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This paper illustrates the use of a computational form-finding method called ParaGen which aids the designer in the exploration of arrays of good solutions. Although the method is guided by a multi-objective optimization program, the goal is to promote the exploration of the solution space based on designer selected combinations of performance objectives. The digital form generation of the bridges is carried out using Formian, a program which uses Formex algebra to describe a wide array of geometric configurations. This form generation is linked to structural simulation and design software (STAAD.Pro) to determine performance values. Finally, ParaGen is used to build a database of all solutions and guide the exploration based on performance values. Using this database, both visual and numeric characteristics are explored.
Performance Based
Exploration Of
Generative Design
Solutions Using Formex
Anahita Khodadadi and Peter von Buelow
issue 3, volume 12international journal of architectural computing
Performance Based Exploration Of Generative
Design Solutions Using Formex Algebra
Anahita Khodadadi and Peter von Buelow
This paper illustrates the use of a computational form-
finding method called ParaGen which aids the designer
in the exploration of arrays of good solutions.Although
the method is guided by a multi-objective optimization
program, the goal is to promote the exploration of the
solution space based on designer selected
combinations of performance objectives.The digital
form generation of the bridges is carried out using
Formian, a program which uses Formex algebra to
describe a wide array of geometric configurations.This
form generation is linked to structural simulation and
design software (STAAD.Pro) to determine
performance values. Finally, ParaGen is used to build a
database of all solutions and guide the exploration
based on performance values. Using this database, both
visual and numeric characteristics are explored.
Designing a form is broadly considered as a creative procedure within
which certain goals are purposefully sought.The designer usually sets some
parameters such as topology or geometry of forms, material properties,
architectural functions and load cases.Then, the design goals are generally
defined by means of some criteria and the extent to which solution(s) can
meet them. In order to expand the designer’s perspective, facilitate
modifications of the forms and explore more possibilities of appropriate
solutions in the early stages of design, the couple of parametric form
generation and evolutionary optimization techniques can be applied [1].
In this research work two methods of form exploration are compared
to study the relation between the geometry and structural performance of
specific types of spatial structures.The first is based on traditional methods
of design exploration including physical modeling and the second is derived
from the coupling of a parametric formulation of the design and the
application of a genetic search process.To demonstrate the application of
computational method in professional context, the design of a trussed
roadway bridge is used, and a comparison is made between solutions found
using the ParaGen exploration method and a successful built bridge.
Furthermore, the solutions are compared to results achieved by design
students through model studies to show the contribution of this method in
an academic context.
A case study of a two-lane truss bridge is opted for in this paper, since it
allows one to consider structural performance as well as other design
concerns like visual characteristics, compatibility with the surrounding
environment and constructability.The truss bridge is based on an actual
design (shown in figure 1) with a width of 8 m and span of 48 m, and is
expected to be composed of two 2D trusses on the two sides that are
braced together laterally.The parametric variables allow for the trusses to
be situated either above or below or both above and below the deck.The
trusses can also have positive, negative or zero curvature (figure 1).
Figure 1:A typical
form of the truss
bridges that are to be
323Performance Based Exploration Of Generative Design Solutions Using Formex Algebra
The questions are raised at the beginning of this study: what are appropriate
solutions regarding the structural performance, visual appearance and a
designer’s individual preference, and how can such a set of suitable solutions
with different geometrical and structural features be found.These questions
involve the subjectivity of the design process which has been the main
concern of recent works considering interactive evolutionary methods of
form exploration in the conceptual design phase [2].
The parametric configuration of the bridge is first processed using
Formex algebra and Formian programming software [3].The geometrical
concepts used within this step are described in the following section. Next,
having produced a geometry, a DXF file is sent to STAAD.Pro for structural
analyses and evaluation.The obtained information including graphic
depictions is stored in a database which is linked to a visual exploration
interface. In the next step pairs of bridges are selected based on the design
objectives to breed further bridges. In selecting a breeding pair, a fitness
function is used to dynamically create a population of the desirable
solutions out of the entire pool of generated forms.The newly generated
truss bridges emerge through the iteration of this cycle to yield an array
increasingly more suitable solutions.This process is described in detail in
section 3 (see figure 5). Finally, a comparison with the Foster Bridge, a
similar, successful constructed bridge over the Huron River in Michigan, and
also the results of form exploration through physical modeling of the truss
bridges, accompany the computational study at the end.
