Institute of Architectural Algorithms & Applications 建筑运算与应用研究所 School of Architecture, Southeast University, Nanjing

Youth Apartment | Vertical Community

Computational design of Residential Architecture – Youth Apartment | Vertical Community
School of Architecture, Southeast University, 2021
Design Tools: Processing 2 + Gurobi 9.1

The pursuit of economy, regulatory overkill, and the preconceived workflow of architects are responsible for the stereotypical massive housing in China; Michael Wolf’s celebrated photograph series, Architecture of Density, reflected the living conditions in metropolitan areas around the Western Pacific Region. The 8-week design and research program Computational Design of Residential Architecture (CDRA) focused on the design of a high-rise youth apartment in Nanjing—a historical city with a population of nine million. The CDRA program centered on the development of computational design methods for the challenge of massive apartment design.

Contrary to the contemporary cliché that digital tools make the design process easier, our approach used computation to challenge architects’ ways of thinking. Architects are proud of creating self-defined geometric operations, such as J.N.L. Durand’s generative operations, Peter Eisenmann’s constructive diagrams, or BIG’s sexy operations of 3D volumes, and they unconsciously presume that their process will result in desirable compositions. But running their operations on a computer may not produce the expected results. The outcomes of virtual experiments (done by running computer programs) help designers to re-think and re-formulate their design methods. Such a cycle between designer and machine will be essential in the architectural design process in the coming AI era.

The CDRA program for the design of youth apartments sought a balance between spatial compactness for economy and the provision of (semi-) public facilities that improve living quality and allow neighborhoods to emerge. One strategy was to break the functional/spatial ontology of apartment buildings. For instance, the study as a private room of a family unit might be transformed into a book and coffee bar as part of the entire building. The fitness center, usually part of an urban facility, might be redesigned as multiple places in an apartment building. By remapping the complex individual needs to various spatial elements, the CDRA program pictured the possible patterns of the urban lives of young people and envisaged new systems for their living quarters.
processingThe coding tool Processing, originally developed by Ben Fry and Casey Reas at MIT, was used to draw 2D and 3D graphics and to implement algorithms. Parametric modeling, cellular automata, and shape grammar were tested in the CDRA program. Running the optimizer Gurobi in Processing solves layout problems in apartment building. Gurobi currently stands as the fastest commercial solver for mathematical optimization. Although it’s widely used in industry, science, and engineering, it rarely enters the central workflow of architectural design, and the combination of Processing and Gurobi is unprecedent in an architectural design studio. Our team used Gurobi to solve Integer Programs (IP) using binary variables to represent spatial layouts in a regular grid. It is interesting that the algebraic thinking involved in such IP formulation can be both elementary and complex, as the following example explains.

Suppose we are going to fill a grid with L shapes (3 cells) and T shapes (4 cells). Let the binary variable Xi (can be 0 or 1) represent whether the i-th cell of the grid is occupied by an L shape; likewise, let Yi represent the same for the presence of the T shape. Zi denotes whether the i-th cell is occupied or void. So, the equation

Xi + Yi = Zi

implies two facts. First, the cell’s occupation is determined by whether any L or T shapes cover it. For example, 1 + 0 = 1 indicates that an L shape covers the cell (Xi = 1), and thus the cell is full (Zi = 1). Second, the cell cannot be occupied by both shapes simultaneously; otherwise, 1 + 1 = 2, where Zi = 2 is impossible for the binary variable Zi. The second implication is tricky since it implicitly imposes a constraint on spatial composition. Such algebra, usually alien to architects, can be very effective in formulating architects’ spatial operations. Thus, computational design is grounded on algebraic (one may say ‘symbolic’, but its meaning in architecture is overloaded) reasoning instead of computer programming. It is much like how Ada Lovelace was able to collaborate on computer programs in the nineteenth century without a computer.tower60ps


经济高效而不失品质与优雅是当下青年对居住环境的追求。课程介绍当今居住建筑体系、空间与功能要素、社会经济需求;引导学生思考住宅的物质构成与日常需求之间的关联,探索当下居住问题的解决途径。本次居住建筑设计课题通过数理逻辑来定义和解析当代青年公寓中的核心问题,并把个性化的设计策略转化为计算机算法(algorithm),最终通过编写代码让程序生成一系列优良的方案。运算化设计(computational design)通过算法来生成传统方法难以企及的个性化方案。本课程探索运算化设计方法在居住建筑设计中的新应用,通过数理方法来剖析居住问题并追求设计创新。

