experimental test of mcdm algorithms in a modular approach abstract the stem algorithm and steuer s filtering procedure were offered to 142 subjects to assist them in solving six car buying problems of various complexity subjects could change between the algorithms and some other program options almost at will we show that the algorithms are evaluated differently and that objective measures of the solution process show differences between the algorithms that support the subjective evaluations if the objective task complexity is noticed at least along one dimension number of objective functions we find that the choice of procedure varies with it as well as with subjective complexity evaluations in general stem is favored by a minority of subjects preferably for smaller sized problems

comments on the cramer rao lower bounds for signals with constant amplitude and polynomial phase for original paper see ieee trans signal processing vol 39 p 749 52 march 1991 different expressions for the cramer rao lower bounds crlbs of constant amplitude polynomial phase signals embedded in white gaussian noise appear in the literature the present paper revisits the derivation of the bounds reported by peleg and porat 1991 and indicates that the resulting expressions depend on the interval over which the signal is defined the proper choice of the interval is the one that centers the signal around zero and results in the minimum lower bounds

reference points and approximation algorithms in multicriteria discrete optimization abstract mathematical research on multicriteria optimization problems predominantly revolves around the set of pareto optimal solutions in practice on the other hand methods that output a single solution are more widespread reference point methods are a successful example of this approach and are widely used in real world multicriteria optimization a reference point solution is the solution closest to a given reference point in the objective space we study the connection between reference point methods and approximation algorithms for multicriteria optimization problems over discrete sets in particular we establish that in terms of computational complexity computing approximate reference point solutions is polynomially equivalent to approximating the pareto set complementing these results we show for a number of general algorithmic techniques in single criteria optimization how they can be lifted to reference point optimization in particular we lift the link between dynamic programming and fptas as well as certain lp rounding techniques the latter applies e g to set cover and several machine scheduling problems

g dominance reference point based dominance for multiobjective metaheuristics abstract one of the main tools for including decision maker dm preferences in the multiobjective optimization mo literature is the use of reference points and achievement scalarizing functions a p wierzbicki the use of reference objectives in multiobjective optimization in g fandel t gal eds multiple criteria decision making theory and application springer verlag new york 1980 pp 469 486 the core idea in these approaches is converting the original mo problem into a single objective optimization problem through the use of a scalarizing function based on a reference point as a result a single efficient point adapted to the dm s preferences is obtained however a single solution can be less interesting than an approximation of the efficient set around this area as stated for example by deb in k deb j sundar n udaya bhaskara rao s chaudhuri reference point based multiobjective optimization using evolutionary algorithms international journal of computational intelligence research 2 3 2006 273 286 in this paper we propose a variation of the concept of pareto dominance called g dominance which is based on the information included in a reference point and designed to be used with any mo evolutionary method or any mo metaheuristic this concept will let us approximate the efficient set around the area of the most preferred point without using any scalarizing function on the other hand we will show how it can be easily used with any mo evolutionary method or any mo metaheuristic just changing the dominance concept and to exemplify its use we will show some results with some state of the art methods and some test problems

the light beam search approach an overview of methodology applications the paper gives a general overview of the light beam search lbs methodology and applications lbs enables an interactive analysis of multiple objective decision problems due to presentation of samples of a large set of non dominated points to the decision maker dm in each iteration a local preference model in the form of an outranking relation is used to define the neighborhood of a current non dominated point the sample comes from the first current point is obtained by projection of an aspiration point onto the non dominated set in the direction of a reservation point the dm can control the search by either modifying the aspiration and reservation points or by shifting the current point to a selected better point from its neighborhood the paper describes applications of the approach to several real life problems and discusses observations made while working on these problems the lbs approach is compared to other existing methods and the class of problems suitable to this methodology is defined

instantaneous frequency estimation of polynomial fm signals using the peak of the pwvd statistical performance in the presence of additive gaussian noise the peak of the polynomial wigner ville distribution pwvd has been previously proposed as an estimator of the instantaneous frequency if for a monocomponent polynomial frequency modulated fm signal in this paper we evaluate the statistical performance of this estimator in the case of additive white gaussian noise and provide an analytical expression for the variance we show that for a given pwvd order the estimator performance can be improved by a proper choice of the kernel coefficients in the pwvd a performance comparison between the pwvd based if estimator and another previously proposed one based on the high order ambiguity function haf is also provided simulation results show that for a signal to noise ratio larger than 3 db the proposed sixth order pwvd outperforms the haf in estimating the if of a third or fourth order polynomial phase signal evaluated at the central point of the observation interval

