852 research outputs found

    The two-dimensional bin packing problem with variable bin sizes and costs

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    AbstractThe two-dimensional variable sized bin packing problem (2DVSBPP) is the problem of packing a set of rectangular items into a set of rectangular bins. The bins have different sizes and different costs, and the objective is to minimize the overall cost of bins used for packing the rectangles. We present an integer-linear formulation of the 2DVSBPP and introduce several lower bounds for the problem. By using Dantzig–Wolfe decomposition we are able to obtain lower bounds of very good quality. The LP-relaxation of the decomposed problem is solved through delayed column generation, and an exact algorithm based on branch-and-price is developed. The paper is concluded with a computational study, comparing the tightness of the various lower bounds, as well as the performance of the exact algorithm for instances with up to 100 items

    PHYSICS-BASED SHAPE MORPHING AND PACKING FOR LAYOUT DESIGN

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    The packing problem, also named layout design, has found wide applications in the mechanical engineering field. In most cases, the shapes of the objects do not change during the packing process. However, in some applications such as vehicle layout design, shape morphing may be required for some specific components (such as water and fuel reservoirs). The challenge is to fit a component of sufficient size in the available space in a crowded environment (such as the vehicle under-hood) while optimizing the overall performance objectives of the vehicle and improving design efficiency. This work is focused on incorporating component shape design into the layout design process, i.e. finding the optimal locations and orientations of all the components within a specified volume, as well as the suitable shapes of selected ones. The first major research issue is to identify how to efficiently and accurately morph the shapes of components respecting the functional constraints. Morphing methods depend on the geometrical representation of the components. The traditional parametric representation may lend itself easily to modification, but it relies on assumption that the final approximate shape of the object is known, and therefore, the morphing freedom is very limited. To morph objects whose shape can be changed arbitrarily in layout design, a mesh based morphing method based on a mass-spring physical model is developed. For this method, there is no need to explicitly specify the deformations and the shape morphing freedom is not confined. The second research issue is how to incorporate component shape design into a layout design process. Handling the complete problem at once may be beyond our reach,therefore decomposition and multilevel approaches are used. At the system level, a genetic algorithm (GA) is applied to find the positions and orientations of the objects, while at the sub-system or component level, morphing is accomplished for select components. Although different packing applications may have different objectives and constraints, they all share some common issues. These include CAD model preprocessing for packing purpose, data format translation during the packing process if performance evaluation and morphing use different representation methods, efficiency of collision detection methods, etc. These common issues are all brought together under the framework of a general methodology for layout design with shape morphing. Finally, practical examples of vehicle under-hood/underbody layout design with the mass-spring physical model based shape morphing are demonstrated to illustrate the proposed approach before concluding and proposing continuing work

    Branching strategies for mixed-integer programs containing logical constraints and decomposable structure

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    Decision-making optimisation problems can include discrete selections, e.g. selecting a route, arranging non-overlapping items or designing a network of items. Branch-and-bound (B&B), a widely applied divide-and-conquer framework, often solves such problems by considering a continuous approximation, e.g. replacing discrete variable domains by a continuous superset. Such approximations weaken the logical relations, e.g. for discrete variables corresponding to Boolean variables. Branching in B&B reintroduces logical relations by dividing the search space. This thesis studies designing B&B branching strategies, i.e. how to divide the search space, for optimisation problems that contain both a logical and a continuous structure. We begin our study with a large-scale, industrially-relevant optimisation problem where the objective consists of machine-learnt gradient-boosted trees (GBTs) and convex penalty functions. GBT functions contain if-then queries which introduces a logical structure to this problem. We propose decomposition-based rigorous bounding strategies and an iterative heuristic that can be embedded into a B&B algorithm. We approach branching with two strategies: a pseudocost initialisation and strong branching that target the structure of GBT and convex penalty aspects of the optimisation objective, respectively. Computational tests show that our B&B approach outperforms state-of-the-art solvers in deriving rigorous bounds on optimality. Our second project investigates how satisfiability modulo theories (SMT) derived unsatisfiable cores may be utilised in a B&B context. Unsatisfiable cores are subsets of constraints that explain an infeasible result. We study two-dimensional bin packing (2BP) and develop a B&B algorithm that branches on SMT unsatisfiable cores. We use the unsatisfiable cores to derive cuts that break 2BP symmetries. Computational results show that our B&B algorithm solves 20% more instances when compared with commercial solvers on the tested instances. Finally, we study convex generalized disjunctive programming (GDP), a framework that supports logical variables and operators. Convex GDP includes disjunctions of mathematical constraints, which motivate branching by partitioning the disjunctions. We investigate separation by branching, i.e. eliminating solutions that prevent rigorous bound improvement, and propose a greedy algorithm for building the branches. We propose three scoring methods for selecting the next branching disjunction. We also analyse how to leverage infeasibility to expedite the B&B search. Computational results show that our scoring methods can reduce the number of explored B&B nodes by an order of magnitude when compared with scoring methods proposed in literature. Our infeasibility analysis further reduces the number of explored nodes.Open Acces

