Download or read book Discrete Optimization in Architecture written by Machi Zawidzki and published by Springer. This book was released on 2016-07-25 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is comprised of two parts, both of which explore modular systems: Pipe-Z (PZ) and Truss-Z (TZ), respectively. It presents several methods of creating PZ and TZ structures subjected to discrete optimization. The algorithms presented employ graph-theoretic and heuristic methods. The underlying idea of both systems is to create free-form structures using the minimal number of types of modular elements. PZ is more conceptual, as it forms single-branch mathematical knots with a single type of module. Conversely, TZ is a skeletal system for creating free-form pedestrian ramps and ramp networks among any number of terminals in space. In physical space, TZ uses two types of modules that are mirror reflections of each other. The optimization criteria discussed include: the minimal number of units, maximal adherence to the given guide paths, etc.

Download or read book Discrete Optimization in Architecture written by Machi Zawidzki and published by Springer. This book was released on 2016-09-15 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the extremely modular systems that meet two criteria: they allow the creation of structurally sound free-form structures, and they are comprised of as few types of modules as possible. Divided into two parts, it presents Pipe-Z (PZ) and Truss-Z (TZ) systems. PZ is more fundamental and forms spatial mathematical knots by assembling one type of unit (PZM). The shape of PZ is controlled by relative twists of a sequence of congruent PZMs. TZ is a skeletal system for creating free-form pedestrian ramps and ramp networks among any number of terminals in space. TZ structures are composed of four variations of a single basic unit subjected to affine transformations (mirror reflection, rotation and combination of both).

Download or read book Discrete Optimization in Architecture written by Machi Zawidzki and published by Springer. This book was released on 2016-07-09 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents three projects that demonstrate the fundamental problems of architectural design and urban composition – the layout design, evaluation and optimization. Part I describes the functional layout design of a residential building, and an evaluation of the quality of a town square (plaza). The algorithm for the functional layout design is based on backtracking using a constraint satisfaction approach combined with coarse grid discretization. The algorithm for the town square evaluation is based on geometrical properties derived directly from its plan. Part II introduces a crowd-simulation application for the analysis of escape routes on floor plans, and optimization of a floor plan for smooth crowd flow. The algorithms presented employ agent-based modeling and cellular automata.

Download or read book Discrete Optimization written by E. Boros and published by Elsevier. This book was released on 2003-03-19 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most frequently occurring types of optimization problems involves decision variables which have to take integer values. From a practical point of view, such problems occur in countless areas of management, engineering, administration, etc., and include such problems as location of plants or warehouses, scheduling of aircraft, cutting raw materials to prescribed dimensions, design of computer chips, increasing reliability or capacity of networks, etc. This is the class of problems known in the professional literature as "discrete optimization" problems. While these problems are of enormous applicability, they present many challenges from a computational point of view. This volume is an update on the impressive progress achieved by mathematicians, operations researchers, and computer scientists in solving discrete optimization problems of very large sizes. The surveys in this volume present a comprehensive overview of the state of the art in discrete optimization and are written by the most prominent researchers from all over the world. This volume describes the tremendous progress in discrete optimization achieved in the last 20 years since the publication of Discrete Optimization '77, Annals of Discrete Mathematics, volumes 4 and 5, 1979 (Elsevier). It contains surveys of the state of the art written by the most prominent researchers in the field from all over the world, and covers topics like neighborhood search techniques, lift and project for mixed 0-1 programming, pseudo-Boolean optimization, scheduling and assignment problems, production planning, location, bin packing, cutting planes, vehicle routing, and applications to graph theory, mechanics, chip design, etc. Key features: • state of the art surveys • comprehensiveness • prominent authors • theoretical, computational and applied aspects. This book is a reprint of Discrete Applied Mathematics Volume 23, Numbers 1-3

Download or read book Handbook on Modelling for Discrete Optimization written by Gautam M. Appa and published by Springer Science & Business Media. This book was released on 2006-08-18 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to demonstrate and detail the pervasive nature of Discrete Optimization. The handbook couples the difficult, critical-thinking aspects of mathematical modeling with the hot area of discrete optimization. It is done with an academic treatment outlining the state-of-the-art for researchers across the domains of the Computer Science, Math Programming, Applied Mathematics, Engineering, and Operations Research. The book utilizes the tools of mathematical modeling, optimization, and integer programming to solve a broad range of modern problems.

