A modified univariate search algorithm
30 May 1999-Vol. 6, pp 306-309
TL;DR: A modified univariateSearch algorithm that overcomes two major limitations of conventional univariate search method, minimizes the probability of premature convergence to poor local minima by utilizing a non-deterministic search procedure based on an analogy with the analytical univariatesearch.
Abstract: This paper describes a modified univariate search algorithm that overcomes two major limitations of conventional univariate search method. It minimizes the probability of premature convergence to poor local minima by utilizing a non-deterministic search procedure based on an analogy with the analytical univariate search, and improves' the quality of solutions by dealing with populations of solutions rather than with single solutions for solving unconstrained as well as constrained optimization problems involving continuous or discrete variables. Unlike Genetic Algorithms (GA's), which also are based on non-deterministic search and exhibit intrinsic parallelism, the solutions do not interact or mix together to produce new solutions (offspring); instead, new solutions are generated by unilaterally updating a single variable at a time in individual solutions. Results of two test problems are presented and compared with those obtained by standard GA, modified GA, and an optimization program based on the method of feasible directions.
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TL;DR: The obtained results show that in the case when the proportional constant of the PI controller varies in time according to the appropriate law, the microinverter output current sinus shape distortions decrease as compared to the cases when the ordinary PI controller is used.
Abstract: The modification of the proportional–integral (PI) controller with the variable proportional constant for tracking of the grid-connected photovoltaic microinverter output current has been proposed. The obtained results show that in the case when the proportional constant of the PI controller varies in time according to the appropriate law, the microinverter output current sinus shape distortions decrease as compared to the case when the ordinary PI controller is used. The operation of the microinverter with the proposed controller was investigated for the cases when the electrical grid voltage sinus shape is not distorted and when it is distorted by the higher harmonics.
11 citations
Cites methods from "A modified univariate search algori..."
...The univariate search method algorithm [39,40] was used for the tuning of controller parameters....
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TL;DR: The digital simulator presented in this paper generates the worst-case waveforms for specified bounds on noise components present in the relay input signals, and determines the performance limits of a computer relay by performing a single test only.
Abstract: Unlike most other digital simulators that generate test waveforms for specific system configurations, playback previously recorded fault waveforms, or randomly generate artificial waveforms, the digital simulator presented in this paper generates the worst case waveforms for specified bounds on noise components present in the relay input signals. As a result, the performance limits of a computer relay can be determined, for specified bounds on its noise components, by performing a single test only. The parameters that define the worst case waveforms; are obtained by utilizing a modified univariate search algorithm. The PC-based simulator was implemented using a general-purpose multifunction card and a graphical programming package called Visual Designer. It did not require any text-based programming for tasks such as interfacing, digital-to-analog conversion, and outputting the discrete analog values of the generated waveform under hardware control. For demonstrating the operation of the digital simulator, a computer relay was also developed in the laboratory and its performance limits were determined.
6 citations
Cites methods from "A modified univariate search algori..."
...Accordingly, an optimization program MOUSE [18], based on a modified univariate search technique, was utilized....
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...For solving a particular optimization problem using MOUSE, a user-supplied routine is required to calculate the value of the fitness function [18]....
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TL;DR: The paper firstly introduces the mathematical model of regression least squares support vector machine (LSSVM), and designs incremental learning algorithms by the calculation formula of block matrix, which is used to model nonlinear system, based on which to control nonlinear systems by model predictive method.
Abstract: Support vector machine is a learning technique based on the structural risk minimization principle, and it is also a class of regression method with good generalization ability. The paper firstly introduces the mathematical model of regression least squares support vector machine (LSSVM), and designs incremental learning algorithms by the calculation formula of block matrix, then uses LSSVM to model nonlinear system, based on which to control nonlinear systems by model predictive method. Simulation experiments indicate that the proposed method provides satisfactory performance, and it achieves superior modeling performance to the conventional method based on neural networks, moreover it achieves well control performance.
4 citations
Cites methods from "A modified univariate search algori..."
