second order analysis for optimal control problems improving results expected from abstract theory an abstract optimization problem of minimizing a functional on a convex subset of a banach space is considered we discuss natural assumptions on the functional that permit establishing sufficient second order optimality conditions with minimal gap with respect to the associated necessary ones though the two norm discrepancy is taken into account the obtained results exhibit the same formulation as the classical ones known from finite dimensional optimization we demonstrate that these assumptions are fulfilled in particular by important optimal control problems for partial differential equations we prove that in contrast to a widespread common belief the standard second order conditions formulated for these control problems imply strict local optimality of the controls not only in the sense of l infty but also of l 2

minimizing total tardiness on one machine is np hard the problem of minimizing the total tardiness for a set of independent jobs on one machine is considered lawler has given a pseudo polynomial time algorithm to solve this problem in spite of extensive research efforts for more than a decade the question of whether it can be solved in polynomial time or it is np hard in the ordinary sense remained open in this paper the problem is shown to be np hard in the ordinary sense

multiple imputation when records used for imputation are not used or disseminated for analysis summary when some of the records used to estimate the imputation models in multiple imputation are not used or available for analysis the usual multiple imputation variance estimator has positive bias we present an alternative approach that enables unbiased estimation of variances and hence calibrated inferences in such contexts first using all records the imputer samples m values of the parameters of the imputation model second for each parameter draw the imputer simulates the missing values for all records n times from these mn completed datasets the imputer can analyse or disseminate the appropriate subset of records we develop methods for interval estima tion and significance testing for this approach methods are presented in the context of multiple imputation for measurement error

second order optimality conditions for semilinear elliptic control problems with finitely many state constraints this paper deals with necessary and sufficient optimality conditions for control problems governed by semilinear elliptic partial differential equations with finitely many equality and inequality state constraints some recent results on this topic for optimal control problems based upon results for abstract optimization problems are compared with some new results using methods adapted to the control problems meanwhile the lagrangian formulation is followed to provide the optimality conditions in the first case the lagrangian and hamiltonian functions are used in the second statement finally we prove the equivalence of both formulations

variable neighborhood search principles and applications abstract systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization called variable neighborhood search vns we present a basic scheme for this purpose which can easily be implemented using any local search algorithm as a subroutine its effectiveness is illustrated by solving several classical combinatorial or global optimization problems moreover several extensions are proposed for solving large problem instances using vns within the successive approximation method yields a two level vns called variable neighborhood decomposition search vnds modifying the basic scheme to explore easily valleys far from the incumbent solution yields an efficient skewed vns svns heuristic finally we show how to stabilize column generation algorithms with help of vns and discuss various ways to use vns in graph theory i e to suggest disprove or give hints on how to prove conjectures an area where metaheuristics do not appear to have been applied before

a multi threaded local search algorithm and computer implementation for the multi mode resource constrained multi project scheduling problem abstract the article describes a solution approach for the multi mode resource constrained multi project scheduling problem our key ideas are based on the concepts of variable neighborhood search together with iterated local search a particular focus of this work is devoted towards the parallel implementation of such local search solution techniques with the increasing availability of parallel multi core computer hardware we believe that such techniques are about to gain attractiveness in the future experiments have been conducted on benchmark instances of the mista 2013 challenge as well as on the well known mmlib datasets the approach described in this article ranked second in the challenge and found new best results to 1371 of the 4320 mmlib instances note that the source code of our implementation has been made available under http dx doi org 10 17632 cw95t56hjv 1 the software may be freely used for non profit research education purposes

generalized pairwise interchanges and machine scheduling abstract in this paper a generalization of pairwise interchanges is considered and applied to machine scheduling problems it is shown how these swap operators can be used to compute bounds for branch and bound procedures to prove dominance properties and to define a high performance neighborhood for local search methods

a branch and bound algorithm for the total weighted tardiness problem this paper presents a new branch and bound algorithm for the single machine total weighted tardiness problem it obtains lower bounds using a lagrangian relaxation approach with subproblems that are total weighted completion time problems the well known subgradient optimization technique is replaced by a multiplier adjustment method that leads to an extremely fast bound calculation the method incorporates various devices for checking dynamic programming dominance in the search tree extensive computational results for problems with up to 50 jobs show the superiority of the algorithm over existing methods

