regulatory assessment of drug dissolution profiles comparability via maximum deviation in drug development comparability of dissolution profiles of 2 different formulations is usually assessed using the similarity factor f2 in practice the drug dissolution profiles are deemed similar if the f2 exceeds 50 which occurs when a 10 maximum difference in the mean percentage of the dissolved drug at each time point between test and reference formulation is obtained according to the guideline on the investigation of bioequivalence cpmp ewp qwp 1401 98 rev 1 corr use of the f2 is however restricted by a set of validity conditions if some of these conditions are not satisfied the f2 is not considered suitable and alternative statistical methods are needed in this article we propose an inferential framework based on the maximum deviation between curves to test the comparability of drug dissolution profiles the new methodology is applicable regardless whether the validity criteria of the f2 are met or not contrary to the f2 this approach also integrates the variability of the measurements over time and not only their average to benchmark our method we performed simulations informed by 3 real case studies provided by the european medicines agency and extracted from dossiers submitted to the centralised procedure for marketing authorisation application in the scenarios of the simulation study the new method controlled its type i error rate when the maximum deviation was greater than the similarity acceptance limit of 10 the power exceeded 80 for small values of the maximum deviation while the test was more conservative for intermediate ones our results were also very robust to sampling variations based on these positive findings we encourage applicants to consider the new maximum deviation based method as a valid alternative to the f2 especially when the validity criteria of the latter are not met

on the equality constraints tolerance of constrained optimization problems the tolerance value plays an important role when converting equality constraints into inequality constraints in solving constrained optimization problems many researchers use a fixed or dynamic setting directly based on trial or experiments without systematic study as a well known constraint handling technique deb s feasibility based rule is widely adopted but it has one drawback as the ranking is not consistent with the actual ranking after introducing the tolerance value after carefully analyzing how the tolerance value influences the ranking difference a novel strategy named ranking adjustment strategy ras is proposed which can be considered as a complement of deb s feasibility based rule the experiment has verified the effectiveness of the proposed strategy this is the first time to analyze the inner mechanism of the tolerance value for equality constraints systematically which can give some guide for future research

cooperative coevolutionary differential evolution with improved augmented lagrangian to solve constrained optimisation problems propose the improved augmented lagrangian method ialf to deal with constraints in a more efficient way propose cooperative coevolutionary method using improved augmented lagrangian ccialf approach for solving constrained optimisation problems solve the cec 2006 constrained optimisation test suite with proposed ccialf algorithm with higher solution quality compared to the state of the art algorithms solve practical engineering problems by proposed ccialf algorithm and improve the best known objective function value that exists in the literature in constrained optimisation the augmented lagrangian method is considered as one of the most effective and efficient methods this paper studies the behaviour of augmented lagrangian function alf in the solution space and then proposes an improved augmented lagrangian method we have shown that our proposed method can overcome some of the drawbacks of the conventional augmented lagrangian method with the improved augmented lagrangian approach this paper then proposes a cooperative coevolutionary differential evolution algorithm for solving constrained optimisation problems the proposed algorithm is evaluated on a set of 24 well known benchmark functions and five practical engineering problems experimental results demonstrate that the proposed algorithm outperforms the state of the art algorithms with respect to solution quality as well as efficiency

an effective co evolutionary differential evolution for constrained optimization many practical problems can be formulated as constrained optimization problems due to the simple concept and easy implementation the penalty function method has been one of the most common techniques to handle constraints however the performance of this technique greatly relies on the setting of penalty factors which are usually determined by manual trial and error and the suitable penalty factors are often problem dependent and difficult to set in this paper a differential evolution approach based on a co evolution mechanism named cde is proposed to solve the constrained problems first a special penalty function is designed to handle the constraints second a co evolution model is presented and differential evolution de is employed to perform evolutionary search in spaces of both solutions and penalty factors thus the solutions and penalty factors evolve interactively and self adaptively and both the satisfactory solutions and suitable penalty factors can be obtained simultaneously simulation results based on several benchmark functions and three well known constrained design problems as well as comparisons with some existed methods demonstrate the effectiveness efficiency and robustness of the proposed method

