in the first methods, (Steadman, Eastman, Mitchel) lot of the research has been done in

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developing a method for calculating all possible configurations, and evaluating them in terms of optimizations and constrains.

In the currently available applications these techniques are used in different software solutions, most of the times separate from popular commercial CAD systems. Many donâ&#x20AC;&#x2122;t integrate big data analysis which could enhance their capabilities, with the exception of Onuma.

The majority of algorithms are focused on the generation method and leave the evaluation method to a set constrains and optimizations defined by the user. There is little participation in algorithms to define constrains and optimizations.

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Simplified version of the plan: A strategy that is recurrent in many computational creative algorithms is analysing previous authors and understand how they create their art, music, poetry etc. To then mimic their decisions. This is true for example in David Cope’s Bach chorales (Garcia, 2015) to the many artistic style transfer algorithms that use deep learning. The plan is to create an algorithm that uses a similar strategy. The following diagram illustrates the desired workflow of the algorithm to be implemented in the thesis.

Input: Database of Previous Designs of a particular author, trend, era, socioeconomic background to be analysed.

Analysis of Traits per Room: • Room Proportion • Room Shortest Dimension • Room Longest Dimension • Room Area • Adjacency to other Rooms • Connectivity to other rooms, • Connection to Exterior The mean and standard deviation/consistence is calculated for each rooms attribute.

Random Typology Generated

Traits of random typology compared to database.

Distance to median x standard deviation of database would be the measurement of fitness

Evolve, lowest fitness value = fittest

Figure 25 Desired Algorithm Structure

*This algorithm would understand what traits are continuous in a specific author, era, trend, and then evaluate future designs as how they compare to the database designs. The more evolved generated floor plan is the floorplan that respects the qualities which are consistent through the dataset.

Defining a Design: Zone allocation defines the architecture major geometrical traits and also the topological relationships between spaces. The designer defines space by physical boundaries to endorse 24

certain activities to certain areas. Although a variety of methods have been used to define spaces, assigning space through zone subdivisions is one of the most used methods for designing and would be used in this example.

Binary tree structures are chosen to keep track of zone subdivisions and room creations.

Binary trees, as used by some extent in Steadman’s and Mitchel’s exhaustive exploration of topological layouts with respectable results. In theory, all floorplans can be constructed using this method (there is no mathematical prove for this) with the exception of spiral configurations. To deal with spiral configurations one would have to use Saed’s algorithm. Since this thesis aims for a heuristic approach spiral configurations are ignored.

Figure 26 Binary Tree to Represent Floorplans

As showed in figure 20, a full binary tree keeps track of zone subdivision. Every zone divides into two zones until the desired floorplan is obtained. The leaves of the resulting tree represent the rooms while the inner nodes represent greater zones. The advantage in using this approach is that every operation to obtain a floor plan design is explicit in the tree. In addition, it resembles a common strategy architects use which is going from general to specific.

Example of House Definition Example House H = a (b, c (d, e)) would result in the following tree:

Figure 27 Sample Tree

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In order to determine the position of subdivision (either x-x or y-y) an option is assigned to each node, either 0 for x-x or 1 for y-y. H = a0 (b, c1 (d, e)), would give as the following floorplan:

Figure 28 Sample Floorplan

A second trait is needed to determine the ratio of subdivision. For each resulting room (leaves of the binary tree) there are architectural variables that define doors, openings etc. The first number indicates the type of aperture (0 = door, 1 = void) the second the location of the door (each corner). In figure 29, you can see an example of room (a 0|5):

Figure 29 Sample Room

The universe of solutions To determine the possible number of results (topologically speaking) of a determine number of rooms we would have to examine enumerative combinatorics. In the field of enumerative combinatorics Catalan numbers determine the total possible combinations of trees for a given number of nodes (Stanley, 2013). The Catalan number describes the relation of the total number of inner nodes to the possible number of trees. In this case the number of leaves (rooms) is a more relevant number to relate to, so, the number of trees is calculated as the Catalan number of leaves minus one. If this number is multiplied times the factorial of n, this would formulate all the possible arrangements of rooms in a determined tree, and times 2 for every inner node to determine if the subdivisions are made in x-x or in y-y. đ?&#x2018;?đ?&#x2018;&#x203A; =

(2đ?&#x2018;&#x203A;)! (n + 1)! n!

