a novel selection evolutionary strategy for constrained optimization the existence of infeasible solutions makes it very difficult to handle constrained optimization problems cops in a way that ensures efficient optimal and constraint satisfying convergence although further optimization from feasible solutions will typically lead in a direction that generates further feasible solutions certain infeasible solutions can also provide useful information about the optimal direction of improvement for the objective function how well an algorithm makes use of these two solutions determines its performance on cops this paper proposes a novel selection evolutionary strategy nses for constrained optimization a self adaptive selection method is introduced to exploit both informative infeasible and feasible solutions from a perspective of combining feasibility with multi objective problem mop techniques since the global optimal solution of a cop is a feasible non dominated solution both non dominated solutions with low constraint violation and feasible ones with low objective values are beneficial to an evolution process thus the exploration and exploitation of both of these two kinds of solutions are preferred during the selection procedure several theorems and properties are given to prove the above assertion furthermore the performance of our method is evaluated using 22 well known benchmark functions experimental results show that the proposed method outperforms state of the art algorithms in terms of the speed of finding feasible solutions and the stability of converging to global optimal solutions in particular when dealing with problems that have zero feasibility ratios and more than one active constraint our method provides feasible solutions within fewer fitness evaluations fes and converges to the optimal solutions more reliably than other popular methods from the literature

cubature formulae of the seventh degree of accuracy for the hypersphere cubature formulae for evaluating integrals on the hypersphere in rn for n 5 are obtained which are exact for any polynomial of degree not exceeding 7 and are invariant with respect to the group of transformations of the regular simplex

sparse grid quadrature nonlinear filtering in this paper a novel nonlinear filter named sparse grid quadrature filter sgqf is proposed the filter utilizes weighted sparse grid quadrature points to approximate the multi dimensional integrals in the nonlinear bayesian estimation algorithm the locations and weights of the univariate quadrature points with a range of accuracy levels are determined by the moment matching method then the univariate quadrature point sets are extended to form a multi dimensional grid using the sparse grid theory compared with the conventional point based methods the estimation accuracy level of the sgqf can be flexibly controlled and the number of sparse grid quadrature points for the sgqf is a polynomial of the dimension of the system which alleviates the curse of dimensionality for high dimensional problems the unscented kalman filter ukf is proven to be a subset of the sgqf at the level 2 accuracy the performance of this filter is demonstrated by an orbit estimation problem the simulation results show that the sgqf achieves higher accuracy than the extended kalman filter ekf the ukf and the cubature kalman filter ckf in addition the sgqf is computationally much more efficient than the multi dimensional gauss hermite quadrature filter ghqf with the same performance

truncated unscented kalman filtering we devise a filtering algorithm to approximate the first two moments of the posterior probability density function pdf the novelties of the algorithm are in the update step if the likelihood has a bounded support we can use a modified prior distribution that meets bayes rule exactly applying a kalman filter kf to the modified prior distribution referred to as truncated kalman filter tkf can vastly improve the performance of the conventional kalman filter particularly when the measurements are informative relative to the prior the application of the tkf to practical problems in which the measurement noise pdf has unbounded support is achieved by imposing several approximating assumptions which are valid only when the measurements are informative this implies that we adaptively choose between an approximation to the kf or the tkf according to the information provided by the measurement the resulting algorithm based on the unscented transformation is referred to as truncated unscented kf

adaptive gaussian sum filters for space surveillance the representation of the uncertainty of a stochastic state by a gaussian mixture is well suited for nonlinear tracking problems in high dimensional data starved environments such as space surveillance in this paper the framework for a gaussian sum filter is developed emphasizing how the uncertainty can be propagated accurately over extended time periods in the absence of measurement updates to achieve this objective a series of metrics constructed from tensors of higher order cumulants are proposed which assess the consistency of the uncertainty and provide a tool for implementing an adaptive gaussian sum filter emphasis is also placed on the algorithm s potential for parallelization which is complemented by the use of higher order unscented filters based on efficient multidimensional gauss hermite quadrature schemes the effectiveness of the proposed gaussian sum filter is illustrated in a case study in space surveillance involving the tracking of an object in a six dimensional state space