statistical tests for multivariate bioequivalence although the u s food and drug administration fda 1992 recommends testing bioequivalence of individual pharmacokinetic parameters one at a time it seems reasonable and interesting to conduct a test simultaneously for all the parameters in this paper we discuss several ways to construct such tests it is shown that the confidence set approach leads to a test which can be uniformly improved by the intersection of schuirmann s two one sided tests procedure the latter test can further be improved upon noticeably by using the one dimensional unbiased test of brown hwang munk 1997 numerical calculations of powers are given to support this claim

an efficient constraint handling method for genetic algorithms many real world search and optimization problems involve inequality and or equality constraints and are thus posed as constrained optimization problems in trying to solve constrained optimization problems using genetic algorithms gas or classical optimization methods penalty function methods have been the most popular approach because of their simplicity and ease of implementation however since the penalty function approach is generic and applicable to any type of constraint linear or nonlinear their performance is not always satisfactory thus researchers have developed sophisticated penalty functions specific to the problem at hand and the search algorithm used for optimization however the most difficult aspect of the penalty function approach is to find appropriate penalty parameters needed to guide the search towards the constrained optimum in this paper ga s population based approach and ability to make pair wise comparison in tournament selection operator are exploited to devise a penalty function approach that does not require any penalty parameter careful comparisons among feasible and infeasible solutions are made so as to provide a search direction towards the feasible region once sufficient feasible solutions are found a niching method along with a controlled mutation operator is used to maintain diversity among feasible solutions this allows a real parameter ga s crossover operator to continuously find better feasible solutions gradually leading the search near the true optimum solution gas with this constraint handling approach have been tested on nine problems commonly used in the literature including an engineering design problem in all cases the proposed approach has been able to repeatedly find solutions closer to the true optimum solution than that reported earlier

combining multiple comparisons and modeling techniques in dose response studies the analysis of data from dose response studies has long been divided according to two major strategies multiple comparison procedures and model based approaches model based approaches assume a functional relationship between the response and the dose taken as a quantitative factor according to a prespecified parametric model the fitted model is then used to estimate an adequate dose to achieve a desired response but the validity of its conclusions will highly depend on the correct choice of the a priori unknown dose response model multiple comparison procedures regard the dose as a qualitative factor and make very few if any assumptions about the underlying dose response model the primary goal is often to identify the minimum effective dose that is statistically significant and produces a relevant biological effect one approach is to evaluate the significance of contrasts between different dose levels while preserving the family wise error rate such procedures are relatively robust but inference is confined to the selection of the target dose among the dose levels under investigation we describe a unified strategy to the analysis of data from dose response studies which combines multiple comparison and modeling techniques we assume the existence of several candidate parametric models and use multiple comparison techniques to choose the one most likely to represent the true underlying dose response curve while preserving the family wise error rate the selected model is then used to provide inference on adequate doses

a hybrid particle swarm optimization with a feasibility based rule for constrained optimization during the past decade hybrid algorithms combining evolutionary computation and constraint handling techniques have shown to be effective to solve constrained optimization problems for constrained optimization the penalty function method has been regarded as one of the most popular constraint handling technique so far whereas its drawback lies in the determination of suitable penalty factors which greatly weakens the efficiency of the method as a novel population based algorithm particle swarm optimization pso has gained wide applications in a variety of fields especially for unconstrained optimization problems in this paper a hybrid pso hpso with a feasibility based rule is proposed to solve constrained optimization problems in contrast to the penalty function method the rule requires no additional parameters and can guide the swarm to the feasible region quickly in addition to avoid the premature convergence simulated annealing sa is applied to the best solution of the swarm to help the algorithm escape from local optima simulation and comparisons based on several well studied benchmarks demonstrate the effectiveness efficiency and robustness of the proposed hpso moreover the effects of several crucial parameters on the performance of the hpso are studied as well