Download or read book Discrete Optimization written by E. Boros and published by JAI Press. This book was released on 2003-03-19 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most frequently occurring types of optimization problems involves decision variables which have to take integer values. From a practical point of view, such problems occur in countless areas of management, engineering, administration, etc., and include such problems as location of plants or warehouses, scheduling of aircraft, cutting raw materials to prescribed dimensions, design of computer chips, increasing reliability or capacity of networks, etc. This is the class of problems known in the professional literature as "discrete optimization" problems. While these problems are of enormous applicability, they present many challenges from a computational point of view. This volume is an update on the impressive progress achieved by mathematicians, operations researchers, and computer scientists in solving discrete optimization problems of very large sizes. The surveys in this volume present a comprehensive overview of the state of the art in discrete optimization and are written by the most prominent researchers from all over the world. This volume describes the tremendous progress in discrete optimization achieved in the last 20 years since the publication of Discrete Optimization '77, Annals of Discrete Mathematics, volumes 4 and 5, 1979 (Elsevier). It contains surveys of the state of the art written by the most prominent researchers in the field from all over the world, and covers topics like neighborhood search techniques, lift and project for mixed 0-1 programming, pseudo-Boolean optimization, scheduling and assignment problems, production planning, location, bin packing, cutting planes, vehicle routing, and applications to graph theory, mechanics, chip design, etc. Key features: . state of the art surveys . comprehensiveness . prominent authors . theoretical, computational and applied aspects. This book is a reprint of Discrete Applied Mathematics Volume 23, Numbers 1-3

Download or read book Parallel Processing of Discrete Optimization Problems written by Panos M. Pardalos and published by American Mathematical Soc.. This book was released on 1995-01-01 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers presented at the Workshop on Parallel Processing of Discrete Optimization Problems held at DIMACS in April 1994. The contents cover a wide spectrum of the most recent algorithms and applications in parallel processing of discrete optimization and related problems. Topics include parallel branch and bound algorithms, scalability, load balancing, parallelism and irregular data structures and scheduling task graphs on parallel machines. Applications include parallel algorithms for solving satisfiability problems, location problems, linear programming, quadratic and linear assignment problems. This book would be suitable as a textbook in advanced courses on parallel algorithms and combinatorial optimization.

Download or read book Nonlinear Discrete Optimization written by Shmuel Onn and published by European Mathematical Society. This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph develops an algorithmic theory of nonlinear discrete optimization. It introduces a simple and useful setup, which enables the polynomial time solution of broad fundamental classes of nonlinear combinatorial optimization and integer programming problems in variable dimension. An important part of this theory is enhanced by recent developments in the algebra of Graver bases. The power of the theory is demonstrated by deriving the first polynomial time algorithms in a variety of application areas within operations research and statistics, including vector partitioning, matroid optimization, experimental design, multicommodity flows, multi-index transportation and privacy in statistical databases. This monograph is intended for graduate students and researchers. It is accessible to anyone with standard undergraduate knowledge and mathematical maturity.

Download or read book Engineering Design Optimization written by Joaquim R. R. A. Martins and published by Cambridge University Press. This book was released on 2021-11-18 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on course-tested material, this rigorous yet accessible graduate textbook covers both fundamental and advanced optimization theory and algorithms. It covers a wide range of numerical methods and topics, including both gradient-based and gradient-free algorithms, multidisciplinary design optimization, and uncertainty, with instruction on how to determine which algorithm should be used for a given application. It also provides an overview of models and how to prepare them for use with numerical optimization, including derivative computation. Over 400 high-quality visualizations and numerous examples facilitate understanding of the theory, and practical tips address common issues encountered in practical engineering design optimization and how to address them. Numerous end-of-chapter homework problems, progressing in difficulty, help put knowledge into practice. Accompanied online by a solutions manual for instructors and source code for problems, this is ideal for a one- or two-semester graduate course on optimization in aerospace, civil, mechanical, electrical, and chemical engineering departments.