a multi model selection framework for unknown and or evolutive misclassification cost problems in this paper we tackle the problem of model selection when misclassification costs are unknown and or may evolve unlike traditional approaches based on a scalar optimization we propose a generic multi model selection framework based on a multi objective approach the idea is to automatically train a pool of classifiers instead of one single classifier each classifier in the pool optimizing a particular trade off between the objectives within the context of two class classification problems we introduce the roc front concept as an alternative to the roc curve representation this strategy is applied to the multi model selection of svm classifiers using an evolutionary multi objective optimization algorithm the comparison with a traditional scalar optimization technique based on an auc criterion shows promising results on uci datasets as well as on a real world classification problem

unscented kalman filter aspects and adaptive setting of scaling parameter this technical note deals with the unscented kalman filter for state estimation of nonlinear stochastic dynamic systems with a special focus on the scaling parameter of the filter its standard choice is analyzed and its impact on the estimation quality is discussed on the basis of the analysis a novel method for adaptive setting of the parameter in the unscented kalman filter is proposed the results are illustrated in a numerical example

sms emoa multiobjective selection based on dominated hypervolume abstract the hypervolume measure or s metric is a frequently applied quality measure for comparing the results of evolutionary multiobjective optimisation algorithms emoa the new idea is to aim explicitly for the maximisation of the dominated hypervolume within the optimisation process a steady state emoa is proposed that features a selection operator based on the hypervolume measure combined with the concept of non dominated sorting the algorithm s population evolves to a well distributed set of solutions thereby focussing on interesting regions of the pareto front the performance of the devised s metric selection emoa sms emoa is compared to state of the art methods on two and three objective benchmark suites as well as on aeronautical real world applications

gaussian filters for nonlinear filtering problems we develop and analyze real time and accurate filters for nonlinear filtering problems based on the gaussian distributions we present the systematic formulation of gaussian filters and develop efficient and accurate numerical integration of the optimal filter we also discuss the mixed gaussian filters in which the conditional probability density is approximated by the sum of gaussian distributions a new update rule of weights for gaussian sum filters is proposed our numerical tests demonstrate that new filters significantly improve the extended kalman filter with no additional cost and the new gaussian sum filter has a nearly optimal performance

fully symmetric interpolatory rules for multiple integrals over hyper spherical surfaces fully symmetric interpolatory integration rules are constructed for multidimensional integrals over un the surface of an n dimensional hyper sphere explicit formulas for the weights are given for odd degrees 3 13 the new rules are efficient and only moderately unstable two randomization methods are described

on a doubly nonlinear diffusion equation in hydrology on considere l equation aux derivees partielles non lineaires u t d u u x x ou d et satisfont certaines hypotheses on etudie le probleme de neumann sur 1 1 avec les conditions aux limites naturelles d u u x 1 t 0 pour t 0 le probleme de cauchy et un probleme de cauchy dirichlet sur 0 avec les conditions aux limites u 0 t a pour t 0 a 0 1

a stochastic algorithm for high dimensional integrals over unbounded regions with gaussian weight abstract details are given for a fortran implementation of an algorithm that uses stochastic spherical radial rules for the numerical computation of multiple integrals over unbounded regions with gaussian weight the implemented rules are suitable for high dimensional problems a high dimensional example from a computational finance application is used to illustrate the use of the rules

multiobjective optimization of classifiers by means of 3d convex hull based evolutionary algorithms the receiver operating characteristic roc and detection error tradeoff det curves are frequently used in the machine learning community to analyze the performance of binary classifiers recently the convex hull based multiobjective genetic programming algorithm was proposed and successfully applied to maximize the convex hull area for binary classification problems by minimizing false positive rate and maximizing true positive rate at the same time using indicator based evolutionary algorithms the area under the roc curve was used for the performance assessment and to guide the search here we extend this research and propose two major advancements firstly we formulate the algorithm in detection error tradeoff space minimizing false positives and false negatives with the advantage that misclassification cost tradeoff can be assessed directly secondly we add complexity as an objective function which gives rise to a 3d objective space as opposed to a 2d previous roc space a domain specific performance indicator for 3d pareto front approximations the volume above det surface is introduced and used to guide the indicator based evolutionary algorithm to find optimal approximation sets we assess the performance of the new algorithm on designed theoretical problems with different geometries of pareto fronts and det surfaces and two application oriented benchmarks 1 designing spam filters with low numbers of false rejects false accepts and low computational cost using rule ensembles and 2 finding sparse neural networks for binary classification of test data from the uci machine learning benchmark the results show a high performance of the new algorithm as compared to conventional methods for multicriteria optimization