The configuration processing of truss bridges is described through
geometrical concepts of Formex algebra [3]. Formex algebra is a
mathematical system that allows a designer to define the geometrical
formulation of forms through concepts that effect movement, propagation,
deformation and curtailment [4].
The creation of any type of spatial structure, such as space trusses,
domes, vaults, hypar shells, polyhedric and free forms, can be carried out by
using this mathematical system and its associated programming language
In the first step, constant parameters, variables and also their acceptable
intervals, described in table 1, are set. Additionally, sketches of truss
patterns, illustrated in figure 2, are provided to assist the designer choosing
the desired pattern more conveniently.
The configuration of trusses can be processed using a 3-directional
reference system similar to the global Cartesian system.Truss elements and
deck members of the bridge are defined in terms of lines, and surfaces
respectively. Figure 3 shows some parts of a simple truss bridge given in an
appropriate reference system and also the related parameters, used to
define such bridges.Trusses are expected to have curvature at the top and
324 Anahita Khodadadi and Peter von Buelow
bottom chords. Curved trusses can be created using the “pellevation”
function which starts with a non-curved truss and deforms it by pushing the
elements up or down, along the z axis, to the prescribed shape.The concept
Table 1: Geometrical parameters on
which the configuration processing of
truss bridges are based.
Figure 2:The truss patterns that are
used for the top and the bottom parts
of the bridges
325Performance Based Exploration Of Generative Design Solutions Using Formex Algebra
Parameters Sign Constant/Variable Acceptable interval/ value
Span of the bridge L Constant 48 m
Width of the bridge W Constant 8 m
Frequency of geometrical modules along the length m variable m should be an even integer.
of the bridge [4 to 20] is recommended.
Total rise of the bridge at the top part HX1 Variable [0.5 to 16] m
Total rise of the bridge at the bottom part HX2 Variable [0.5 to 16] m
The rise of the arch at the top truss X1 Variable [0.01 to 16] m
The rise of the arch at the bottom truss X2 Variable [0.01 to 16] m
The top rise in non-arched part of the truss H1 H1 = HX1 - X1 [0.49 to 16) m
The bottom rise in non-arched part of the truss H2 H2 = HX2 - X2 [0.49 to 16) m
Curvature sign of the top truss Sign1 Variable 1= positive curvature
-1 = negative curvature
0 = none
Curvature sign of the bottom truss Sign1 Variable 1= positive curvature
-1 = negative curvature
0 = none
Pattern of top truss Top Variable D1, D3, D5, D7, D9, D11, D13, D15, D17
(see figure 2)
Pattern of bottom truss Bottom Variable D2, D4, D6, D8, D10, D12, D14, D16, D18
(see figure 2)
of pellevation has been presented in a variety of ways that can be applied to
create different forms. In this study,“circular barrel pellevation” is used, see
Hofmann, 1999 [5]. The configurations generated by Formian can be
exported in DXF format and used in the next stage of study which includes
a full structural analysis and design of members.
Form exploration and traditional optimization can both be used in form finding,
however, optimization generally is carried out to search for one single best
solution and exploration seeks a set of significantly different good solutions.
Exploration can be used at the early stages of design to study a wider range
of possibilities for reasonably good or even unexpected solutions. Form
exploration usually can be accomplished efficiently using parametric tools.
Evolutionary computation methods provide means to search a range of
generated solutions in a directed way [1] [6].
Form optimization can be accomplished in different stages.Topology,
geometry and determination of member sections.This can take place
recursively or all at once.Topology is the highest level at which forms can
be explored.An instance of a topology will have a specific geometry which
can either be explored in a range under a single topology or linked to
differing topologies. Solutions can be sorted in a database which can be
inspected visually in a relevantly easy way. Specific solutions of a certain
topology and geometry are further composed of members which can be
optimized as well, but with which designers usually have less direct
interaction in terms of form finding. In this research work, form exploration
is accomplished at topology and geometry levels.
