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Global Optimization (global + optimization)
Terms modified by Global Optimization Selected AbstractsGlobal optimization of SixHy at the ab initio level via an iteratively parametrized semiempirical methodINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4-5 2003Yingbin Ge Abstract Previously we searched for the ab initio global minima of several SixHy clusters by a genetic algorithm in which we used the AM1 semiempirical method to facilitate a rapid energy calculation for the many different cluster geometries explored. However, we found that the AM1 energy ranking significantly differs from the ab initio energy ranking. To better guarantee locating the ab initio global minimum while retaining the efficiency of the AM1 method, we present an improved iterative global optimization strategy. The method involves two separate genetic algorithms that are invoked consecutively. One is the cluster genetic algorithm (CGA), mentioned above, to find the semiempirical SixHy cluster global minimum. A second and separate parametrization genetic algorithm (PGA) is used to reparametrize the AM1 method using some of the ab initio data generated from the CGA to form a training set of different reference clusters but with fixed SixHy stoichiometry. The cluster global optimization search (CGA) and the semiempirical parametrization (PGA) steps are performed iteratively until the semiempirical GA reparametrized AM1 (GAM1) calculations give low-energy optimized structures that are consistent with the globally optimized ab initio structure. We illustrate the new global optimization strategy by attempting to find the ab initio global minima for the Si6H2 and Si6H6 clusters. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003 [source] Global optimization for robust control synthesis based on the Matrix Product Eigenvalue ProblemINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9 2001Yuji Yamada Abstract In this paper, we propose a new formulation for a class of optimization problems which occur in general robust control synthesis, called the Matrix Product Eigenvalue Problem (MPEP): Minimize the maximum eigenvalue of the product of two block-diagonal positive-definite symmetric matrices under convex constraints. This optimization class falls between methods of guaranteed low complexity such as the linear matrix inequality (LMI) optimization and methods known to be NP-hard such as the bilinear matrix inequality (BMI) formulation, while still addressing most robust control synthesis problems involving BMIs encountered in applications. The objective of this paper is to provide an algorithm to find a global solution within any specified tolerance , for the MPEP. We show that a finite number of LMI problems suffice to find the global solution and analyse its computational complexity in terms of the iteration number. We prove that the worst-case iteration number grows no faster than a polynomial of the inverse of the tolerance given a fixed size of the block-diagonal matrices in the eigenvalue condition. Copyright 2001 © John Wiley & Sons, Ltd. [source] A multi-objective optimization approach to polygeneration energy systems designAICHE JOURNAL, Issue 5 2010Pei Liu Abstract Polygeneration, typically involving co-production of methanol and electricity, is a promising energy conversion technology which provides opportunities for high energy utilization efficiency and low/zero emissions. The optimal design of such a complex, large-scale and highly nonlinear process system poses significant challenges. In this article, we present a multiobjective optimization model for the optimal design of a methanol/electricity polygeneration plant. Economic and environmental criteria are simultaneously optimized over a superstructure capturing a number of possible combinations of technologies and types of equipment. Aggregated models are considered, including a detailed methanol synthesis step with chemical kinetics and phase equilibrium considerations. The resulting model is formulated as a non-convex mixed-integer nonlinear programming problem. Global optimization and parallel computation techniques are employed to generate an optimal Pareto frontier. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source] Global optimization of mixed-integer nonlinear problemsAICHE JOURNAL, Issue 9 2000C. S. Adjiman Two novel deterministic global optimization algorithms for nonconvex mixed-integer problems (MINLPs) are proposed, using the advances of the ,BB algorithm for nonconvex NLPs of Adjiman et al. The special structure mixed-integer ,BB algorithm (SMIN-,BB) addresses problems with nonconvexities in the continuous variables and linear and mixed-bilinear participation of the binary variables. The general structure mixed-integer ,BB algorithm (GMIN-,BB) is applicable to a very general class of problems for which the continuous relaxation is twice continuously differentiable. Both algorithms are developed using the concepts of branch-and-bound, but they