Figure 30 Catalan Number (Stanley, 2013)

đ?&#x2018;?đ?&#x2018;&#x203A; =

(2(đ?&#x2018;&#x203A; â&#x2C6;&#x2019; 1))! đ?&#x2018;&#x203A;! 2(đ?&#x2018;&#x203A; â&#x2C6;&#x2019; 1) n! (n â&#x2C6;&#x2019; 1)!

Figure 31 Possible combinations

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As in Steadman’s work, this numbers would reduce substantially if work is done to eliminate repeated typologies. Since the approach taken in the thesis is using a genetic algorithm (heuristic approach) such reduction is not essential, but would be useful if the algorithm would take an exhaustive approach. Nevertheless, calculating the topological possibilities for the search space can give you a brief idea of the range of possible solutions.

Method for defining the “optimal” So far, a system for random typology creation with an immense possibility for solutions is created. This by itself brings nothing new to existing methodologies. The next step is defining optimal solutions. This part is extremely important and should not be defined as a mere optimization to a manually inputted list of desired qualities. The most criticized aspect of floorplan automation has been this part of the process. The reason for this critique is because it reduces the architectural problem to an engineering solution. It forces the qualities to be described as hard coded facts to comply, but architecture many times works in subtler territories.

Intuition is an extremely important skill for an architect, and an architect may sometimes weight certain rules as more important than others. This would be extremely difficult to hardcode into a program as a user. If you have to answer for example the ideal area for a living room, well it depends on the size of the house. The ideal area of the bathroom, this is a bit more restrictive and should not vary that much. Are bathrooms always connected to the exterior? This is recommended but it is not always possible. If not every ideal measurement can be achieved, which is more important to maintain? The list of constrains and optimizations is endless and ambiguous and would be so laborious to create as to design floorplans without any aid.

So how can an algorithm learn from these subtle laws governing architecture? If we want to understand an architect instead of making him enumerate his rules for design it would be better to study their work. If something is consistently repeated through a series of floorplans it is probable important. If something is not consistent then it is more flexible. This method would allow the algorithm to work with the same level of intuition as the architect, and without having any previous knowledge of what a “living room” is understand how a “living room” should be measured and located within the floorplan.

Variables and Criteria taken into account An important aspect that would influence immensely in the resulting typologies is the criteria and variables that are considered and the importance (weight) that these variables pose in defining the fitness of the house. This aspect is highly subjective and would be different depending on architect and background.

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A method that extracts which qualities are used and given importance by architects would be useful. This is not an easy task, due to the fact that different qualities have different units, scales etc. and therefore are not comparable. Due to the limited amount of data extracted during this thesis is not sufficient to elaborate such a method. So, instead this method relies on definitions and criteria which have been used previously by renowned architects, in either their build work or have been mentioned in their theories.

Neufert, Ching, Hsu, Elezkurtaj, Lobos have written extensively on the subject. Lobos separates design criteria into two main categories: rational and general. While rational criteria are measurable, general criteria are more abstract and hard to measure. (Lobos & Donath, 2010) Lobo’s research in design criteria is displayed below.

Rational design criteria: 1) Solar Orientation: Seek optimal orientation in relation to the sun for each room, enables natural illumination and optimal climate depending on geographical location. (Glenn Murcutt: Marie Short House) 2) Views: Seek best views for the living areas. (Luis Barragán: Casa Barragán) 3) Adjacency and Room dependence: Rooms are placed depending on their desired adjacencies. Either adjacencies could be required, irrelevant or avoidable. (Systematic Layout planning: Flow Matrix) 4) Accessibility: Seek optimal distance paths from the entrance to each room. (Le Corbusier: "promenade architecturale") 5) Circulation Efficiency: Seek optimal distance (usually minimize) between rooms to optimize the circulation spaces. (Craft Method) 6) Minimal size: The minimal size either length or width of a room must have in order to function. (Neufert).

7) Proportions: The ideal width/height a room must have to function (Le Corbusier: Modulor) 8) Area: The optimal area of a space for a specific function. (Plazola, Neufert) General design criteria: 9) Geometric Composition: The building as a whole must be adapted to fit a geometric form (square, circle, rectangles, etc.) (Rem Koolhaas: CCTV Headquarters, Delirious New York) 10) Hidden Proportions: A seek for establishing hidden proportions that result in aesthetic or spiritual qualities. (Golden ration, Feng shui, etc.)