order matters a variable neighborhood search for the swap body vehicle routing problem abstract this article presents investigations on the performance of standard and problem specific neighborhood operators for the swap body vehicle routing problem more specifically our work analyzes the contribution of each operator to the solution quality in addition an experimental setting is defined that can be utilized to identify promising sequences in a variable neighborhood search the experiments verify that the sequence matters since two best known solutions can be equaled and 16 out of 18 solutions can be improved with a maximal improvement of 2 25 and an average improvement of 0 70

multiple imputation methods for multivariate one sided tests with missing data summary multivariate one sided hypotheses testing problems arise frequently in practice various tests have been developed in practice there are often missing values in multivariate data in this case standard testing procedures based on complete data may not be applicable or may perform poorly if the missing data are discarded in this article we propose several multiple imputation methods for multivariate one sided testing problem with missing data some theoretical results are presented the proposed methods are evaluated using simulations a real data example is presented to illustrate the methods

large sample significance levels from multiply imputed data using moment based statistics and an f reference distribution abstract we present a procedure for computing significance levels from data sets whose missing values have been multiply imputed data this procedure uses moment based statistics m 3 repeated imputations and an f reference distribution when m we show first that our procedure is essentially the same as the ideal procedure in cases of practical importance and second that its deviations from the ideal are basically a function of the coefficient of variation of the canonical ratios of complete to observed information for small m our procedure s performance is largely governed by this coefficient of variation and the mean of these ratios using simulation techniques with small m we compare our procedure s actual and nominal large sample significance levels and conclude that it is essentially calibrated and thus represents a definite improvement over previously available procedures furthermore we compare the large sample power of the procedure as a function of m and other factors such as the di

a green s formula for quasilinear elliptic operators abstract we prove a theorem of traces which allows us to define the boundary condition of the neumann problem associated to a quasilinear elliptic operator in divergence form later we prove a green s formula that justifies the variational formulation of the problem

optimal control of semilinear parabolic equations by bv functions optimal control problems for semilinear parabolic equations with control costs involving the total bounded variation seminorm are analyzed this choice of control cost favors optimal controls which are piecewise constant and it penalizes the number of jumps it is an appropriate choice if a simple structure of the optimal controls is desired which however is still sufficiently flexible so that good tracking properties can be maintained existence of optimal controls necessary and sufficient optimality conditions and sparsity properties of the derivatives are obtained convergence of a finite element approximation is analyzed and numerical examples illustrating structural properties of the optimal controls are provided

second order sufficient optimality conditions for some state constrained control problems of semilinear elliptic equations this paper deals with a class of optimal control problems governed by elliptic equations with nonlinear boundary condition the case of boundary control is studied pointwise constraints on the control and certain equality and set constraints on the state are considered second order sufficient conditions for local optimality of controls are established

on heuristic search for the single machine total weighted tardiness problem some theoretical insights and their empirical verification the article presents theoretical and experimental investigations of computational intelligence techniques for machine sequencing problems contrary to other approaches which are experimentally driven only our work is motivated by gaining insights in the underlying principles of heuristic search for this particular problem we therefore first theoretically analyze local search neighborhoods deriving expectations about their relative performance an empirical study on benchmark data follows verifying the initial propositions in result we may conclude theoretically and empirically on the relative performance of neighborhood search operators for the single machine total weighted tardiness problem the results are useful for the proposition of heuristic search procedures based on local search as they lead to an order of neighborhood structures with respect to their relative performance the obtained insights are verified by investigating the effectiveness of a multi operator variable neighborhood search approach for the problem at hand we are able to show that most known benchmark instances are reliably solved to optimality leaving an overall average gap of around 1 above the optimum

a tabu search algorithm for the single machine total weighted tardiness problem abstract in this study a tabu search ts approach to the single machine total weighted tardiness problem smtwt is presented the problem consists of a set of independent jobs with distinct processing times weights and due dates to be scheduled on a single machine to minimize total weighted tardiness the theoretical foundation of single machine scheduling with due date related objectives reveal that the problem is np hard rendering it a challenging area for meta heuristic approaches this paper presents a totally deterministic ts algorithm with a hybrid neighborhood and dynamic tenure structure and investigates the strength of several candidate list strategies based on problem specific characteristics in increasing the efficiency of the search the proposed ts approach yields very high quality results for a set of benchmark problems obtained from the literature

