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Acommodating Change in Parametric Design
... Yan et al. [52] mentioned before, also used Octopus stating that multi objective genetic optimizers have the advantageous of being global optimization algorithms, can find multiple pareto front solutions for MOO problems in one time and there is no need for the objective function of the genetic algorithm to be continues. Quoting, [24,30,50] highlighted the effectiveness of using genetic algorithms that was developed based on the theory of natural selection by Darwin. They also highlighted their suitability for optimizing building energy that was demonstrated before in many recent studies using genetic algorithms to optimize building form, envelope, HVAC and renewable energy systems. ...
With the increasing demand for sustainable built environments, energy performance is becoming essential in the early design stage. Several previous studies using optimization of building form for energy performance considered simple hypothetical forms. In addition, previous multi-objective optimization (MOO) of building form and envelope did not consider views percentage to the outdoor (VPO) despite of its importance for human mental health and its conflict with energy performance. This paper proposes a novel lattice incubates boxes (LIB) method that optimizes a cellular office building form. It considers the entire building with 27 thermal zones in an attempt to mimic a real case study. In addition, it considers VPO as an objective in the MOO of building form and envelope. First, the study performs single-objective optimization (SOO) of architectural form and orientation for annual thermal Energy Use Intensity (EUI) in Cairo, London, and Chicago. Second, it performs multidisciplinary MOO of Cairo’s form, window to wall ratio (WWR) and horizontal shading devices (HSD) for annual thermal EUI, annual Useful Daylight Illuminance (UDI-100–2000), and VPO. Third, it develops the LIB method to make it more applicable in professional practice through considering 72 individual thermal zones while adding more constraints. Compared to the initial forms, first part EUI savings were between 16.86% and 12.9 %. EUI, UDI, and VPO savings for Cairo in the second part were 20.16%, 11.5%, and 19.5 %. Scatterplots are developed for the second part that show rows motion has the highest positive impact on UDI and VPO, WWR has a positive impact on all objectives and HSD has high positive impact on EUI only. Savings in the third part are 11 % EUI, 8.77 % UDI, 2.86% Daylight Autonomy (DLA) and 7.8 % VPO. Scatterplots in the third part show that almost all proposed form dynamic parameters have strong impact on all objectives.
... For instance, computational, generative, and parametric design may be sought as pragmatic actors in concrete projects and experiences. Thanks to their adaptive and transformative interventions, the design outcome is not only meant to simply translate the multispecies perspectives but also to let the technology add further elements to design projects and experiences, i.e., multiple alternatives through generative design [27,28]. However, the role of technology should be critically considered, paying attention to its way of mediating different multispecies agencies and/or participating in the designed experience, avoiding human-biased actions of technology or anthropocentric outcomes [24,29]. ...
The research aims at analyzing the theme of human-nature interactions mediated by technologies from different perspectives and applying three lenses: the first one is more pragmatic and oriented by technological applications, and, thus, with relapses on design practices, while the other two are theoretical – decolonization and post-human feminism – and they provide a critical vision of the topics of interest from an ontological and epistemological point of view, with relapses on design theories. Therefore, the goal of the research is to provide a first draft of a framework, designed through a process of literature review and case studies analysis, that can stimulate more-than-human connections as collaborative and symbiotic processes between human and non-human agents, oriented by new perspectives upon technology.
... In recent years, MOGO has been extensively used to optimize building forms, envelope HVAC, and renewable energy systems [43,44]. The Octopus is a component of Grasshopper, which was used to perform the optimization in this study [45]. It allows multi-objective optimization of competing objectives within a seamless workflow and allows the entire optimization process to be visualized and controlled. ...