    From algorithm selection to generation using deep learning

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    Algorithm selection and generation techniques are two methods that can be used to exploit the performance complementarity of different algorithms when applied to large diverse sets of combinatorial problem instances. As there is no single algorithm that dominates all others on all problem instances, algorithm selection automatically selects an algorithm expected to perform best for each problem instance. Meanwhile, algorithm generation refers to combining different algorithms in a manner that allows the resulting method to improve the efficacy of a pool of algorithms. This thesis examines algorithm selection and generation within a single streaming problem domain, that is Bin-Packing, where novel approaches are proposed and evaluated on large problem sets. This research starts with presenting a novel feature-free approach to select the best performing heuristic by capturing the sequential information implicit in a streaming instance and using this as direct input to two Deep Learning (DL) models, Long-Short-Term Memory (LSTM) or Gated Recurrent Unit (GRU), to learn a mapping from an instance to an algorithm. Results obtained using the proposed approach show that the performance of the feature-free selectors significantly outperforms the performance of both the single best solver and the classical feature-based approach using well-known Machine Learning (ML) classifiers when applied to large sets of diverse problem instances. Next, a more radical approach is proposed: bypass algorithm selection altogether by training encoder-decoder LSTM using solutions obtained from a set of algorithms to directly predict a solution from the instance data behaving as an automatically generated algorithm. Experiments conducted on large datasets using problem batches of varying sizes show that the generated algorithm is able to accurately predict solutions, particularly with small batch sizes. Finally, the thesis develops the proposed encoder-decoder approach by introducing a novel neural approach for generating algorithms, in which a neural network acts as an algorithm by generating decisions. Two architectures are evaluated, an encoder-decoder LSTM and a feed-forward Neural Network (NN), and trained using the decisions output from existing algorithms on a large set of instances. Experiments show that the new generated algorithms are capable of solving a subset of instances better than the well-known bin-packing algorithms, and hence they can significantly improve the overall performance when they are added to a pool of algorithms

    Learning for Optimization with Virtual Savant

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    Optimization problems arising in multiple fields of study demand efficient algorithms that can exploit modern parallel computing platforms. The remarkable development of machine learning offers an opportunity to incorporate learning into optimization algorithms to efficiently solve large and complex problems. This thesis explores Virtual Savant, a paradigm that combines machine learning and parallel computing to solve optimization problems. Virtual Savant is inspired in the Savant Syndrome, a mental condition where patients excel at a specific ability far above the average. In analogy to the Savant Syndrome, Virtual Savant extracts patterns from previously-solved instances to learn how to solve a given optimization problem in a massively-parallel fashion. In this thesis, Virtual Savant is applied to three optimization problems related to software engineering, task scheduling, and public transportation. The efficacy of Virtual Savant is evaluated in different computing platforms and the experimental results are compared against exact and approximate solutions for both synthetic and realistic instances of the studied problems. Results show that Virtual Savant can find accurate solutions, effectively scale in the problem dimension, and take advantage of the availability of multiple computing resources.Los problemas de optimización que surgen en múltiples campos de estudio demandan algoritmos eficientes que puedan explotar las plataformas modernas de computación paralela. El notable desarrollo del aprendizaje automático ofrece la oportunidad de incorporar el aprendizaje en algoritmos de optimización para resolver problemas complejos y de grandes dimensiones de manera eficiente. Esta tesis explora Savant Virtual, un paradigma que combina aprendizaje automático y computación paralela para resolver problemas de optimización. Savant Virtual está inspirado en el Sı́ndrome de Savant, una condición mental en la que los pacientes se destacan en una habilidad especı́fica muy por encima del promedio. En analogı́a con el sı́ndrome de Savant, Savant Virtual extrae patrones de instancias previamente resueltas para aprender a resolver un determinado problema de optimización de forma masivamente paralela. En esta tesis, Savant Virtual se aplica a tres problemas de optimización relacionados con la ingenierı́a de software, la planificación de tareas y el transporte público. La eficacia de Savant Virtual se evalúa en diferentes plataformas informáticas y los resultados se comparan con soluciones exactas y aproximadas para instancias tanto sintéticas como realistas de los problemas estudiados. Los resultados muestran que Savant Virtual puede encontrar soluciones precisas, escalar eficazmente en la dimensión del problema y aprovechar la disponibilidad de múltiples recursos de cómputo.Fundación Carolina Agencia Nacional de Investigación e Innovación (ANII, Uruguay) Universidad de Cádiz Universidad de la Repúblic