improved instantaneous frequency estimation using an adaptive short time fourier transform instantaneous frequency estimation ife arises in a variety of important applications including fm demodulation we present here a new time frequency representation tfr based approach to ife based on an adaptive short time fourier transform astft this tfr leads naturally to a type of short term ml estimator of the if to further improve the performance we apply a multistate hidden markov model hmm based post estimation tracker the end result is up to a 16 db reduction in the threshold snr over the frequency discriminator fd and an 8 db improvement over the phase locked loop pll for a rayleigh fading channel

an interactive multiple objective linear programming method for a class of underlying nonlinear utility functions this paper develops a method for interactive multiple objective linear programming assuming an unknown pseudo concave utility function satisfying certain general properties the method is an extension of our earlier method published in this journal zionts s wallenius j 1976 an interactive programming method for solving the multiple criteria problem management sci 22 6 652 663 various technical problems present in predecessor versions have been resolved in addition to presenting the supporting theory and algorithm we discuss certain options in implementation and summarize our practical experience with several versions of the method

a combined tchebycheff aspiration criterion vector interactive multiobjective programming procedure in this paper we combine the tchebycheff method of steuer and choo with wierzbicki s aspiration criterion vector method in order to form an improved procedure for interactive multiple objective programming the combined procedure is sensible because the tchebycheff and aspiration criterion vector methods possess complementary distinguishing characteristics solve similar optimization problems to probe the nondominated set and share a similar computer user interface in the early iterations tchebycheff probes of the nondominated set might be conducted to locate promising neighborhoods of search in later iterations aspiration criterion vector probes might be used to pinpoint a final solution computational experience is reported showing the improved effectiveness of the combined procedure when employed in this fashion when compared against the tchebycheff and aspiration criterion vector methods run separately

including preferences into a multiobjective evolutionary algorithm to deal with many objective engineering optimization problems abstract in this paper we introduce a new preference relation based on a reference point approach this relation offers an easy approach to integrate decision maker s preferences into a moea without modifying its basic structure besides finding the optimal solution of the achievement scalarizing function the new preference relation allows the decision maker to find a set of solutions around that optimal solution then a moea equipped with the proposed preference relation can be integrated into an interactive optimization method one of the main advantages of the new method is that setting its parameters is an intuitive task to the decision maker the other advantage is that since our preference relation induces a finer order on vectors of objective space than that achieved by the pareto dominance relation it is appropriate to cope with problems having a high number of objectives we evaluated the proposed preference relation an engineering problem the optimization of an airfoil design with 6 objectives

dupin hypersurfaces with three principal curvatures using the method of moving frames we prove that any locally irreducible dupin hypersurface in sn with three distinct principal curvatures is equivalent by lie sphere transformation to an isoparametric hypersurface in sn

cramer rao bounds and maximum likelihood estimation for random amplitude phase modulated signals the problem of estimating the phase parameters of a phase modulated signal in the presence of colored multiplicative noise random amplitude modulation and additive white noise both gaussian is addressed closed form expressions for the exact and large sample cramer rao bounds crbs are derived it is shown that the crb is significantly affected by the color of the modulating process when the signal to noise ratio snr or the intrinsic snr is small maximum likelihood type estimators that ignore the noise color and optimize a criterion with respect to only the phase parameters are proposed these estimators are shown to be equivalent to the nonlinear least squares estimators which consist of matching the squared observations with a constant amplitude phase modulated signal when the mean of the multiplicative noise is forced to zero closed form expressions are derived for the efficiency of these estimators and are verified via simulations

quantitative performance analysis of scalogram as instantaneous frequency estimator instantaneous frequency if estimation through the estimation of peak locations in the time frequency plane is an important approach for signals contaminated with additive white gaussian noise in this paper the forementioned analysis is carried out for continuous wavelet transform the analysis of the scalogram as the instantaneous frequency estimator is performed for any fm signal regardless of the mother wavelet accurate expressions for the bias and the variance of the estimator are derived and reveal that the bias and the variance are signal dependent results are statistically confirmed through the numerical analysis for several mother wavelets and among considered wavelets the morlet wavelet produces the smallest estimation error furthermore the performance of the if estimator based on the scalogram and the spectrogram were compared through analysis of mean square error these results showed that the scalogram with the morlet wavelet exhibited good performance for the sample linear fm signal and the sample hyperbolic fm signal in comparison to the spectrogram

