We propose a mathematical framework for developing social-choice games that are designed to mediate decision-making processes for city planning, urban area redevelopment, and architectural configuration of urban housing complexes. The proposed framework features a digital serious gaming approach for participatory design to support transparency and inclusion in the process of decision-making and ensure an equitable balance of sustainable development goals in spatial design outcomes. The mathematical process consists of a Markovian design machine for balancing the design decisions of actors, a massing configurator equipped with fuzzy logic and multi-criteria decision analysis, algebraic graph-theoretical accessibility evaluators, and automated solar-climatic evaluators using geospatial computational geometry. We demonstrate the effectiveness of the framework by implementing a multi-player online game that facilitates a participatory decision-making workshop for forming multi-functional building complexes by providing a generative configurator equipped with automated appraisal/scoring mechanisms for revealing the aggregate impact of alternatives. The EquiCity game empowers a group of decision-makers to reach a fair consensual spatial design by mathematically simulating many rounds of reasonable trade-offs between their decisions, with different levels of interest or control over various types of investments. The novelty of the framework is in its capability to encompass decision-making about the most idiosyncratic aspects of a site related to its heritage status and cultural significance to the most generic aspects such as balancing access to sunlight for the site while respecting ‘the right to sunlight’ of the neighbours of the site, ensuring coherence of the entire configuration with regards to a network of desired closeness ratings, the satisfaction of a programme of requirements, and intricately balancing individual development goals in conjunction with communal goals and environmental design codes.

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How can we assess the ergonomic comfort of a sizeable spatial configuration such as the indoor space of a complex building or an urban landscape when we design, plan, and manage the space? Is there a fundamental difference between indoor [architectural] spatial configurations and outdoor [urban] spatial configurations with respect to ergonomics? Can we have a unified approach to the computational study of spatial ergonomics? This paper addresses these fundamental questions while providing a brief taxonomic review of the scholarly literature on these matters from a mathematical point of view, including a brief introduction to the modelling-based approaches to the computational ways of studying the fundamental effects of spatial configuration on human behaviours. Furthermore, the paper proposes a computational approach for ergonomic assessment of spatial configurations that explicitly allows for combined accessibility and visibility analyses in the built environment. The gist of this approach is the conceptualisation of spatial configurations as rasterised (voxelated) 2D manifold walkable terrains whose voxels have 3D vistas, unifying the simulations and analyses of accessibility and visibility. The paper elaborates on how such a representation of space can provide for conducting various sorts of computational queries, analyses, and simulation experiments for research in spatial ergonomics. The paper concludes with a mapping of the computational modelling approaches pertinent to the study and assessment of spatial ergonomics; and marks avenues of future research on various categories of exploratory, generative, and associative models for ex-ante and ex-post assessment of ergonomic matters at spatial scales.@en

In contrast to the contemporary aesthetic account, Muqarnas are geometrically complex variations of Squinches used for structural integration of rectilinear geometries and curved geometries. Inspired by the historical functionality of Muqarnas, we present a generalized computational workflow for generating dry-fit stacking modules from two-dimensional patterns in order to construct a dome. Similar to Muqarnas these blocks are modular in nature, complex in geometry, and compression-only in their structural behavior. We demonstrate the design of such structures based on the exemplary Penrose pattern and showcase the variations & potentials of this method in comparison to conventional approaches.@en

Hospital facilities are known as functionally complex buildings. There are usually configurational problems that lead to inefficient transportation processes for patients, medical staff, and/or logistics of materials. The Quadratic Assignment Problem (QAP) is a well-known problem in the field of Operations Research from the category of the facility's location/allocation problems. However, it has rarely been utilized in architectural design practice. This paper presents a formulation of such logistics issues as a QAP for space planning processes aimed at renovation of existing hospitals, a heuristic QAP solver developed in a CAD environment, and its implementation as a computational design tool designed to be used by architects. The tool is implemented in C# for Grasshopper (GH), a plugin of Rhinoceros CAD software. This tool minimizes the internal transportation processes between interrelated facilities where each facility is assigned to a location in an existing building. In our model, the problem of assignment is relaxed in that a single facility may be allowed to be allocated within multiple voxel locations, thus alleviating the complexity of the unequal area assignment problem. The QAP formulation takes into account both the flows between facilities and distances between locations. The distance matrix is obtained from the spatial network of the building by using graph traversal techniques. The developed tool also calculates spatial geodesic distances (walkable, easiest, and/or shortest paths for pedestrians) inside the building. The QAP is solved by a heuristic optimization algorithm, called Iterated Local Search. Using one exemplary real test case, we demonstrate the potential of this method in the context of hospital layout design/re-design tasks in 3D. Finally, we discuss the results and possible further developments concerning a generic computational space planning framework.@en