Figure 3:A part of a curved
bridge configuration and the
related parameters within a 3-
direcional reference system
326 Anahita Khodadadi and Peter von Buelow
A genetic algorithm, originally described by John Holland, is a search method
that progresses through iterating cycles to find solutions that meet certain
goals [7]. Using mechanisms like recombination and mutation, good
solutions may be found which are not anticipated by designers.The
solutions which are inherently parametric, are described in terms of a list of
variables which are analogous to genes on chromosomes.These
chromosomes are bred to form children that inherit characteristics through
the genes of their parents.
ParaGen uses a non-conventional genetic algorithm called a Non-
Destructive Dynamic Population GA (NDDP GA). It incorporates HUX as
described above in the breeding step and incorporates a database to
maintain a general pool of all solutions found. ParaGen incorporates the
following steps:
1. The problem is described in terms of parametric variables: a
2. An initial pool of solutions is generated and stored in a database.
3. A population of parents is dynamically pulled from the full solution
pool based on given criteria (the fitness function).
4. Two parents are randomly selected from the dynamic population.
5. A child is bred (HUX) from the selected parents.
6. The chromosome (parametric values) of the child is translated into
a geometric solution.
7. The performance of the solution is evaluated based various
simulation software.
8. The resulting performance values along with the parametric values
are uploaded to the database. Images are also included and linked
to the solution.
Figure 4: Half Uniform Crossover
(HUX):The characteristics of parents
1 and 2 are described in terms of
shapes.The child may inherit some
exact characteristics of parent 1 or
exactly those of parent 2 or a
combination of both through a
“breeding” of the genes.
327Performance Based Exploration Of Generative Design Solutions Using Formex Algebra
Steps 3 through 8 form an iterative cycle which continues until satisficing
solutions are found.
ParaGen is designed to run using a parallel cluster of PCs linked to a
web server through the internet.The solution database and design interface
are placed on the web server (the interface is a www site), and steps 3-5
run on that web server. Each child is downloaded to a PC linked to the
server simply by connecting to the ParaGen website.
Figure 5: Schematic of the ParaGen
cyclic method
328 Anahita Khodadadi and Peter von Buelow
In a traditional GA approach, any defective or poor performing solutions
are usually removed from the breeding population (killed off). However, in
the NDDP GA all solutions, both well performing and poorly performing
solutions are stored in the database. ParaGen simply stores all performance
values and defers any ranking of these values to the moment of breeding
(thus “dynamic” selection). By retaining data on all solutions, the designer is
able to learn from ill solutions and increase the knowledge of what would
make a good solutions [8]. Recent studies have shown the value of sub-
optimal solutions in the exploration process [9]. Furthermore, in case of any
modification of criteria, the poor performing solutions can also be re-
considered and re-used in the breeding process to form new solutions.
ParaGen guided by the multi-objective performance criteria set by the
designers, concentrates the generation of new solutions in the area of the
solution space defined by the fitness function of the GA, and the focus of
the exploration becomes more defined.Within a productive exploration,
thousands of solutions are evaluated by the program.The designer uses the
ParaGen web interface to filter and sort these solution based on any
combination of geometry or performance data. In this way, a well
performing set of solutions is defined as a manageable quantity, which is
reasonable for the designer to visually inspect and possibly make manual
selections for further breeding.The web interface provides interaction
between the designer and the form exploration system which eventually
leads to choosing the final desirable solutions.The designer’s interaction can
be also based on a totally aesthetic preference.
The incorporation of a relational database into a genetic algorithm gives
ParaGen several advantages over traditional population bases generational
methods [8].These include being able to:
Store all solutions without duplicates;
•Use multi-objective fitness functions with SQL queries;
•Create dynamic parent populations;
Change search direction instantaneously;
Explore solution space with interactive search;
Graph parameters to determine Pareto trade-off sets;
Utilize parallel hardware for efficient computation.
The above points all enhance to the ability of ParaGen to function beyond
the range of traditional search and optimization methods when dealing with
design exploration.