equivalence of regression curves sharing common parameters in clinical trials the comparison of two different populations is a common problem nonlinear parametric regression models are commonly used to describe the relationship between covariates such as concentration or dose and a response variable in the two groups in some situations it is reasonable to assume some model parameters to be the same for instance the placebo effect or the maximum treatment effect in this paper we develop a parametric bootstrap test to establish the similarity of two regression curves sharing some common parameters we show by theoretical arguments and by means of a simulation study that the new test controls its significance level and achieves a reasonable power moreover it is demonstrated that under the assumption of common parameters a considerably more powerful test can be constructed compared with the test that does not use this assumption finally we illustrate the potential applications of the new methodology by a clinical trial example

equivalence of regression curves this article investigates the problem whether the difference between two parametric models m1 m2 describing the relation between a response variable and several covariates in two different groups

a new fuzzy programming approach for multi period portfolio optimization with return demand and risk control abstract this paper considers a multi period portfolio selection problem imposed by return demand and risk control in a fuzzy investment environment in which the returns of assets are characterized by fuzzy numbers a fuzzy lower semi deviation is originally defined as the risk control of portfolio a proportion entropy constraint is added as the divergence measure of portfolio based on the theories of possibility and necessity measures a new multi period portfolio optimization model with return demand and risk control is proposed and then the proposed model is transformed into a crisp nonlinear programming problem by using fuzzy programming approach furthermore an improved differential evolution algorithm is designed for obtaining the optimal strategy finally a numerical example is given to illustrate the practicality and efficiency of the proposed model and the corresponding algorithm

differential evolution with dynamic stochastic selection for constrained optimization how much attention should be paid to the promising infeasible solutions during the evolution process is investigated in this paper stochastic ranking has been demonstrated as an effective technique for constrained optimization in stochastic ranking the comparison probability will affect the position of feasible solution after ranking and the quality of the final solutions in this paper the dynamic stochastic selection dss is put forward within the framework of multimember differential evolution firstly a simple version named dss mde is given where the comparison probability decreases linearly the algorithm dss mde has been compared with two state of the art evolution strategies and three competitive differential evolution algorithms for constrained optimization on 13 common benchmark functions dss mde is also evaluated on four well studied engineering design examples and the experimental results are significantly better than current available results secondly other dynamic settings of the comparison probability for dss mde are also designed and tested from the experimental results dss mde is effective for constrained optimization finally dss mde with a square root adjusted comparison probability is evaluated on the 22 benchmark functions in cec 06 and the experimental results on most functions are competitive

assessing nonsuperiority noninferiority or equivalence when comparing two regression models over a restricted covariate region in many scientific problems the purpose of the comparison of two regression models which describe the relationship between a same response variable and several same covariates for two different groups is to demonstrate that one model is no higher than the other by a negligible amount or to demonstrate that the models have only negligible differences and so they can be regarded as describing practically the same relationship between the response variable and the covariates in this article methods based on one sided pointwise confidence bands are proposed for assessing the nonsuperiority of one model to the other and for assessing the equivalence of two regression models examples from qt qtc study and from drug stability study are used to illustrate the methods

assessing the similarity of dose response and target doses in two non overlapping subgroups we consider two problems that are becoming more and more frequent in dose finding studies first we assess the similarity of two non linear regression models for two non overlapping subgroups of patients over a restricted covariate space to this end we derive a confidence interval for the maximum difference between the two given models if this confidence interval excludes the equivalence margins similarity of dose response can be claimed second we address the problem of demonstrating the similarity of two target doses for two non overlapping subgroups using again a confidence interval based approach the proposed methods are illustrated with a real case study and their operating characteristics coverage probabilities type i error rates power are investigated via simulation

hecke theory and equidistribution for the quantization of linear maps of the torus 1 1 background one of the key issues of quantum chaos is the nature of the semiclassical limit of eigenstates of classically chaotic systems when the classical system is given by the geodesic flow on a compact riemannian manifoldm or rather on its cotangent bundle one can formulate the problem as follows the quantum hamiltonian is in suitable units represented by the positive laplacian on m to measure the distribution of its eigenstates we start with a smooth classical observable that is a smooth function on the unit cotangent bundle s m via some choice of quantization from symbols to pseudodifferential operators we form its quantization op f this is a zero order pseudodifferential operator with principal symbol f the expectation value of op f in the eigenstate is op f let j be a sequence of normalized eigenfunctions j j j 0 m j 2 1 the problem then is to understand the possible limits as j of the distributions f c s m op f j j 1 1

