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Exploration of Urban Street Patterns – Multi-Criteria Evolutionary Optimisation Using Axial Line Analysis

Authors:
EXPLORATION OF URBAN STREET PATTERNS
Multi-criteria evolutionary optimisation using axial line analysis
CHEE Zong Jie and Patrick JANSSEN
National University of Singapore
a0048719@nus.edu.sg, akiphtj@nus.edu.sg
Abstract. In urban design, researchers have developed techniques to auto-
mate both the generation and evaluation of urban street patterns. In most
cases, these approaches are investigated in isolation from one another.
Recently, a number of researchers have attempted to couple these
approaches, in order to enable larger numbers of street patterns to be gener-
ated and evaluated in an iterative loop. However, to date, the possibility of
fully automating the generative-evaluative loop using optimisation algo-
rithms has not been explored. This research proposes an explorative design
method in which urban street patterns can be optimised for multiple con-
flicting performance criteria. The optimisation process uses evolutionary
algorithms to evolve populations of design variants by iteratively applying
three key procedures: development, evaluation, and feedback. For develop-
ment, a generative technique is proposed for constructing street patterns. For
evaluation, various performance measures are used, including in particular
Space Syntax based Axial Line analysis. For feedback, a Pareto-ranking
algorithm is used that ranks street patterns according to multiple criteria.
The proposed method is demonstrated using an abstract scenario in which
orthogonal street patterns are evolved for a small urban area.
Keywords. Axial line analysis; generative modelling; evolutionary algo-
rithms; decision chain encoding; urban street patterns.
1. Introduction
The idea of automating certain parts of the urban design process has been around
since 1960s. Since then, researchers have developed a wide variety of techniques
to automate both the generation and evaluation of urban design. This research will
focus in particular on the generation and evaluation of street patterns.
For generating street patterns, researchers have investigated a number of gen-
erative techniques. Duarte et al. (2006) described the generative modelling of the
R. Stouffs, P. Janssen, S. Roudavski, B. Tunçer (eds.), Open Systems: Proceedings of the 18th International
Conference on Computer-Aided Architectural Design Research in Asia (CAADRIA 2013), 695–704. © 2013,
The Association for Computer-Aided Architectural Design Research in Asia (CAADRIA), Hong Kong, and
Center for Advanced Studies in Architecture (CASA), Department of Architecture-NUS, Singapore.
695
6B-198.qxd 4/28/2013 4:47 AM Page 695
Medina of Marrakech by combining a top-down and bottom-up hybrid models.
Braach and Fritz (2010) used Voronoi partitioning in the generative modelling of
street patterns. Both Parish and Muller (2009) and Chen et al. (2008) generated
urban street patterns using Lidenmayer systems (L-systems).
For evaluating street patterns, researchers in the field of Space Syntax have
since the 1970s been developing and refining various tools and theories (Hillier
and Hanson, 1984; Hillier, 1996; Hanson 1998). Space Syntax methods translate
overlapping convex spaces into a series of graph structures that can be analysed
and interpreted in terms of their two-dimensional spatial characteristics. One of
the key methods is the Axial Line method, which creates such a graph by generat-
ing a set of overlapping sight lines, referred to as Axial Lines.
For Axial Line methods, the main concepts are that of depth and integration.
Depth described the minimum number of Axial Lines that need to be traversed in
order to get from one space to another space. Integration describes the minimum
depth between one space and all other spaces. Integration can also be calculated
for a certain radius n, in which case it measures the total number of spaces that can
be reached from a particular space by traversing nAxial Lines. Integration at a low
radius (for example n = 3) is referred to a local integration, while integration
without specifying any radius is referred to as a global integration.
Depth and integration are measures associated with particular spaces within a
spatial configuration. However, these measures can also be used as a basis for cal-
culating some more general measures that describe characteristic of the overall
spatial configuration. Two such measures are the mean depth and the R2correla-
tion. The mean depth measures the mean of all the depths from every space to
every other space in the spatial configuration. A low mean depth may be desirable,
as it is seen to represent better integrated spatial configurations. The R2correla-
tion is slightly more complex. To calculate R2, both local and global integration
values are calculated for every space in the spatial configuration, and a scatter plot
is generated of local versus global integration. The R2correlation is then calcu-
lated as the statistical correlation between these two sets of values, also referred to
as the coefficient of determination. A high R2correlation may be desirable, as it is
seen to represent the intelligibility of the spatial configuration (Hillier, 2002).
