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”
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Architectural Functional Layout Optimization in a Coarse Grid
Abstract 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.
1.1 Introduction According to Ref. [16], Architecture can be defined in two thousand ways. This shows the level of ambiguity and difficulty with the nomenclature and proper mathematical formulation of the problems. This is due to the expressive power of the natural language, which according to Ref. [26]: can easily generate contradictions and paradoxes. Moreover, the communication in this field is mostly visual, through: diagrams, plans, perspective and parallel projections, etc. Finally, an architectural design can not be formulated as simple algorithmic steps. It is rather a number of interrelated processes involving: sketching of the functional relationships, visualizations of imagined aesthetics appearance, followed by detailed drafting and approval procedures, etc. Usually, there several re-iterations and re-considerations before the project is completed, and rarely the final result satisfies all the personnel involved, which is likely due to: © The Author(s) 2016 M. Zawidzki, Discrete Optimization in Architecture, SpringerBriefs in Architectural Design and Technology, DOI 10.1007/978-981-10-1106-1_1
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1 Architectural Functional Layout Optimization in a Coarse Grid
1. The problems in Architecture are “hard”. 2. The constraints, conditions, and in particular user’s requirements for a project are often ill-defined. 3. The “ideal” solution is the sense of optimization has not been found. Such a solution corresponds to the point in the objective space whose coordinates have minimal (maximal) values of the objective functions. It is quite common that such “ideal” solution does not exist—then it is necessary to select one of the permissible solutions (called an “admissible solution”). Since in pr
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