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Genetic algorithms for structural design
... Overall, GAs are particularly suitable for architectural design problems in which various performance aspects and design criteria can be quantified and used as fitness criteria in order to guide the evolution of design solutions. Examples include lighting (Caldas and Norford 2002), acoustics (Sato et al. 2004;Spaeth and Menges 2011), view exposure (Menges 2012) or structural aspects (Dimčić 2011;Coelho et al. 2014). One advantage of GAs is their conceptual ease of use in a design environment and the lack of requirement for gradient information upon which many other optimization techniques depend, e.g. ...
... Examples of design problems that have been tackled by using evolutionary computation include, but are not limited to, free-form curved surface design (Hemberg et al. 2001(Hemberg et al. , 2008, spatial layout (Jo and Gero 1998;Michalek et al. 2002), building envelope design (Tuhus-Dubrow and Krarti 2010), thermal and lighting performance (Caldas and Norford 2002;Wright et al. 2002) and urban design (Finucane et al. 2006). Evolutionary computation has also been applied in the related field of structural engineering; for example, Dimčić (2011) and Coelho et al. (2014) have shown the way that GAs can be used to optimize the design of shell structures. Menges (2012) presented two case studies in which design solutions were generated by using an evolutionary approach. ...
Biological evolution drives morphological diversity via genetic variation and results in a high level of adaptation, performance and resource efficiency. However, “biological design” arising from evolution is often counterintuitive and unexpected in a non-linear way. Evolutionary processes are undirected and very good at exploring novel design possibilities in an open-ended manner. Biological evolution thus differs profoundly from the gradualistic and constantly converging character of technical optimization with defined and static fitness functions. Evolutionary algorithms based on Darwinian principles are mainly developed for solving multi-criteria problems in technology. Technical goals are defined as fitness functions and the evolutionary mechanisms of selection, heredity, reproduction and mutation are employed as stochastic optimization processes. These metaheuristic algorithms do not include recent insights into micro- and macro-evolutionary mechanisms derived from genomics, phylogenomics and population genomics. Similar to natural evolution, the architectural design process is an open-ended process exploring possible solutions. However, in order to navigate this vast and dynamic design space, most design methodologies in architecture are based on a typological approach. The designers, based on their knowledge and understanding of the problems, usually limit the solution space to a particular structural, constructional, spatial or programmatic type that is iteratively adapted to the particular design requirements. The constraints inherent in typology-based design methodologies exclude a vast range of potentially more effective and better design variants. In contrast, the dynamics of biological evolution suggest ways of continuously expanding the design space towards new and unexplored possibilities, that can potentially in a new set of typologies that still satisfy the constraints. Thus, in architecture, evolutionary processes are more relevant as exploratory processes than as optimization tools.
... Thus, they can theoretically be applied to any problem where a performance parameter can be well-defined. These characteristics explain the GA's robustness (Filomeno Coelho, et al. 2014) as well as their popularity for structural optimization. ...
... Standard GA's operate on the problem using three 'genetic' operators to generate new populations of candidate solutions based on previous populations as follows (Filomeno Coelho, et al. 2014) (see Figure 2): ...
Current modeling and analysis tools are extremely powerful and allow one to generate and analyze virtually any structural shape. However, most of them do not allow designers to integrate structural performance as an objective during conceptual design. As structural performance is highly linked to architectural geometry, there is a need for computational strategies allowing for performance-oriented structural design in architecture. In order to address these issues, this research combines interactive evolutionary optimization and parametric modeling to develop a new computational strategy for creative and high-performance conceptual structural design. Parametric modeling allows for quick exploration of complex geometries and can be combined with analysis and optimization algorithms for performance-driven design. However, this methodology often questions the designer's authorship as it is based on the use of black-box optimizers. On the other hand, interactive evolutionary optimization empowers the user by acknowledging his or her input as fundamental and includes it in the evolutionary optimization process. This approach aims at improving the structural performance of a concept without limiting the creative freedom of designers. Taking advantage of the two frameworks, this research implements an interactive evolutionary structural optimization framework in the widely used parametric modeling environment constituted by Rhinoceros and Grasshopper. Previous work has illustrated the benefits of combining parametric modeling and genetic algorithms for design space exploration. Comparatively, the implemented design tool capitalizes on Grasshopper's versatility for geometry generation but supplements the visual programming interface with a flexible portal increasing the designer's creative freedom through enhanced interactivity. The tool can accommodate a wide range of structural typologies and geometrical forms in an integrated environment. This research offers a versatile, performance- and user-oriented environment for creative and efficient conceptual structural design.
... Structural design and optimization problems often present i) variables of different nature (continuous, discrete, integer, and/or categorical), ii) objective and constraint functions whose derivatives are too complex or impossible to calculate, and iii) noisy and multimodal solution space [11]. GAs are particularly suitable to address these types of problems as i) they can handle different types of variables, ii) they require no auxiliary information but the value of the objective function itself, and iii) they are a population-based approach making them less likely to be trapped in local optima. ...