11) Readability of Plan: Possible configuration distributions so that the final layout is readable as a whole. Some examples are: Linear scheme, L Shape scheme, U Shape scheme (Bjarke Ingels Group: 8 House) 28

12) Sustainable Criteria: Space should be distributed to optimize energy efficiency in building.

(Norman Foster: Commerzbank HQ in Frankfurt) 13) Semantics: A building must adapt to prescribed spiritual or symbolic forms. (Traditional Romanic Church Scheme) As seen in the list showed above, the range for defining architectural floorplans is quite complex and many times unmeasurable. Some criteria are inherently incompatible with each other. For example, geometric composition, and semantics have to sacrifice circulation efficiency and proportions. Also, combinations of certain pairs of criteria may be incompatible in specific situations. If views are opposed to favourable solar orientation there has to be some hierarchy to determine which criteria plays a more important role.

Therefore, it is important to state that floorplan automation doesn’t seek to substitute the architect or be a simple click a button procedure to generate results. It has to be seen as a tool for exploration rather than a recipe for creation. In Autodesk studies in generative design this is widely recognized and in the many interviews with Autodesk CTFO Jeff Kowalski he highlights that “the augmentation of designer is the purpose of generative design and not the designer substitution”. (Kowalski, 2016) In this thesis, the purpose is first to identify what are the minimal criteria to create a consistent floorplan to then enhance the automation with secondary criteria. The first essential criteria for floorplan creation are taken from the first attempts in floor plan automation. In synthesis and optimization of small rectangular floorplans Mitchells works with adjacency, short side size, and area. These three criteria would be first explored and later on some other aspects such as long side, proportion, connection and relation of area/total house area are added.

Determining how to measure Consistence In summary, criteria’s (minimal size, area, and adjacency, etc) for each room, are measured in an entire database of floorplans. The mean (average) of the criteria becomes the optimal to represent the floorplan. The standard deviation from the mean would measure how consistent / inflexible these criteria is through the database. For minimal size and area this measurement is really straight forward. For adjacencies, the method is slightly more complicated, and does by defining how often a room is adjacent to another room as a percentage. To compare all criteria with comparable units percentage of consistence is measured. This is defined by how much a trait of a criteria is repeated through the database. A 100% consistence indicates that the pattern is repeated in all plans through the database. 0% indicates that the pattern is not repeated through

29

the database. When comparing measurements, a standard deviation of 0.00 would mean that there is a 100% consistence, and a consistence of 0% would result in the maximum possible distribution of data. All standard deviations are mapped in a linear relationship taking the lower standard deviation as 0 and the higher standard deviation as 1. This procedure can be better appreciated with the following example: From a database of floorplans two roomsâ&#x20AC;&#x2122; data are displayed:

Sample Size: 81 Average Most Common 4.19 6.37 26.80 0.67 0.31 Ki Ha Mb Ba

Stand. Dev. Consistence 0.88|90% 1.70|14% 11.45|55.53% 0.16|29.87% 11.45|0% 73% 64% 43.21% 0.00%

Figure 32 Example 1 for Room Criteria

Sample Size: 81 Average Most Common 1.62 2.77 4.46 0.86 0.05 Ha Be Ki Li

Stand. Dev. Consistence 0.21|93.47% 0.52|86% 0.96|89.18% .20|43% 3.12|100% 93.83% 38.27% 22.22% 0.00%

Figure 33 Example 2 for Room Criteria

Note that without any previous knowledge of design principles or the function of rooms an algorithm can learn important traits from analysing data. It can be objectively concluded for instance that the minimal size of the living-dining room tends to be around 4.19 m while the minimum size of a bathroom tends to be around 1.62 m. Also, that the area of the bathroom of 4.246 m2 tends to be more consistent (89.18%) than the area of the living dining room (55.53%) It can also be concluded that the living room tends to be connected to the kitchen, or that the bathroom tends to be connected to a hall.

30

If more criteria are added, then more patterns emerge and start to determine design patterns for a particular database of floorplans. If criteria x is consistent through a database then it can be implied that it is important for design, and therefore to evaluate a new floorplan in terms of how well it resembles a database of designs the fitness should be determined on how its criteria qualities are alike the criteria qualities of a database of designs.

