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Exploring the Evoluon of Meta

Parametric Models

1 An exmaple of evolon of atumat-

ically generated oor plans shonw

conanted in the grey backgrounds

based on user preference shown by

circe size.

Sam Conrad Joyce

Meta Design Lab, Singapore Uni-

versity of Tecnology and Design

Nazim Ibrahim

Meta Design Lab, Singapore Uni-

versity of Tecnology and Design

1

ABSTRACT

Parametric associave logic can describe complex design scenarios but are typically non-trivial

and me consuming to develop. Opmizaon is being applied widely in many elds to nd high

preforming soluons to objecve design needs and this is being extended further to include user

input to sasfy subjecve preferences. However, whilst convenonal opmizaon approaches can

set good parameters for a model it cannot currently improve the underlying logic dened by the

associave topology of the model leaving it limited to predened domain of designs.

This work looks at the applicaon of Cartesian Genec Programming as a method for allowing auto-

mac generaon, combinaon and modicaon of valid parametric models including topology. This

has value as it allows much greater ranges of soluons, and potenally computaonal ‘creavity’ as

it can develop unique and surprising soluons. However, the applicaon of a genome based deni-

on and evoluonary opmizaon to describe parametric models and develop beer models for a

problem respecvely introduces many unknowns into how model generaon works.

This paper explains CGP as applied to parametric design and invesgates the dierence between

using mang mung and both strategies as a way of combining aspects of parent models, under

selecon by Genec Algorithm under random, objecve and user (Interacve GA) preferences. We

look into how this eects the resultant over iterated interacon in relaon to both the geometry

and the parametric model.

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INTRODUCTION

Computaonal design, specically parametric associave design

has become widely adopted. This method has many strengths,

leveraging a formal but exible relaonal geometry denion

to capture design logic, to drive advanced form generaon and

support analysis and opmisaon. Parametric design is oen

used in early concept stage; where many opons are considered

over a short me in order to explore the design and soluon

space, with parametric variability speeding up exploraon

signicantly. Despite its popular use during the exploratory phase

parametric associave models (PM) are not easy to recongure

especially if a change has not been designed into the model from

the start (Davis et al 2011). To rephrase this more technically:

parametric changes (modifying variables) are trivial, whereas

associave changes (modifying the topology) of a parametric

associave model is dicult.

Considering computaonally assisted design exploraon, we

see a similar bias towards parametric over associave support.

For example, mul-objecve opmisaon allows for explora-

on of trade-os in parameter spaces and performance spaces

(Lin and Gerber 2014) (Vierlinger anda Hofmann 2013) and

interacve-evoluonary-opmisaon allows for user driven

parametric exploraon of design needs and soluons (Mueller

and Ochsendorf 2015). Despite the power of evoluonary

algorithms, there are no equivalent methods to opmise and

explore variaons in associavely dierent models (Harding et al

2013). A principal issue is generavely dening working associa-

ve links suciently complex or variable enough to sasfy real

2 Visual idencaon of the three

data sets comprising of a full CGP

denion of a small parametric

model: A 2D Funconal ‘F’ array of

component types, a 3D Topology ‘T’

array of input links for each compo-

nent and a 1D array of Metric ‘M’

numeric values.

design requirements and produce meaningful working geom-

etry. However, if realized it has great potenal for exible even

‘creave’ systems which could generate new innovave soluons

unaided (DeLanda 2002).

The relave complexity of manipulang parameters vs associaons

can be demonstrated if we consider changing one at random; if

a parametric value is changed it is likely that the model will sll

funcon; but if a component link or component type is changed

randomly then it is likely to break the model. One soluon to

eecvely algorithmically create and change valid topological

denions is applying Cartesian Genec Programming (CGP)

with is a Genec Programming method which uses evoluonary

algorithms to algorithmically create funconal and opmal

designs. Originally developed for designing circuits specically

logic gate based chips (Miller et al 2000). The main innovaon

of CGP is to develop an eecve schema which enables the

‘genome’ of the design (an encoded numerical represenaon

which is easy to manipulate computaonally and which when

processed into a ‘phenotype’ denes a design) to encompass

both topological and funconal elements of a directed-acy-

clic-graph (DAG). In the electrical circuit use case the DAG’s

deinfes the circit with electrical messages passing from inputs

through a potenally large set of logic gates and then producing

outputs, the funcons being the which type of logic gate is used

at each node and the topology dening how they are connected.

