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34
Genetic Algorithms for Multiobjective Optimization: Formulation, Discussion and Generalization
, 1993
"... The paper describes a rankbased fitness assignment method for Multiple Objective Genetic Algorithms (MOGAs). Conventional niche formation methods are extended to this class of multimodal problems and theory for setting the niche size is presented. The fitness assignment method is then modified to a ..."
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Cited by 633 (15 self)
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The paper describes a rankbased fitness assignment method for Multiple Objective Genetic Algorithms (MOGAs). Conventional niche formation methods are extended to this class of multimodal problems and theory for setting the niche size is presented. The fitness assignment method is then modified to allow direct intervention of an external decision maker (DM). Finally, the MOGA is generalised further: the genetic algorithm is seen as the optimizing element of a multiobjective optimization loop, which also comprises the DM. It is the interaction between the two that leads to the determination of a satisfactory solution to the problem. Illustrative results of how the DM can interact with the genetic algorithm are presented. They also show the ability of the MOGA to uniformly sample regions of the tradeoff surface.
The efficient evaluation of the hypergeometric function of a matrix argument
 MATH. COMP
, 2005
"... We present new algorithms that efficiently approximate the hypergeometric function of a matrix argument through its expansion as a series of Jack functions. Our algorithms exploit the combinatorial properties of the Jack function, and have complexity that is only linear in the size of the matrix. ..."
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Cited by 79 (17 self)
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We present new algorithms that efficiently approximate the hypergeometric function of a matrix argument through its expansion as a series of Jack functions. Our algorithms exploit the combinatorial properties of the Jack function, and have complexity that is only linear in the size of the matrix.
Accurate and efficient evaluation of Schur and Jack functions
 Math. Comp
, 2006
"... Abstract. We present new algorithms for computing the values of the Schur sλ(x1,x2,...,xn)andJackJ α λ (x1,x2,...,xn) functions in floating point arithmetic. These algorithms deliver guaranteed high relative accuracy for positive data (xi,α>0) and run in time that is only linear in n. 1. ..."
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Cited by 13 (4 self)
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Abstract. We present new algorithms for computing the values of the Schur sλ(x1,x2,...,xn)andJackJ α λ (x1,x2,...,xn) functions in floating point arithmetic. These algorithms deliver guaranteed high relative accuracy for positive data (xi,α>0) and run in time that is only linear in n. 1.
A toolkit for the development and application of parsimonious hydrological models, To appear in: Mathematical models of small watershed hydrology – Volume 2
 Resources Publications LLC
, 2001
"... ABSTRACT: A modelling toolkit is described which has been developed to produce parsimonious model structures with a high degree of parameter identifiability. This is necessary if sensible relationships between model parameters and catchment characteristics are to be established, for example for regi ..."
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Cited by 10 (6 self)
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ABSTRACT: A modelling toolkit is described which has been developed to produce parsimonious model structures with a high degree of parameter identifiability. This is necessary if sensible relationships between model parameters and catchment characteristics are to be established, for example for regionalization studies. The toolkit contains two major components. The first is a rainfallrunoff modeling system with a generic architecture of lumped, conceptual or metricconceptual model elements, which allows alternative model structures to be rapidly constructed and tested. The second component is a MonteCarlo analysis toolbox combining a number of analysis tools to investigate parameter identifiability, model behaviour and prediction uncertainty. Two example applications are presented. These illustrate the use of multiple objective functions to extract information from a single output timeseries for analysis of parameter sensitivity and identifiability, and the tradeoff between model complexity and identifiability. 1.
2000 Databased mechanistic modelling and forecasting of hydrological systems
 J. Hydroinformatics
"... The paper presents a datadriven approach to the modelling and forecasting of hydrological systems based on nonlinear timeseries analysis. Time varying parameters are estimated using a combined Kalman filter and fixedintervalsmoother, and statedependent parameter relations are identified leading ..."