    Operational Research IO2017, Valença, Portugal, June 28-30

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    This proceedings book presents selected contributions from the XVIII Congress of APDIO (the Portuguese Association of Operational Research) held in Valença on June 28–30, 2017. Prepared by leading Portuguese and international researchers in the field of operations research, it covers a wide range of complex real-world applications of operations research methods using recent theoretical techniques, in order to narrow the gap between academic research and practical applications. Of particular interest are the applications of, nonlinear and mixed-integer programming, data envelopment analysis, clustering techniques, hybrid heuristics, supply chain management, and lot sizing and job scheduling problems. In most chapters, the problems, methods and methodologies described are complemented by supporting figures, tables and algorithms. The XVIII Congress of APDIO marked the 18th installment of the regular biannual meetings of APDIO – the Portuguese Association of Operational Research. The meetings bring together researchers, scholars and practitioners, as well as MSc and PhD students, working in the field of operations research to present and discuss their latest works. The main theme of the latest meeting was Operational Research Pro Bono. Given the breadth of topics covered, the book offers a valuable resource for all researchers, students and practitioners interested in the latest trends in this field.info:eu-repo/semantics/publishedVersio

    Algorithm-aided Information Design: Hybrid Design approach on the edge of associative methodologies in AEC

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    Dissertação de mestrado em European Master in Building Information ModellingLast three decades have brought colossal progress to design methodologies within the common pursuit toward a seamless fusion between digital and physical worlds and augmenting it with the of computation power and network coverage. For this historically short period, two generations of methodologies and tools have emerged: Additive generation and parametric Associative generation of CAD. Currently, designers worldwide engaged in new forms of design exploration. From this race, two prominent methodologies have developed from Associative Design approach – Object-Oriented Design (OOD) and Algorithm-Aided Design (AAD). The primary research objective is to investigate, examine, and push boundaries between OOD and AAD for new design space determination, where advantages of both design methods are fused to produce a new generation methodology which is called in the present study AID (Algorithm-aided Information Design). The study methodology is structured into two flows. In the first flow, existing CAD methodologies are investigated, and the conceptual framework is extracted based on the state of art analysis, then analysed data is synthesized into the subject proposal. In the second flow, tools and workflows are elaborated and examined on practice to confirm the subject proposal. In compliance, the content of the research consists of two theoretical and practical parts. In the first theoretical part, a literature review is conducted, and assumptions are made to speculate about AID methodology, its tools, possible advantages and drawbacks. Next, case studies are performed according to sequential stages of digital design through the lens of practical AID methodology implementation. Case studies are covering such design aspects as model & documentation generation, design automation, interoperability, manufacturing control, performance analysis and optimization. Ultimately, a set of test projects is developed with the AID methodology applied. After the practical part, research returns to the theory where analytical information is gathered based on the literature review, conceptual framework, and experimental practice reports. In summary, the study synthesizes AID methodology as part of Hybrid Design, which enables creative use of tools and elaborating of agile design systems integrating additive and associative methodologies of Digital Design. In general, the study is based on agile methods and cyclic research development mixed between practice and theory to achieve a comprehensive vision of the subject.Last three decades have brought colossal progress to design methodologies within the common pursuit toward a seamless fusion between digital and physical worlds and augmenting it with the of computation power and network coverage. For this historically short period, two generations of methodologies and tools have emerged: Additive generation and parametric Associative generation of CAD. Currently, designers worldwide engaged in new forms of design exploration. From this race, two prominent methodologies have developed from Associative Design approach – Object-Oriented Design (OOD) and Algorithm-Aided Design (AAD). The primary research objective is to investigate, examine, and push boundaries between OOD and AAD for new design space determination, where advantages of both design methods are fused to produce a new generation methodology which is called in the present study AID (Algorithm-aided Information Design). The study methodology is structured into two flows. In the first flow, existing CAD methodologies are investigated, and the conceptual framework is extracted based on the state of art analysis, then analysed data is synthesized into the subject proposal. In the second flow, tools and workflows are elaborated and examined on practice to confirm the subject proposal. In compliance, the content of the research consists of two theoretical and practical parts. In the first theoretical part, a literature review is conducted, and assumptions are made to speculate about AID methodology, its tools, possible advantages and drawbacks. Next, case studies are performed according to sequential stages of digital design through the lens of practical AID methodology implementation. Case studies are covering such design aspects as model & documentation generation, design automation, interoperability, manufacturing control, performance analysis and optimization. Ultimately, a set of test projects is developed with the AID methodology applied. After the practical part, research returns to the theory where analytical information is gathered based on the literature review, conceptual framework, and experimental practice reports. In summary, the study synthesizes AID methodology as part of Hybrid Design, which enables creative use of tools and elaborating of agile design systems integrating additive and associative methodologies of Digital Design. In general, the study is based on agile methods and cyclic research development mixed between practice and theory to achieve a comprehensive vision of the subject
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