A floorplan can be thought of as a point in a multidimensional space. Every criterion for every room is a dimension. The position of the point is determined in every dimension by the amount measured in the criteria. The point located in the average of all positions of a database determines the most representative floorplan. To determine how a new floorplan relates to an existing database the distance from that point times the consistence (normalized standard deviation) from the mean for every dimension would define how much a new design follows the design criteria established in a database.

Total weighted distance from Mean represents how much a new design follows the criteria of a database

average position of database int

mos

mos

Distance in x dimension x New design

int mos Consistence (normalized standard deviation) int Figure 34 Multidimensional Representation of Designs

mosof a database to represent a It has to be accepted that by picking the average position design may be too simplistic. For future studies more indebt analysis should be done to databases using cluster analysis. This way different typologies of designs could be recognized within a database, and generated new designs would be compared to these clusters rather that only the mean.

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The GA Once a method for comparing designs is developed now it is important to state how this method would be used in generating new designs. Since genetic algorithms are good in heuristic approaches and have been explored before in similar problems, (Doulgerakis, 2007, Coohon 1991.) the same method would be used here. Genetic algorithms have the following advantages over other methods: â&#x20AC;&#x153;there is no need to determine restrictive assumptions, dimensions can be explored in continuity, and explores answers within an acceptable efficiencyâ&#x20AC;?. (Jo & Gero, 2006) Genes are divided into 4 main categories depending on the function they perform. By varying all genes, a fitter solution is searched from all possible rectangular arrangements (excluding spiral arrangements).

Gene type 1 controls the full binary tree number. There is one global gene type 1 for the (2đ?&#x2018;&#x203A;)!

tree. If n is the number of rooms (leafs) there are đ?&#x2018;?đ?&#x2018;&#x203A; = (n+1)!n! possible outcomes for this gene (Catalan number).

0

0

0

1

2

0

0

0

3

4

0

0

Figure 35 Gene Type 1 Diagram

Gene type 2 controls how rooms are assigned to the corresponding leaf. There is one global gene type 2 for every tree. If there are n number of rooms, there are n! number of possible outcomes for this gene.

0

0

0

0

1

0

0

2

0

32

3

0

4

0

5

Figure 36 Gene Type 2 Diagram

Genes type 3 controls the arrangement of the subdivision. If there are n number of rooms there are n-1 number of genes (number of inner nodes). Genes type 3 can either be 0 or 1. If the geneâ&#x20AC;&#x2122;s value is 0 the inner node would subdivide in x-x. If the genes value is 1 the inner node would subdivide in y-y.

0

1

Figure 37 Gene Type 4 Diagram

Genes type 4 control the percentage of space given to each subdivision. It goes from 0 â&#x20AC;&#x201C; 1 by steps of 0.01. There are the same amount of genes type 4 as genes type 3.

0.2

0.4

0.6

Figure 38 Gene Type 4 Diagram

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0.8

For testing the above-mentioned method with examples, the space layout method was divided into two main steps. The first step would be to create an algorithm capable of producing designs that evolve to satisfy hardcoded fitness criteria. This part would interpret the subdivision as a series of parameters and create a housing solution with measurements and locations. The second part would evaluate housing according to how its design traits resemble the traits from a database. This step would require analysing previous typologies and interpreting their consistent attributes.

First Step: (Hardcode Fitness) Given the complexity of the problem, a first algorithm was created with the following purpose: Given a typology x (tree definition) or desired rooms, determine how its traits need to be adjusted so that it fits the following hardcoded dimensions and connections. This was made as a first step to understand how the genetic algorithms behaves, and which conditions (best number of individuals in population, etc.) finds acceptable solutions without running into a local maximum.

It was found that a population of 625 members is sufficient enough to determine until a maximum number of 8 rooms. It was also determined that for all elements to have similar importance in the genetic algorithm, dimensional differences must be squared while maintaining areas difference units. Displayed below is a simple example that uses this method, the fitness algorithm used and the results obtained.

Figure 39 Input for Hardcoded Designs

To create the following results, a fixed short side, long side, area, proportion and adjacency were given. Cost weights for each room quality were given a same value of 1. (This weight would be adjusted in future steps according to standard deviation | consistence in database for each room).