This represents a system where the messages go in one direcon

and there is no feedback or recursion hence directed-acyclic.

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CGP has been shown to be successfully extended to para-

metric modelling (Harding and Shepherd 2016). The reason

for this is that Parametric Modelling as used in packages such

as Grasshopper, Generave-Components and Dynamo-BIM,

essenally dene a graph like representaon of data ows which

must be a DAG. If we replace the logic gates for components and

the circuits with data connecons then the two systems operate

the same. This is a novel and new approach and potenally very

powerful enabling opmisaon or machine learning to operate

on parametric models both at the parametric and accusave

levels. However, the complexity of automated model generaon

by CGP is lile understood; especially relaonships between

the CGP representaon, the PM and the resultant geometry,

especially the eects of iteravely combining models which is

a principal mechanism for evoluonary approaches, this paper

invesgates these relaonships.

METHOD

The eld of CGP is relavely new and experience and thus experse in

applying it eecvity is growing with the research. Whilst there is not

yet consensus about eecve approaches to applicaon as there is in

Genec Algorithms say, most current applicaons of CGP follow broadly

similar methods, the current authority on this method can be found in

(Miller 2011). For this study a relavely standard implementaon of the

CGP schema was used for dening a parametric model on a xed-grid

(hence Cartesian) of components.

In our case three arrays were used to dene a complete parametric model

; a 2D ‘Funcon’ array dening the component types from a collecon

of possible components, a 3D ‘Topology’ array for which determines for

each component which input links to which component output and a 1D

3 An example of a mutaon of an

exisng model (le) showing the

result (right) with changes in the

T,F,M genotype and the resultant

parametric and geometric model

shown in red.

‘Metrics’ array of the values of the input parameters; as shown in gure 2.

The use of CGP is similar to its applicaon in circuit programming however

importantly the data is ‘typed’. Whereas circuits simply transfer binary

on-o messages; a parametric system is using a range of incompable

data type such as numbers characters and geometry (points, lines,

surfaces etc.) as inputs which complicates the generaon. As such there

is a DAG generaon constraint that nodes/component inputs must be

connected to the right upstream outputs to to allow the funcon of the

component to work, for example the denion of a line must take two

points if one input is a number then the line cannot be dened adequate.

More detail on this issue is discussed in (Harding and Sheppard 2016).

With this formal but exible denion of a parametric model consistent

with the CGP schema, it is possible to undertake evoluonary process to

generate, change and mix dierent models together. The CGP generaon

works by inially assigning random values for F, T and M. It is possible

to constrain the values of F & T so that all inputs to the components

have the right type. Here we can see that the components or funcons

used in this process are important, these are dened by the user and can

theorecally be any parametric component, for any component to actually

have a chance of working all inputs of a chosen component must be

represented in other component outputs or the metric values M so that

the component will actually have a chance of working.

Beyond inial generaon, to change a model the most simple approach

is ‘mutang’ a model by randomly changing some values in some or all of

F,T or M. Doing this to M is the same as changing parametres in a typical

genec opmizaon. Changing T or F generates a new logic in the model

and assuming only a few elements are changed can result in small but

signicant eects on the results in output geometry, as demonstrated in

gure 3.

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We can also ‘mate’ mulple models by mixing the values in T,F,M of two

(or more) models to make a new derivave models. The approach applied

here uses a quite typical spling method where the genome of both

models is cut into pieces and then alternate pieces are used to generate

a new genome, gure 4 shows the process and eect of this. It is worth

nong that this spling is realised by the CGP by using a xed grid size

of elements. However there are other techniques which can remove this

limitaon. This simplies the process as the genome remains the same

size and the locaon of individual genes/values in the genome/matrix are

comparable between models and discernible in the phenotype/generated

parametric model. In our case a simple single but variable posion cross

over point was used.