We present a modular generative design framework for design processes in thebuilt environment that provides for the unification of participatory design andoptimization to achieve mass-customization and evidence-based design. Thepaper articulates this framework mathematically as three meta proceduresframing the typical design problems as multi-dimensional, multi-criteria,multi-actor, and multi-value decision-making problems: 1) space-planning, 2)configuring, and 3) shaping; structured as to the abstraction hierarchy of thechain of decisions in design processes. These formulations allow for applyingvarious problem-solving approaches ranging from mathematical derivation &artificial intelligence to gamified play & score mechanisms and grammaticalexploration. The paper presents a general schema of the framework; elaborateson the mathematical formulation of its meta procedures; presents a spectrum ofapproaches for navigating solution spaces; discusses the specifics of spatialsimulations for ex-ante evaluation of design alternatives. The ultimatecontribution of this paper is laying the foundation of comprehensive SpatialDecision Support Systems (SDSS) for built environment design processes. (3) (PDF) GoDesign: A modular generative design framework for mass-customization and optimization in architectural design. Available from: https://www.researchgate.net/publication/353931074_GoDesign_A_modular_generative_design_framework_for_mass-customization_and_optimization_in_architectural_design [accessed Aug 27 2021].@en

Formalization of knowledge within a scientific paradigm unifies sporadic efforts through converging glossary and notation, thus enabling scientists to identify knowledge gaps and discrepancies easier. Formalization reveals potential bridges to various domain sciences and facilitates the utilization of methods that have proven effective in scientific problem-solving. In the case of Architecture and Built Environment, there is a long history of scattered efforts for identifying and formalizing design problems and design methodologies, but the big picture is yet missing. In this short piece, we name and frame some of these efforts to identify their parallels with Mathematics, Computer Science, and Systems Theory, as well as to illustrate new opportunities that methodical design unlocks.@en

This article explains the motivation and the theoretical underpinnings of a master's level course on generative design for earth and masonry architecture.@en

The paper reports the formulation, the design, and the results of a serious game developed for structuring negotiations concerning the redevelopment of a university campus with various stakeholders. The main aim of this research was to formulate the redevelopment planning problem as an abstract and discrete decision-making problem involving multiple actions, multiple actors with preconceived gains and losses with respect to the comprising actions, and decisions as combinations of actions. Using fictitious and yet realistic scenarios and stakeholders as simulation, the results evidence how different levels of democratic participation and different modes of moderation can affect reaching a consensus and present in a mathematical characterisation of a consensus as a state of equilibrium. The small set of actions and actors enabled a chance to compute a theoretically optimal state of consensus, where the efficiency and the effectiveness of different modes of moderation and participatory rights could be observed and analysed.

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Building optimal free-form compression-only adobe shells requires sophisticated molds, scaffolding, critical supervision and an expert labor force as pointed out in [1]; this is because the optimality of a compu-tationally designed shell depends on achieving the right geometric shape in construction. The objective of our research is to find ways to simplify the construction of compression-only adobe shell structures to be built as shelters. This paper presents a computational work-flow for approximating the shape of an adobe shell structure, with space filling polyhedral bricks[18], through a topological polyhedralization process. The work flow is devised to simplify the construction of an adobe structure with the prospect of participatory construction of adobe shelters. The process takes in a dynamically-relaxed optimized shape for an adobe thin shell structure as a manifold surface, approximates it with space-filling polyhedrons as a volumetric representation; forms a finite element mesh as the lattice dual to the polyhedrons; and analyzes the structures to validate their stability. We argue that the proposed approach simplifies the construction process for untrained labor forces and thus makes it possible to quickly build adobe shell structures as temporary shelters. A possible application of this method could be the participatory construction of adobe shelters for displaced communities with in-situ soil as an alternative to long-term stay in tents.@en