Research using Axial Line methods focuses mostly on the analysis of existing
street patterns rather than the synthesis of new street patterns. A number of
researchers have been exploring how these techniques can be used as a way of
evaluating alternative urban design proposals. Hillier et al. (2008) used Axial Line
analysis to evaluate design proposals in the Jeddah Urban Regeneration Master
plan. Existing urban fabric and the old local plan were examined in order to
observe the connectedness of neighbouring towns to the historic core. The pro-
posed design option was then simulated to predict its effectiveness. Stonor (2009)
696 CHEE Z. J. AND P. JANSSEN
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showed similar evaluation of the design proposal for Trafalgar Square, London.
Both cases used Axial Line analysis in an “analyse, observe, predict” framework.
Recently, a number of researchers have combined generative urban modelling
and Axial Line analysis in an iterative manner, where each iteration is applied
manually. For example, Al-Sayed (2012) used Axial Line analysis to evaluate dif-
ferent iterations for hypothetical urban street patterns. Generative modelling
techniques were used to create a variety of street patterns, which were subse-
quently evaluated for their R2correlation. Certain street patterns were then
selected and further analysed. In another experiment, Canuto (2012) created dif-
ferent iterations of an abstracted urban grid followed by evaluation using Axial
Line measures, as well as a set of other measures known as urbanity ratios. Both
experiments showed the possibility of iteratively combining the generation and
evaluation of urban street patterns to optimise a number of design variants.
Despite significant research in the areas of urban street pattern generation and
evaluation, no research has explored the automated optimisation of street patterns
using optimisation algorithms. This paper proposes such a method for the automated
evolution of street patterns. The proposed method is demonstrated using an abstract
scenario in which orthogonal street patterns are evolved for a small urban area.
2. Demonstration
The proposed method combines three techniques: the generative modelling of
street patterns (generation), Axial Line analysis of street patterns (evaluation), and
optimisation of street patterns using Evolutionary Algorithms.
Evolutionary design (Frazer, 1995; Bentley, 1999; Caldas, 2001; Bentley, and
Corne, 2002; Janssen, 2004) is an approach that evolves populations of design
variants through the iterative application of a set of computational procedures. The
developmental procedure generates design variants, one or more evaluation pro-
cedures assess the performance of design variants, and the feedback procedure
drives the evolutionary process by applying selective pressure to the population.
The use of Evolutionary Algorithms allow large numbers of alternative design
variants to be considered in a fully automated way, thereby allowing optimised
street patterns to be generated. The Evolutionary Algorithms here act as a way of
“closing the loop” between generative modelling of street patterns and Axial Line
analysis of street patterns.
The evolutionary process is executed using Dexen, a distributed execution
environment for population based algorithms (Janssen et al., 2011). This system is
coupled to a procedural modelling environment called SideFX Houdini, which is
used for creating both the developmental and evaluation procedures (Janssen and
Chen, 2011). The feedback procedure is generated automatically by Dexen, and
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uses a Pareto-ranking algorithm that ranks street patterns according to multiple
criteria. The results of the evolutionary process are plotted as a scatter plot using
a data analytics package called Tableau.
2.1. DEVELOPMENTAL PROCEDURE
For the developmental procedure, a generative technique called decision chain
encoding is used to generate street patterns (Janssen and Kaushik, 2013). The
decision chain encoding technique structures the street pattern generation process
as a sequential chain of decision points, where each decision consists of a ‘design
move’ that inserts an urban block into the urban grid. Each time a block needs to
be inserted, a gene will be used to select a move from a list of possible valid
moves.
The starting condition for the developmental procedure consists of a library of
urban blocks together with an empty urban area with a boundary condition at the
periphery. The task is then to fill the empty urban area with some combination of
blocks from the urban block library. The way that the blocks are inserted and ori-
entated results in a variety of urban streets and squares with varying spatial
qualities. Figure 1 shows the starting condition on the left and six steps in the deci-
sion chain process on the right.
The decision chain process continues to add blocks until either no more blocks
can be inserted or until a certain maximum is reached. In this case, the maximum
698 CHEE Z. J. AND P. JANSSEN
Figure 1. Sequence of generative street modelling.
6B-198.qxd 4/28/2013 4:47 AM Page 698
was set to be 100 blocks (which was in fact never reached). Since 100 blocks
require 100 decision points, the genotype is also set to be 100 genes long. Genes
are real values in the range {0, 1}, which are used to select valid moves by map-
ping to an integer range {1, n}, where n is the number of valid moves for that
particular decision point.