To explore the eects of mutaon and mang on the development

of soluons a custom lightweight parametric system was developed

in JavaScript with a limited range of components. As (Harding 2014)

elaborates on the choice of components used essenally determines the

pallet of geometry available to the algorithm and thus directs the type

of results achieved, to ensure a level of focus on the design a relavely

limited set of components is preferable to produce meaningful relevant

4 An example of a mang of two

models (top) showing the result

(boom) with the descendent parts

of the T,F,M genotype and the

resultant parametric model colored

respecvely.

6

5 Example output from the CGP

system: Right: the dense parametric

model produced by CGP with some

ineecve components in read

and the resultant design. Le: a

rendered generated model from the

last generaon

6 A small sample evoluonary

hereditary history plot using the

‘Farnsworth set’ components plot-

ng 16 models over 4 generaons

(each shown in plan) ordered top

to boom by age (oldest above

youngest) and posioned le

to right by parametric model

complexity .

designs which are comparable between themselves. For this study a

component set was used for CGP orientated towards producing single

story modernist plans, nicknamed the ‘Farnsworth set’; it includes basic

geometry but also special components to dene the actual ‘built elements’

namely: rectangle oor, rectangle roof, solid wall, glazed wall. An example

automacally generated example is shown in gure 5. The system was

set up to support genec evoluonary processes, using ‘roulee wheel’

selecon based and as part of this exploraon we compared both

objecve tness values, and subjecve tness (user input preference

scores) inpued via the web browser.

To ascertain the potenal of generated models, we explored useful

objecve metrics to measure models, nong that there is an important

dierenaon between parametric model and the geometry model.

Since the sample design is not intended for a parcular programmac

requirement, other aributes were calculated as indicators to determine

whether the resulng model is useful as a design arfact. Indicators such

as number of geometry elements created (number of points, lines etc)

, type and variety of elements (diversity of geometry vs few repeang

elements – all walls, all oors…). Similarly evaluaon metrics were

developed for the parametric model to determine model tness, these

were based on exisng approaches used to analyse computer programs

(Davis et al 2013). This was to get values to masure how ‘correct’ and

well the model was working independent of its actual geometry output.

The main metrics were: stascal variance of components especially the

number of ‘built element’ components, ‘eciency’ the percentage of

components used, and metrics for the complexity of the model (cyclo-

mac complexity). A detailed list and explanaon of the metrics used can

be found in the appendix.

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We then setup an experimental approach to look at the eect of an

evoluonary process applied to a pool of parametric models, specically

how the iterated applicaon of a genec algorithm using the CGP schema

to manipulate the deigns eects the models. An inial xed number of

models are randomly generated based on the predened CGP schema/

genome. The key properes of the CGP schema as menoned above are;

components to use, grid size and number of numerical inputs. The GA is

inialized which also requires inputs; primarily: the size of the generaon

and how many generaons to run the algorithm for. The GA can opmize

the models based on a tness based on one of three approaches, 1/

completely random, 2/ objecve model tness metrics, 3/ subjecve

user preference. The GA can be run to user dened evoluonary method

(mate/mutate/both) to create a new generaon of CGP models. A small

example of this process is shown in gure 6. Note that unlike typical

heredity trees, models are ordered on the x-axis le to right based on

their objecve performance values so that we can see how this changes

over me, a larger version of which is shown in gure 8.

As outlined this was applied looking at three key CGP generaon

approaches, mutaon only, mang only and mang then mutaon. The

intent was to idenfy any interesng eects of the methods and see if

it was possible to develop any idenable ‘best’ approach. For objecve

tness the metric was the amount of geometry generated by the soluon;

and the subjecve tness was the vong preference of one user making

model from 1 to 10 based on personal preference; in that case making

the study a use of an interacve evoluonary algorithm.

The system is publically available online and can be trialed here:

hp://www.metadesignlab.com/demo/arcadia-2017

INITIAL RESULTS

The results are complex and sll being analysed more deeply for insight;

however some interesng inial ndings have been found. Current

analysis looks at comparing all the aforemenoned CGP combinaon

methods with all of the dierent GA opmisaon criteria.