(Ideal area – actual area) X 1 (in this case cost weight is 1 for each room) (Ideal short side – actual short side) ² x 1 (Ideal long side – actual long side) ² x 1 (Ideal proportion – actual proportion) x 20 x 1 (Ideal area / total house area – actual area / total house area) x 20 x 1 (For each ideal adjacent not adjacent in actual plan) + 5 x 1 + (for each ideal connection not connected in actual plan) + 25 x 1 _______________________________________________________________ Fitness (add all rooms to get total fitness)

34

Figure 40 Results Hard Coded Designs

35

More complex designs using same fitness criteria:

Figure 41 Hardcoded Result 1 in Interface

Figure 42 Hardcoded Result 2 in Interface

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Extracting Criteria from Existing Typologies: A program was implemented to get housing schematics from images of floorplans. This program was distributed among friends both architects and non-architects to help gather large databases. This program displays images of floorplans, the user first determines the scale by selecting a door. Then by drawing over rooms; dimensions, position and adjacencies are calculated for the floorplan and stored in a database.

Figure 43 Processing Program for Area Selection

Furthermore, to extract criteria from existing floorplans a script was developed in dynamo.

From this script rooms are transcribed to an excel list instantly from a floorplan drawn in Revit or Archicad. This would facilitate future augmentations of the research and also to understand designs without having to manually input all of its traits.

Figure 44 Floorplan Trait Extraction

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Database 1: Random Floorplan Selection (Google Search) A first database of floorplans was selected from a sample of images from google search with no previous specifications, they all come from a search of â&#x20AC;&#x153;floorplans 2 bedroomsâ&#x20AC;?. The idea is that by emulating these traits a generative design can understand the main components in making a coherent house. No style is predefined to the house. From this search, a total of 112 rooms were selected with 1147 rooms to extract information. The violin plot can give a better reading of patterns, but for the algorithm to work the table summary is sufficient. Some patterns start to emerge that are easy to identify. These patterns may appear obvious to trained architects but take into account that the program has no previous knowledge of what every room function is and how it should be designed.

DATABASE 1: Random Floorplan Selection (Floorplan Source: Google Search)

Bathroom

Bedroom

Bed Ex.

Closet

Dining

Foyer

Hall

Kitchen

Living

Master B.