constrained optimization based on modified differential evolution algorithm this paper presents a novel constrained optimization based on modified differential evolution algorithm comde in the new algorithm a new directed mutation rule based on the weighted difference vector between the best and the worst individuals at a particular generation is introduced the new directed mutation rule is combined with the modified basic mutation strategy de rand 1 bin where only one of the two mutation rules is applied with the probability of 0 5 the proposed mutation rule is shown to enhance the local search ability of the basic differential evolution de and to get a better trade off between convergence rate and robustness two new scaling factors are introduced as uniform random variables to improve the diversity of the population and to bias the search direction additionally a dynamic non linear increased crossover probability is utilized to balance the global exploration and local exploitation comde also includes a modified constraint handling technique based on feasibility and the sum of constraints violations a new dynamic tolerance technique to handle equality constraints is also adopted the effectiveness and benefits of the new directed mutation strategy and modified basic strategy used in comde has been experimentally investigated the effect of the parameters of the crossover probability function and the parameters of the dynamic tolerance equation on the performance of comde have been analyzed and evaluated by different experiments numerical experiments on 13 well known benchmark test functions and five engineering design problems have shown that the new approach is efficient effective and robust the comparison results between the comde and the other 28 state of the art evolutionary algorithms indicate that the proposed comde algorithm is competitive with and in some cases superior to other existing algorithms in terms of the quality efficiency convergence rate and robustness of the final solution

adaptive memetic differential evolution with global and local neighborhood based mutation operators differential evolution de is one of the most popular optimization methods for real valued problems and a large number of its variants have been proposed so far however bringing together different ideas that already led to successful de versions is rare in the literature in the present paper a novel de algorithm is proposed in which three among the most efficient concepts already applied separately within de framework are gathered together namely 1 the adaptation of algorithm control parameters and probabilities of using different mutation strategies 2 the use of nelder mead algorithm as a local search method hybridized with de and 3 the splitting mutation into global and local models when local mutation model is based on the concept of neighborhood of individuals organized on a ring topology the performance of the novel algorithm called adaptive memetic de with global and local neighborhood based mutation operators is compared with 13 different de variants on a set of 25 popular problems which include rotated shifted and hybrid composition functions it is found that although none de algorithm outperforms all the others for the majority of problems on average the proposed approach perform better than all 13 de algorithms selected for comparison the proposed algorithm is another heuristic approach developed to solve optimization problems the question may arise whether proposing novel methods is useful as no free lunch theorems for optimization state that the expected performance of all possible heuristics on all possible problems is equal in the last section of the paper the limitations and implications of no free lunch theorems are discussed based on rich but unfortunately frequently neglected literature a very simple continuous and differentiable minimization problem is proposed for which it is empirically verified that each among considered 14 de algorithms perform poorer than random sampling it is also empirically shown that when all considered de algorithms search for the maximum of the proposed problem they found lower minimum than de algorithms searching for the minimum such result is not unexpected according to no free lunch theorems and should be considered as a precaution from generalization of good performance of heuristic optimization methods

optimal designs for the emax log linear and exponential models we derive locally d and edp optimal designs for the exponential log linear and three parameter emax models for each model the locally d and ed p optimal designs are supported at the same set of points while the corresponding weights are different this indicates that for a given model d optimal designs are efficient for estimating the smallest dose that achieves 100p of the maximum effect in the observed dose range conversely ed p optimal designs also yield good d efficiencies we illustrate the results using several examples and demonstrate that locally d and ed p optimal designs for the emax log linear and exponential models are relatively robust with respect to misspecification of the model parameters

ergodic properties of quantized toral automorphisms we study the ergodic properties for a class of quantized toral automorphisms namely the cat and kronecker maps the present work uses and extends the results of klimek and le niewski ann phys 244 173 198 1996 we show that quantized cat maps are strongly mixing while kronecker maps are ergodic and nonmixing we also study the structure of these quantum maps and show that they are effected by unitary endomorphisms of a suitable vector bundle over a torus this allows us to exhibit explicit relations between our toeplitz quantization and the semiclassical quantization of cat maps proposed by hannay and berry physica d 1 267 290 1980