2.2. EVALUATION PROCEDURES
Three separate evaluation procedures are defined which are used to evaluate each
street pattern. The three procedures are used to calculate three performance crite-
ria: the R2correlation, the average line length, and the total footprint. The R2
correlation has already been described above and in this case measures the corre-
lation between local integration with a radius of 3 and global integration. The
average line length measures the average length of all Axial Lines. Lastly, the total
building footprint measures the total footprint of all urban blocks.
The R2correlation is seen as measuring intelligibility, and therefore the opti-
misation system is set to maximise this performance criteria. One way of
achieving this is by generating a regular urban grid with long straight streets. For
such a grid, the average line length will therefore be very high. However, research
by Hillier (2002) has suggested that historical urban street patterns typically have
a few long Axial Lines combined with many short Axial Lines. For the optimisa-
tion algorithm, we therefore set the average line length to be minimised. The first
two performance criteria are therefore defined to be in conflict with one another,
as street patterns cannot have both a high R2correlation and a low average line
length. Such a conflict is seen as being desirable, as it is likely to result in a range
of performance trade-offs. Lastly, in order to encourage the optimisation system to
generate high density street patterns, the third performance criteria is added for the
maximisation of building footprint.
This research is not suggesting that the selected performance criteria are suffi-
cient as a basis for evaluating the quality of a particular street pattern. Performance
criteria will vary on a case-by-case basis and may include a wide range of factors.
Rather than being used as a tool for global optimisation, this research imagines
such tools to be used in a more exploratory mode. The solutions that are evolved
should therefore not be seen as being the best answers, but instead as a provoca-
tion for deeper analysis and exploration.
In order to calculate the R2correlation and the average line length, Axial Lines
need to be generated and analysed. A Space Syntax software tool exists that can
be used for this, called Depthmap. However, the tool cannot be easily automated
by another program and as a result it was not used in this case. Instead, a custom
plugin was created for Houdini. Within Houdini, two separate algorithms were
EXPLORATION OF URBAN STREET PATTERNS 699
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implemented: one for generating the Axial Lines, and another for analysing the
Axial Lines. The Axial Line generation algorithm is implemented using built-in
ray functions within Houdini following the method described in the Space Syntax
literature (Turner et al., 2004; Ostwald, 2011). The Axial Line analysis algorithm
first translates the Axial Lines into a graph representation and then calculates inte-
gration values. The graph calculations are performed using a general-purpose
graph library called NetworkX.
In order to validate the results, a number of tests were carried out, comparing
the generation and analysis of Axial Lines in Houdini to the results obtained from
Depthmap. Although the Houdini technique was found to generate slightly fewer
Axial Lines than Depthmap, there was only a 1.4% difference in mean depth and
0.2–5% difference in integration values.
Houdini was therefore used to define all three evaluation procedures: R2cor-
relation, average line length, and total footprint. The first two required Axial Line
techniques while the last one consists of a simple area calculation.
3. Experiment Outcome
The evolutionary system was run with a population of 100 street patterns, for a
total of 10,000 births. Street patterns with very low total footprints were first fil-
tered out, resulting in 5500 remaining street patterns. A scatter-plot was created
where each point represents a different street pattern. For the scatter plot, the R2
correlation was plotted against average line length. The scatter plot is shown at
the centre of Figure 3. Dark circles represent street patterns with larger total foot-
prints, while light circles represent street patterns with smaller total footprints.
In the scatter plot, the most desirable area is the top-left corner, where the aver-
age line length is minimised and the R2correlation is maximised. The closer a
point is to this area, the higher its rank. Conversely, the further away they are from
this area, the lower their rank.
700 CHEE Z. J. AND P. JANSSEN
Figure 2. Axial Line generation in Houdini.
6B-198.qxd 4/28/2013 4:47 AM Page 700
Various street patterns were selected to be examined in more detail. Figure 3, the
three street patterns at the top have a high rank while the three street patterns at the
bottom have a low rank. At first sight, it is hard to tell why one set would be more
highly ranked than another set. However, certain key characteristics can be identified.
In general, the high rank street patterns have grid-like configurations where the
urban blocks are evenly distributed and densely packed, thereby resulting in a high
total footprint. They typically include a number of long, straight streets. These
make the journey from one end of the street pattern to the other end easier as more
EXPLORATION OF URBAN STREET PATTERNS 701
Figure 3. Scatter plot of 5500 individuals.
6B-198.qxd 4/28/2013 4:47 AM Page 701
direct routes can be used. The locations of open spaces are more well defined and
easily accessible (Figure 4a).