This section describes in more detail the 8 step process enumerated in
section 3 as the ParaGen method. In step 1. Formian was used to describe a
wide range of truss bridge types and geometries. In the parametric
formulation, 11 independent variables plus 2 additional values were used -
(Total Top Height and Total Bottom Height) which are depended on others,
but useful in formulating constraints.These 13 parametric input variables for
Formian are listed in table 1.
For this trial, Span was set to 48 m and Width set to 8 m.These 13
variables constituted the “chromosome” description of a solution which is
eventually downloaded to Formian for processing into a geometry (step 6).
This “chromosome” is bred from two parents in step 5 using a GA
crossover technique called HUX [10].The two parents are randomly
selected from a dynamic population (step 4), which is gleaned from the full
database using a SQL query (step 3).This SQL query formulates the search
objective or fitness function for the GA.
329Performance Based Exploration Of Generative Design Solutions Using Formex Algebra
Once the input variables (the “chromosome”) are passed to Formian,
Formian processes the variables to produce one instance of the parametric
bridge geometry. Formian generates a visual perspective view as well as a
DXF file which can be read by other simulation software. In this example a
finite element analysis (FEA) was carried out using STAAD.Pro (step 7).The
process makes use of scripts written in each software used plus a general
Windows interface script (AutoHotkey) to automate the process. Steps 6
and 7 are performed in parallel using a cluster of PCs.At the completion of
the analysis, the original input data (the “chromosome”) plus all of the
associated performance data collected through the simulation software, plus
any number of descriptive images and files, are all uploaded to the server
through the web site interface (step 8). On the server all numeric data is
placed in a database and tagged to the images.The ParaGen web site then
offers a graphic window into this database by displaying the images and
associated performance values.The ParaGen web interface also allows the
designer to sort and filter the displayed images and data in a variety of ways
to enhance the exploration of the solution space. Figure 6 shows the query
Figure 6: Display of solutions
comparable with the properties of
Foster Bridge.They show the variety
of possible solutions if the bridge was
to be design as the Foster Bridge.The
solutions are sorted according to their
weight from lighter to heavier and are
also represented in figures 7 and 8
where structural performance and
number of joints are compared.
330 Anahita Khodadadi and Peter von Buelow
boxes that allow the designer to display different ranges of the solutions. In
this example, the solutions are filtered in a way that provides a suitable
comparison with the Foster Bridge (table 2, figure 9).This demonstrates
how the website can display a set of solutions for any particular list of
requirements and preferences. In this example, the better final solutions
have fewer joints that contribute to better constructablity or they may be
lighter or have less deflection, indicating better structural performance.All
in all, the final decision will be made regarding the designer’s informed
intuition and preferences.
In addition to solution displays, the ParaGen website provides graphs in
which the designer can compare two specific properties and choose the
most desirable solution. Figures 7 and 8, show graphs in which solutions are
distributed regarding the maximum deflection or total weight versus
number of joints. For example the designer may look for a solution which
has the least maximum deflection and least number of joints at the same
time. Or a designer may opt for a solution with greater weight but fewer
joints which provides better constructability. It is possible to click on the
specific chosen solution and find out more detail regarding the other
geometrical and structural properties or the diagram of the modal shape.
Properties Desired value
Number of panels = 8
Max deflection 3
Total weight 400
Number of joints 85
Table 2: Filtering properties for a
series of solutions in the ParaGen
interface which compare to the Foster
Figure 7: Number of joints vs.
maximum deflection.The highlighted
solutions are depicted in figure 6
331Performance Based Exploration Of Generative Design Solutions Using Formex Algebra
The physical modeling and testing of truss bridges was carried out in the
context of a structures course at University of Michigan, School of
Architecture. Groups of students were asked to make a 1/64 scale model of
a bridge using balsa wood, and to the best of their knowledge choose a
suitable geometrical pattern to reach a high strength-to-weight ratio.Then,
Figure 8: Number of joints vs. total
weight.The highlighted solutions are
depicted in figure 6
Figure 9:The Foster Bridge in Ann
Arbor, Michigan. Build in 1876 by the
Wrought Iron Bridge Co.
