a half product based approximation scheme for agreeably weighted completion time variance a recent informs journal on computing paper presents a fully polynomial time approximation scheme for minimizing the completion time variance with agreeable weights on a single machine this paper presents a much faster scheme for this problem

control of flat systems by quasi static feedback of generalized states generalized states the state representations of which depend on time derivatives of the input are naturally used in the control design for flat systems quasi static feedback of these generalized states which involves time derivatives of the closedloop input is shown to allow control of all flat systems by feedback linearization of the tracking error dynamics this is then used in a method proposed for the analysis and design by subsystems of certain flat series connections the results are illustrated on a gantry crane example

extended newton methods for multiobjective optimization majorizing function technique and convergence analysis we consider the extended newton method for approaching a pareto optimum of a multiobjective optimization problem establish quadratic convergence criteria and estimate a radius of convergence ball

preconditioned adaptive multipole accelerated iterative methods for three dimensional first kind integral equations of potential theory this paper presents a preconditioned krylov subspace iterative algorithm where a modified multipole algorithm with a novel adaptation scheme is used to compute the iterates for solving dense matrix problems generated by galerkin or collocation schemes applied to three dimensional first kind integral equations that arise in potential theory a proof is given that this adaptive algorithm reduces both matrix vector product computation time and storage to order n and experimental evidence is given to demonstrate that the combined preconditioned adaptive multipole accelerated pama method is nearly order n in practice examples from engineering applications are given to demonstrate that the accelerated method is substantially faster than standard algorithms on practical problems

the single machine weighted mean squared deviation problem abstract this paper studies a single machine problem related to the just in time jit production objective in which the goal is to minimize the sum of weighted mean squared deviation of the completion times with respect to a common due date in order to solve the problem several structural and dominance properties of the optimal solution are investigated these properties are then integrated within a branch and cut approach to solve a time indexed formulation of the problem the results of a computational experiment with the proposed algorithm show that the method is able to optimally solve instances with up to 300 jobs within reduced running times improving other integer programming approaches

fast single domain subdomain bem algorithm for 3d incompressible fluid flow and heat transfer in this paper acceleration and computer memory reduction of an algorithm for the simulation of laminar viscous flows and heat transfer is presented the algorithm solves the velocity vorticity formulation of the incompressible navier stokes equations in 3d it is based on a combination of a subdomain boundary element method bem and single domain bem the cpu time and storage requirements of the single domain bem are reduced by implementing a fast multipole expansion method the laplace fundamental solution which is used as a special weighting function in bem is expanded in terms of spherical harmonics the computational domain and its boundary are recursively cut up forming a tree of clusters of boundary elements and domain cells data sparse representation is used in parts of the matrix which correspond to boundary domain clusters pairs that are admissible for expansion significant reduction of the complexity is achieved the paper presents results of testing of the multipole expansion algorithm by exploring its effect on the accuracy of the solution and its influence on the non linear convergence properties of the solver two 3d benchmark numerical examples are used the lid driven cavity and the onset of natural convection in a differentially heated enclosure

earliness tardiness scheduling problems ii derivation of completion times about a restrictive common due date a companion paper part i considers the problem of minimizing the weighted earliness and tardiness of jobs scheduled on a single machine around a common due date d which is unrestrictively late this paper part ii considers the problem of minimizing the unweighted earliness and tardiness of jobs allowing the possibility that d is early enough to constrain the scheduling decision we describe several optimality conditions the recognition version of the problem is shown to be np complete in the ordinary sense confirming a well known conjecture moreover this complexity definition is precise since we describe a dynamic programming algorithm which runs in pseudopolynomial time this algorithm is also extremely efficient computationally providing an improvement over earlier procedures of almost two orders of magnitude in the size of instance that can be solved finally we describe a special case of the problem which is polynomially solvable

constrained model predictive manifold stabilization based on transverse normal forms the optimization based stabilization of manifolds for nonlinear dynamical systems with constraints is investigated manifolds in the state or output space are considered for which the original system description can be transformed into a so called transverse normal form with this formulation the motion of the system transverse and tangential to the manifold can be separately described the transverse normal form is combined with a tailored model predictive control scheme to achieve the objectives of stabilizing the manifold rendering it invariant and imposing a desired motion on the manifold under due consideration of constraints furthermore the stabilization of the manifold is prioritized over the movement on the manifold convergence of the model predictive control scheme is proven the applicability of the proposed concept is demonstrated by an illustrative simulation example

a tight lower bound for the completion time variance problem abstract we consider the completion time variance problem our main result is a tight lower bound for the mean completion time of an optimal sequence this result can be applied to reduce the time required to solve the problem

conditions for the existence of a flat input we introduce the concept of an affine flat input to a non linear system with a given output function this approach can be seen as dual to the search for a flat output of a control system with given input our results provide a necessary and sufficient condition for the existence of a flat input in the siso case which also allows to construct of the vector field associated to the flat input in addition a relation between the flat input vector field and non linear observer design is discussed a population model is used to illustrate the construction of a flat input