In contrast, the low rank street patterns exhibit a more random configuration.
The urban blocks are tightly packed in some areas and loosely distributed in other
areas with some large open spaces in-between, thereby resulting in a low total foot-
print. This makes the journey from one end to another more complex (Figure 4b).
Overall, the highly ranked street patterns seem to have a more legible spatial
pattern as compared to the lower ranked street patterns. This represents one phase
in the evolutionary exploration process. Subsequent phases would tweak the gen-
erative technique in order to generate street patterns that differ more significantly
with regards to R2correlation and average line length. In particular, increasing the
block library to include a wider variety of urban blocks may result in more tightly
interlocking patterns.
702 CHEE Z. J. AND P. JANSSEN
Figure 4. (a) Individual 2776 (b) Individual 3551.
6B-198.qxd 4/28/2013 4:47 AM Page 702
4. Conclusions
This paper has demonstrated how evolutionary algorithms can be used to link gen-
erative modelling techniques to Axial Line evaluation techniques. This suggests
an alternative explorative design method for the early phases of urban design,
when overall urban patterns and textures need to be developed. Future research
will further develop this design method taking into account a wider range of per-
formance criteria, including in particular environmental criteria such as solar
radiation and daylight.
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This paper addresses the problem of interactively modeling large street networks. We introduce an intuitive and flexible modeling framework in which a user can create a street network from scratch or modify an existing street network. This is achieved through designing an underlying tensor field and editing the graph representing the street network. The framework is intuitive because it uses tensor fields to guide the generation of a street network. The framework is flexible because it allows the user to combine various global and local modeling operations such as brush strokes, smoothing, constraints, noise and rotation fields. Our results will show street networks and three-dimensional urban geometry of high visual quality.
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"October 2004" Thesis (Ph.D.)--The Hong Kong Polytechnic University, 2005. Includes bibliographical references.
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The fewest-line axial map, often simply referred to as the 'axial map', is one of the primary tools of space syntax. Its natural language definition has allowed researchers to draw consistent maps that present a concise description of architectural space; it has been established that graph measures obtained from the map are useful for the analysis of pedestrian movement patterns and activities related to such movement: for example, the location of services or of crime. However, the definition has proved difficult to translate into formal language by mathematicians and algorithmic implementers alike. This has meant that space syntax has been criticised for a lack of rigour in the definition of one of its fundamental representations. Here we clarify the original definition of the fewest-line axial map and show that it can be implemented algorithmically. We show that the original definition leads to maps similar to those currently drawn by hand, and we demonstrate that the differences between the two may be accounted for in terms of the detail of the algorithm used. We propose that the analytical power of the axial map in empirical studies derives from the efficient representation of key properties of the spatial configuration that it captures.
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This dissertation dwells in the interstitial spaces between the fields of architecture, environmental design and computation. It introduces a Generative Design System that draws on evolutionary concepts to incorporate adaptation paradigms into the architectural design process. The initial aim of the project focused on helping architects improving the environmental performance of buildings, but the final conclusions of the thesis transcend this realm to question the process of incorporating computational generative systems in the broader context of architectural design. The Generative System [GS] uses a Genetic Algorithm as the search and optimization engine. The evaluation of solutions in terms of environmental performance is done using DOE2.1E. The GS is first tested within a restricted domain, where the optimal solution is previously known, to allow for the evaluation of the system's performance in locating high quality solutions. Results are very satisfactory and provide confidence to extend the GS to complex building layouts. Comparative studies using other heuristic search procedures like Simulated Annealing are also performed. The GS is then applied to an existing building by Alvaro Siza, to study the system's behavior in a complex architectural domain, and to assess its capability for encoding language constraints, so that solutions generated may be within certain design intentions. An extension to multicriteria problems is presented, using a Pareto-based method.
Multi-source synthesis: Intelligent Cities -A Climate for Change, Architectural Design
  • G Battle
  • C Mccarthy
Battle, G., and McCarthy, C.: 1994, Multi-source synthesis: Intelligent Cities -A Climate for Change, Architectural Design, 66(9/10).
The Organisation of Plots
  • London Academic
  • M Braach
  • O Friz
Bentley, P. J. and Corne, D. W. (eds.): 2002, Creative Evolutionary Systems, Academic, London. Braach, M. and Friz, O.: 2010, The Organisation of Plots, in Hovestadt, L. (ed.), Beyond the Grid -Architecture and Information Technology, Birkhauser, Berlin, 24-31.