332 Anahita Khodadadi and Peter von Buelow
the models were loaded until the breakage point and the structural
performance was presented in terms of held load to weight ratio.The ratio
and geometrical features were added to a data base and with a similar
fashion to computational study, the web site allows to sort and filter the
results and offers a graphic window with all the images of the models. In
figure 10 a graph presents the load capacity to weight ratio of the bridges
versus number of joints. In this graph the capacity to self-weight ratio
(structural performance) versus the number of joints (constructability) is
Figure 10:A plot of load capacity to
weight ratio vs. number of joints
within the 219 bridge models.
Figure 11:The display of
highlighted models in figure
10 chosen as probable
desirable solutions
333Performance Based Exploration Of Generative Design Solutions Using Formex Algebra
plotted.The highlighted models in this figure show the best tradeoff
combinations of these two factors and may be considered as desirable
solutions (Pareto optimal).The web site also provides a graphic window that
shows the images and associated performance values of the models.
This paper has looked at the results of two different forms of design
exploration. One which can be considered “traditional” in which solutions
were found by designers (students) using physical modeling techniques; and
a second, computational approach based on what has been described as the
“ParaGen method”.Although both studies were based on the same
geometric limits (two lane, 48 m span), the loading was approached
differently. In the physical models although a target was set at the same level
as the computational model (AASHTO HL93) in testing the load was
applied until attaining ultimate failure, which was usually much higher. So,
whereas the computational database contained solutions with a safe
capacity of HL93, the physical models tended to range at much higher loads.
Looking at the results it is not surprising to find that the form is effected by
the level of loading.
Figure 12: Graph of number of
joints vs. total weight from the
computational exploration.
334 Anahita Khodadadi and Peter von Buelow
Figure 12 shows the computational counterpart to figure 10 which used
the physical models.The lighter load level combined with the stronger
material (steel vs wood) results in solutions with much less depth. In the
computational version, the top bracing was removed at any height below 3
m so as not to interfere with traffic.Thus the lightest solutions found in the
graph shown in figure 12 are simple pony truss bridges using only the deck
for lateral bracing. Figure 13 shows solutions on the Pareto frontier of this
graph.These solutions are certainly good solutions, but the designer may
also explore the forms of nearby solutions (near optimal) by simply clicking
on the graphed dots.
Figure 13: Pareto optimal set from
the graph in figure 12.
335Performance Based Exploration Of Generative Design Solutions Using Formex Algebra
In studying the results of the physical tests a few other points can be
The solutions with best load to weight ratio were lenticular
(curved top and bottom) but tended to have more joints. Flat
chord trusses tended to have fewer joints, but lower load to
weight ratios.
The quality of construction undoubtedly played a role in the
strength, which was not present in the computational models.
Because of the longer time required per solution, the traditional
method with physical modeling was more limited in the number of
solutions which could be considered.
Using physical modeling makes the form finding process more
tangible and comprehensible. It is therefore arguably better in
developing an initial intuition, and sometimes it helps the designer
to gain a firsthand sense of structural performance.
Coupling the Formex configuration processing and evolutionary
optimization based on the ParaGen method can be applied in early stages of
design process like the conceptual design phase.The method assists the
designer exploring forms and at the same time considering multiple design
objectives. It can expand the designer’s perspective by providing a number
of suitable solutions with different topology, geometrical and structural
properties.The results are not limited to a single best solution, but generate
arrays of good solutions in dynamic response to given criteria.
The application domain of the ParaGen method can be extended to
different simulation works such as structural performance, energy efficiency,
lighting or acoustic analysis.Therefore, any kind of simulation software or
tool which allows scripting and parametric design can be used within the
iterating cycle of form exploration.This method is mainly applicable in
design projects in which multi-objective criteria are considered. However, it
can certainly also contribute in academic projects to expand the designers’
perspective and facilitate exploring the possible solutions.The Foster Bridge
and also the student models indicate that the provided solutions using the
ParaGen method are reasonable and close to what designers intuitively
expect.This verifies the applicability of the method in both professional and
academic fields.
Compared to similar computational form exploration methods, the one
that is described in this paper has the following characteristics:
Once the solution database is created, the exploration of different
sets of well performing solutions based on different sets of criteria
is very quick and certainly interactive.