multiple imputation after 18 years abstract multiple imputation was designed to handle the problem of missing data in public use data bases where the data base constructor and the ultimate user are distinct entities the objective is valid frequency inference for ultimate users who in general have access only to complete data software and possess limited knowledge of specific reasons and models for nonresponse for this situation and objective i believe that multiple imputation by the data base constructor is the method of choice this article first provides a description of the assumed context and objectives and second reviews the multiple imputation framework and its standard results these preliminary discussions are especially important because some recent commentaries on multiple imputation have reflected either misunderstandings of the practical objectives of multiple imputation or misunderstandings of fundamental theoretical results then criticisms of multiple imputation are considered and finally comparisons are made to alt

biometrika centenary sample surveys summary despite karl pearson s stated aim that the evolutionist has to become in the widest sense of the words a registrar general for all forms of life the papers published in biometrika on sample surveys have been mainly theoretical and do not start to appear until the 1940s there has been little work on sampling in the life sciences with the exception of capture recapture methods the major areas have been in variable probability designs the foundations of inference for finite populations analytic surveys and the role of selection mechanisms in inference in recent years the work on survey analysis has been the outcome of an interaction between sample selection mechanisms and mainstream theory with interesting consequences for both areas

single machine scheduling to minimize total weighted tardiness abstract the problem of minimizing the total weighted tardiness in single machine scheduling is a well known strongly np hard problem in this paper we present an o n 2 time approximation algorithm for the problem where n is the number of jobs we further investigate different sub models of the problem and obtain interesting properties and results we begin with the model where the job due dates are affine linear functions of their processing times and the job tardiness weights are proportional to their processing times for this model we classify the np hardness of the problem with respect to different affine linear functions and provide an o n log n algorithm for each of the polynomially solvable problems the second model we investigate is one where all job due dates have equal slacks namely the slk due date model results for this model include the problem is np hard in the ordinary sense a pseudo polynomial algorithm with time complexity o n 2 p is derived where p is the sum of all of the processing times and a fully polynomial time approximation scheme is constructed

a variable neighborhood search heuristic for periodic routing problems the aim of this paper is to propose a new heuristic for the periodic vehicle routing problem pvrp without time windows the pvrp extends the classical vehicle routing problem vrp to a planning horizon of several days each customer requires a certain number of visits within this time horizon while there is some flexibility on the exact days of the visits hence one has to choose the visit days for each customer and to solve a vrp for each day our method is based on variable neighborhood search vns computational results are presented that show that our approach is competitive and even outperforms existing solution procedures proposed in the literature also considered is the special case of a single vehicle i e the periodic traveling salesman problem ptsp it is shown that slight changes of the proposed vns procedure is also competitive for the ptsp

characterization of local quadratic growth for strong minima in the optimal control of semi linear elliptic equations in this article we consider an optimal control problem of a semi linear elliptic equation with bound constraints on the control our aim is to characterize local quadratic growth for the cost function j in the sense of strong solutions this means that the function j growths quadratically over all feasible controls whose associated state is close enough to the nominal one in the uniform topology the study of strong solutions classical in the calculus of variations seems to be new in the context of pde optimization our analysis based on a decomposition result for the variation of the cost combines pontryagin s principle and second order conditions while these two ingredients are known we use them in such a way that we do not need to assume that the hessian of lagrangian of the problem is a legendre form or that it is uniformly positive on an extended set of critical directions

pontryagin s principle for state constrained boundary control problems of semilinear parabolic equations this paper deals with state constrained optimal control problems governed by semilinear parabolic equations we establish a minimum principle of pontryagin s type to deal with the state constraints we introduce a penalty problem by using ekeland s principle the key tool for the proof is the use of a special kind of spike perturbations distributed in the domain where the controls are defined conditions for normality of optimality conditions are given

an improved branch and bound algorithm for the two machine total completion time flow shop problem we consider the two machine total completion time flow shop scheduling problem this problem is known to be np hard in the strong sense an improved lagrangean relaxation approach is proposed two new dominance criteria are introduced to curtail the enumeration tree a branch and bound algorithm capable of solving to optimality medium size problem instances is presented