本设计聚焦单栋高层青年公寓设计,探讨当下年轻人的生活工作模式,营造空间集约的垂直社区。基地为南京市江北新区国际健康城人才公寓3号楼地块,面积2163 m2。公寓不高于100米,建筑面积22000-27000m2,其中公寓总面积不低于16000m2。本设计强调青年公寓的居住品质、性价比,追求都市环境中垂直居住模式的创新。

课程采用Processing编程工具与Gurobi优化器。教学过程中介绍了Truchet拼贴、细胞自动机、整数规划(Integer programming)、形式语法的基本原理与编程。中期答辩时每位同学单独用Processing生成各自的初步方案,之后以小组的方式继续发展方案,最终共有5组设计作品: CUBE+、拼多多、瓣·宅 、 生长·聚居、ACROSS THE LAYER。



CUBE+ revisits the wisdom of Japanese Metabolism architecture from the 1960–70s. Compared with Kurokawa’s iconic Capsule Tower, which is composed of uniform capsule units, CUBE+ employs the configurable cube (typically 12×12×11.2m) consisting of dozens of apartment units. Each cube presents a community of common interest, while the types of residential modules within the cube vary according to the demands. Various apartment units, including duplex apartments across two floors, can be fit into a cube by running IP via Gurobi. The gaps between the cubes become public spaces (e.g., restaurants, bars, gyms) or green spaces for nearby communities.



拼多多  Pin House


The subgroups within the CDRA program proposed five systems of youth apartments. The first proposal, Pin House, was inspired by the controversial but fast-growing e-commerce platform PinDuoDuo. The idea is that a group of people can gain economic and social advantages more effectively than unorganized individuals. Thus, multi-level communities center on public–private spaces within the high-rise building, large public zones exist for the entire building, middle-sized semi-public spaces are allotted for supporting nearby neighborhoods, and small units with private balconies offer living space for individuals. The irregular arrangement of these spaces allows for the self-organizing of social communities rather than imposing fixed grouping. Pin House uses IP to explore apartment compositions on three levels. First, all (or the best portion of) possible layouts for a certain unit can be created from any given program specifying the sizes of rooms and the adjacency between them. For example, IP found 176 layouts for a program of single apartment. Second, IP organized various apartment units (constructed in the first step) on each floor to optimize orientations, accessibility, and compactness. Finally, the entire building was automatically shaped by a set of global parameters, such as the geometry of core tube(s) and the prescribed percentages of different units.




瓣·宅  Floral House











该方案将公共空间打造成富有活力的垂直街道,形成一条螺旋上升公共廊道,其中设有放映室、开放客厅、健身房、便利店、阅读空间等等。公共空间在局部贯穿楼层,楼面形成折板,提高空间的趣味性和利用效率。ACROSS THE LAYER公寓内的户型十分丰富性,可以适应不同人生阶段和经济水平的住户需求。除单人间和家庭间外,还安排了舒适的家庭跃层和层高较低的合租户型。将设计好的户型用整数规划(由Gurobi实现)满铺在建筑中,限制条件为:户型不出界、不重叠、每户均接到走廊、每种户型在整个建筑中至少出现一定次数。




Another three projects of the CDRA program are CROSS THE LAYER, which includes a spiral ‘street’ through the entirety of a skyscraper; Floral House with a curved facade; and Generative Community, which has a complex fabric of apartments, outdoor spaces, and public spaces. Each project attempts to break the preconceived design rules for high-rise apartment buildings. Programming (in Processing) enables designers to go back and forth between architectural conceptualization and mathematical modeling.

What’s the role of computing in architectural design? This is a recurring question rising not only in architecture but also in other fields like AI. I bet that computer scientists like Paul Merrell at Standard have significantly different opinions than those of architects. Our computer programs were written to 1) implement design ideas and create a vast number of diverse solutions and 2) echo designers’ reasoning so that they become self-conscious about their own design thinking. So, in our opinion, computation acts as both a pragmatic tool and an externalized faculty of thinking.

The cases shown above indicate that computational method and architectural conceptualization can be deeply entwined; however, the two are grounded in their own realms. Computing (and the algebraic thinking behind it) belongs first to the realm of natural science, though it can play an essential role in generating architectural design. Developing design concepts is an architect’s job, and—at least so far—is unable to be done by machines. But architects can use computation to see their design ideas more clearly. That is to say that we can teach ourselves through machines, leading to ever-evolving ways of looking at problem solving, reasoning, and design.


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