Tv Room

Washing Waking Cl

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

1.62

2.77

4.46

0.86

0.05

Ha

Mb

Wm

Ck

0.21|39%

0.52|33%

0.96|30%

0.19|46%

0.01|29%

67%

35%

34%

1%

3.42

4.07

13.95

0.90

0.16

Cb

Ha

Li

Be

0.26|46%

0.42|26%

1.92|53%

0.11|29%

0.02|52%

77%

65%

43%

0%

0.60

1.07

0.64

0.80

0.01

Be

Be

Ha

Wa

0.003|10%

0.22|10%

0.13|10%

0.22|51%

0.002|10%

63%

63%

60%

1%

0.60

3.09

1.85

0.64

0.02

Ha

Be

Mb

Di

0.005|10%

0.86|59%

0.51|19%

0.4|90%

0.007|21%

63%

58%

48%

1%

2.82

3.40

9.68

0.90

0.10

Ki

Li

Ha

Mb

0.44|72%

0.48|30%

2.59|69%

0.14|36%

0.03|62%

82%

71%

59%

0%

1.58

3.16

5.05

0.62

0.06

Ki

Ki

Ha

Fo

0.4|66%

0.97|67%

1.99|55%

0.24|56%

0.02|53%

86%

86%

54%

1%

1.40

2.56

3.58

0.88

0.04

Ba

Mb

Li

Ck

0.24|43%

1.27|90%

1.82|51%

0.22|51%

0.02|48%

72%

62%

61%

1%

2.81

3.42

9.68

0.93

0.11

Li

Fo

Wa

Ki

0.42|68%

0.59|38%

2.52|67%

0.12|30%

0.03|66%

91%

40%

27%

0%

4.19

5.83

24.37

0.83

0.27

Ki

Ha

Be

Li

0.35|58%

0.84|57%

3.46|90%

0.16|39%

0.04|90%

94%

65%

43%

0%

3.83

4.86

18.70

0.86

0.21

Ha

Wm

Cm

Mb

0.29|50%

0.55|35%

2.91|77%

0.12|31%

0.03|64%

67%

51%

44%

0%

2.75

3.75

10.38

0.73

0.10

Ha

Ha

Ba

Ki

0.35|59%

0.35|20%

2.3|62%

0.03|10%

0.02|41%

100%

100%

50%

0%

1.47

2.73

4.00

0.73

0.04

Ki

Ha

Ba

Wa

0.57|90%

0.66|44%

1.78|50%

0.3|68%

0.02|44%

74%

45%

43%

1%

1.66

2.23

3.76

0.90

0.04

Mb

Bm

Ha

Bb

0.25|45%

0.45|28%

1.11|34%

0.16|38%

0.01|29%

76%

69%

49%

1%

Figure 45 Database 1 Summary from Google Search

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For example, there is a clear indicator that to respect the traits of this database a closet short size should be around 0.60, and since there is none variation (standard deviation), this measurement is highly inflexible. This in contrast with kitchen, laundry and bedrooms which because of their higher standard deviation (lower consistence) are more flexible in terms of short size.

Figure 46 Roomâ&#x20AC;&#x2122;s Short Side Dimensions for DB1

There is a bigger variation regarding long sides in almost every room except the bathroom that seems to maintain its proportions. Halls have a wider variance in contrast to their shorter side.

Figure 47 Roomâ&#x20AC;&#x2122;s Long Side Dimensions for DB1

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Areas and proportion of area to total area have similar results, with some exceptions. The variations in areas appear to be superior in served spaces rather servant spaces. Areas such as living rooms and bedrooms tend to vary more than bathrooms and closets. Again, this may be obvious to an architect but may be hard to explain to a program.

Figure 48 Room's Area for DB1

One would expect less variance in the living relation to the total house area, but in this database, it appears that this relation has a big variation, which would suggest that living rooms area donâ&#x20AC;&#x2122;t depend directly on the total area of the house.

Figure 49 Rooms Area/ Total House Area for DB1

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Proportions seem to have no value in this database with some exceptions. Bedrooms, living rooms and master bedrooms do seem to maintain their proportions.

Figure 50 Roomâ&#x20AC;&#x2122;s Proportions for DB1

Adjacencies are harder to visualize but the information is available and valuable for the program to run. Therefore, the matrix for the most adjacencies is also shown. The three most common adjacencies are used for the G.A. with their respective cost weights. The diagram showed is created by displaying each adjacency with transparency so that common adjacencies are visible.

1st Adj. a Ha Cl Cl Ha Ki Ki Ba Li Ki Ha Ha Ki Ba

p 68.75% 75.23% 97.78% 64.29% 85.71% 85.71% 87.30% 91.74% 94.50% 66.97% 100.00% 69.64% 96.00%

2nd Adj. a Wc Ha Be Be Li Ki Be Fo Ha Cl Ha Ba Mb

p 43.18% 68.81% 64.44% 54.55% 71.43% 85.71% 59.52% 38.53% 65.14% 56.88% 100.00% 48.21% 72.00%

3th Adj. a Mb Li Ha Mb Ha Ha Mb Wa Be Ba Ba Ha Ha

p 37.50% 44.95% 62.22% 45.45% 61.90% 59.18% 58.73% 36.70% 44.95% 52.29% 50.00% 42.86% 49.33%

Figure 51 Adjacencies Matrix and Graph

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Then by adding all these traits for every room, the ideal fitness would be obtained by generating the average house, and the difference in consistence would determine the fitness cost for every element.

Figure 52 Inserted Fitness Parameters for floorplan Generation

The evolution process resulted in the housing typologies displayed in figure 54 to 56. The results to a certain degree show a vague degree of understating how a house works. With some minor problems. It is clear than some cases a genetic algorithm may sometimes favour designs that meet all of the criteria but one and still have a good fitness. For example, in figure 54 although the majority of rooms work fine the bedroom has really unusual proportions.

Generated housing before evolution:

Figure 53 Unevolved Population

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Generated designs using database 1:

Figure 54 Generated Example 1 using DB1

Figure 55 Generated Example 2 using DB1

Figure 56 Generated Example 3 using Db1

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Other Examples in Interface:

Figure 57 Evolved Examples using Db1

Figure 58 Evolved Example 2 using DB1

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DATABASE 2: Collective Housing in Mexico Given the results in the previous database the next step was to compare this results with other databases from particular cultural backgrounds, architects, eras etc. Although a particular architect would have more constant patterns in design which would be easier to identify using this method since there needs to be a big database to create such comparison particular architects were not selected but cultural backgrounds. In this case a recompilation of Mexican architecture made by Fernanda Canales was used.

