An Algorithmic Optimization Model for High-Density Urban Settings○Mohammed Aqil Cheddadi *1 and Yasushi Ikeda *2*1 Ph.D. Student, Graduate School of Media & Governance, Keio University, Dipl. Arch.
*2 Professor, Graduate School of Media & Governance, Keio University, Ph.D.
Keywords: Urban form; multi-objective optimization; Pareto efficiency; generative design.

1. Introduction
The research presented in this paper discusses the use of

3. Multi-objective optimization evolutionary algorithms

algorithmic design in the generation and evaluation of urban form.

The use of evolutionary algorithms or genetic algorithms goesWith the use of Multi-objective optimization evolutionary

back to the early 1960s. It refers to algorithms that use a numberalgorithms (MOEA),

constraints andof variables, referred to as “genes” that are changed in order toobjectives are outlined for a simulation model. Based on this,find the best combinations of input variables that satisfy andesigning an urban generation model seeks to explore self-objective function and find the highest value in what is known asorganizing geometries through objective evaluation. Considering

the “fitness landscape”.

severalfunctional

the degree of design intricacy that an urban development model
implies, our study makes use of multi-objective optimization

3.1. EVOLUTIONARY SOLVERS

methodologies to interpret the intrinsic complexity of conflicting

Evolutionary solvers in algorithmic design software, such as

objectives present in a living urban system. For this, anGalapagos or WallaceiX plugins in Grasshopper (GH), areevolutionary computing solver and Pareto front evaluation

programs that apply evolutionary principles to problem-solving

methodology are used in order to evaluate and rank a myriad ofin the design process. This means that the chosen input

optimized solutions.

parameters, or “genes” will be selected as variables to bemodified by the solver in order to achieve the best possible range

2. Backgroundof solutions for the prescribed problem. The optimization data

While considering cities as complex organisms it is essential forand geometry are referred to as “phenotypes”, it is logged into

urban designers to think of design practices that can allow for

GH and specific solutions can be reinstated as 3D geometry inevolutive growth and adaptability of the urban scenery. During

Rhinoceros 3D. While Galapagos is a single-objective

the 1980s, Christopher Alexander(1) proposed an urban design

optimization solver, WallaceiX is a multi-objective solver,

methodology that is characterized by an organic, bottom-up

meaning that it can optimize a model with a more complex design

design concept that offers means to better adapt and adapt toproblem requiring differing objectives, and consequently moreliving spaces for the designers and users of the urban space alike.

calculation time.

To achieve this design concept with the use of algorithmic design,
it is necessary to establish a logical conceptual framework that

3.2. PARETO FRONT OPTIMIZATION

can define a model capable of formulating, generating andIn architecture and urbanism, a design problem is every so often

evaluating the urban form(2).

complex and require to be represented through multiple

Subsequently, this kind of framework for urban generative

objectives. These design objectives can often be conflicting indesign models, such as urban shape grammars(3), when couplednature and require evaluation criteria to be well designed. In suchwith a comprehensive, site-specific formulation model and acomplex problems, the Pareto front methodology refers to thedynamic evaluation methodology such through evolutionary

selection of solutions with the optimum distribution of resources

algorithms can offer a relative diversification and optimization inwhen there is no alternative to finding a better ranking position

results while also keeping a cohesive logic to the urban space.

for all the criteria. This means that there is no single dominating

Following this, we can notice a paradigm shift in the designsolution for all the criteria, but rather multiple solutions variably

process where the subject of the design shifts from the actual

optimized for all criteria. For a solution in the Pareto frontline,

architectural or urban space to the formulation of the system andmaking one criterion better will necessarily result in the decline

process of it.

of the others.

日本建築学会情報システム技術委員会
第 42 回情報･システム･利用･技術シンポジウム論文集， 24-27 ， 2019 年 12 月，東京
Proceedings of the 42nd Symposium on Computer Technology of Information ，Systems and Applications ， AIJ ， 24-27 ， Dec. ， 2019 ， Tokyo－ 24 －In order to attain objectives relative to the above points, a
4. Previous work

complex generative system must show enough adaptability to be

Previously(4), our research was centered on urban settlements inresilient against physical constraints and dynamic change in

Morocco, it studied the distinctiveness of urban form in urban

context. Also, it should be capable of diversifying of solutions,settings known for their self-growth and organization. The

which indicates variation in possible spatial configurations, thus

subject of our precedent study was one of the last remaining

enabling enough interactions between elements of the generative

slums in the urban perimeter of Rabat city in Morocco(5). Its

systems on lower levels.