differ in their approach to each of the required steps. The SMIN-,BB algorithm is based on the convex underestimation of the continuous functions, while the GMIN-,BB algorithm is centered around the convex relaxation of the entire problem. Both algorithms rely on optimization or interval-based variable-bound updates to enhance efficiency. A series of medium-size engineering applications demonstrates the performance of the algorithms. Finally, a comparison of the two algorithms on the same problems highlights the value of algorithms that can handle binary or integer variables without reformulation. [source] Video completion and synthesisCOMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 3-4 2008Chunxia Xiao Abstract This paper presents a new exemplar-based framework for video completion, allowing aesthetically pleasing completion of large space-time holes. We regard video completion as a discrete global optimization on a 3D graph embedded in the space-time video volume. We introduce a new objective function which enforces global spatio-temporal consistency among patches that fill the hole and surrounding it, in terms of both color similarity and motion similarity. The optimization is solved by a novel algorithm, called weighted priority belief propagation (BP), which alleviates the problems of slow convergence and intolerable storage size when using the standard BP. This objective function can also handle video texture synthesis by extending an input video texture to a larger texture region. Experiments on a wide variety of video examples with complex dynamic scenes demonstrate the advantages of our method over existing techniques: salient structures and motion information are much better restored. Copyright © 2008 John Wiley & Sons, Ltd. [source] Seamless Montage for Texturing ModelsCOMPUTER GRAPHICS FORUM, Issue 2 2010Ran Gal Abstract We present an automatic method to recover high-resolution texture over an object by mapping detailed photographs onto its surface. Such high-resolution detail often reveals inaccuracies in geometry and registration, as well as lighting variations and surface reflections. Simple image projection results in visible seams on the surface. We minimize such seams using a global optimization that assigns compatible texture to adjacent triangles. The key idea is to search not only combinatorially over the source images, but also over a set of local image transformations that compensate for geometric misalignment. This broad search space is traversed using a discrete labeling algorithm, aided by a coarse-to-fine strategy. Our approach significantly improves resilience to acquisition errors, thereby allowing simple and easy creation of textured models for use in computer graphics. [source] Integrative optimization by RBF network and particle swarm optimizationELECTRONICS & COMMUNICATIONS IN JAPAN, Issue 12 2009Satoshi Kitayama Abstract This paper presents a method for the integrative optimization system. Recently, many methods for global optimization have been proposed. The objective of these methods is to find a global minimum of nonconvex function. However, large numbers of function evaluations are required, in general. We utilize the response surface method to approximate function space to reduce the function evaluations. The response surface method is constructed from sampling points. The RBF Network, which is one of the neural networks, is utilized to approximate the function space. Then Particle Swarm Optimization (PSO) is applied to the response surface. The proposed system consists of three parts: (Part 1) generation of the sampling points, (Part 2) construction of response surface by RBF Network, (Part 3) optimization by PSO. By iterating these three parts, it is expected that the approximate global minimum of nonconvex function can be obtained with a small number of function evaluations. Through numerical examples, the effectiveness and validity are examined. © 2009 Wiley Periodicals, Inc. Electron Comm Jpn, 92(12): 31,42, 2009; Published online in Wiley InterScience (www.interscience. wiley.com). DOI 10.1002/ecj.10187 [source] Analog circuit design by nonconvex polynomial optimization: Two design examplesINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 1 2010Siu-Hong Lui Abstract We present a framework for synthesizing low-power analog circuits through global optimization over generally nonconvex multivariate polynomial objective function and constraints. Specifically, a nonconvex optimization problem is formed, which is then efficiently solved through convex programming techniques based on linear matrix inequality (LMI) relaxation. The framework allows both polynomial inequality and equality constraints, thereby facilitating more accurate device modelings and parameter tuning. Compared to traditional nonlinear programming (NLP), the proposed methodology exhibits superior computational efficiency, and guarantees convergence to a globally optimal solution. As in other physical design tasks, circuit knowledge and insight are