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Cited by 8 (1 self)
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The paper presents a datadriven approach to the modelling and forecasting of hydrological systems based on nonlinear timeseries analysis. Time varying parameters are estimated using a combined Kalman filter and fixedintervalsmoother, and statedependent parameter relations are identified leading to nonlinear extensions to common timeseries models such as the autoregressive exogenous (ARX) and general transfer function (TF). This nonlinear timeseries technique is used as part of a databased mechanistic modelling methodology where models are objectively identified from the data, but are only accepted as a reasonable representation of the system if they have a valid mechanistic interpretation. To this end it is shown that the TF model can represent a general linear storage model that subsumes many common hydrological flow forecasting models, and that the rainfallrunoff process can be represented using a nonlinear input transformation in combination with a TF model. One advantage of the forecasting models produced is that the Kalman filter can be used for realtime state updating leading to improved forecasts and an estimate of associated forecast uncertainty. Rainfallrunoff and flood routing case studies are included to demonstrate the power of the modelling and forecasting methods. One important conclusion is that optimal system identification techniques are required to objectively identify parallel flow pathways.
Accurate and efficient expression evaluation and linear algebra
, 2008
"... We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By ‘accurate ’ we mean that the computed answer has relative error less than 1, i.e., has some correc ..."
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Cited by 6 (0 self)
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We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By ‘accurate ’ we mean that the computed answer has relative error less than 1, i.e., has some correct leading digits. We also address efficiency, by which we mean algorithms that run in polynomial time in the size of the input. Our results will depend strongly on the model of arithmetic: most of our results will use the socalled traditional model (TM), where the computed result of op(a, b), a binary operation like a + b, is given by op(a, b) ∗ (1 + δ) where all we know is that δ  ≤ε ≪ 1. Here ε is a constant also known as machine epsilon.
Implicit Standard Jacobi Gives High Relative Accuracy
, 2008
"... We prove that the Jacobi algorithm applied implicitly on a decomposition A = XDX T of the symmetric matrix A, where D is diagonal, and X is well conditioned, computes all eigenvalues of A to high relative accuracy. The relative error in every eigenvalue is bounded by O(εκ(X)), where ε is the machin ..."
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Cited by 6 (0 self)
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We prove that the Jacobi algorithm applied implicitly on a decomposition A = XDX T of the symmetric matrix A, where D is diagonal, and X is well conditioned, computes all eigenvalues of A to high relative accuracy. The relative error in every eigenvalue is bounded by O(εκ(X)), where ε is the machine precision and κ(X) ≡ ‖X‖2 · ‖X −1 ‖2 is the spectral condition number of X. The eigenvectors are also computed accurately in the appropriate sense. We believe that this is the first algorithm to compute accurate eigenvalues of symmetric (indefinite) matrices that respects and preserves the symmetry of the problem and uses only orthogonal transformations.
Composite Constructs For ObjectOriented Modeling
 Proc. Eurosim Simulation Congress
, 1995
"... Object orientation in modeling, i.e. the possibility to structure a model according to the objects present in the system under consideration, promotes reuse and simplifies maintenance. This paper is mainly devoted to composite language constructs, like matrix notation, multiple inheritance and gener ..."
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Cited by 3 (0 self)
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Object orientation in modeling, i.e. the possibility to structure a model according to the objects present in the system under consideration, promotes reuse and simplifies maintenance. This paper is mainly devoted to composite language constructs, like matrix notation, multiple inheritance and generic class parameters, that are introduced in order to further facilitate reuse and maintenance of models.
Development of a Morphological Index of the Nutritional Status
"... Abstract.—We describe the morphological changes associated with starvation in larval largemouth bass Micropterus salmoides and develop bivariate and multivariate morphological indices of nutritional status. We obtained hatcheryreared largemouth bass, raised them until completion of fin development ..."
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Cited by 2 (0 self)
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Abstract.—We describe the morphological changes associated with starvation in larval largemouth bass Micropterus salmoides and develop bivariate and multivariate morphological indices of nutritional status. We obtained hatcheryreared largemouth bass, raised them until completion of fin development, and divided them into two randomized experimental groups of fed and unfed fishes. Fed fishes were provided with newly hatched brine shrimp twice daily. We quantified morphological changes in body shape using 23 morphometric characters. After only 3 d of food deprivation, we were able to detect statistically significant differences in morphology between the fed and unfed fish using multivariate analysis. The magnitude of the mean difference increased over time. An unexpected result suggested that a simple, bivariate ratio of standard length to body depth at the anus was almost as efficient and robust at classifying fed and unfed largemouth bass from an independent data set as a multivariate index based on all 23 morphometric characters. The relative ease of use, combined with a small level of misclassification error rate and a firm foundation in wholebody changes, makes these ratio indices effective tools for detecting food deprivation in larval largemouth bass. High and variable mortality rates among larval