characteristics were used for setting up the model’s site
constraints and discussed the use of an MOEA in order to5.2. RESEARCH AIM

incorporate characteristics of old Islamic urban form as a base for

The main outcome of the research is to propose a self-organizing

the optimization of spatial solutions. Two conflicting objectives

urban simulation model through algorithmic design that canwere used in order to test the model, the first one is physicalpropose an optimized abstractive urban form while also offering

accessibility whereas the second one was environmental sun

a degree of resiliency and adaptiveness to change. Using aexposure. With this, a set of algorithmic rules and functional

generative solver as a self-organizing system is expected to offerobjectives were used for an abstractive urban form-defining

the advantage of adaptability while exploring a diversity ofmodel.

possibilities in the urban form that break from the redundancy

Based on these features, the development of a parametricand lack of flexibility of modern planning.

model sought to grasp certain characteristics of spontaneous
urban tissues in old Islamic cities and incorporate them into an

5.3. PRESENTATION OF THE URBAN FORM SIMULATION

experimental social housing proposal. Using genetic algorithms,

5.2.2. Algorithm workflow

the model offers better adaptability and more diversification
while keeping a degree of preservation to the distinctive aspects
that define those settlements. The use of a genetic solver showed
itself to be a method that can simulate and offer a wide range ofobjective-based spatial that are considerably adaptive to urban
contexts.
5. The experiment5.1. THE METHODOLOGYAs presented in our previous research(4), the model initiated its
conceptual framework on the observation of self-organizing
urban tissues in the city of Fes, Morocco and how an algorithmic
design methodology can be correlated to the same organic urban
generation and growth process.
The concept behind this algorithmic model is to generate acityscape that is optimized for sun exposure and accessibility
while also being diversified enough in its spatial configuration.
Basic modules or units are combined randomly by the program
to generate a clustered geometry that forms a housing complex
that is evaluated by objective functions. The algorithm isFigure 1. Urban generative design algorithm workflow.

designed in a way as to aim for a range of population density andfor a range of hours of exposure to sunlight per day for each

The GH parametric model is made to follow a logical data flow

housing unit. The results resemble heterogeneous porous units

that loops in order to optimize form-finding (Figure 1). First, itthat allow sun rays to get through, consequently allowing ansubdivides the site’s surface into smaller plots and then generates

aesthetical diversity as well. Although the algorithm is

a 3D geometry based on a grid system that represents theprogrammed to only obey the sun exposure condition, it can also

dimensions of precast modules. These modules are duplicatedbe modified to include multiple agents that reflect otherfollowing a 3D grid and then randomly reduced to fit the target

evaluation factors if necessary.

density. Weather data in the form of sun vectors are also inputted

報告 H55－ 25 －into the algorithmic model, sun exposure has been set to a

• Random reduction seeds.

specific period. The resulting geometry is then meshed and run• Random 2D population for plot subdivision.

through a color gradient visualization algorithm that reflects the• Number of plot subdivisions

number of sun vectors that can reach each surface of the geometry.
After that, the resulting geometry is meshed and run throughAs for the fixed inputs in the algorithm, those include:• Random reduction seeds.

a color gradient visualization algorithm that reflects the number• Maximum building heights

of sun vectors that can reach each surface of the geometry. Finally,• Weather data

the algorithm is run through the evolutionary solver in order to• Population density

generate, evaluate and rank the solutions dynamically.

• A few fixed 2D population for plot subdivisions

Based on two objective fitness functions that seek tomaximize sun exposure and accessibility, the Octopus solver

5.4. MOEA EVALUATION STRATEGY

evaluates each output of 3D geometry in order to generate a betterWallaceiX, an MOEA solver is used to optimize, evaluate andfitting form. For this simulation, the solver is set to a maximum

visualize the generative algorithm results. The simulation is setof 50 generations with a population of 50.

to a maximum generation count of 50 by size of 50, making for a

Because the design logic starts from the basis of modules, sun

population of 2500. The input genes include plot counts andexposure optimization should be made by optimizing units andvariation seeds, density definition and variation seeds with a total

not the global evaluation which is the average of all units. Theof 9 sliding values. The phenotypes (Figure 2) in this case include

problem is that we could end up with a huge disparity in thethe meshes and geometry of the building cells and plot surfaces.

optimization curve, with some units having no sunlight at all

There are three conflicting fitness objectives, including

while others having maximum sunlight. The idea is to have a

optimizing density count (FO1), optimizing and equalizing thelarge median base rather than two large extremes. We could

number of hours of sun exposure (FO2) and optimizing physicalanswer this problem by setting a minimum percentage andaccessibility (FO3). The first two objectives are set to be

maximum percentage in order to limit the domain better.

maximized whereas the third one is to be minimized (i.e.