In the results obtained there appears to be a bigger variation in traits than the database obtained from google. This would suggest that Mexican architecture is more diverse than typologies that can be found on google, and also that Mexican architecture is less constrained in terms of regulations that determine the nature of spaces.

Collective Hosing in Mexico (Floorplan Source: Canales, 2017)

Bathroom

Bedroom

Bed Ex.

Closet

Dining

Foyer

Hall

Kitchen

Living

Master B.

Tv Room

Washing Waking Cl

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

Avg. /Most Com. Stand.

Dev./Persis.

1.75

2.85

5.08

0.63

0.06

Ha

Mb

Be

Tv

0.41|36%

0.6|70%

1.79|84%

0.16|31%

1.79|84%

62%

42%

36%

2%

3.09

3.80

12.11

0.83

0.13

Ha

Cl

Ba

Tv

0.59|58%

0.73|63%

4.11|64%

0.12|46%

4.11|64%

60%

55%

43%

3%

0.79

1.58

1.70

0.62

0.02

Cl

Ba

Ha

Fo

0.36|31%

0.84|57%

1.79|84%

0.16|27%

1.79|84%

80%

73%

65%

1%

0.73

2.51

1.83

0.34

0.02

Mb

Ha

Be

Wa

0.18|10%

1.07|46%

0.88|92%

0.17|26%

0.88|92%

54%

52%

49%

1%

3.17

3.90

12.55

0.81

0.13

Ki

Li

Ha

Bx

0.69|69%

0.64|68%

4.33|62%

0.13|44%

4.33|62%

86%

83%

57%

1%

1.59

3.20

5.24

0.51

0.06

Li

Ki

Ha

Fo

0.62|61%

0.95|52%

3.53|69%

0.18|18%

3.53|69%

89%

74%

48%

1%

1.25

3.17

4.08

0.49

0.04

Ba

Li

Be

Tv

0.39|34%

1.98|0%

3.08|73%

0.22|0%

3.08|73%

72%

64%

53%

3%

2.43

3.60

9.00

0.70

0.11

Li

Ba

Ha

Ki

0.57|54%

0.77|61%

3.47|70%

0.17|26%

3.47|70%

73%

43%

42%

0%

4.03

6.37

26.80

0.67

0.31

Ki

Ha

Mb

Li

0.88|90%

1.7|14%

11.45|0%

0.16|30%

11.45|0%

73%

65%

43%

0%

3.40

4.19

14.49

0.82

0.17

Cl

Ha

Ba

Mb

0.53|50%

0.87|56%

4.72|59%

0.11|50%

4.72|59%

62%

55%

53%

0%

3.30

4.45

14.08

0.71

0.13

Li

Mb

Be

Ki

0.65|64%

0.61|69%

3.77|67%

0.14|37%

3.77|67%

100%

86%

57%

0%

2.08

2.85

5.76

0.71

0.06

Ki

Li

Ba

Bx

0.62|60%

0.98|50%

4.06|65%

0.21|8%

4.06|65%

97%

25%

19%

1%

2.12

2.87

5.53

0.69

0.05

Ba

Mb

Ha

Cl

0.39|35%

0.96|51%

2.54|78%

0.17|25%

2.54|78%

83%

56%

50%

0%

Figure 59 Database 2 Summary from Google Search

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The variations of short sides in database 2 are greater than the ones in database 1 nevertheless patterns seem to maintain. Living rooms show the biggest variation while closets and laundries show less variation.

Figure 60 Rooms Short Side Dimension for DB2

The longer side of each room seems also to have similar variations in every room, with the exception of the living room.

Figure 61 Rooms Long Side Dimension for DB2

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Areas are also similar to database 1. With a greater variance for living rooms. It can be appreciated that the variations in areas appear in both living rooms and bedroom.

Figure 62 Room's Areas for DB2

Figure 63 Rooms Area / Total House Area for DB2

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Proportions are much more varied than in database #1 it is hard to determine which rooms have a consistent proportion.

Figure 64 Room's Proportion for DB2

Adjacencies have similar results than in data base 1 with a smaller frequency of master bedroom to living room connection.

Figure 65 Rooms Adjacencies for DB2

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These results were then used in the genetic algorithm in a similar way to the method used for database 1.