the use of cone shaped kernels for generalized time frequency representations of nonstationary signals generalized time frequency representations gtfrs which use cone shaped kernels for nonstationary signal analysis are presented the cone shaped kernels are formulated for the gtfrs to produce good resolution simultaneously in time and frequency specifically for a gtfr with a cone shaped kernel finite time support is maintained in the time dimension along with an enhanced spectrum in the frequency dimension and the cross terms are smoothed out experimental results on simulated data and real speech show the advantages of the gtfrs with the cone shaped kernels through comparisons to the spectrogram and the pseudo wigner distribution

asymptotic wavelet and gabor analysis extraction of instantaneous frequencies the behavior of the continuous wavelet and gabor coefficients in the asymptotic limit using stationary phase approximations are investigated in particular it is shown how under some additional assumptions these coefficients allow the extraction of some characteristics of the analyzed signal such as frequency and amplitude modulation laws applications to spectral line estimations and matched filtering are briefly discussed

the monogenic wavelet transform this paper extends the 1 d analytic wavelet transform to the 2 d monogenic wavelet transform the transformation requires care in its specification to ensure suitable transform coefficients are calculated and it is constructed so that the wavelet transform may be considered as both local and monogenic this is consistent with defining the transform as a real wavelet transform of a monogenic signal in analogy with the analytic wavelet transform classes of monogenic wavelets are proposed with suitable local properties it is shown that the monogenic wavelet annihilates anti monogenic signals that the monogenic wavelet transform is phase shift covariant and that the transform magnitude is phase shift invariant a simple form for the magnitude and orientation of the isotropic transform coefficients of a unidirectional signal when observed in a rotated frame of reference is derived the monogenic wavelet ridges of local plane waves are given

the achievable accuracy in estimating the instantaneous phase and frequency of a constant amplitude signal the approach is based on modeling the signal phase by a polynomial function of time on a finite interval the phase polynomial is expressed as a linear combination of the legendre basis polynomials first the cramer rao bound crb of the instantaneous phase and frequency of constant amplitude polynomial phase signals is derived then some properties of the crbs are used to estimate the order of magnitude of the bounds the analysis is extended to signals whose phase and frequency are continuous but not polynomial the crb can be achieved asymptotically if the estimation of the phase coefficients is done by maximum likelihood the maximum likelihood estimates are used to show that the achievable accuracy in phase and frequency estimation is determined by the crb of the polynomial coefficients and the deviation of true phase and frequency from the polynomial approximations

mobius curvature laguerre curvature and dupin hypersurface abstract in this paper we show that a dupin hypersurface with constant mobius curvatures is mobius equivalent to either an isoparametric hypersurface in the sphere or a cone over an isoparametric hypersurface in a sphere we also show that a dupin hypersurface with constant laguerre curvatures is laguerre equivalent to a flat laguerre isoparametric hypersurface these results solve the major issues related to the conjectures of cecil et al on the classification of dupin hypersurfaces

molp with an interactive assessment of a piecewise linear utility function the paper presents a methodology for multi objective linear programming molp problems it relies on three steps 1 generation of a subset of feasible efficient solutions from 10 to 50 as representative as possible of the efficient set 2 assessment of an additive utility function using an interactive method prefcalc 3 optimization of the additive utility function on the original set of feasible alternatives following this methodology enables the user to find compromise solutions which can be different from the vertices it is particularly adapted for large scale linear programs where traditional multiobjective methods would be too costly to use since the interactive phase is limited to step 2 using prefcalc on a micro computer a micro computer version of the method prefchat is available

an interactive weighted tchebycheff procedure for multiple objective programming the procedure samples the efficient set by computing the nondominated criterion vector that is closest to an ideal criterion vector according to a randomly weighted tchebycheff metric using filtering techniques maximally dispersed representatives of smaller and smaller subsets of the set of nondominated criterion vectors are presented at each iteration the procedure has the advantage that it can converge to non extreme final solutions especially suitable for multiple objective linear programming the procedure is also applicable to integer and nonlinear multiple objective programs