fast fully polynomial approximation schemes for minimizing completion time variance abstract we present fully polynomial approximation schemes fpass for the problem of minimizing completion time variance ctv of a set of n jobs on a single machine the fastest of these schemes runs in time o n2 e and thus improves on all fully polynomial approximation schemes presented in the literature

a fast elastostatic solver based on fast fourier transform on multipoles fftm in this paper we present a fast algorithm to solve elasticity problems governed by the navier equation using the boundary element method bem this fast algorithm is based on the fast fourier transform on multipoles fftm method that has been developed for the laplace equation the fftm method uses multipole moments and their kernel functions together with the fast fourier transform fft to accelerate the far field computation the memory requirement of the original fftm tends to be high especially when the method is extended to the navier equation that involves vector quantities in this paper we used a compact representation of the translation matrices for the navier equation based on solid harmonics this reduces the memory usage significantly allowing large elasticity problems to be solved efficiently the improved fftm is compared with the commonly used fmm revealing that the fftm requires shorter computational time but more memory than the fmm to achieve comparable accuracy finally the method is applied to calculate the effective young s modulus of a material containing numerous voids of various shapes sizes and orientations copyright 2008 john wiley sons ltd

scheduling about a common due date with kob dependent asymmetric earliness and tardiness penalties abstract this paper is concerned with the problem of scheduling n jobs with a common due date on a single machine so as to minimize the total cost arising from earliness and tardiness a general model is examined in which earliness penalty and tardiness penalty are respectively arbitrary non decreasing functions moreover the model includes two important features that commonly appear in practical problems namely 1 earliness and tardiness are penalized with different weights which are job dependent and 2 the earliness or tardiness penalty consists of two parts one is a variable cost dependent on the length of earliness or tardiness while the other is a fixed cost incurred when a job is early or tardy this model provides a general and flexible performance measure for earliness tardiness scheduling which has not been addressed before we establish a number of results on the characterizations of optimal and sub optimal solutions and propose two algorithms based on these results the first algorithm can find under an agreeable weight condition an optimum in time o n2 pn and the second algorithm can generate a sub optimum in time o npn where pn is the sum of the processing times further we derive an upper bound on the relative error of the sub optimal solution and show that under certain conditions the error tends to zero as n increases computational results are also reported to demonstrate the effectiveness of the algorithms proposed

approximability issues for unconstrained and constrained maximization of half product related functions we address the boolean programming problem of maximizing a half product function with and without a linear knapsack constraint maximizing the half product can be done in polynomial time adding a knapsack constraint makes the problem non approximable within a constant factor provided that the coefficients in the linear part of the function are negative for maximizing a function with positive coefficients in the linear part we develop a fully polynomial time approximation scheme

minimizing total completion time and total deviation of job completion times from a restrictive due date we study a single machine scheduling problem with the objective of minimizing a linear combination of total job completion times and total deviation of job completion times from a common due date the due date is assumed to be restrictive i e it may be sufficiently small to have an impact on the optimal sequence when more weight is allocated to total job completion times the problem is shown to have a polynomial time solution when more weight is allocated to total completion time deviations from the due date the problem is np hard in the ordinary sense for the latter case we introduce an efficient dynamic programming algorithm which is shown numerically to perform well in all our tests

exact feedforward linearization based on differential flatness this article deals with the trajectory aspect of differential flatness from a feedforward point of view the notion of exact feedforward linearization based on differential flatness is introduced a differentially flat system to which a nominal feedforward deduced from flatness is applied is equivalent by change of coordinates to a linear multivariable brunovsk form if the initial condition is consistent with the one considered in the design of the nominal trajectory in its second part the new notion states that there exist unique solutions in the vicinity of the desired trajectory when applying a nominal feedforward to the corresponding flat system to the end of stabilizing the desired trajectory the information from the brunovsk form is used to design the combination of the nominal feedforward and an additional feedback part in the case of extended pid controls for the latter stability is proven using a theorem by kelemen thus the overall control structure turns out to be quite simple and e

minimization of half products in this paper a special class of quadratic functions the so called half products are considered it is shown that while the minimization over the set of binary n vectors for half products is np complete an e approximating solution can be found in polynomial time for any e 0

single machine scheduling with coefficient of variation minimization abstract the problem of scheduling n jobs on a single machine so as to minimize the coefficient of variation of the job completion times is considered in this paper some results on the characterization of an optimal schedule including its v shape are proved explicit optimal schedules for some small values of n are also given a heuristic method for solving the problem is proposed and its efficiency is investigated