a general variable neighborhood search for the one commodity pickup and delivery travelling salesman problem abstract we present a variable neighborhood search approach for solving the one commodity pickup and delivery travelling salesman problem it is characterized by a set of customers such that each of the customers either supplies pickup customers or demands delivery customers a given amount of a single product and by a vehicle whose given capacity must not be exceeded that starts at the depot and must visit each customer only once the objective is to minimize the total length of the tour thus the considered problem includes checking the existence of a feasible travelling salesman s tour and designing the optimal travelling salesman s tour which are both np hard problems we adapt a collection of neighborhood structures k opt double bridge and insertion operators mainly used for solving the classical travelling salesman problem a binary indexed tree data structure is used which enables efficient feasibility checking and updating of solutions in these neighborhoods our extensive computational analysis shows that the proposed variable neighborhood search based heuristics outperforms the best known algorithms in terms of both the solution quality and computational efforts moreover we improve the best known solutions of all benchmark instances from the literature with 200 to 500 customers we are also able to solve instances with up to 1000 customers

small sample degrees of freedom for multi component significance tests with multiple imputation for missing data summary when performing multi component significance tests with multiply imputed datasets analysts can use a wald like test statistic and a reference f distribution the currently employed degrees of freedom in the denominator of this f distribution are derived assuming an infinite sample size for modest complete data sample sizes this degrees of freedom can be unrealistic for example it may exceed the complete data degrees of freedom this paper presents an alternative denominator degrees of freedom that is always less than or equal to the complete data denominator degrees of freedom and equals the currently employed denominator degrees of freedom for infinite sample sizes its advantages over the currently employed degrees of freedom are illustrated with a simulation

error estimates for the numerical approximation of dirichlet boundary control for semilinear elliptic equations we study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control the control is the trace of the state on the boundary of the domain which is assumed to be a convex polygonal open set in mathbb r 2 piecewise linear finite elements are used to approximate the control as well as the state we prove that the error estimates are of order o h 1 1 p for some p 2 which is consistent with the w 1 1 p p gamma regularity of the optimal control

a hybrid rank based evolutionary algorithm applied to multi mode resource constrained project scheduling problem abstract we consider the multi mode resource constrained project scheduling problem mrcpsp where a task has different execution modes characterized by different resource requirements due to the nonrenewable resources and the multiple modes this problem is np hard therefore we implement an evolutionary algorithm looking for a feasible solution minimizing the makespan in this paper we propose and investigate two new ideas on the one hand we transform the problem of single objective mrcpsp to bi objective one to cope with the potential violation of nonrenewable resource constraints relaxing the latter constraints allows to visit a larger solution set and thus to simplify the evolutionary operators on the other hand we build the fitness function not on a priori grid of the bi objective space but on an adaptive one relying on clustering techniques this proposed idea aims at more relevant fitness values we show that a clustering based fitness function can be an appealing feature in multi objective evolutionary algorithms since it may promote diversity and avoid premature convergence of the algorithms clustering heuristics require certainly computation time but they are still competitive with respect to classical niche formation multi objective genetic algorithm

an adaptive ts approach to jit sequencing with variable processing times and sequence dependent setups this paper addresses a single machine sequencing problem with variable processing times and sequence dependent setups the objective is to find the best trade off between the jit goal and the processing time compression and extension costs by simultaneously determining the job sequence and processing times for concerned jobs due to the combinatorial nature of the problem it cannot be optimally solved in polynomial time a tabu search approach is used to provide good and quick solutions to improve the computational efficiency an adaptive neighbourhood generation method is proposed and used in the tabu search algorithm a total of 100 problems of different sizes have been solved to test the proposed approach our computational experience shows that the adaptive approach outperforms several other neighbourhood generation methods in terms of both convergence rate and solution quality the effects of the search parameters are also discussed

less is more basic variable neighborhood search for minimum differential dispersion problem abstract in this paper we propose a basic variable neighborhood search for solving minimum differential dispersion problem using only the swap neighborhood structure in both descent intensification and shaking diversification steps it has become a trend in the metaheuristic literature to use hybrid metaheuristics i e combination of several metaheuristic paradigms for solving some particular optimization problem we show that our simple method which relies on the basic variable neighborhood search significantly outperforms the hybrid one that combines grasp variable neighborhood search and exterior path relinking metaheuristics thus simplicity is not only the desired user friendly property of a heuristic but can lead to more efficient and effective method than if complex hybrid metaheuristic is used less is more