...And we use an optimization method given in [10] to solve the above optimization problem in predictive control, then we will get the predictive control signal sequence u(k)....
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01 Jan 2020
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References
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Book•
01 Jan 1983
TL;DR: Theoretical Equivalence of Mayer, Lagrange, and Bolza Problems of Optimal Control, and the Necessary Conditions and Sufficient Conditions Convexity and Lower Semicontinuity.
Abstract: 1 Problems of Optimization-A General View.- 1.1 Classical Lagrange Problems of the Calculus of Variations.- 1.2 Classical Lagrange Problems with Constraints on the Derivatives.- 1.3 Classical Bolza Problems of the Calculus of Variations.- 1.4 Classical Problems Depending on Derivatives of Higher Order.- 1.5 Examples of Classical Problems of the Calculus of Variations.- 1.6 Remarks.- 1.7 The Mayer Problems of Optimal Control.- 1.8 Lagrange and Bolza Problems of Optimal Control.- 1.9 Theoretical Equivalence of Mayer, Lagrange, and Bolza Problems of Optimal Control. Problems of the Calculus of Variations as Problems of Optimal Control.- 1.10 Examples of Problems of Optimal Control.- 1.11 Exercises.- 1.12 The Mayer Problems in Terms of Orientor Fields.- 1.13 The Lagrange Problems of Control as Problems of the Calculus of Variations with Constraints on the Derivatives.- 1.14 Generalized Solutions.- Bibliographical Notes.- 2 The Classical Problems of the Calculus of Variations: Necessary Conditions and Sufficient Conditions Convexity and Lower Semicontinuity.- 2.1 Minima and Maxima for Lagrange Problems of the Calculus of Variations.- 2.2 Statement of Necessary Conditions.- 2.3 Necessary Conditions in Terms of Gateau Derivatives.- 2.4 Proofs of the Necessary Conditions and of Their Invariant Character.- 2.5 Jacobi's Necessary Condition.- 2.6 Smoothness Properties of Optimal Solutions.- 2.7 Proof of the Euler and DuBois-Reymond Conditions in the Unbounded Case.- 2.8 Proof of the Transversality Relations.- 2.9 The String Property and a Form of Jacobi's Necessary Condition.- 2.10 An Elementary Proof of Weierstrass's Necessary Condition.- 2.11 Classical Fields and Weierstrass's Sufficient Conditions.- 2.12 More Sufficient Conditions.- 2.13 Value Function and Further Sufficient Conditions.- 2.14 Uniform Convergence and Other Modes of Convergence.- 2.15 Semicontinuity of Functionals.- 2.16 Remarks on Convex Sets and Convex Real Valued Functions.- 2.17 A Lemma Concerning Convex Integrands.- 2.18 Convexity and Lower Semicontinuity: A Necessary and Sufficient Condition.- 2.19 Convexity as a Necessary Condition for Lower Semicontinuity.- 2.20 Statement of an Existence Theorem for Lagrange Problems of the Calculus of Variations.- Bibliographical Notes.- 3 Examples and Exercises on Classical Problems.- 3.1 An Introductory Example.- 3.2 Geodesics.- 3.3 Exercises.- 3.4 Fermat's Principle.- 3.5 The Ramsay Model of Economic Growth.- 3.6 Two Isoperimetric Problems.- 3.7 More Examples of Classical Problems.- 3.8 Miscellaneous Exercises.- 3.9 The Integral I = ?(x?2 ? x2)dt.- 3.10 The Integral I = ?xx?2dt.- 3.11 The Integral I = ?x?2(1 + x?)2dt.- 3.12 Brachistochrone, or Path of Quickest Descent.- 3.13 Surface of Revolution of Minimum Area.- 3.14 The Principles of Mechanics.- Bibliographical Notes.- 4 Statement of the Necessary Condition for Mayer Problems of Optimal Control.