critical for initial problem formulation, while the nonconvex optimization machinery provides a versatile tool and systematic way to locate the optimal parameters meeting design specifications. Two circuit design examples are given, namely, a nested transconductance(Gm),capacitance compensation (NGCC) amplifier and a delta,sigma (,,) analog-to-digital converter (ADC), both of them being the key components in many electronic systems. Copyright © 2008 John Wiley & Sons, Ltd. [source] Thermodynamic optimization of a solar system for cogeneration of water heating and absorption coolingINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 13 2008R. Hovsapian Abstract This paper presents a contribution to understanding the behavior of solar-powered air conditioning and refrigeration systems with a view to determining the manner in which refrigeration rate, mass flows, heat transfer areas, and internal architecture are related. A cogeneration system consisting of a solar concentrator, a cavity-type receiver, a gas burner, and a thermal storage reservoir is devised to simultaneously produce heat (hot water) and cooling (absorption refrigerator system). A simplified mathematical model, which combines fundamental and empirical correlations, and principles of classical thermodynamics, mass and heat transfer, is developed. The proposed model is then utilized to simulate numerically the system transient and steady-state response under different operating and design conditions. A system global optimization for maximum performance (or minimum exergy destruction) in the search for minimum pull-down and pull-up times, and maximum system second law efficiency is performed with low computational time. Appropriate dimensionless groups are identified and the results are presented in normalized charts for general application. The numerical results show that the three-way maximized system second law efficiency, ,II,max,max,max, occurs when three system characteristic mass flow rates are optimally selected in general terms as dimensionless heat capacity rates, i.e. (,ss, ,wxwx, ,Hs)opt=(0.335, 0.28, 0.2). The minimum pull-down and pull-up times, and maximum second law efficiencies found with respect to the optimized operating parameters are sharp and, therefore, important to be considered in actual design. As a result, the model is expected to be a useful tool for simulation, design, and optimization of solar energy systems in the context of distributed power generation. Copyright © 2008 John Wiley & Sons, Ltd. [source] Parameter optimization for a PEMFC model with a hybrid genetic algorithmINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 8 2006Zhi-Jun Mo Abstract Many steady-state models of polymer electrolyte membrane fuel cells (PEMFC) have been developed and published in recent years. However, models which are easy to be solved and feasible for engineering applications are few. Moreover, rarely the methods for parameter optimization of PEMFC stack models were discussed. In this paper, an electrochemical-based fuel cell model suitable for engineering optimization is presented. Parameters of this PEMFC model are determined and optimized by means of a niche hybrid genetic algorithm (HGA) by using stack output-voltage, stack demand current, anode pressure and cathode pressure as input,output data. This genetic algorithm is a modified method for global optimization. It provides a new architecture of hybrid algorithms, which organically merges the niche techniques and Nelder,Mead's simplex method into genetic algorithms (GAs). Calculation results of this PEMFC model with optimized parameters agreed with experimental data well and show that this model can be used for the study on the PEMFC steady-state performance, is broader in applicability than the earlier steady-state models. HGA is an effective and reliable technique for optimizing the model parameters of PEMFC stack. Copyright © 2005 John Wiley & Sons, Ltd. [source] Reduction constraints for the global optimization of NLPsINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 1 2004Leo Liberti Abstract Convergence of branch-and-bound algorithms for the solution of NLPs is obtained by finding ever-nearer lower and upper bounds to the objective function. The lower bound is calculated by constructing a convex relaxation of the NLP. Reduction constraints are new linear problem constraints which are (a) linearly independent from the existing constraints; (b) redundant with reference to the original NLP formulation; (c) not redundant with reference to its convex relaxation. Thus, they can be successfully employed to reduce the feasible region of the convex relaxation without cutting the feasible region of the original NLP. [source] Conformational search of peptides and proteins: Monte Carlo minimization with an adaptive bias method applied to the heptapeptide deltorphinJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 4 2004S. Banu Ozkan Abstract The energy function of a protein consists of a tremendous number of minima. Locating