an iterated local search algorithm for the vehicle routing problem with backhauls abstract the vehicle routing problem with backhauls vrpb is an extension of the vrp that deals with two types of customers the consumers linehaul that request goods from the depot and the suppliers backhaul that send goods to the depot in this paper we propose a simple yet effective iterated local search algorithm for the vrpb its main component is an oscillating local search heuristic that has two main features first it explores a broad neighborhood structure at each iteration this is efficiently done using a data structure that stores information about the set of neighboring solutions second the heuristic performs constant transitions between feasible and infeasible portions of the solution space these transitions are regulated by a dynamic adjustment of the penalty applied to infeasible solutions an extensive statistical analysis was carried out in order to identify the most important components of the algorithm and to properly tune the values of their parameters the results of the computational experiments carried out show that this algorithm is very competitive in comparison to the best metaheuristic algorithms for the vrpb additionally new best solutions have been found for two instances in one of the benchmark sets these results show that the performance of existing metaheuristic algorithms can be considerably improved by carrying out a thorough statistical analysis of their components in particular it shows that by expanding the exploration area and improving the efficiency of the local search heuristic it is possible to develop simpler and faster metaheuristic algorithms without compromising the quality of the solutions obtained

boundary control of semilinear elliptic equations with pointwise state constraints this paper is concerned with state constrained optimal control problems of semilinear elliptic equations the control being on the boundary optimality conditions are derived and regularity of the optimal solution is investigated

second order analysis for bang bang control problems of pdes in this paper we derive some sufficient second order optimality conditions for control problems of partial differential equations pdes when the cost functional does not involve the usual quadratic term for the control or higher nonlinearities for it though not always in this situation the optimal control is typically bang bang two different control problems are studied the second differs from the first in the presence of the l 1 norm of the control this term leads to optimal controls that are sparse and usually take only three different values we call them bang bang bang controls though the proofs are detailed in the case of a semilinear elliptic state equation the approach can be extended to parabolic control problems some hints are provided in the last section to extend the results

the k dissimilar vehicle routing problem abstract in this paper we define a new problem the aim of which is to find a set of k dissimilar solutions for a vehicle routing problem vrp on a single instance this problem has several practical applications in the cash in transit sector and in the transportation of hazardous materials a min max mathematical formulation is proposed which requires a maximum similarity threshold between vrp solutions and the number k of dissimilar vrp solutions that need to be generated an index to measure similarities between vrp solutions is defined based on the edges shared between pairs of alternative solutions an iterative metaheuristic to generate k dissimilar alternative solutions is also presented the solution approach is tested using large and medium size benchmark instances for the capacitated vehicle routing problem

job shop scheduling by simulated annealing we describe an approximation algorithm for the problem of finding the minimum makespan in a job shop the algorithm is based on simulated annealing a generalization of the well known iterative improvement approach to combinatorial optimization problems the generalization involves the acceptance of cost increasing transitions with a nonzero probability to avoid getting stuck in local minima we prove that our algorithm asymptotically converges in probability to a globally minimal solution despite the fact that the markov chains generated by the algorithm are generally not irreducible computational experiments show that our algorithm can find shorter makespans than two recent approximation approaches that are more tailored to the job shop scheduling problem this is however at the cost of large running times

performing likelihood ratio tests with multiply imputed data sets summary existing procedures for obtaining significance levels from multiply imputed data either i require access to the completed data point estimates and variance covariance matrices which may not be available in practice when the dimensionality of the estimand is high or ii directly combine p values with less satisfactory results taking advantage of the well known relationship between the wald and log likelihood ratio test statistics we propose a complete data log likelihood ratio based procedure it is shown that for any number of multiple imputations the proposed procedure is equivalent in large samples to the existing procedure based on the point estimates and the variance covariance matrices yet it only requires the point estimates and evaluations of the complete data log likelihood ratio statistic as a function of these estimates and the completed data the proposed procedure therefore is especially attractive with highly multiparameter incomplete data problems since it does not involve the computation of any matrices

diagnosing missing always at random in multivariate data models for analyzing multivariate data sets with missing values require strong often unassessable assumptions the most common of these is that the mechanism that created the missing data is ignorable a twofold assumption dependent on the mode of inference the first part which is the focus here under the bayesian and direct likelihood paradigms requires that the missing data are missing at random in contrast the frequentist likelihood paradigm demands that the missing data mechanism always produces missing at random data a condition known as missing always at random under certain regularity conditions assuming missing always at random leads to an assumption that can be tested using the observed data alone namely the missing data indicators only depend on fully observed variables here we propose three different diagnostic tests that not only indicate when this assumption is incorrect but also suggest which variables are the most likely culprits although missing always at random is not a necessary condition to ensure validity under the bayesian and direct likelihood paradigms it is sufficient and evidence for its violation should encourage the careful statistician to conduct targeted sensitivity analyses

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea