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A Global Optimization Algorithm (GOP) for Certain Classes of Nonconvex NLPs : II. Application of Theory and Test Problems
 Engng
, 1990
"... In Part I (Floudas and Visweswaran, 1990), a deterministic global optimization approach was proposed for solving certain classes of nonconvex optimization problems. An algorithm, GOP, was presented for the rigorous solution of the problem through a series of primal and relaxed dual problems until th ..."
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Cited by 54 (21 self)
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In Part I (Floudas and Visweswaran, 1990), a deterministic global optimization approach was proposed for solving certain classes of nonconvex optimization problems. An algorithm, GOP, was presented for the rigorous solution of the problem through a series of primal and relaxed dual problems until the upper and lower bounds from these problems converged to an fflglobal optimum. In this paper, theoretical results are presented for several classes of mathematical programming problems that include : (i) the general quadratic programming problem, (ii) quadratic programming problems with quadratic constraints, (iii) pooling and blending problems, and (iv) unconstrained and constrained optimization problems with polynomial terms in the objective function and/or constraints. For each class, a few examples are presented illustrating the approach. Keywords : Global Optimization, Quadratic Programming, Quadratic Constraints, Polynomial functions, Pooling and Blending Problems. Author to whom...
Simulated Annealing Algorithms For Continuous Global Optimization
, 2000
"... INTRODUCTION In this paper we consider Simulated Annealing algorithms (SA in what follows) applied to continuous global optimization problems, i.e. problems with the following form f = min x2X f(x); (1.1) where X ` ! n is a continuous domain, often assumed to be compact, which, combined with ..."
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Cited by 30 (1 self)
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INTRODUCTION In this paper we consider Simulated Annealing algorithms (SA in what follows) applied to continuous global optimization problems, i.e. problems with the following form f = min x2X f(x); (1.1) where X ` ! n is a continuous domain, often assumed to be compact, which, combined with the continuity or lower semicontinuity of f , guarantees the existence of the minimum value f . SA algorithms are based on an analogy with a physical phenomenon: while at high temperatures the molecules in a liquid move freely, if the temperature is slowly decreased the thermal mobility of the molecules is lost and they form a pure crystal which also corresponds to a state of minimum energy. If the temperature is decreased too quickly (the so called quenching) a liquid metal rather ends up in a polycrystalline or amorphous state with
Approximating Bayesian Belief Networks by Arc Removal
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1997
"... Bayesian belief networks or causal probabilistic networks may reach a certain size and complexity where the computations involved in exact probabilistic inference on the network tend to become rather time consuming. Methods for approximating a network by a simpler one allow the computational complex ..."
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Cited by 21 (0 self)
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Bayesian belief networks or causal probabilistic networks may reach a certain size and complexity where the computations involved in exact probabilistic inference on the network tend to become rather time consuming. Methods for approximating a network by a simpler one allow the computational complexity of probabilistic inference on the network to be reduced at least to some extend. We propose a general framework for approximating Bayesian belief networks based on model simplification by arc removal. The approximation method aims at reducing the computational complexity of probabilistic inference on a network at the cost of introducing a bounded error in the prior and posterior probabilities inferred. We present a practical approximation scheme and give some preliminary results. 1 Introduction Today, more and more applications based on the Bayesian belief network 1 formalism are emerging for reasoning and decision making in problem domains with inherent uncertainty. Current applicati...
Cut Size Statistics of Graph Bisection Heuristics
 SIAM JOURNAL ON OPTIMIZATION
, 1999
"... We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut sizes found by “local” algorithms becomes peaked as the number ..."
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Cited by 20 (5 self)
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We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut sizes found by “local” algorithms becomes peaked as the number of vertices in the graphs becomes large. Evidence is given that this distribution tends towards a Gaussian whose mean and variance scales linearly with the number of vertices of the graphs. Given the distribution of cut sizes associated with each heuristic, we provide a ranking procedure which takes into account both the quality of the solutions and the speed of the algorithms. This procedure is demonstrated for a selection of local graph bisection heuristics.
New Properties and Computational Improvement of the GOP Algorithm For Problems With Quadratic Objective Function and Constraints
 Journal of Global Optimization
, 1993
"... In Floudas and Visweswaran (1990, 1992), a deterministic global optimization approach was proposed for solving certain classes of nonconvex optimization problems. An algorithm, GOP, was presented for the solution of the problem through a series of primal and relaxed dual problems that provide valid ..."
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Cited by 20 (10 self)
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In Floudas and Visweswaran (1990, 1992), a deterministic global optimization approach was proposed for solving certain classes of nonconvex optimization problems. An algorithm, GOP, was presented for the solution of the problem through a series of primal and relaxed dual problems that provide valid upper and lower bounds respectively on the global solution. The algorithm was proved to have finite convergence to an fflglobal optimum. In this paper, new theoretical properties are presented that help to enhance the computational performance of the GOP algorithm applied to problems of special structure. The effect of the new properties is illustrated through application of the GOP algorithm to a difficult indefinite quadratic problem, a multiperiod tankage quality problem that occurs frequently in the modeling of refinery processes, and a set of pooling/blending problems from the literature. In addition, extensive computational experience is reported for randomly generated concave and in...
Simulated Annealing for Noisy Cost Functions
 Journal of Global Optimization
, 1996
"... : We generalize a classical convergence result for the Simulated Annealing algorithm to a stochastic optimization context, i.e., to the case where cost function observations are disturbed by random noise. It is shown that for a certain class of noise distributions, the convergence assertion remains ..."
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Cited by 14 (2 self)
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: We generalize a classical convergence result for the Simulated Annealing algorithm to a stochastic optimization context, i.e., to the case where cost function observations are disturbed by random noise. It is shown that for a certain class of noise distributions, the convergence assertion remains valid, provided that the standard deviation of the noise is reduced in the successive steps of cost function evaluation (e.g., by repeated observation) with a speed O(k ), where is an arbitrary constant larger than one. Key words: Simulated Annealing, stochastic optimization, noisy cost functions. 1 Introduction The Simulated Annealing algorithm, introduced about ten years ago by Kirkpatrick, Gelatt and Vecchi [8] into the area of combinatorial optimization, has developed into a well{known and thoroughly studied optimization technique with a large (and still rapidly growing) number of applications. (Cf. Laarhoven and Aarts [9], Aarts and Korst [1]; see also the bibliography in [7].) ...
Power Optimization in DiskBased RealTime Application Specific Systems
 In Proceedings of the International Conference on ComputerAided Desi gn (ICCAD
, 1996
"... A flurry of modern communications, video, and DSP applications, such as world wide web, interactive high resolution television, videoondemand, video conferencing, and wireless communications, are mainly data management oriented. In this type of systems, magnetic disk performance is quickly becomin ..."
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Cited by 13 (0 self)
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A flurry of modern communications, video, and DSP applications, such as world wide web, interactive high resolution television, videoondemand, video conferencing, and wireless communications, are mainly data management oriented. In this type of systems, magnetic disk performance is quickly becoming a primary bottleneck which dictates key design metrics of the overall system. At the same time, technology trends imply reduced importance of classical design objectives, such as area and throughput, and together with consumers demand for portability promote power consumption as the principal design metric. While numerous power optimization techniques have been proposed at all levels of design process abstractions for electronic components, until now, power minimization in mixed mechanicalelectronic subsystems, such as disks, has not been addressed. We first analyze optimization degrees of freedom for power minimization in diskbased application specific systems. Next, we propose a concep...
Constrained Optimalities in Query Personalization
 In Proceedings of the ACM International Conference on Management of Data, SIGMOD
, 2005
"... Personalization is a powerful mechanism that helps users to cope with the abundance of information on the Web. Database query personalization achieves this by dynamically constructing queries that return results of high interest to the user. This, however, may conflict with other constraints on the ..."
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Cited by 13 (3 self)
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Personalization is a powerful mechanism that helps users to cope with the abundance of information on the Web. Database query personalization achieves this by dynamically constructing queries that return results of high interest to the user. This, however, may conflict with other constraints on the query execution time and/or result size that may be imposed by the search context, such as the device used, the network connection, etc. For example, if the user is accessing information using a mobile phone, then it is desirable to construct a personalized query that executes quickly and returns a handful of answers. Constrained Query Personalization (CQP) is an integrated approach to database query answering that dynamically takes into account the queries issued, the user’s interest in the results, response time, and result size in order to build personalized queries. In this paper, we introduce CQP as a family of constrained optimization problems, where each time one of the parameters of concern is optimized while the others remain within the bounds of range constraints. Taking into account some key (exact or approximate) properties of these parameters, we map CQP to a state search problem and provide several algorithms for the discovery of optimal solutions. Experimental results demonstrate the effectiveness of the proposed techniques and the appropriateness of the overall approach. 1.
LatticeBased Search Strategies For Large Vocabulary Speech Recognition
, 1995
"... The design of search algorithms is an important issue in recognition, particularly for very large vocabulary, continuous speech. It is an especially crucial problem when computationally expensive knowledge sources are used in the system, as is necessary to achieve high accuracy. Recently, multipass ..."
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Cited by 11 (1 self)
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The design of search algorithms is an important issue in recognition, particularly for very large vocabulary, continuous speech. It is an especially crucial problem when computationally expensive knowledge sources are used in the system, as is necessary to achieve high accuracy. Recently, multipass search strategies have been used as a means of applying inexpensive knowledge sources early on to prune the search space for subsequent passes using more expensive knowledge sources. Three multipass search algorithms are investigated in this thesis work: the Nbest search algorithm, a lattice dynamic programming search algorithm and a lattice local search algorithm. Both the lattice dynamic programming and lattice local search algorithms are shown to achieve comparable performance to the Nbest search algorithm while running as much as 10 times faster on a 20,000 word vocabulary task. The lattice local search algorithm is also shown to have the additional advantage over the lattice dynamic programming search algorithm of allowing sentencelevel knowledge sources to be incorporated into the search.
On the Computation of Protein Backbones by using Artificial Backbones of Hydrogens
"... NMR experiments provide information from which some of the distances between pairs of hydrogen atoms of a protein molecule can be estimated. Such distances can be exploited in order to identify the threedimensional conformation of the molecule: this problem is known in the literature as the Molecu ..."
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Cited by 11 (8 self)
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NMR experiments provide information from which some of the distances between pairs of hydrogen atoms of a protein molecule can be estimated. Such distances can be exploited in order to identify the threedimensional conformation of the molecule: this problem is known in the literature as the Molecular Distance Geometry Problem (MDGP). In this paper, we show how an artificial backbone of hydrogens can be defined which allows the reformulation of the MDGP as a combinatorial problem. This is done with the aim of solving the problem by the Branch and Prune (BP) algorithm, which is able to solve it efficiently. Moreover, we show how the real backbone of a protein conformation can be computed by using the coordinates of the hydrogens found by the BP algorithm. Formal proofs of the presented results are provided, as well as computational experiences on a set of instances whose size ranges from 60 to 6000 atoms.