- 4.1 Some General Assumptions.- 4.2 The Necessary Condition for Mayer Problems of Optimal Control.- 4.3 Statement of an Existence Theorem for Mayer's Problems of Optimal Control.- 4.4 Examples of Transversality Relations for Mayer Problems.- 4.5 The Value Function.- 4.6 Sufficient Conditions.- 4.7 Appendix: Derivation of Some of the Classical Necessary Conditions of Section 2.1 from the Necessary Condition for Mayer Problems of Optimal Control.- 4.8 Appendix: Derivation of the Classical Necessary Condition for Isoperimetric Problems from the Necessary Condition for Mayer Problems of Optimal Control.- 4.9 Appendix: Derivation of the Classical Necessary Condition for Lagrange Problems of the Calculus of Variations with Differential Equations as Constraints.- Bibliographical Notes.- 5 Lagrange and Bolza Problems of Optimal Control and Other Problems.- 5.1 The Necessary Condition for Bolza and Lagrange Problems of Optimal Control.- 5.2 Derivation of Properties (P1?)-(P4?) from (P1)-(P4).- 5.3 Examples of Applications of the Necessary Conditions for Lagrange Problems of Optimal Control.- 5.4 The Value Function.- 5.5 Sufficient Conditions for the Bolza Problem.- Bibliographical Notes.- 6 Examples and Exercises on Optimal Control.- 6.1 Stabilization of a Material Point Moving on a Straight Line under a Limited External Force.- 6.2 Stabilization of a Material Point under an Elastic Force and a Limited External Force.- 6.3 Minimum Time Stabilization of a Reentry Vehicle.- 6.4 Soft Landing on the Moon.- 6.5 Three More Problems on the Stabilization of a Point Moving on a Straight Line.- 6.6 Exercises.- 6.7 Optimal Economic Growth.- 6.8 Two More Classical Problems.- 6.9 The Navigation Problem.- Bibliographical Notes.- 7 Proofs of the Necessary Condition for Control Problems and Related Topics.- 7.1 Description of the Problem of Optimization.- 7.2 Sketch of the Proofs.- 7.3 The First Proof.- 7.4 Second Proof of the Necessary Condition.- 7.5 Proof of Boltyanskii's Statements (4.6.iv-v).- Bibliographical Notes.- 8 The Implicit Function Theorem and the Elementary Closure Theorem.- 8.1 Remarks on Semicontinuous Functionals.- 8.2 The Implicit Function Theorem.- 8.3 Selection Theorems.- 8.4 Convexity, Caratheodory's Theorem, Extreme Points.- 8.5 Upper Semicontinuity Properties of Set Valued Functions.- 8.6 The Elementary Closure Theorem.- 8.7 Some Fatou-Like Lemmas.- 8.8 Lower Closure Theorems with Respect to Uniform Convergence.- Bibliographical Notes.- 9 Existence Theorems: The Bounded, or Elementary, Case.- 9.1 Ascoli's Theorem.- 9.2 Filippov's Existence Theorem for Mayer Problems of Optimal Control.- 9.3 Filippov's Existence Theorem for Lagrange and Bolza Problems of Optimal Control.- 9.4 Elimination of the Hypothesis that A Is Compact in Filippov's Theorem for Mayer Problems.- 9.5 Elimination of the Hypothesis that A Is Compact in Filippov's Theorem for Lagrange and Bolza Problems.- 9.6 Examples.- Bibliographical Notes.- 10 Closure and Lower Closure Theorems under Weak Convergence.- 10.1 The Banach-Saks-Mazur Theorem.- 10.2 Absolute Integrability and Related Concepts.- 10.3 An Equivalence Theorem.- 10.4 A Few Remarks on Growth Conditions.- 10.5 The Growth Property (?) Implies Property (Q).- 10.6 Closure Theorems for Orientor Fields Based on Weak Convergence.- 10.7 Lower Closure Theorems for Orientor Fields Based on Weak Convergence.- 10.8 Lower Semicontinuity in the Topology of Weak Convergence.- 10.9 Necessary and Sufficient Conditions for Lower Closure.- Bibliographical Notes.- 11 Existence Theorems: Weak Convergence and Growth Conditions.- 11.1 Existence Theorems for Orientor Fields and Extended Problems.- 112 Elimination of the Hypothesis that A Is Bounded in Theorems (11.1. i-iv).- 11.3 Examples.- 11.4 Existence Theorems for Problems of Optimal Control with Unbounded Strategies.- 11.5 Elimination of the Hypothesis that A Is Bounded in Theorems (11.4.i-v).- 11.6 Examples.- 11.7 Counterexamples.- Bibliographical Notes.- 12 Existence Theorems: The Case of an Exceptional Set of No Growth.- 12.1 The Case of No Growth at the Points of a Slender Set. Lower Closure Theorems..- 12.2 Existence Theorems for Extended Free Problems with an Exceptional Slender Set.- 12.3 Existence Theorems for Problems of Optimal Control with an Exceptional Slender Set.- 12.4 Examples.- 12.5 Counterexamples.- Bibliographical Notes.- 13 Existence Theorems: The Use of Lipschitz and Tempered Growth Conditions.- 13.1 An Existence Theorem under Condition (D).- 13.2 Conditions of the F, G, and H Types Each Implying Property (D) and Weak Property (Q).- 13.3 Examples.- Bibliographical Notes.- 14 Existence Theorems: Problems of Slow Growth.- 14.1 Parametric Curves and Integrals.- 14.2 Transformation of Nonparametric into Parametric Integrals.- 14.3 Existence Theorems for (Nonparametric) Problems of Slow Growth.- 14.4 Examples.- Bibliographical Notes.- 15 Existence Theorems: The Use of Mere Pointwise Convergence on the Trajectories.- 15.1 The Helly Theorem.- 15.2 Closure Theorems with Components Converging Only Pointwise.- 15.3 Existence Theorems for Extended Problems Based on Pointwise Convergence.- 15.4 Existence Theorems for Problems of Optimal Control Based on Pointwise Convergence.- 15.5 Exercises.- Bibliographical Notes.- 16 Existence Theorems: Problems with No Convexity Assumptions.- 16.1 Lyapunov Type Theorems.- 16.2 The Neustadt Theorem for Mayer Problems with Bounded Controls.- 16.3 The Bang-Bang Theorem.- 16.4 The Neustadt Theorem for Lagrange and Bolza Problems with Bounded Controls.- 16.5 The Case of Unbounded Controls.- 16.6 Examples for the Unbounded Case.- 16.7 Problems of the Calculus of Variations without Convexity Assumptions.- Bibliographical Notes.- 17 Duality and Upper Semicontinuity of Set Valued Functions.- 17.1 Convex Functions on a Set.- 17.2 The Function T(x z).- 17.3 Seminormality.- 17.4 Criteria for Property (Q).- 17.5 A Characterization of Property (Q) for the Sets $$\tilde Q$$(t, x) in Terms of Seminormality.- 17.6 Duality and Another Characterization of Property (Q) in Terms of Duality.- 17.7 Characterization of Optimal Solutions in Terms of Duality.- 17.8 Property (Q) as an Extension of Maximal Monotonicity.- Bibliographical Notes.- 18 Approximation of Usual and of Generalized Solutions.- 18.1 The Gronwall Lemma.- 18.2 Approximation of AC Solutions by Means of C1 Solutions.- 18.3 The Brouwer Fixed Point Theorem.- 18.4 Further Results Concerning the Approximation of AC Trajectories by Means of C1 Trajectories.- 18.5 The Infimum for AC Solutions Can Be Lower than the One for C1 Solutions.- 18.6 Approximation of Generalized Solutions by Means of Usual Solutions.- 18.7 The Infimum for Generalized Solutions Can Be Lower than the One for Usual Solutions.- Bibliographical Notes.- Author Index.
2,371 citations
TL;DR: This book discusses the construction of mental ray, a model for synthetic lighting, and some of the techniques used to design and implement such models.