analysis of kalman filter approximations for nonlinear measurements a theoretical analysis is presented of the correction step of the kalman filter kf and its various approximations for the case of a nonlinear measurement equation with additive gaussian noise the kf is based on a gaussian approximation to the joint density of the state and the measurement the analysis metric is the kullback leibler divergence of this approximation from the true joint density the purpose of the analysis is to provide a quantitative tool for understanding and assessing the performance of the kf and its variants in nonlinear scenarios this is illustrated using a numerical example

the iterated kalman filter update as a gauss newton method it is shown that the iterated kalman filter ikf update is an application of the gauss newton method for approximating a maximum likelihood estimate an example is presented in which the iterated kalman filter update and maximum likelihood estimate show correct convergence behavior as the observation becomes more accurate whereas the extended kalman filter update does not

technical communique a zakai equation derivation of the extended kalman filter a discrete time filter is considered where both the observation and signal process have non linear dynamics with additive gaussian noise using the reference probability framework a convolution type zakai equation is obtained which updates the unnormalized conditional density using first order approximations this equation can be solved recursively and the extended kalman filter can be derived

monomial cubature rules since stroud a compilation a bibliography of references to cubature rules which have appeared since the publication of stroud s book 1971 is presented the standard regions that are treated in this paper are the n cube the n simplex the n sphere and the entire space

a new method for the nonlinear transformation of means and covariances in filters and estimators this paper describes a new approach for generalizing the kalman filter to nonlinear systems a set of samples are used to parametrize the mean and covariance of a not necessarily gaussian probability distribution the method yields a filter that is more accurate than an extended kalman filter ekf and easier to implement than an ekf or a gauss second order filter its effectiveness is demonstrated using an example

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

multiobjective genetic optimization of diagnostic classifiers with implications for generating receiver operating characteristic curves it is well understood that binary classifiers have two implicit objective functions sensitivity and specificity describing their performance traditional methods of classifier training attempt to combine these two objective functions or two analogous class performance measures into one so that conventional scalar optimization techniques can be utilized this involves incorporating a priori information into the aggregation method so that the resulting performance of the classifier is satisfactory for the task at hand the authors have investigated the use of a niched pareto multiobjective genetic algorithm ga for classifier optimization with niched pareto ga s an objective vector is optimized instead of a scalar function eliminating the need to aggregate classification objective functions the niched pareto ga returns a set of optimal solutions that are equivalent in the absence of any information regarding the preferences of the objectives the a priori knowledge that was used for aggregating the objective functions in conventional classifier training can instead be applied post optimization to select from one of the series of solutions returned from the multiobjective genetic optimization the authors have applied this technique to train a linear classifier and an artificial neural network ann using simulated datasets the performances of the solutions returned from the multiobjective genetic optimization represent a series of optimal sensitivity specificity pairs which can be thought of as operating points on a receiver operating characteristic roc curve all possible roc curves for a given dataset and classifier are less than or equal to the roc curve generated by the niched pareto genetic optimization

quantum behaved discrete multi objective particle swarm optimization for complex network clustering abstract complex network research has attracted lots of attention in both academic community and various application fields complex network clustering as one of the key issues in complex network explores the internal organization of the nodes in a complex network the discrete particle swarm optimization strategy has been successfully proposed for network clustering while the existing method works with weak robust in this paper we model the task of complex network clustering as a multi objective optimization problem and solve the problem with the quantum mechanism based particle swarm optimization algorithm which is a parallel algorithm to our knowledge this is the first attempt to apply the quantum mechanism based discrete particle swarm optimization algorithm into network clustering in addition the non dominant sorting selection operation is employed for individual replacement consequently a quantum behaved discrete multi objective particle swarm optimization algorithm is proposed for complex network clustering the experimental results demonstrate that the proposed algorithm performs effectively and achieves competitive performance with the state of the art approaches on the extension of girvan and newman benchmarks and real world networks especially on large scale networks

existence and uniqueness of radial solutions for fresh salt water interface equation in a confined aquifer abstract we prove existence and uniqueness of radial weak solutions of the doubly nonlinear parabolic equation u t div d u u where d and satisfy some hypothesis this cover the particular case where d s s 1 s and p p 1 p 2 which is the hydrological case numerical simulations are provided also