Download or read book Discrete Structural Optimization as a Sequential Decision Process Solved Using Deep Reinforcement Learning written by Maximilian Edward Ororbia and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology optimization is a mathematical framework that in general seeks to determine the optimal layout of material in a design domain. If the design variables are continuous, then often sensitivities can be derived and used with gradient based optimization techniques. However, for certain applications the design variables are inherently discrete, for example the design of steel structures that are constructed of standardized steel sections. This work focuses on the latter, whereby the optimization of structures with discrete elements and discrete design variables is formulated as a sequential decision process solved using reinforcement learning (RL) and deep reinforcement learning (DRL), which has been shown to efficiently provide adept solutions to a variety of high-dimensional planning and learning problems. Hence, this work mathematically models the discrete optimization of planar structures, including trusses and frames, as a Markov decision process (MDP). By modeling discrete structural optimization as an MDP, the set of all feasible design solutions can be precisely represented and the MDP naturally, but not exclusively, accommodates discrete actions. Within this framing, the MDP states correspond to specific structural designs represented as finite graph configurations and the actions correspond to specific topological and parametric grammars that are applied to alter the structure, transitioning the design to a new state and graph configuration. Key to modeling discrete optimization as an MDP is the relation of the rewards to the change in the design's performance as the agent explores alternate design configurations. Through this relation, the agent learns an optimal policy, that is, a sequence of necessary alteration actions, that maximizes its cumulative reward and simultaneously synthesizes a high-performing design solution, if not the global optimal, with respect to the specified design problem's objective and specified constraints. The discrete MDP model solved using RL and DRL is applied to the discrete optimization of planar truss and frame structures. To demonstrate the merit of the idea and because elements of the MDP tuple are unknown to the agent a priori, a tabular implementation of reinforcement learning (RL), specifically a Q-learning algorithm, was employed to solve the MDP due to its strong convergence properties. However, for problems with high dimensional state and action spaces, that is, with a large set of feasible design solutions, the number of state visits required to converge to the optimal policy becomes intractable, a problem commonly referred to as the curse of dimensionality. Tabular RL algorithms can become inefficient for solving design problems with relatively large state and action spaces due to their memory limitation and need for an excessive number of experiences to learn the optimal policy. Hence by extending the general discrete structural optimization MDP to be solved using DRL, a deep neural network architecture is specifically developed to approximate the state-action value function, such that the network has far fewer parameters than the cardinality of the state space of feasible design solutions. This enables the MDP framework to adeptly solve discrete topology optimization design problems with large state and action spaces. A benefit of the suggested method, in comparison to other discrete optimization approaches, is that the MDP framework is grounded in mathematics and is not dependent on the specifics of the structural model. The framework is evaluated in the context of the discrete structural optimization of planar trusses and frames with discrete elements and multiple discrete cross-sectional areas, and its utility is investigated through several numerical examples, each with different state space cardinalities. The objective of the design task is to determine both the layout of structural elements and the assignment of cross-sectional areas that minimize the displacement at a specified node for a given external force(s) determined using either linear or nonlinear finite element analysis, subject to stability and volume constraints. In this work, both the agent's learned optimal policy and the resulting synthesized design solution are validated against the policy determined by using a state-action value iteration dynamic programming algorithm, chosen for its strong convergence guarantees, and the global optimal design configuration identified from an exhaustive evaluation of all feasible design solutions, respectively. Also through qualitative and quantitative comparison with other considered alternative methods, the MDP framework is observed to adeptly learn optimal policies that synthesize optimal design solutions with lower computational effort.

Download or read book Discretization Methods and Structural Optimization Procedures and Applications written by Hans A. Eschenauer and published by Springer. This book was released on 1989-03-23 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main subject of this GAMM-Seminar is research in the field of discretization methods and structural optimization. The topics are procedures, strategies and algorithms for structural optimization based on modern discretization techniques. In particular, sensitivity and mesh-generation, large-scale structural systems and decomposition for finite element systems are covered. Structural optimization is presented as multipurpose and multistage optimization. Optimal design and shape optimization are treated in analytical form and as an interactive process. Finally, knowledge-based algorithms for design optimization and expert systems are discussed.

Download or read book Benchmarking Discrete Optimization Heuristics written by and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Discrete Structural Optimization written by Witold Gutkowski and published by Springer. This book was released on 1994 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Discrete Optimization written by R. Gary Parker and published by Elsevier. This book was released on 2014-06-28 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats the fundamental issues and algorithmic strategies emerging as the core of the discipline of discrete optimization in a comprehensive and rigorous fashion. Following an introductory chapter on computational complexity, the basic algorithmic results for the two major models of polynomial algorithms are introduced--models using matroids and linear programming. Further chapters treat the major non-polynomial algorithms: branch-and-bound and cutting planes. The text concludes with a chapter on heuristic algorithms.Several appendixes are included which review the fundamental ideas of linear programming, graph theory, and combinatorics--prerequisites for readers of the text. Numerous exercises are included at the end of each chapter.

Download or read book Discrete Optimization I written by and published by Elsevier. This book was released on 2000-04-01 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrete Optimization I

Download or read book Discrete Optimization Methods in Scheduling and Computer aided Design written by J.-M. Proth and published by . This book was released on 2000 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Discrete Optimization Algorithms written by Maciej M. Sys?o and published by Courier Corporation. This book was released on 2006-01-01 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rich in publications, the well-established field of discrete optimization nevertheless features relatively few books with ready-to-use computer programs. This book, geared toward upper-level undergraduates and graduate students, addresses that need. In addition, it offers a look at the programs' derivation and performance characteristics. Subjects include linear and integer programming, packing and covering, optimization on networks, and coloring and scheduling. A familiarity with design, analysis, and use of computer algorithms is assumed, along with knowledge of programming in Pascal. The book can be used as a supporting text in discrete optimization courses or as a software handbook, with twenty-six programs that execute the most common algorithms in each topic area. Each chapter is self-contained, allowing readers to browse at will.