Incorporating intelligent optimization algorithms in the early stages of office building design facilitates a better response to the local climate. The indoor and outdoor thermal performances of office buildings, such as solar radiation, indoor lighting, and outdoor thermal comfort, must be jointly evaluated during the conceptual design phase. Based on the technical framework of “performance-based generative architectural design”, this study constructs a data-driven workflow for comprehensive performance assessment and rapid prediction of office buildings. The method was then applied to an office building in the hot summer and cold winter regions of China. Based on a total of 6000 data samples generated by the iterative process of genetic optimization, this study achieved a precision of 0.77, recall of 0.59, and F-1 score of 0.75 for categorical prediction by the XGBoost algorithm. The method facilitates the optimization potential of integrated solar and thermal performances in the early design phase of office buildings while significantly improving the efficiency of interaction and feedback between design decisions and their performance evaluation.
The adaptive façades serve as the interface between the indoor and outdoor energy of the building. Adaptive façade optimization design can improve daylighting performance, the thermal environment, view performance, and solar energy utilization efficiency, thus reducing building energy consumption. However, traditional design frameworks often neglect the influence of building envelope performance characteristics on adaptive façade optimization design. This paper aims to reveal the potential functional relationship between building façade performance characteristics and adaptive façade design. It proposes an adaptive façade optimization design framework based on building envelope performance characteristics. The method was then applied to a typical office building in northern China. This framework utilizes a K-means clustering algorithm to analyze building envelope performance characteristics, establish a link to adaptive façade design, and use the optimization algorithm and machine learning to make multi-objective optimization predictions. Finally, Pearson’s correlation analysis and visual decision tools were employed to explore the optimization potential of adaptive façades concerning indoor daylighting performance, view performance, and solar energy utilization. The results showed that the optimized adaptive façade design enhances useful daylight illuminance (UDI) by 0.52%, quality of view (QV) by 5.36%, and beneficial solar radiation energy (BSR) by 14.93% compared to traditional blinds. In addition, each office unit can generate 309.94 KWh of photovoltaic power per year using photovoltaic shading systems. The framework provides new perspectives and methods for adaptive façade optimization design, which helps to achieve multiple performance objectives for buildings.
Rapid population growth accelerates urbanization, and human activities exacerbate climate change, leading to a series of urban thermal environment problems, especially in hot and humid regions. In China, regulatory planning is a crucial aspect of urban planning significantly impacting the emergence and development of urban thermal environment problems. However, the current methods for evaluating and optimizing the urban thermal environment at the regulatory planning level are relatively insufficient. In-depth study on the urban thermal environment at the regulatory planning level in hot and humid regions, assessment of the impact and risk of meteorological background on the environment and residents, and then regulation of the thermal environment through parameterization of planning control elements, can consider the urban heat island effect, thermal safety and thermal comfort, building energy consumption and other multi-objectives to effectively mitigate urban thermal environment problems.
Numerical simulation is an important way to study the urban thermal environment, and at the regulatory planning level, new models that combine multi-parameter and multi-objective evaluation are needed. In order to do this, this study shows how the algorithms and functions of the Urban Weather Generator (UWG) model can be made better and how they can be added to. In terms of algorithms, the radiant energy allocation algorithm for uniform three-dimensional rectangular building arrays, the roughness algorithm that takes into account vegetation, the vegetation energy allocation algorithm that takes into account weather, and the convective heat transfer calculation algorithm that improves the wind speed reference height are introduced. In terms of functions, the mean radiant temperature and the water temperature are extended. Following that, simulations are carried out using the improved and extended new UWG model in Guangzhou and Nanning, typical cities in hot and humid regions, and the air temperature, relative humidity, and mean radiant temperature at the regulatory planning level are evaluated using the measured data. The results show that the new UWG model performs well in predicting the trends and numerical results of the evaluated parameters (taking Guangzhou as an example, the coefficients of determination of the predicted air temperature, relative humidity, and mean radiant temperature are 0.966, 0.720, and 0.828, respectively, and the root mean square errors are 0.93 ℃, 6.59 %, and 2.34 ℃, respectively, and the mean bias errors are 0.10 ℃, 1.41 %, and −0.69 ℃, respectively), and the model has sufficient stability to simulate the changes in the thermal environment over long time periods.