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

a parallel multiple reference point approach for multi objective optimization this paper presents a multiple reference point approach for multi objective optimization problems of discrete and combinatorial nature when approximating the pareto frontier multiple reference points can be used instead of traditional techniques these multiple reference points can easily be implemented in a parallel algorithmic framework the reference points can be uniformly distributed within a region that covers the pareto frontier an evolutionary algorithm is based on an achievement scalarizing function that does not impose any restrictions with respect to the location of the reference points in the objective space computational experiments are performed on a bi objective flow shop scheduling problem results quality measures as well as a statistical analysis are reported in the paper

generalized instantaneous parameters and window matching in the time frequency plane the concept of instantaneous parameters which has previously been associated exclusively with 1 d measures like the instantaneous frequency and the group delay are extended to the 2 d time frequency plane such generalized instantaneous parameters are associated with the short time fourier transform they may also be interpreted as local moments of certain time frequency distributions it is shown that these measures enable local signal behavior to be characterized in the time frequency plane for nonstationary deterministic signals the usefulness of the generalized instantaneous parameters is demonstrated in their application to optimal selection of windows for spectrograms this is achieved through window matching in the time frequency plane an algorithm is provided that illustrates the performance of this window matching results based on simulated and real data are presented

parameter estimation for random amplitude chirp signals we consider the problem of estimating the parameters of a chirp signal observed in multiplicative noise i e whose amplitude is randomly time varying two methods for solving this problem are presented first an unstructured nonlinear least squares approach nls is proposed it is shown that by minimizing the nls criterion with respect to all samples of the time varying amplitude the problem reduces to a two dimensional 2 d maximization problem a theoretical analysis of the nls estimator is presented and an expression for its asymptotic variance is derived it is shown that the nls estimator has a variance that is very close to the cramer rao bound the second approach combines the principles behind the high order ambiguity function hbf and the nls approach it provides a computationally simpler but suboptimum estimator a statistical analysis of the haf based estimator is also carried out and closed form expressions are derived for the asymptotic variance of the haf estimators based on the data and on the squared data numerical examples attest to the validity of the theoretical analyzes and establish a comparison between the two proposed methods

cramer rao bounds for wavelet transform based instantaneous frequency estimates we use an asymptotic integral approximation of a wavelet transform as a model for the estimation of instantaneous frequency if our approach allows the calculation of the cramer rao bound for the if variance at each time directly without the need for explicit phase parameterization this is in contrast to other approaches where the cramer rao bounds rely on a preliminary decomposition of the if with respect to a usually polynomial basis attention is confined to the morlet wavelet transform of single component signals corrupted with additive gaussian noise potential computationally and statistically efficient if extraction algorithms suggested by the analysis are also discussed

using box indices in supporting comparison in multiobjective optimization because of the conflicting nature of criteria or objectives solving a multiobjective optimization problem typically requires interaction with a decision maker who can specify preference information related to the objectives in the problem in question due to the difficulties of dealing with multiple objectives the way information is presented plays a very important role questions posed to the decision maker must be simple enough and information shown must be easy to understand for this purpose visualization and graphical representations can be useful and constitute one of the main tools used in the literature in this paper we propose to use box indices to represent information related to different solution alternatives of multiobjective optimization problems involving at least three objectives box indices are an intelligible and easy to handle way to represent data they are based on evaluating the solutions in a natural and rough enough scale in order to let the decision maker easily recognize the main characteristics of a solution at a glance and to facilitate comparison of two or more solutions in an easily understandable way

on the analytic wavelet transform an exact and general expression for the analytic wavelet transform of a real valued signal is constructed resolving the time dependent effects of nonnegligible amplitude and frequency modulation the analytic signal is first locally represented as a modulated oscillation demodulated by its own instantaneous frequency and then taylor expanded at each point in time the terms in this expansion called the instantaneous modulation functions are time varying functions which quantify at increasingly higher orders the local departures of the signal from a uniform sinusoidal oscillation closed form expressions for these functions are found in terms of bell polynomials and derivatives of the signal s instantaneous frequency and bandwidth the analytic wavelet transform is shown to depend upon the interaction between the signal s instantaneous modulation functions and frequency domain derivatives of the wavelet inducing a hierarchy of departures of the transform away from a perfect representation of the signal the form of these deviation terms suggests a set of conditions for matching the wavelet properties to suit the variability of the signal in which case our expressions simplify considerably one may then quantify the time varying bias associated with signal estimation via wavelet ridge analysis and choose wavelets to minimize this bias

multiplicities of dupin hypersurfaces all known examples of isoparametric hypersurfaces of spheres are of the following two types 1 the homogeneous examples which are principal orbits of isotropy representations of symmetric spaces of rank 2 2 the clifford examples of ferus karcher munzner which are constructed from modules over clifford algebras our main result which extends work of munzner thorbergsson and grove halperin is that any isoparametric hypersurface has the same number of principal curvatures and the same multiplicities as some hypersurface of type 1 or 2 more generally this holds for any dupin hypersurface the proof is homotopy theoretic the main tools are the hopf invariant and the ehp sequence