Existing Transformation Approaches Research Articles

Transformation and Linearization Techniques in Optimization: A State-of-the-Art Survey

To formulate a real-world optimization problem, it is sometimes necessary to adopt a set of non-linear terms in the mathematical formulation to capture specific operational characteristics of that decision problem. However, the use of non-linear terms generally increases computational complexity of the optimization model and the computational time required to solve it. This motivates the scientific community to develop efficient transformation and linearization approaches for the optimization models that have non-linear terms. Such transformations and linearizations are expected to decrease the computational complexity of the original non-linear optimization models and, ultimately, facilitate decision making. This study provides a detailed state-of-the-art review focusing on the existing transformation and linearization techniques that have been used for solving optimization models with non-linear terms within the objective functions and/or constraint sets. The existing transformation approaches are analyzed for a wide range of scenarios (multiplication of binary variables, multiplication of binary and continuous variables, multiplication of continuous variables, maximum/minimum operators, absolute value function, floor and ceiling functions, square root function, and multiple breakpoint function). Furthermore, a detailed review of piecewise approximating functions and log-linearization via Taylor series approximation is presented. Along with a review of the existing methods, this study proposes a new technique for linearizing the square root terms by means of transformation. The outcomes of this research are anticipated to reveal some important insights to researchers and practitioners, who are closely working with non-linear optimization models, and assist with effective decision making.

An algorithm to facet curved walls in IFC BIM for building energy analysis

Abstract The automatic transformation of a Building Information Model (BIM) in Industry Foundation Classes (IFC) to a building energy model (BEM) demonstrates significant benefits on the improvement of efficiency and accuracy in a building energy modeling process. However, so far, building objects with curved surfaces in IFC models are not supported by existing transformation approaches as they only handle polyhedral geometries. This study presents an algorithm to automatically facet curved walls and convert their geometries into polyhedrons, so that they can be further processed by existing transformation approaches. In the process of faceting curved walls, geometric connections between each target wall and adjacent walls are detected and handled to maintain the connections in the results. Furthermore, the algorithm updates the geometries of relevant building objects, including straight walls connected to curved walls, openings (i.e., windows and doors) on curved walls and spaces enclosed by curved walls, based on the faceted geometries. This removes curved surfaces of these objects on the one hand, and maintains their geometric relationships on the other. Moreover, slabs with the curved surfaces are also faceted. This algorithm takes an IFC BIM that pertains to the model view definition Concept Design BIM 2010 as an input. It generates a new IFC BIM, in which all curved walls and relevant building objects are represented as polyhedral geometries with correct geometric relationships. A prototype application that implements the algorithm was developed to evaluate the performance of the algorithm with a simple building model and a complex real-world building model. In the results, all the curved walls were faceted, and all relevant straight walls, openings, spaces and slabs were correctly updated, which indicated that the algorithm worked as intended.

Multi-dimensional classification via a metric approach

Abstract Multi-dimensional classification (MDC) refers to learning an association between individual inputs and their multiple dimensional output discrete variables, and is thus more general than multi-class classification (MCC) and multi-label classification (MLC). One of the core goals of MDC is to model output structure for improving classification performance. To this end, one effective strategy is to firstly make a transformation for output space and then learn in the transformed space. However, existing transformation approaches are all rooted in label power-set (LP) method and thus inherit its drawbacks (e.g., class imbalance and class overfitting). In this study, we first analyze the drawbacks of the LP, then propose a novel transformation method which can not only overcome these drawbacks but also construct a bridge from MDC to MLC. As a result, many off-the-shelf MLC methods can be adapted to our newly-formed problem. However, instead of adapting these methods, we propose a novel metric learning based method, which can yield a closed-form solution for the newly-formed problem. Interestingly, our metric learning based method can also naturally be applicable to MLC, thus itself can be of independent interest as well. Extensive experiments justify the effectiveness of our transformation approach and our metric learning based method.

Molecular Characterization of Gasoline and Diesel Streams

A novel methodology to characterize gasoline and diesel streams into the molecular level is developed on the basis of molecular type homologous series (MTHS) matrix framework (Chem. Eng. Sci. 2005, 60, 6702−6717). The method comprises the enhancements of both representation matrix construction and transformation methodology of bulk properties into molecular composition. To improve the accuracy and adequacy of the representation model, different strategies are set up separately for gasoline and diesel streams for the consideration of isomers. By introducing statistical distribution and applying extensive bulk properties, the transformation approach is revolutionized to increase the usability, and tackle the challenge of possibly achieving significantly different molecular compositions from the same bulk properties of refining streams by existing transformation approaches. The proposed method is verified with both gasoline and diesel streams, and the results show a good agreement with measured data.

The Classification Framework for Model Transformation

Wide usage of model transformation in the Information Systems has resulted in a number of transformation approaches recently. In order to provide an insight into the existing transformation approaches, to draw out the practicability and analyze the strengths and weaknesses of these approaches a multidimensional classification is required. In this paper, a classification framework is proposed which provides a multidimensional, faceted and measure based viewpoint to give a clear and better insight into the existing model transformation approaches.