In civil engineering there is a need for lightweight structural elements, specifically in applications such as the rehabilitation of degraded floors in existing buildings and modular construction. Metaheuristic search procedures are suitable to tackle optimization problems concerning material efficiency, but their use in real design applications is still limited. This paper presents the preliminary design in terms of structural, thermal, and acoustic performance of a floor system based on steel web core sandwich panels with polyurethane (PUR) foam core and a new genetic algorithm (GA) procedure developed to optimize its mass. The optimization study also addresses the minimization of cost and environmental impact and includes a wide range of practical engineering requirements. The constraints stemming from the building codes are incorporated in a new adaptive penalty function whose formulation and performance are thoroughly investigated. Examples of how to formulate the optimization problem in terms of Eurocode verifications are provided to foster the use of optimization procedures in current design practice. The results are presented in terms of design variables and constraints search histories as well as optimal feasible and unfeasible solutions. General conclusions and specific recommendations are drawn based on the case study presented for the design of sandwich floor panels and steel web core sandwich panels, respectively.
... A multi-objective GA was developed for the optimization of the SP1 solution since this metaheuristic approach present intrinsic features which makes it particularly suitable for the solution of this class of problems. These optimization procedures often involve the use of different types of variables which can be easily handled by the GA [2], as opposed to, gradient-based methods which are devoted to problems with continuous variables. GAs only consider the value of the function itself with no additional information required. ...
In the scope of the research project “Lightslab - development of innovative slab solutions using sandwich panel” a new floor system based on sandwich panel has been developed. The lightweight structural system shall be a competitive solution when compared to traditional rehabilitation technique of degraded timber floors in old buildings. The layout of the sandwich prototypes designed involved the use of steel face sheet and: i) steel webs and polyurethane (PUR) foam core system; ii) glass fiber-reinforced polymer (GFRP) webs and PUR foam core system; and iii) outer steel webs and balsa wood core. The design of the sandwich panels included an optimization procedure. A multi-objective genetic algorithm (GA) was developed for this purpose as it is a search method well suited for the solution of optimization problems. The multi-objective GA aims at the minimization of the three objective functions, i.e. cost, mass and environmental footprint of the sandwich panel. The definition of the main feature of the algorithm includes consideration about encoding procedure, fitness scaling, selection method and handling of constraints. The boundary conditions are imposed so that the retrieved solutions will represent a feasible solution to the problem. These boundary conditions are the analytical formulation of the serviceability, ultimate limit state and thermal transmittance verifications imposed by the building codes to sandwich panels. The present paper deals with the introduction of all the aspects of the optimization problems providing as an example the optimization of the panel with steel face sheets, webs and PUR foam.
... In order to find and study the best-fit solution, the size and location of the shell perforations were controlled by a multi-objective optimization algorithm, minimizing mass and deflection to determine the distribution on the shell surface. The central aim of the optimization routine is to search for a set of best-tradeoff solutions, according to multiple objective functions, so-called fitness functions [4]. This project, as most other real design problems, had multiple competing objectives leading to a set of Pareto Optimal solutions. ...
In this paper the design of a perforated free-form concrete shell structure is discussed, demonstrating the practical implementation of form-finding and optimization in a real-world design. This project is designed as an architecturally expressive building with undulating, exposed material across several levels, housing interior and exterior living spaces. As one of the most significant features of the project, the upper surface of the building is envisioned as a perforated concrete shell, which is the focus of this paper. This surface is supported at the center of the shell, housing a swimming pool, and touches down at four locations at the perimeter. A form-finding procedure, respecting the design intent of the shell was carried out, demonstrating the material-savings that can be achieved with minimal visual impact on the design. The topology of the shell perforations is controlled by a multi-objective optimization algorithm, minimizing mass and deflection to determine the size and distribution of the perforations on the shell surface. This iterative algorithm is constrained by maximum peak stresses for the envelope load combinations and architectural considerations. Options for visualizing the optimization problem are presented at the end of this paper.
... The use of MOGA is a proven resource to find structurally sound solutions for designs that are out of the funicular spectrum or when a trade between different optimization goals is required [14], [15]. For the purposes of this research, the MOGA was set to minimize the bending energy and displacement data obtained from the FEA analysis. ...
The current work presents a novel method to form find efficient funnel shell structures beyond the constraints of funicularity. The so-called Bending-driven Dynamic Corrugation method is introduced within the framework of corrugated shell design and that of integrated computational form finding workflows. The hereby presented method employs the analysis of bending energy of an initial non-funicular shell design as the driver for defining the location and modulation of a corrugation of its surface. The parameters of this corrugation are further manipulated by a multi-objective optimization algorithm to generate a set of performative solutions. The form found solutions exhibit an improved bending and buckling stiffness compared with a traditional cross-section optimized version of the same initial design. Most importantly, these dynamically corrugated designs achieve these improvements using significantly less material. Along with the performance gains, the resulting designs are deemed as a contribution to the expressiveness of the shell structure.