The evolution process resulted in the following prototypes. There is little difference from the housing types developed from the google database that the one created from the Mexican social housing. Although the rooms using this database have more variations, the results ended up undistinguishable from the database of google search floorplans. As it was hypothesised from the observation of the graphs, constrains are more flexible in these floorplans allowing a greater amount of variety.

Unevolved Examples:

Figure 66 Unevolved Population DB2

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Figure 67 Evolved Example DB2

Figure 68 Evolved Example DB2

Figure 69 Evolved Example DB2

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Comparison It is hard to state major differences between both databases that would be sufficient to create notable differences in their generated designs. Both typologies have subtle differences that would need many examples and a lot of evolutionary iterations to be appreciated. There seems to be a clearer distinction between each room in the database, than a distinction between databases. This would imply that in both databases used there are more “universal rules” followed for design, than “local rules” followed; nevertheless, to make this statement more robust databases would be needed and more criteria should be examined. Database 1 designs are colored green and Database 2 designs are colored orange.

Figure 70 Examples Db1 vs Db2

Figure 71 Short Side Dimension Comparison

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Figure 72 Examples Db1 vs Db2

Figure 73 Long Dimension Comparison

Figure 74 Area Comparison

52

Figure 75 Examples Db1 vs Db2

Figure 76 Proportion Comparison

Figure 77 Area / Total Area Comparison

53

Figure 78 Examples Db1 vs Db2

Figure 79 Comparison in Radar Graph

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The degree of success of the method used in this thesis for generating new floorplan designs is satisfactory for generating coherent designs. Nevertheless, some adjustments need to be done to improve the generation and give more distinctive characteristics that relate designs generated to different cultural backgrounds. There are plenty of observations that should be considered in future studies.

First of all, there needs to be a more rigorous method in defining the cost of each criterion in the fitness function. There is no objective simple way to determine how important is a trait in comparison to other traits, so, taking this into account more empirical experimentation should be done to determine what weights give more accurate results.

Something else to consider for further experimentations is to choose socio-cultural backgrounds that have more defined characteristics in terms of housing solutions. Using Mexico as a unified culture is too broad and the variety in its floorplans are too big to be analysed as a whole. This is something that is particularly challenging more and more through the years because globalization is making buildings more similar, regardless of culture. Nevertheless, this could also lead in an interesting area of exploration and critique. By comparing resulting databases from different periods, a study on how a culture has changed evolved, and diluted to globalization could be analysed in debt.

A very interesting domain to explore in further research would be to alter how databases determine fitness values for the genetic algorithm. Incorporating more complex data analysis systems could lead to better generated results. Methods such as cluster analysis could identify subgroups within a database and could lead to better identifying traits that are consistent within a cluster.

Exploring other methods for heuristic search may also be advisable for further explorations. Genetic algorithms are competent in identify global characteristics for architectural designs but neural networks may prove to be better at identifying more local characteristics. While many neural network models work to discriminate data (classify) generative adversarial neural networks are competent in producing new data from a determined database. They use a generative network and a discriminatory network (both competing to create and select/discard data samples) Goodfellow & Pouget-Abadie used generative adversarial neural networks for image creation with promising results. (Goodfellow & Pouget-Abadie, 2014) An architectural design problem would take significantly less data to analyse.

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Another domain could be to mix databases to experiment on how different authors/ cultures could blend to create new typologies. Incorporating author A and B could develop a hybrid design that uses both authors. Furthermore, if two databases are merged there is no reason why not to select particular traits from particular databases. For example, Le Corbusierâ&#x20AC;&#x2122;s proportions in housing could mix with Mies Van der Roheâ&#x20AC;&#x2122;s connectivity within a house.

Although much more work should be done, this system has a great potential as an aid to people with little access to professionals. An office called Micro Housing Solutions proposes a similar automation approach to structural consultancy, and has been working for some years in informal settlements in India. (Ferrario, 2017) If structural parameters and economic parameters are added, a more robust system could aid in informal settlements. By giving a robust consultancy to non-professionals many could dramatically improve their construction conditions. The general objective of this investigation is to rethink architectural practice in places were the current techniques are not sufficient to deliver quality solutions. As the vast majority of constructions in the world tend to be informal, technology should help widen the gap between quality and resources available. Therefore, automation should attempt to use collective knowledge to obtain solutions that can adapt to resolve particular problems.

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