To carry out urban thermal environment assessment at the regulatory planning level, it is necessary to parameterize various types of thermal environment information and conduct a comprehensive evaluation from multiple dimensions. In order to do this, this study proposes a multi-dimensional urban thermal environment information extraction and evaluation method and analyzes the central city of Guangzhou as an example. First, the thermal environment information is extracted from multiple data sources such as remote sensing inversion, visual interpretation, field research, and social perception by combining the Local Climate Zone (LCZ) system and building classification, and a thermal environment database is established for the central urban area of Guangzhou. Then, relevant thermal environment parameters were input into the new UWG model to analyze the thermal environment differences in the central area of Guangzhou from three objectives: urban heat island intensity, universal thermal climate index (UTCI), and building cooling energy demand. The research results reveal that there is some variation in the degree of superiority and inferiority of the thermal environment in each LCZ area under different thermal evaluation objectives, and the thermal environment of the area represented by LCZ 3 (compact low-rise building areas) is the most unsatisfactory. The global PAWN sensitivity analysis further shows that building height, building density, and wall-to-ground area ratio are the three factors with the greatest influence on the thermal environment, with their PAWN indices all greater than 0.2. Planning-related factors like urban morphology, blue-green infrastructure, anthropogenic heat from transportation, albedo, and building function type distribution have different effects on the thermal environment over time and space. By quantitatively analyzing each factor, the degree of influence and stability of the spatial and temporal variation of each factor can be developed into a targeted planning strategy to achieve the best thermal mitigation effect.
Uncertainty in the planning and design process could affect the thermal environment, which makes it harder to get the planning results that were wanted. To address this issue, this study constructs a multi-objective parametric thermal environment optimization design platform based on the new UWG model within the parametric plug-in Grasshopper in the planning scheme modeling software Rhinoceros 3D. The platform can evaluate the thermal environment at the regulatory planning level, provide suggestions on the values of planning control elements with full consideration of robustness, generate Pareto-optimal solution sets, and realize multifaceted evaluation and optimization of the thermal environment in the planning and design processes. Further, a climate adaptation planning process with the thermal environment as the core is proposed to incorporate the impact of the thermal environment into the decision-making process at the regulatory planning level. The multi-objective evaluation of thermal environment and parametric optimization applications is carried out with two regulatory planning cases as examples. The former compares the changes in urban heat island intensity, outdoor human thermal safety and comfort, and cooling energy demand for 8,760 hours of a typical meteorological year before and after the program modification and provides a quantitative method for comparing and selecting different control schemes from the thermal environment perspective. The latter provides an effective multi-objective parameterization method for optimizing the thermal environment by filtering out the thermal environment control units that need to be optimized based on the rapid calculation of multiple thermal environment control unit-related parameters, conducting a parametric search to obtain the Pareto-optimal solution set, and then outputting the corresponding proposed values of the planning control elements for the decision of the planner.
In summary, this study suggests a method for evaluating and improving the urban thermal environment at the level of regulatory planning. The method uses the new UWG model to extract multivariate urban thermal environment parameters based on the LCZ system and building classification perspective, constructs a multi-objective parametric thermal environment optimization design platform, evaluates the multidimensional impact of planning control elements on the urban thermal environment, realizes rapid, quantitative, and multi-objective regulation of the thermal environment at the regulatory planning level, and provides a theoretical basis and technical support for evaluating and optimizing the thermal environment at the regulatory planning level.
Embedding circular economy (CE) principles in early design requires iterative evaluation across multiple lifecycle phases, with trade-offs between objectives complicating the identification of best solutions. This paper puts forward methods to automatically discover diverse, yet well-performing solution types within complex multi-objective CE design optimisation models. Working with a parametric model derived from a furniture design for CE case study, a comparison is made between weighted-sum single objective optimisation and multi-objective optimisation augmented with clustered solution types targeted by the reference point-based NSGA-II optimisation algorithm. Efficiency of optimisation, quality of results and distinctiveness of solution types presented by each method is compared in an effort to understand which will best assist designers to manage complexity in CE design. The generalisability of the presented methods to larger scale CE design problems is discussed and future areas of work on computational design for CE are extrapolated from the presented results.