the global energy minimum (GEM) structure, which corresponds approximately to the native structure, is a severe problem in global optimization. Recently we have proposed a conformational search technique based on the Monte Carlo minimization (MCM) method of Li and Scheraga, where trial dihedral angles are not selected at random within the range [,180°,180°] (as with MCM) but with biased probabilities depending on the increased structure-energy correlations as the GEM is approached during the search. This method, called the Monte Carlo minimization with an adaptive bias (MCMAB), was applied initially to the pentapeptide Leu-enkephalin. Here we study its properties further by applying it to the larger peptide with bulky side chains, deltorphin (H-Tyr-D-Met-Phe-His-Leu-Met-Asp-NH2). We find that on average the number of energy minimizations required by MCMAB to locate the GEM for the first time is smaller by a factor of approximately three than the number required by MCM,in accord with results obtained for Leu-enkephalin. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 565,572, 2004 [source] Evolution of physics-based methodology for exploring the conformational energy landscape of proteinsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 1 2002Harold A. Scheraga Abstract The evolution of our physics-based computational methods for determining protein conformation without the introduction of secondary-structure predictions, homology modeling, threading, or fragment coupling is described. Initial use of a hard-sphere potential captured much of the structural properties of polypeptide chains, and subsequent more refined force fields, together with efficient methods of global optimization provide indications that progress is being made toward an understanding of the interresidue interactions that underlie protein folding. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 28,34, 2002 [source] Piecewise linear relaxation of bilinear programs using bivariate partitioningAICHE JOURNAL, Issue 7 2010M. M. Faruque Hasan Abstract Several operational and synthesis problems of practical interest involve bilinear terms. Commercial global solvers such as BARON appear ineffective at solving some of these problems. Although recent literature has shown the potential of piecewise linear relaxation via ab initio partitioning of variables for such problems, several issues such as how many and which variables to partition, which partitioning scheme(s) and relaxation model(s) to use, placement of grid points, etc., need detailed investigation. To this end, we present a detailed numerical comparison of univariate and bivariate partitioning schemes. We compare several models for the two schemes based on different formulations such as incremental cost (IC), convex combination (CC), and special ordered sets (SOS). Our evaluation using four process synthesis problems shows a formulation using SOS1 variables to perform the best for both partitioning schemes. It also points to the potential usefulness of a 2-segment bivariate partitioning scheme for the global optimization of bilinear programs. We also prove some simple results on the number and selection of partitioned variables and the advantage of uniform placement of grid points (identical segment lengths for partitioning). © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source] Improving the performance of natural gas pipeline networks fuel consumption minimization problemsAICHE JOURNAL, Issue 4 2010F. Tabkhi Abstract As the gas industry has developed, gas pipeline networks have evolved over decades into very complex systems. A typical network today might consist of thousands of pipes, dozens of stations, and many other devices, such as valves and regulators. Inside each station, there can be several groups of compressor units of various vintages that were installed as the capacity of the system expanded. The compressor stations typically consume about 3,5% of the transported gas. It is estimated that the global optimization of operations can save considerably the fuel consumed by the stations. Hence, the problem of minimizing fuel cost is of great importance. Consequently, the objective is to operate a given compressor station or a set of compressor stations so that the total fuel consumption is reduced while maintaining the desired throughput in the line. Two case studies illustrate the proposed methodology. Case 1 was chosen for its simple and small-size design, developed for the sake of illustration. The implementation of the methodology is thoroughly presented and typical results are analyzed. Case 2 was submitted by the French Company Gaz de France. It is a more complex network containing several loops, supply nodes, and delivery points, referred as a multisupply multidelivery transmission network. The key points of implementation of an optimization framework are presented. The treatment of both case studies provides some guidelines for optimization of the operating performances of pipeline networks, according to the complexity of the involved problems. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source] Deterministic global optimization of nonlinear dynamic systemsAICHE JOURNAL, Issue 4 2007Youdong Lin Abstract A new approach is described for the deterministic global optimization of dynamic systems, including optimal control problems. The method is based on interval analysis and Taylor models and employs a type of sequential approach. A key feature of the method is the use of a new validated solver for parametric ODEs, which is used to produce guaranteed bounds on the solutions of dynamic systems with interval-valued parameters. This is combined with a new technique for domain reduction based on the use of Taylor models in an efficient constraint propagation scheme. The result is that an ,-global optimum can be found with both mathematical and computational certainty. Computational studies on benchmark problems are presented showing that this new approach provides significant improvements in computational efficiency, well over an order of magnitude in most cases, relative to other recently described methods. © 2007 American Institute of Chemical Engineers AIChE J, 2007 [source] Quality by design: Optimization of a liquid filled pH-responsive macroparticles using Draper-Lin composite designJOURNAL OF PHARMACEUTICAL SCIENCES, Issue 7 2009Hasan Rafati Abstract In this study, pH responsive macroparticles incorporating peppermint oil (PO) were prepared using a simple emulsification/polymer precipitation technique. The formulations were examined for their properties and the desired quality was then achieved using a quality by design (QBD) approach. For this purpose, a Draper-Lin small composite design study was employed in order to investigate the effect of four independent variables, including the PO to water ratio, the concentration of pH sensitive polymer (hydroxypropyl methylcellulose phthalate), acid and plasticizer concentrations, on the encapsulation efficiency and PO loading. The analysis of variance showed that the polymer concentration was the most important variable on encapsulation efficiency (p,<,0.05). The multiple regression analysis of the results led to equations that adequately described the influence of the independent variables on the selected responses. Furthermore, the desirability function was employed as an effective tool for transforming each response separately and encompassing all of these responses in an overall desirability function for global optimization of the encapsulation process. The optimized macroparticles were predicted to yield 93.4% encapsulation efficiency and 72.8% PO loading, which were remarkably close to the experimental values of 89.2% and 69.5%, consequently. © 2009 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 98:2401,2411, 2009 [source] Diffusion-equation method for crystallographic figure of meritsACTA CRYSTALLOGRAPHICA SECTION A, Issue 5 2010Anders J. Markvardsen Global optimization methods play a significant role in crystallography, particularly in structure solution from powder diffraction data. This paper presents the mathematical foundations for a diffusion-equation-based optimization method. The diffusion equation is best known for describing how heat propagates in matter. However, it has also attracted considerable attention as the basis for global optimization of a multimodal function [Piela et al. (1989). J. Phys. Chem.93, 3339,3346]. The method relies heavily on available analytical solutions for the diffusion equation. Here it is shown that such solutions can be obtained for two important crystallographic figure-of-merit (FOM) functions that fully account for space-group symmetry and allow the diffusion-equation solution to vary depending on whether atomic coordinates are fixed or not. The resulting expression is computationally efficient, taking the same order of floating-point operations to evaluate as the starting FOM function measured in terms of the number of atoms in the asymmetric unit. This opens the possibility of implementing diffusion-equation methods for crystallographic global optimization algorithms such as structure determination from powder diffraction data. [source] Verified global optimization with GloptLabPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007Ferenc Domes GloptLab is a testing and development platform for solving quadratic constraint satisfaction problems, written in MATLAB. All applied methods are rigorous, hence it is guaranteed that no feasible point is lost. Some emphasis is given to finding a bounded initial box containing all feasible points, in cases where other complete solvers rely on non-rigorous heuristics. The algorithms implemented in GloptLab are used to reduce the search space: scaling, constraint propagation, linear relaxations, strictly convex enclosures, conic methods, and branch and bound. From the method repertoire custom made strategies can be built, with a user friendly graphical interface. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||||||||