an effective memetic differential evolution algorithm based on chaotic local search this paper proposes an effective memetic differential evolution de algorithm or decls that utilizes a chaotic local search cls with a shrinking strategy the cls helps to improve the optimizing performance of the canonical de by exploring a huge search space in the early run phase to avoid premature convergence and exploiting a small region in the later run phase to refine the final solutions moreover the parameter settings of the decls are controlled in an adaptive manner to further enhance the search ability to evaluate the effectiveness and efficiency of the proposed decls algorithm we compared it with four state of the art de variants and the ipop cma es algorithm on a set of 20 selected benchmark functions results show that the decls is significantly better than or at least comparable to the other optimizers in terms of convergence performance and solution accuracy besides the decls has also shown certain advantages in solving high dimensional problems

a note on teaching learning based optimization algorithm teaching learning based optimization tlbo seems to be a rising star from amongst a number of metaheuristics with relatively competitive performances it is reported that it outperforms some of the well known metaheuristics regarding constrained benchmark functions constrained mechanical design and continuous non linear numerical optimization problems such a breakthrough has steered us towards investigating the secrets of tlbo s dominance this paper reports our findings on tlbo qualitatively and quantitatively through code reviews and experiments respectively our findings have revealed three important mistakes regarding tlbo 1 at least one unreported but important step 2 incorrect formulae on a number of fitness function evaluations and 3 misconceptions about parameter less control additionally unfair experimental settings conditions were used to conduct experimental comparisons e g different stopping criteria the experimental results for constrained and unconstrained benchmark functions under fairly equal conditions failed to validate its performance supremacy the ultimate goal of this paper is to provide reminders for metaheuristics researchers and practitioners in order to avoid similar mistakes regarding both the qualitative and quantitative aspects and to allow fair comparisons of the tlbo algorithm to be made with other metaheuristic algorithms

differential evolution in constrained numerical optimization an empirical study motivated by the recent success of diverse approaches based on differential evolution de to solve constrained numerical optimization problems in this paper the performance of this novel evolutionary algorithm is evaluated three experiments are designed to study the behavior of different de variants on a set of benchmark problems by using different performance measures proposed in the specialized literature the first experiment analyzes the behavior of four de variants in 24 test functions considering dimensionality and the type of constraints of the problem the second experiment presents a more in depth analysis on two de variants by varying two parameters the scale factor f and the population size np which control the convergence of the algorithm from the results obtained a simple but competitive combination of two de variants is proposed and compared against state of the art de based algorithms for constrained optimization in the third experiment the study in this paper shows 1 important information about the behavior of de in constrained search spaces and 2 the role of this knowledge in the correct combination of variants based on their capabilities to generate simple but competitive approaches

cultured differential evolution for constrained optimization a cultural algorithm with a differential evolution population is proposed in this paper this cultural algorithm uses different knowledge sources to influence the variation operator of the differential evolution algorithm in order to reduce the number of fitness function evaluations required to obtain competitive results comparisons are provided with respect to three techniques that are representative of the state of the art in the area the results obtained by our algorithm are similar in quality to those obtained by the other approaches with respect to which it was compared however our approach requires a lower number of fitness function evaluations than the others

an improved differential evolution algorithm with fitness based adaptation of the control parameters differential evolution de is arguably one of the most powerful stochastic real parameter optimization algorithms of current interest de operates through the similar computational steps as employed by a standard evolutionary algorithm ea however unlike the traditional eas the de variants perturb the current generation population members with the scaled differences of randomly selected and distinct population members therefore no separate probability distribution has to be used which makes the scheme self organizing in this respect scale factor f and crossover rate cr are two very important control parameters of de since the former regulates the step size taken while mutating a population member in de and the latter controls the number of search variables inherited by an offspring from its parent during recombination this article describes a very simple yet very much effective adaptation technique for tuning both f and cr on the run without any user intervention the adaptation strategy is based on the objective function value of individuals in the de population comparison with the best known and expensive variants of de over fourteen well known numerical benchmarks and one real life engineering problem reflects the superiority of proposed parameter tuning scheme in terms of accuracy convergence speed and robustness