Looking broadly at the models generated linier correlaons were found

between component use eciency and geometry output irrespecve

of the generaon criteria (random, objecve or subjecve/user driven)

however an unintuive lack of correlaon between parametric model

complexity and output geometry complexity. It was also shown that

models developed by CGP have higher complexity properes than

human produced counterparts shown in (Davis 2013), implying an ability

solve problems radically dierently but also produce soluons which are

not easily human readable. It was also shown that by looking at large

numbers of randomly generated models that one could show relaon-

ships or not between dierent model metrics, examples of this are shown

in gure 7.

The discussed metrics where applied to provide insight to understand

the eect of model creaon over the whole duraon of an evoluonary

processes looking at the eect of selecon (subjecve vs objecve)

and the method of making new models (mang, mutang or both). It

was found that subjecve human selecon was much more eecve in

converging the design, whereas objecve selecon always produced a

much wider range of soluons. It was also shown that by controlling the

use of mang or mutaon that the metric qualies of the models could

be controlled. As mang tended towards generang more geometrically

complex models, whereas mutaon reduced the complexity and output

7 A collecon of 1000 dierent parametric models (shown as plan models on grey backgrounds) generated by CGP, showing top a linier correlaon between geometry

x-axis and eciency y-axis , and boom a lowly correlated behavior for geometry x-axis and cyclo-mac complexity y-axis.

8

8 The evoluonary tree of an automated design session using genec algorithm, with 30 generaons containing 30 models per generaon. The models are shown

contained in grey boxes with redlines showing hereditary links from direct mang using CGP. The oldest models are shown at the top with ‘children’ and other decedents

ordered going down. We observe that using only mang the diversity in geometry output (horizontal axis) is broad and tends towards large outputs relave to the inial

generated models but is not convergent

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geometry amongst other factors, mang and mutang a CGP model also

reduced the model complexity. The eect of mang was also to result in

disparate ranges of model complexity over the more convergent eects

of mang regimes. The eect of geometric complexity for the dierent

CGP generaon methods over generaons can be seen in gure 9.

FURTHER WORK

This study is by all means not complete and further analysis of current

results are the rst priority. However even based on the inintla ndings,

areas that require further research/exploraon have been idened along

with a few limitaons and potenal new direcons.

One of the main areas that requires deeper consideraon is how to

handle Model complexity. As described in the ndings, the computer

can generate much more complex networks than typical manually built

models, which leads to two issues. Firstly, the more complex models

become more inecient (they have more failed or ‘junk’ components

and does not create more complexity in geometry) and secondly, these

models become increasingly illegible.

To address these two issues, we could examine how humans create asso-

ciave models and develop certain network criteria or similar to ‘guide’

the generave process to create more working complex models, reducing

junk components. We could also develop addional logic that lters and

translates these generated networks into more legible components and

connecons which could be further modied by a designer.

Another area, which requires further invesgaon. is the evoluonary

process using mang. While Mang allowed for much geometrically

diverse soluons to be generated, it oen resulted in inecient CGP

models which reduced the geometric complexity. This issue is a conse-

quence of incompable ‘input’ types that get passed on during slicing and

recombinaon of dierent typologies. An experiment which explores the

eect of dierent types ‘Cross-over’ could be set up to determine which

approach or approaches are most eecve to be used in CGP Parametric

models.

Lastly, the techniques discussed in this study could be further enhanced

by exploring addional metrics and associang them with the models

9 The evoluonary tree of 3 separate interacve sessions 15 generaons containing 15

models per generaon. Each plot shows models ordered top to boom by age, with

the x-axis showing model geometry. Top le uses mutaon to generate next genera-

on models models, top right uses mang and boom uses mang then mutaon for

each new generaon.

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created in order for the computer to make beer judgements about

which models are the ‘est’. More metrics that ‘describe’ the visual

quality of the designs would help reduce the gap in convergence

between subjecve selecon and objecve selecon.

CONCLUSIONS

The applicaon of CGP to parametric modelling demonstrates an

approach which is able to control exisng widely used design systems

to automacally generate models and with a much wider amount a

variability and potenal as compared to convenonal opmizaons based

on solely input values; but this will only be useful if these methods are

controllable directable and human readable. Inial ndings highlight the

lack of knowledge and understanding in applying computaonal methods

to control parametric modelling and the need for further analysis and

work. The complexity of these models requires new ways to gain insights

into the tractability and eecveness of applying CGP in this context. It

has been shown that some metrics are able to idenfy and potenally

seer resultant evoluon of these models in producve ways for designers.