With additive manufacturing, greater degrees of design freedoms can be afforded via design optimization and mass customization of part geometries. One way to leverage the geometrical and hierarchical complexities of additively manufactured parts is the manufacturing of functionally-graded lattice structures – a tall order for conventional manufacturing technologies. Yet, the selection of suitable unit cell types and strut diameters to generate lattice structures with desirable mechanical performance for specific applications remains a challenge for engineers due to the lack of computational design support tools integrating domain experts’ knowledge and past empirical outcomes across the stages of the engineering design process. This study proposes a digital design workflow which aids decision-making by redefining design features as parametric problems to be solved using algorithmic methods. Using a visual programming application, the 3D model is first parameterized, then fed into a simulation and optimization workflow. Solutions are then generated by iterating all possibilities within the ranges of the design parameters given by the human designer. The methodology presented here is examined through a case study of a bike saddle for fabrication via Multi Jet Fusion, taking into consideration the minimum unit cell gap and minimum strut diameter to ensure the model’s printability. Preliminary results indicated that comparisons between different design alternatives can be made easily via the visualization and feedback of the interface. The potential of such an integrated workflow can be further demonstrated in products that can benefit from the mechanical advantages of lattice structures, such as orthotics, personalized sports equipment, and more.
Origami‐based designs refer to the application of the ancient art of origami to solve engineering problems of different nature. Despite being implemented at dimensions that range from the nano to the meter scale, origami‐based designs are always defined by the laws that govern their geometrical properties at any scale. It is thus not surprising to notice that the study of their applications has become of cross‐disciplinary interest. This article aims to review recent origami‐based applications in engineering, design methods and tools, with a focus on research outcomes from 2015 to 2020. First, an introduction to origami history, mathematical background and terminology is given. Origami‐based applications in engineering are reviewed largely in the following fields: biomedical engineering, architecture, robotics, space structures, biomimetic engineering, fold‐cores, and metamaterials. Second, design methods, design tools, and related manufacturing constraints are discussed. Finally, the article concludes with open questions and future challenges. This article reviews the state of the art of origami‐based applications in engineering. Publications of origami‐based applications are reviewed according to the following fields: biomedical engineering, architecture, robotics, space structures, biomimetic engineering, fold‐cores, and metamaterials. Design methods and tools are also reviewed. Manufacturing considerations are provided and future challenges discussed.
The contemporary development and digital culture in architecture, from the idea to the realization, lead to a rewriting of the coordinates of the deep relation between model and pre-figuration, especially in the timber structure field. Artificial intelligence opened new potentialities that rewrite the project paths through the evaluation of computational design, with a model set as the place of simulation and experimentation, in order to locate solutions for more and more high requests made by architecture. Wood’s natural intelligence inspires artificial intelligence’s principles, and it is projected as the new frontier of the research, in its possibility of defying optimized solutions also in function of multiples objectives and parameters. Wooden architecture design correlated to a history of tradition, which is established on descriptive geometry, finds today multiple application fields for the research. In this sense, representation supports the knowledge and the innovation, able to continue and express its operative aspect full of culture and, at the same time, its tecné sense, which etymologically it is meant as art and technique. The present chapter shows different ways to apply the contemporary principle of descriptive geometry in digital wood design research, in a multidisciplinary and contaminated learning environment. In all the illustrated cases, the generative design has a central role, in an integration addressed to the need of optimization of architectural form, using Genetic algorithms in order to analyze and to understand the relationship between form, geometry, and construction.