Because performance data about not only a single best solution,
but in fact all solutions is provided, exploration of suboptimal
solutions is also possible.
The visual display of solutions allows the designer to interact with
the solutions and make selections with regards to visual criteria
Because all solutions are held in the SQL database, the designer
can use queries and sorts to define solution sets which respond to
a variety of multi-objective criteria.
On the other hand using Formex configuration processing in conjunction
with the ParaGen method requires certain knowledge, skills and facilities.
336 Anahita Khodadadi and Peter von Buelow
Running the form exploration cycle requires certain knowledge in
programming and working with the specific simulation software. Each
software also has its own limitations in terms of programming and
application. Furthermore, license requirements depend on the simulation
software being used. Finally, because of the time required to run the digital
simulations, hardware requirements can be significant. In this example a
cluster of 10 dual core PCs was used.
All in all, the examples of actual constructed bridges as well as the
examples of student models, verify that the pool of suitable solutions found
by the design method is reasonable. Furthermore, in cases of professional
projects where multiple objectives of both a quantitative and qualitative
nature are considered, this form exploration technique should provide
significant help.
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International Association for Shell and Spatial Structures,2012, December.53 (4).
2. Mueller, C., and Ochsendorf, J., An Integrated Computational Approach for
Creative Conceptual Structural Design, International Association of Shell and Spatial
Structures (IASS) Symposium 2013 “Beyond the Limits of Man”, Poland, 2013.
3. Nooshin, H., and Disney, P., Formex Configuration Processing I., (H. Nooshin, &
Z. S. Makowski, Eds.), International Journal of Space Structures, 2000, 15(1), pp. 1-52.
4. Nooshin, H., Disney, P. L., and Champion, O. C., Computer-Aided Processing of
Polyhedric Configurations., In J. F. Gabriel (Ed.), Beyond the Cube:The Architecture of
Space Frames and Polyhedra,New York, Chichester,Weinheim, Brisbane, Singapore,
To r onto: John Wiley & Sons, Inc, 1997, pp. 343-384.
5. S. Hofmann, I., The Concept of Pellevation for Shaping of Structural Forms,University
of Surrey, Department of Civil Engineering, Guilford: Space Structures Research
Centre, 1999.
6. Byrne, J., Fenton, M., Hemberg, E., McDermott, J., O’Neill, M., Shotton, E., & Nally,
C., Combining Structural Analysis and Multi-Objective Criteria for Evolutionary
Architectural Design, In G. Goos, J. Hartmanis, & J. van Leeuwen (Ed.), Application
of Evolutionary Optimization, Springer, 2011, pp. 204-213.
7. Holland, J. H.,Adaptation in Natural and Artificial Systems,Ann Arbor:The
University of Michigan Press, 1975.
8. von Buelow, P.,Techniques for more Productive Genetic Design: Exploration with
GAs using Non-Destructive Dynamic Populations, In K. S. Beesley (Ed.),
Proceedings of the Assoc. for Computer-Aided Design in Architecture (ACADIA),
Cambridge, Ontario, Canada, 2013, pp. 24-26.
9. Sosa, R and Gero, JS., The Creative Value of Bad Ideas – A Computational Model
of Creative Ideation , R Stouffs, P Janssen, S Roudavski and B Tuncer (eds), Open
Systems:CAADRIA 2013,National University of Singapore, 2013, pp. 853-862.
10. Syswerda, G., Uniform Crossover in Genetic Algorithms, Morgan Kaufmann, Third
International Conference of Genetic Algorithms, 1989, pp. 2-9.
337Performance Based Exploration Of Generative Design Solutions Using Formex Algebra
Anahita Khodadadi and Peter von Buelow
University of Michigan
Taubman College of Architecture and Urban Planning
2000 Bonisteel Blvd.
Ann Arbor, MI48109
... In this study, the ParaGen method is used to accomplish the form generation and exploration. ParaGen steps of form exploration can be described as follows (von Buelow 2012) (Khodadadi and von Buelow 2014): ...
... A schematic demonstration of Half Uniform Crossover (HUX). Source:Khodadadi, von Buelow 2014. ...