Encouraging is that the results of such methods are made more useful

with the introducon of human input poinng to producve methods of

human machine interacon.

More work is required to develop good underlying methods for

combining models producvely in a similar way as a human designer

would as well as interfaces which allow the human designer ecient

and praccal ways of direcng this powerful method able to make many

designs into the ones that are actually relevant and desirable by the

designer.

ACKNOWLEDGEMENTS

We would like to acknowledge the support of SUTD and the SUTD MIT

Internaonal Design Center

REFERENCES

Davis, Daniel, Jane Burry, and Mark Burry. 2011 "Untangling parametric

schemata: enhancing collaboraon through modular programming." In

Proceedings of the 14th internaonal conference on Computer Aided

Architectural Design, University of Liege, Liege.

Davis, Daniel., Burry, Jane Burry, and Mark Burry. 2013. "Modelled

on Soware Engineering: Flexible Parametric Models in the Pracce of

Architecture", PhD Theisis, RMIT

DeLanda, Manuel. 2002 "Deleuze and the Use of the Genec Algorithm

in Architecture." Architectural Design 71, no. 7 (2002): 9-12.

Harding, John, Sam Joyce, Paul Shepherd, and Chris Williams. 2013

"Thinking Topologically at Early Stage Parametric Design." In Advances in

Architectural Geometry 2012, pp. 67-76. Springer, Vienna.

Harding, John, and Paul Shepherd. 2016 "Meta-parametric design."

Design Studies (2016).

Lin, Shih-Hsin Eve, and David Jason Gerber. 2014 "Designing-in

performance: A framework for evoluonary energy performance feed-

back in early stage design." Automaon in Construcon 38 (2014): 59-73.

Miller, Julian F., Dominic Job, and Vesselin K. Vassilev. 2000 "Principles in

the evoluonary design of digital circuits—Part I." Genec programming

and evolvable machines 1, no. 1-2 (2000): 7-35.

Miller, J.F., Job, D. and Vassilev, V.K., 2000. Principles in the evoluonary

design of digital circuits—Part I. Genec programming and evolvable

machines, 1(1-2), pp.7-35.

Miller, Julian F. 2011 "Cartesian Genec Programming." In Cartesian

Genec Programming, pp. 17-34. Springer Berlin Heidelberg.

Mueller, Caitlin T., and John A. Ochsendorf. 2015 "Combining structural

performance and designer preferences in evoluonary design space

exploraon." Automaon in Construcon 52 (2015): 70-82.

Vierlinger, Robert, and Arne Hofmann. 2013 "A Framework for exible

search and opmizaon in parametric design." In Proceedings of the

Design Modeling Symposium Berlin. .

APPENDIX

A graphical explanaon of the metrics used to measure model and output

geometry is shown on the opposite page.

IMAGE CREDITS

All gures copyright of the authors.

Sam Conrad Joyce is an Assistant Professor in Architecture and

Sustainable Design at the Singapore University of Technology and Design.

Prior to this he was an Associate at Foster + Partners, in the Applied

Research and Development group leading structural integraon. Before

this he held a role as Design Systems Analyst at Buro Happold working

on geometrical, structural and master-planning projects. His group the

Meta Design Lab focuses on data rich systems for eecve design space

exploraon and decision making. To enable this his work synthesizes and

applies new techniques in distributed and scalable compung, mul-ob-

jecve opmizaon, big data analycs, arcial intelligence and web

based visualizaon.

Nazim Ibrahim has more than seven years of experience as a researcher.

His work focuses on the use of Parametric tools and Computaonal

workows in the exploraon and evaluaon of various design related

issues. He earned his Masters in Architecture from NUS where he

explored the use of parametric tools and digital fabricaon technologies

at various stages of design. He rmly believes that computaon design

should be employed extensively to resolve the complex issues faced by

design and architecture. He currently works as a Research assistant in

Meta Design Lab, exploring web frameworks in creang generave and

parametric design environments.

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Visual explanion of the various

metrics captured for this study

measuring both for the parametric

model itself and the output geom-

etry that it produces