... Each individual in the population is called a chromosome, and these represent the candidate solution to the problem at hand (Gen and Cheng 1997). GAs generate successively improved populations of solutions (better generations) by applying three main genetic operators: selection, crossover, and mutation (Amjadi et al. 2010;Coelho et al. 2014;Kunt et al. 2011). ...
This study has proposed and empirically tested for the first time genetic algorithm optimization models for modelling Australia's domestic airline passenger demand, as measured by enplaned passengers (GAPAXDE model) and revenue passenger kilometres performed (GARPKSDE model). Data was divided into training and testing datasets; 74 training datasets were used to estimate the weighting factors of the genetic algorithm models and 13 out-of-sample datasets were used for testing the robustness of the genetic algorithm models. The genetic algorithm parameters used in this study comprised population size (n): 200; the generation number: 1,000; and mutation rate: 0.01. The modelling results have shown that both the quadratic GAPAXDE and GARPKSDE models are more accurate, reliable, and have greater predictive capability as compared to the linear models. The mean absolute percentage error in the out of sample testing dataset for the GAPAXDE and GARPKSDE quadratic models are 2.55 and 2.23%, respectively.
... Each individual in the population is called a chromosome, and these represent the candidate solution to the problem at hand (Gen and Cheng 1997). GAs generate successively improved populations of solutions (better generations) by applying three main genetic operators: selection, crossover, and mutation (Amjadi et al. 2010;Coelho et al. 2014;Kunt et al. 2011). ...
This study has proposed and empirically tested for the first time genetic algorithm optimization models for modelling Australia’s domestic airline passenger demand, as measured by enplaned passengers (GAPAXDE model) and revenue passenger kilometres performed (GARPKSDE model). Data was divided into training and testing datasets; 74 training datasets were used to estimate the weighting factors of the genetic algorithm models and 13 out-of-sample datasets were used for testing the robustness of the genetic algorithm models. The genetic algorithm parameters used in this study comprised population size (n): 200; the generation number: 1,000; and mutation rate: 0.01. The modelling results have shown that both the quadratic GAPAXDE and GARPKSDE models are more accurate, reliable, and have greater predictive capability as compared to the linear models. The mean absolute percentage error in the out of sample testing dataset for the GAPAXDE and GARPKSDE quadratic models are 2.55 and 2.23%, respectively. © 2015, Journal of Aerospace Technology and Management. All Rights Reserved.
... Galapagos, a 'black-box' Genetic Algorithm implemented in Grasshopper® , is used to perform the optimisation. Genetic Algorithms (GAs) are meta-heuristic search algorithms based on the mechanics of natural selection and natural genetics (Coelho et al., 2014). They provide a robust and flexible tool to solve complex problems and their meta-heuristic way of exploring suitable solutions seems to be particularly helpful in architecture – designers generally benefit from comparing several sub-optimal outcomes rather than converging to a single optimal one. ...
Before the introduction of NURBS-based CAD software and optimisation, the design of form-resistant structures was based on the use of either experimental tools (physical form-finding) or analytical surfaces, and architects were challenged in the articulation of spaces from the intrinsic characteristics/rules of structural forms. An outstanding example of this kind is provided by the Church of Longuelo, which was built by architect Pino Pizzigoni in Italy, between 1961-1966. It was conceived as composed by two major elements – an irregular frame and a set of shells suspended to it. The entire design process was based on the calculation of the frame on which the shells have been just added as a dead load. This paper presents one possible way to redesign the church parametrically. Comparison with the original design is not performed at the final formal level, which can logi-cally differ, but around the concepts behind the project. The aim is to show how current digital design and optimisation tools are affecting the way architects design. But, at a higher level, the purpose is also to highlight where conceptual design is now taking place in the process.
Unfolding double-curvature surfaces is a problem that is widely encountered in engineering and increasingly met in architecture and digital fabrication processes. In the context of building construction, the process used to unfold the complex surface matters more than the unfolded result. Mastering the process of developable surfaces is fundamental to the construction method in order to keep the resulting geometry faithful to the initial one, to increase structural efficiency and material savings. The interest in unfolding a surface lies in its feasibility, in order to build surfaces with materials that can be elastically bent. This study is based on geodesic curves on surfaces and involves a process including parameters such as the number of geodesics and the division of these geodesics depending on the curvature of the surface, to be as close as possible to the initial surface. The algorithm approximates the initial surface by building developable strips between two successive geodesic curves.
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