Combining graph-based parametric design with metaheuristic solvers has to date focused solely on performance-based criteria and solving clearly defined objectives. In this article, we outline a new method for combining a parametric modelling environment with an interactive Cluster-Orientated Genetic Algorithm. In addition to performance criteria, evolutionary design exploration can be guided through choice alone, with user motivation that cannot be easily defined. As well as numeric parameters forming a genotype, the evolution of whole parametric definitions is discussed through the use of genetic programming. Visualisation techniques that enable mixing small populations for interactive evolution with large populations for performance-based optimisation are discussed, with examples from both academia and industry showing a wide range of applications.
The research is based on the project of a free-form roofing system with double curved glass panels that are cladding the structure. One of the challenges is a load-bearing structure that follows a free-form NURBS surface. The load-bearing members are going to be manufactured from bended metal tubes. Technology of production allows bending pipes in circular shapes, therefore, initially designed free-form NURBS curvature is difficult to transfer into buildable load-bearing structure due to its complex geometry. For the fabrication purposes the curve elements needs to be simplified to a set of arcs in order to achieve profiles for bending. To solve this problem, the Genetic Algorithm had been applied for fitting arcs into initial geometry. The algorithm fits elements to minimize Deviation from an initial curve and maximize Continuity between arcs. Base set up can be modified due to other parameters such as Length or a Number of elements etc. The aim is to achieve design methodology which will give full freedom of design, on the same time, but also to reassure possibility of construction.
This paper speculates on the applicability of methods from artificial intelligence in generative design. In particular, Cppn-Neat as a recent concept is implemented and tested on an established platform for procedural design. The method evolves artificial neural networks and has proven successful in control of robotic navigation, cognition, and collaboration, therefore is proposed to control the behaviour of drawing agents for architectural optimization tasks. A projected goal is the development of networks which, once evolved, instantly perform specific tasks on generic geometries, to be re-used on different projects and save run-time in the optimization process. Potentials of the method regarding general encoding and novel modes of formal articulation are examined in a first set of parameterization-studies. Further examples are testing the scalability of results from different problem domains and work towards the evolution of large ANNs to be suitable for the synthesis of higher level concepts.
Today architectural design processes are more and more influenced by parametric methods. As these allow for a multiplicity of alternatives, the design process can be enriched by computational optimization. Extensive research has shown the efficiency of optimization in engineering and design disciplines. Though, optimization is hereby rather a technical than a design task; it is limited to different autonomous specialist areas and does not enable a comprehensive approach. Advanced optimization methods facilitate the generation of complex systems, but these procedures are directed and do not provide turnoffs, multiple solutions or altering circumstances. These however are things that are essential for architectural design processes, which mostly do not have clearly defined starting and end points. This practice subdivides the workflow into two independent and recurring tasks: the generation of a parametric model followed by optimization of its driving parameters. The result is then assessed with respect to its actual qualities. The design either is kept, or modifications on the parametric model, its auxiliary conditions and parameters are made and the optimization process starts again from scratch. The aim of the research project, this paper is referring to, is the development of a flexible generation and optimization framework for practical use in the sense of a continuously accompanying design explorer, in which parameterization is adaptable and objective functions are changeable at any time during the design process. The user is supported in his/her understanding of correlations by identifying a multiplicity of optimal solutions utilizing state-of-the-art multi-objective search algorithms within the core of the framework. Considering the tool as an interactive design aid, an intuitive interface allowing for extensive manual guidance and verification of the search process is featured. Zooming, filtering and weighting within the genotypic, phenotypic and objective space comply with an extensive support of man-machine-dialogue and incorporation of non-or not-yet quantifiable measures. A reusable search history aids examination of design alternatives and the redefinition of constraints, maintaining the continuity of the search process and traceability of results in the sense of rational design verification. Within this work it is not planned to focus on specific optimization targets, but to build an open framework to allow for all kinds of objective functions and in particular the mediation between conflicting targets. In a broader context of general design research, the process of design development from early to final solution is examined, where not even optimization itself but the entire search for an adequate optimization setup is targeted. Even the research process is at its very beginning, in this paper we already propose a tool that integrates key features of a continuous design-assistant. User guided, adaptive multi-objective search algorithms, re-entrant history records, parallelization of computation, and a user interface that allows control in a manifold and intuitive way.