Abstract: Introduction. Chapter 1: Introduction to mental ray. What Is mental ray? Why Use mental ray? The Structure of mental ray. mental ray Integration. Command-Line Rendering and the Stand-Alone Renderer. mental ray Shaders and Shader Libraries. Indirect Illumination. Chapter 2: Rendering Algorithms. Introduction to Synthetic Lighting. Rendering under the Hood. mental ray Rendering Algorithms. Scanline Rendering in Depth. Raytrace Rendering in Depth. Hardware Rendering. Chapter 3: mental ray Output. mental ray Data Types. The Frame Buffer. Frame Buffer Options. mental ray Cameras. Output Statements. Chapter 4: Camera Fundamentals. Camera Basics and Aspect Ratios. Camera Lenses. Host Application Settings. Chapter 5: Quality Control. Sampling and Filtering in Host Applications. Raytrace Acceleration. Diagnostic and BSP Fine-Tuning. Chapter 6: Lights and Soft Shadows. mental ray Lights. Area Lights. Host Application Settings. Light Profiles. Chapter 7: Shadow Algorithms. Shadow Algorithms. Raytrace Shadows. Depth-Based Shadows. Stand-Alone and Host Settings. Chapter 8: Motion Blur. mental ray Motion Blur. Motion-Blur Options. Motion-Blur Render Algorithms. Host Settings. Chapter 9: The Fundamentals of Light and Shading Models. The Fundamentals of Light. Light Transport and Shading Models. mental ray Shaders. Chapter 10: mental ray Shaders and Shader Trees. Installing Custom Shaders. DGS and Dielectric Shading Models. Glossy Reflection and Refraction Shaders. Brushed Metals with the Glossy and Anisotropic Shaders. The Architectural (mia) Material. Chapter 11: mental ray Textures and Projections. Texture Space and Projections. mental ray Bump Mapping. mental ray Projection and Remapping Shaders. Host Application Settings. Memory Mapping, Pyramid Images, and Image Filtering. Chapter 12: Indirect Illumination. mental ray Indirect Illumination. Photon Shaders and Photon-Casting Lights. Indirect Illumination Options and Fine-Tuning. Participating Media (PM) Effects. Chapter 13: Final Gather and Ambient Occlusion. Final Gather Fundamentals. Final Gather Options and Techniques. Advanced Final Gather Techniques. Ambient Occlusion. Chapter 14: Subsurface Scattering. Advanced Shading Models. Nonphysical Subsurface Scattering. An Advanced Shader Tree. Physical Subsurface Scattering. Appendix: About the Companion CD. Index.
1,022 citations
Book•
01 Jan 2010
TL;DR: VLSI Physical Design Automation is an essential introduction for senior undergraduates, postgraduates and anyone starting work in the field of CAD for VLSI.
Abstract: From the Publisher:
VLSI is an important area of electronic and computer engineering: however, there are few textbooks available for undergraduate education in VLSI design automation and chip layout. VLSI Physical Design Automation fills the void and is an essential introduction for senior undergraduates, postgraduates and anyone starting work in the field of CAD for VLSI. It covers all aspects of physical design, together with such related areas as automatic cell generation, silicon compilation, layout editors and compaction. A problem solving approach has been adopted and each solution has been illustrated with examples. Each topic is treated in a standard format of Problem Definition, Cost Functions and Constraints, Possible Approaches and Latest Developments.
273 citations
16 Nov 1996
TL;DR: It turns out that the performance of GALME is remarkably superior to that of the traditional GA, and its theoretical justification is described.
Abstract: Genetic algorithms (GAs) are promising for function optimization. Methods for function optimization are required to perform local search as well as global search in a balanced way. It is recognized that the traditional GA is not well suited to local search. I have tested algorithms combining various ideas to develop a new genetic algorithm to obtain the global optimum effectively. The results show that the performance of a genetic algorithm using large mutation rates and population-elitist selection (GALME) is superior. This paper describes the GALME and its theoretical justification, and presents the results of experiments, compared to the traditional GA. Within the range of the experiments, it turns out that the performance of GALME is remarkably superior to that of the traditional GA.
36 citations