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2016 | Book

Discrete Optimization in Architecture

Architectural & Urban Layout


About this book

This book presents three projects that demonstrate the fundamental problems of architectural design and urban composition – the layout design, evaluation and optimization. Part I describes the functional layout design of a residential building, and an evaluation of the quality of a town square (plaza).

The algorithm for the functional layout design is based on backtracking using a constraint satisfaction approach combined with coarse grid discretization. The algorithm for the town square evaluation is based on geometrical properties derived directly from its plan.

Part II introduces a crowd-simulation application for the analysis of escape routes on floor plans, and optimization of a floor plan for smooth crowd flow. The algorithms presented employ agent-based modeling and cellular automata.

Table of Contents


Layout Optimization & Evaluation

Chapter 1. Architectural Functional Layout Optimization in a Coarse Grid
This chapter describes the method for creating optimal architectural functional layouts. The methodology is based on coarse grid and three general steps: i. generation of layouts satisfying requirements given by the designer, ii. selection of the “proper” layouts, and iii. ranking of the “proper” layouts according to multiple objectives. Presented methodology can be used in architectural practice, urban or graphic design, and wherever the allocation of interrelated shapes is to be optimized. For clarity, simplified examples of a single-story two-apartment residential building are shown. Despite this simplicity, presented layouts resemble realistic functional solutions. One example of a practical-size floor-plan of three apartments of total twenty rooms is generated. The material is organized as follows: the concept of space discretization with coarse grid is introduced; the backtrack (depth-first) search algorithm is implemented for the generation of a number “potentially good” layouts. A machine learning method (feed-forward artificial neural network) is implemented for the classification of “proper” and “improper” layouts based on the “corridor criterion”. Simple examples of dynamic multi-criterial ranking of “proper” layouts are demonstrated.
Machi Zawidzki
Chapter 2. Evaluation of the Quality of an Urban Square
As shown in the previous chapter, the evaluation of a building layout is difficult. The same applies to an urban layout. However, the basic evaluation of the quality of a plaza (P), that is the basic element of urban composition, is relatively straightforward. This chapter presents a method for an Automated Geometrical Evaluation (AGE) of a P. Firstly, nineteen plazas from various countries have been evaluated by twenty respondents in so called Human Subjective Evaluation (HSE). Secondly, a preliminary investigation of HSE including the identification of categories which are redundant is demonstrated. Thirdly, three normalized properties derived directly from a plan of P are introduced: smallness (S), enclosure (E), and regularity (R). Finally, the evaluation method of P based on these properties is discussed. AGE based on S, E, and R (\(NP_{SER}\)) shows good agreement with HSE. The quality rating based on \(NP_{SER}\) of P, namely: fair, good, and excellent is presented. Some outlying cases are shortly discussed.
Machi Zawidzki

Crowd Simulation

Chapter 3. Crowd-Z
This chapter presents Crowd-Z (CZ): a user-friendly framework for crowd simulations (CS) in any floor-plans. The crowd dynamics component of CZ is a straightforward agent-based model. Such CSs can be carried out at every stage of architectural or urban design process: from early sketches to the final blue-prints. Most importantly, CZ accepts the initial input in practically any form, e.g.: pre-processed drawings produced by Computer-Aided Design (CAD) software, digital images, free-hand drawings, etc. Selected methods of acquisition of the CS environment are demonstrated and illustrative with practical examples. Finally CZ is evaluated against commercially available software and with some “classic” CS experiments.
Machi Zawidzki
Chapter 4. The Influence of Various Factors on Crowd Behavior
This chapter presents a number of experiments performed in Crowd-Z (CZ). The objective is to investigate the influence of various factors on the collective behavior of the crowd. These factors include: the type of metric & neighborhood, agents’ perkiness and type of tessellation. The robustness of models based on different tessellations are examined by grid rotation. Three platonic tessellations, that is: hexagonal, triangular and square are compared. Two experiments based on the literature are presented:
The egress of 200 agents from a square room (SRE) in grid rotated by: \(0^{\circ }\), \(15^{\circ }\), \(30^{\circ }\), and \(45^{\circ }\).
The one-directional flow (ODF) in grid rotated by: \(15^{\circ }\), \(18.434\ldots ^{\circ }\), \(26.565\ldots ^{\circ }\), \(30^{\circ }\), and \(45^{\circ }\).
The basic CZ setup is used for the experiments: the crowds are homogeneous, and the agents’ walking speed is unitary and constant. The qualitative analysis is based in heat maps. The quantitative analysis is based on density-flow rate and evacuation time diagrams.
Machi Zawidzki
Chapter 5. Application of Crowd Simulation for a Layout Improvement
This chapter presents a creative experiment, where a series of simulations in Crowd-Z have been used for improvement of an architectural floor-plan. As an example one floor of a retail store has been used for this experiment. A simple scenario of crowd passing from the entrance towards the exit has been implemented. The objective is to possibly uniform the usage of space, in other words to reduce the number of unvisited areas and congestion in other places. Two types of layout elements are introduced: fixed and modifiable. The fixed elements represent structural members such as construction walls, pillars, other unmodifiable elements such as elevators, escalators, etc. The modifiable elements represent partition walls, sale stands, etc. The heat maps (HMs) are used to determine the use of spaces. A semi-totalistic two-dimensional cellular automaton has been defined to “melt” modifiable elements of the layout if the value of HM exceeds a given threshold and to “create” wall-cells in the unvisited areas. The process is iterative. A brief interpretation of the results has been presented.
Machi Zawidzki
Discrete Optimization in Architecture
Machi Zawidzki
Copyright Year
Springer Singapore
Electronic ISBN
Print ISBN