nonlinear kalman filtering with divergence minimization we consider the nonlinear kalman filtering problem using kullback leibler kl and alpha divergence measures as optimization criteria unlike linear kalman filters nonlinear kalman filters do not have closed form gaussian posteriors because of a lack of conjugacy due to the nonlinearity in the likelihood in this paper we propose novel algorithms to approximate this posterior by optimizing the forward and reverse forms of the kl divergence as well as the alpha divergence that contains these two as limiting cases unlike previous approaches our algorithms do not make approximations to the divergences being optimized but use monte carlo techniques to derive unbiased algorithms for direct optimization we assess performance on radar and sensor tracking and options pricing showing general improvement over the extended unscented and ensemble kalman filters as well as competitive performance with particle filtering

cubature kalman filters in this paper we present a new nonlinear filter for high dimensional state estimation which we have named the cubature kalman filter ckf the heart of the ckf is a spherical radial cubature rule which makes it possible to numerically compute multivariate moment integrals encountered in the nonlinear bayesian filter specifically we derive a third degree spherical radial cubature rule that provides a set of cubature points scaling linearly with the state vector dimension the ckf may therefore provide a systematic solution for high dimensional nonlinear filtering problems the paper also includes the derivation of a square root version of the ckf for improved numerical stability the ckf is tested experimentally in two nonlinear state estimation problems in the first problem the proposed cubature rule is used to compute the second order statistics of a nonlinearly transformed gaussian random variable the second problem addresses the use of the ckf for tracking a maneuvering aircraft the results of both experiments demonstrate the improved performance of the ckf over conventional nonlinear filters

high degree cubature kalman filter the cubature kalman filter ckf which is based on the third degree spherical radial cubature rule is numerically more stable than the unscented kalman filter ukf but less accurate than the gauss hermite quadrature filter ghqf to improve the performance of the ckf a new class of ckfs with arbitrary degrees of accuracy in computing the spherical and radial integrals is proposed the third degree ckf is a special case of the class the high degree ckfs of the class can achieve the accuracy and stability performances close to those of the ghqf but at lower computational cost a numerical integration problem and a target tracking problem are utilized to demonstrate the necessity of using the high degree cubature rules to improve the performance the target tracking simulation shows that the fifth degree ckf can achieve higher accuracy than the extended kalman filter the ukf the third degree ckf and the particle filter and is computationally much more efficient than the ghqf

adaptive unscented gaussian likelihood approximation filter this paper focuses on the update step of bayesian nonlinear filtering we first derive the unscented gaussian likelihood approximation filter uglaf which provides a gaussian approximation to the likelihood by applying the unscented transformation to the inverse of the measurement function the uglaf approximation is accurate in the cases where the unscented kalman filter ukf is not and the other way round as a result we propose the adaptive uglaf auglaf which selects the best approximation to the posterior ukf or uglaf based on the kullback leibler divergence this enables auglaf to outperform both the ukf and uglaf

regularizing effects for ut aϑ u 0 in l1 abstract various initial boundary value problems and cauchy problems can be written in the form du dt a u 0 where r r is nondecreasing and a is the linear generator of strongly continuous nonexpansive semigroup e ta in an l1 space for example if a subject perhaps to suitable boundary conditions we obtain equations arising in flow in a porous medium or plasma physics depending on the choice of while if a x acting in l1 r we have a scalar conservation law in this paper we show that if m m 0 and m 2 m 2 where 1 1 then roughly speaking the norm of t du dt may be estimated in terms of the initial data u0 in l1 such estimates give information about the regularity of solutions asymptotic behaviour etc in applications side issues such as the introduction of sufficiently regular approximate problems on which estimates can be made and the assignment of a precise meaning to the operator a are also dealt with these considerations are of independent interest

relations between sparse grid quadrature rule and spherical radial cubature rule in nonlinear gaussian estimation the recently emerging cubature kalman filter and the sparse grid quadrature filter approximate the numerical integrations for the mean and covariance in gaussian filters using the spherical radial cubature rule and the sparse grid quadrature rule respectively this technical note reveals that 1 spherical rules can be obtained by the projection of sparse grid quadrature rules 2 the third and some of the fifth degree spherical radial cubature rules can be directly constructed from sparse grid quadrature rules