Evolutionary computation is emerging as a new engineering computational paradigm, which may significantly change the present structural design practice. For this reason, an extensive study of evolutionary computation in the context of structural design has been conducted in the Information Technology and Engineering School at George Mason University and its results are reported here. First, a general introduction to evolutionary computation is presented and recent developments in this field are briefly described. Next, the field of evolutionary design is introduced and its relevance to structural design is explained. Further, the issue of creativity/novelty is discussed and possible ways of achieving it during a structural design process are suggested. Current research progress in building engineering systems’ representations, one of the key issues in evolutionary design, is subsequently discussed. Next, recent developments in constraint-handling methods in evolutionary optimization are reported. Further, the rapidly growing field of evolutionary multiobjective optimization is presented and briefly described. An emerging subfield of coevolutionary design is subsequently introduced and its current advancements reported. Next, a comprehensive review of the applications of evolutionary computation in structural design is provided and chronologically classified. Finally, a summary of the current research status and a discussion on the most promising paths of future research are also presented.
In evolutionary computation, the fitness function normally measures progress toward an objective in the search space, effectively acting as an objective function. Through deception, such objective functions may actually prevent the objective from being reached. While methods exist to mitigate deception, they leave the underlying pathology untreated: Objective functions themselves may actively misdirect search toward dead ends. This paper proposes an approach to circumventing deception that also yields a new perspective on open-ended evolution. Instead of either explicitly seeking an objective or modeling natural evolution to capture open-endedness, the idea is to simply search for behavioral novelty. Even in an objective-based problem, such novelty search ignores the objective. Because many points in the search space collapse to a single behavior, the search for novelty is often feasible. Furthermore, because there are only so many simple behaviors, the search for novelty leads to increasing complexity. By decoupling open-ended search from artificial life worlds, the search for novelty is applicable to real world problems. Counterintuitively, in the maze navigation and biped walking tasks in this paper, novelty search significantly outperforms objective-based search, suggesting the strange conclusion that some problems are best solved by methods that ignore the objective. The main lesson is the inherent limitation of the objective-based paradigm and the unexploited opportunity to guide search through other means.
In this thesis I consider the relationship between the design of software and the design of flexible parametric models.
There is growing evidence that parametric models employed in practice lack the flexibility to accommodate certain design changes. When a designer attempts to change a model’s geometry (by modifying the model’s underlying functions and parameters) they occasionally end up breaking the model. The designer is then left with a dilemma: spend time building a new model, or abandon the changes and revise the old model. Similar dilemmas exist in software engineering. Despite these shared concerns, Robert Woodbury (2010, 66) states that there is currently “little explicit connection” between the practice of software engineering and the practice of parametric modelling.
In this thesis I consider, using a reflective practice methodology, how software engineering may inform parametric modelling. Across three case studies I take aspects of the software engineering body of knowledge (language paradigms; structured programming; and interactive programming) and apply them to the design of parametric models for the Sagrada Família, the Dermoid pavilion, and the Responsive Acoustic Surface. In doing so I establish three new parametric modelling methods.
The contribution of this research is to show there are connections between the practice of software engineering and the practice of parametric modelling. These include the following:
Shared challenges: Both practices involve unexpected changes occurring within the rigid logic of computation.
Shared research methods: Research methods from software engineering apply to the study of parametric modelling.
Shared practices: The software engineering body of knowledge seems to offer a proven pathway for improving the practice of parametric modelling.
These connections signal that software engineering is an underrepresented and important precedent for architects using parametric models; a finding that has implications for how parametric modelling is taught, how parametric models are integrated with practice, and for how researchers study and discuss parametric modelling.