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Conference Paper
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A design task usually begins with a conceptual design phase where requirements and objectives are defined and synthesized into design alternatives. Although there have been successful accomplishments in developing computational methods and tools in the conceptual design of spatial structures, the initial step of problem structuring needs more consideration. A designer may spend several hours to build a parametric model and explore the suitable solutions through an iterative process of generation, evaluation, and modification of design alternatives. But the parametric model may not initially include some determining variables. The process of exploring design alternatives and choosing the suitable one/s may be more of a challenge when contradictory design objectives exist in a project. In such a case, the designer may give privilege to only one design criterion over the others, or compromise (trade-off) and choose a solution among a group of suitable ones. This study addresses the extent to which TRIZ can contribute to computational early design exploration of spatial structures. The focus of the paper is on presenting a map of the design process which allows a better problem structuring and, also, elimination of the contradiction among design objectives. The proposed model is founded on the Lawson's map of design process. The matrix of contradictions and 40 Inventive Principles of TRIZ, and a genetic algorithm in the framework of ParaGen are incorporated in this model.
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The products of generative design are ever more commonly explored and refined through evolutionary search techniques. Genetic algorithms (GAs) belong to this class of stochastic procedures, and are particularly well suited for the way designers investigate a problem. GAs search through mixing and matching different parts of a solution (represented as parametric variables) to find new solutions that out perform their predecessors. Generally the method proceeds through generations of populations in which the better solutions out survive their less desirable siblings. Inherent to this approach, however, is the fact that all but the select solutions perish. This paper discusses a non-destructive GA that uses dynamic populations drawn from a bottomless pool of solutions to find the most productive breeding pairs. In a typical GA the survival or destruction of a solution depends on a well defined fitness function. By not enforcing the destruction of less fit individuals, the possibility is held open to modify the fitness function at any time, and allow different parts of the solution space to be explored. This ability is ideal for multi-objective (more complex) problems that are not easily described by a single fitness function. Generally design is just such a problem.
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Spatial structures often embody generative systems. Both analog (physical modeling) as well as computational methods have been uses to explore the range of design possibilities. Whereas many of the favored physical modeling techniques, such as soap films or catenary nets, inherently generate forms based on certain performative properties, many of the parametric form generating computational methods derive form based solely on geometry, detached from physical performance. ParaGen has been developed as a tool to explore parametric geometry based on aspects of performance. Within the cyclic structure of a genetic algorithm, it incorporates parametric geometry generation, simulation for performance evaluation, and the ability to sort and compare a wide range of solutions based on single or multiple objectives. The results can be visually compared by teams of designers across a graphic web interface which includes the potential for human interaction in parent selection and breeding of further designs. The result is a tool which allows the exploration of the generative design space based on performance as well as visual criteria.
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This study evolves and categorises a population of conceptual designs by their ability to handle physical constraints. The design process involves a trade-off between form and function. The aesthetic considerations of the designer are constrained by physical considerations and material cost. In previous work, we developed a design grammar capable of evolving aesthetically pleasing designs through the use of an interactive evolutionary algorithm. This work implements a fitness function capable of applying engineering objectives to automatically evaluate designs and, in turn, reduce the search space that is presented to the user.
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A different crossover operator, uniform crossover, is presented. It is compared theoretically and empirically with one-point and two-point crossover and is shown to be superior in most cases.
This is the first paper in a series of papers that are intended to cover the present state of knowledge in the field of formex configuration processing. This field of knowledge has been developed during the last three decades and has now reached a level of maturity that makes it an ideal medium for configuration processing in many disciplines. In particular, it provides a rich assortment of concepts that are of great value to the engineers and architects involved in the design of space structures.
This is the second paper in a series of papers that are intended to provide a comprehensive coverage of the concepts of formex configuration processing and their applications in relation to structural configurations. In the present paper, attention is focused on the configuration processing for a number of families of space structures, namely, pyramidal forms, towers, foldable systems and diamatic domes. Also included is a section on information export as well as an Appendix on basic formex functions. The section on information export describes the manner in which the information about the details of a configuration, generated by the programming language Formian, can be exported to graphics, draughting and structural analysis packages.