The accessibility objective function calculates the distanceproximity of blocks to streets).

between each module and the nearest street, thus evaluating theaccessibility of each module from the exterior. As for the sun

6. Findings

exposure objective function, it is set to reward the algorithm if

6.1. RESULTS

the optimization result is between the range of 30% to 60% (3 toThe solutions calculated through the MOEA solver have been run

6 hours of sun exposure). Thus, it seeks to homogenize the results

through data analysis and have shown a global trend for evolving

in order to come up with a larger median base rather than twooptimization through the flow of the simulation generations.

curves that cluster in the maximum and minimum edges.

While analyzing the solution's data (Figure 3), there is a cleartrend for further optimizing the mean value of the evaluation
scores for all three objectives. Moreover, narrowing the standard
deviation graphs through the generations, especially for FO1 andFO2, proves the system’s ability for diversification of results.
Beyond the study of general optimization trends, it is also
crucial in this methodology to select the optimum outputs for thedesign problem. This is achieved with the exploration of thePareto front results.
6.2 SELECTION
After a generation count of 50, the number of solutions
represented on the Pareto line is 20. The dynamic change andFigure 2. Phenotypes of the Pareto front distributed on a grid.

diversification of results have also shown that the solutions
represented on the Pareto front have changed throughout the5.2.2. Solver and genes
In order to set up the solver, the genes that are input include:

報告 H55generations. Visualizing the Pareto front results (Figure 2) is key
to select the appropriate solutions and comparing any physicaldiscrepancies between the results and the visual forms. Some first－ 26 －iterations of the model have indeed show inconsistencies

compared to decide of the most suitable design strategy for thisbetween data and generated form, this was caused by a poorly

self-organizing urban model.

defined evaluation factor.
Acknowledgements
This research was only possible with the valuable input and contribution
the help of Kensuke Hotta, project assistant professor of Keio University.

References
1) Alexander C.: 1987, A New theory of urban design. New York: Oxford
University Press.
2) Duarte J, Beirão J, Montenegro N, Gil J.: 2012, City Induction: A
Model for Formulating, Generating, and Evaluating Urban Designs.
Communications in Computer and Information Science. 242: Springer
Berlin Heidelberg. p. 73-98.
3) Mandić M, Tepavčević B.: 2015, Analysis of shape grammar
application as a tool for urban design. Environment and Planning B:
Planning and Design. 42(4):675-87.
4) Cheddadi MA, Hotta K, Ikeda Y.: 2019, An Urban Form-Finding
Parametric Model Based on the Study of Spontaneous Urban Tissues.
The 24th International Conference of the Association for Computer-Figure 3. Standard deviation through the generations and Meanvalue trendline for the fitness objectives scores.
7. Conclusion and prospects
Through the study of this experimental tool for self-organizing
urban form, the results have shown potential for optimizing
morphology to design constraints. It also showed that there is also

Aided Architectural Design Research in Asia (CAADRIA); Victoria
University of Wellington, Wellington, New Zealand: The Association
for Computer-Aided Architectural Design Research in Asia(CAADRIA). p. 181-90.
5) Cheddadi MA.: 2018, Towards a Digital Design Approach for
Rehousing Slums: The Case Of Douar Al Garaa in Morocco. Japan:Keio University.

still ample room to optimize and better develop the algorithmic
model itself to address various issues such as calculation times,
and poorly defined objective functions, However, to further
proof-check this algorithmic model also requires an externalevaluation factor for the solutions outside the application ofMOEA solvers.
While the model might have partially answered to themorphological and organizational factors discussed in the paper,
there is still a need to better define evaluation factors that canoptimize social aspects. Comparing and cross-checking, theoptimized model with factors external to the multi-objectiveoptimization algorithm can be methods to evaluate its reliability
and adaptiveness. Thus, it would be relevant to check thesolutions with a participative methodology that can take the inputof the target users to better define the urban program.
To conclude, in order to verify the reliability of thiscomputational design model, it is also necessary to experimentwith multi-objective optimization algorithms other thanevolutionary solvers such as the use of machine learning. Thesevarious methodologies should be separately developed and報告 H55－ 27 －