The Karamba plug-in developed by Clemens Preisinger in collaboration with Bollinger + Grohmann Engineers has been developed to predict the behaviour of structures under external loads. Intended to be used by architects rather than being solely confined to an engineering setting, it enables a seamless flow of data between structural and geometric models. Preisinger here describes the program's evolution and application.
Design is complex. This is because it involves conflicting goals that are often vague. Also, prior to the design it is generally not clear how important goals are relative to each other. And finally the amount of possible solutions is large in general. These bottlenecks are addressed in this thesis. A novel approach for design is proposed, where computation is used to reach most suitable solutions. The approach is based on a novel concept of the objects forming a design. This concept is termed intelligent design objects. Such objects exhibit intelligent behavior in the sense that they approach most desirable solutions for conflicting, vague goals put forward by a designer. That is, the objects know ‘themselves’ what to do to satisfy a designer’s goals. This is accomplished using methods from the domain of computational intelligence, as these are uniquely able to deal with the complexity of design mentioned above. The result from the approach is that designers and decision makers have great certainty about the satisfaction of their goals and are able to concentrate on second order aspects they were not aware of prior to the execution. The approach is implemented for two applications from the domain of architecture demonstrating its effectiveness. The thesis addresses to students, researchers and executives in the field of architecture, and other areas of design. It may be also interesting for researchers in the domain of computational intelligence, as it provides a formalism of intelligent design, and it exemplifies the use of these modern technologies in the design domain. Due to its generic nature, this formalism may have some significance in the development of the science of design.
The Strength Pareto Evolutionary Algorithm (SPEA) (Zitzler and Thiele 1999) is a relatively recent technique for finding or approximating the Pareto-optimal set for multiobjective optimization problems. In different studies (Zitzler and Thiele 1999; Zitzler, Deb, and Thiele 2000) SPEA has shown very good performance in comparison to other multiobjective evolutionary algorithms, and therefore it has been a point of reference in various recent investigations, e.g., (Corne, Knowles, and Oates 2000). Furthermore, it has been used in different applications, e.g., (Lahanas, Milickovic, Baltas, and Zamboglou 2001). In this paper, an improved version, namely SPEA2, is proposed, which incorporates in contrast to its predecessor a fine-grained fitness assignment strategy, a density estimation technique, and an enhanced archive truncation method. The comparison of SPEA2 with SPEA and two other modern elitist methods, PESA and NSGA-II, on different test problems yields promising results. 1
In this paper, a flexible yet efficient algorithm for solving engineering design optimization problems is presented. The algorithm is developed based on both binary-coded and realcoded genetic algorithms (GAs). Since both GAs are used, the variables involving discrete, continuous, and zero-one variables are handled quite efficiently. The algorithm restricts its search only to the permissible values of the variables, thereby reducing the search effort in converging to the optimum solution. The efficiency and ease of application of the proposed method is demonstrated by solving three different mechanical component design problems borrowed from the optimization literature. The proposed technique is compared with binarycoded genetic algorithms, Augmented Lagrange multiplier method, Branch and Bound method and Hooke and Jeeves pattern search method. In all cases, the solutions obtained using the proposed technique are superior than those obtained with other methods. These results ...
The success of binary-coded genetic algorithms (GAs) in problems having discrete search space largely depends on the coding used to represent the problem variables and on the crossover operator that propagates building-blocks from parent strings to children strings. In solving optimization problems having continuous search space, binary-coded GAs discretize the search space by using a coding of the problem variables in binary strings. However, the coding of real-valued variables in finite-length strings causes a number of difficulties---inability to achieve arbitrary precision in the obtained solution, fixed mapping of problem variables, inherent Hamming cliff problem associated with the binary coding, and processing of Holland's schemata in continuous search space. Although, a number of real-coded GAs are developed to solve optimization problems having a continuous search space, the search powers of these crossover operators are not adequate. In this paper, the search power...
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IMAGE CREDITS
All image credits to Robert Vierlinger (2014).