stochastic binary problems with simple penalties for capacity constraints violations this paper studies stochastic programs with first stage binary variables and capacity constraints using simple penalties for capacities violations in particular we take a closer look at the knapsack problem with weights and capacity following independent random variables and prove that the problem is weakly mathcal n mathcal p hard in general we provide pseudo polynomial algorithms for three special cases of the problem constant weights and capacity uniformly distributed subset sum with gaussian weights and strictly positively distributed random capacity and subset sum with constant weights and arbitrary random capacity we then turn to a branch and cut algorithm based on the outer approximation of the objective function we provide computational results for the stochastic knapsack problem i with gaussian weights and constant capacity and ii with constant weights and capacity uniformly distributed on randomly generated instances inspired by computational results for the knapsack problem

the boolean quadric polytope some characteristics facets and relatives we study unconstrained quadratic zero one programming problems havingn variables from a polyhedral point of view by considering the boolean quadric polytope qpn inn n 1 2 dimensions that results from the linearization of the quadratic form we show that qpn has a diameter of one descriptively identify three families of facets of qpn and show that qpn is symmetric in the sense that all facets of qpn can be obtained from those that contain the origin by way of a mapping the naive linear programming relaxation qpnlp of qpn is shown to possess the trubin property and its extreme points are shown to be 0 1 2 1 valued furthermore o n3 facet defining inequalities of qpn suffice to cut off all fractional vertices of qpnlp whereas the family of facets described by us has at least o 3n members the problem is also studied for sparse quadratic forms i e when several or many coefficients are zero and conditions are given for the previous results to carry over to this case polynomially solvable problem instances are discussed and it is shown that the known polynomiality result for the maximization of nonnegative quadratic forms can be obtained by simply rounding the solution to the linear programming relaxation in the case that the graph induced by the nonzero coefficients of the quadratic form is series parallel a complete linear description of the associated boolean quadric polytope is given the relationship of the boolean quadric polytope associated to sparse quadratic forms with the vertex packing polytope is discussed as well

minimizing mean squared deviation of completion times about a common due date this paper addresses a nonpreemptive single machine scheduling problem where all jobs have a common due date and have zero ready time the scheduling objective is to minimize mean squared deviation msd of job completion times about the due date this nonregular measure of performance is appropriate when earliness and tardiness are both penalized and when large deviations of completion time from the due date are undesirable a special case of the msd problem referred to as the unconstrained msd problem is shown to be equivalent to the completion time variance problem ctv studied by merten and muller merten a g m e muller 1972 variance minimization in single machine sequencing problems management sci 18september 518 528 and schrage schrage l 1975 minimizing the time in system variance for a finite jobset management sci 21may 540 543 strong results for this latter problem are combined with several new propositions to develop a reasonably efficient procedure for solving the unconstrained msd problem this enables us to improve the existing procedures for the ctv problem we also propose a branching procedure for the constrained msd problem and present computational results

on the minimization of completion time variance with a bicriteria extension we discuss a single machine scheduling problem where the objective is to minimize the variance of job completion times to date the problem has not been solved in polynomial time this paper presents a dynamic programming algorithm that is pseudopolynomial in complexity we also propose a fully polynomial approximation scheme and derive a lower bound that is useful in its implementation furthermore we show that the dynamic programming solution is easy to extend to a bicriteria version of the problem in which it is desired to simultaneously minimize the mean completion time

scheduling about a given common due date to minimize mean squared deviation of completion times abstract in this paper the problem of minimizing the mean squared deviation msdp of job completion times about a given common due date in n job single machine scheduling is considered the release times for all jobs are assumed to be zero no polynomial time algorithms have been found to identify an optimal solution to msdp for the tightly restricted version of msdp no even pseudo polynomial time algorithms have been found to identify an optimal solution we present some dominance properties for msdp based on which a pseudo polynomial dynamic programming algorithm which is an extension of the dynamic programming algorithm proposed by lee danusaputro and lin is presented to optimally solve the tightly restricted version of msdp computational results show that the proposed dynamic programming algorithm can optimally solve tightly restricted instances of msdp with up to 100 jobs in less than two seconds

on the construction of static stabilizers and static output trackers for dynamically linearizable systems related results and applications it is shown that the property of dynamic linearizability to be understood as linearizability by means of the dynamic extension algorithm implies the existence of static possibly time varying control laws yielding asymptotic output tracking with arbitrary speed of convergence and asymptotic stabilization with a computable bound on the region of attraction similar results hold for systems which are only input output linearizable by means of dynamic state feedback provided that the inverse dynamics possess certain stability properties applications of these results to the problem of regional stabilization of a vtol aircraft is considered together with the tracking problem for a class of flexible joints robots moreover a novel parameterization for flexible joint robots is also proposed

continuous time non linear flatness based predictive control an exact feedforward linearisation setting with an induction drive example a general flatness based framework for non linear continuous time predictive control is presented it extends the results of fliess and marquez 2000 to the non linear case the mathematical setting which is valid for multivariable systems is provided by the theory of flatness based exact feedforward linearisation introduced by the authors hagenmeyer and delaleau 2003b thereby differential flatness does not only yield an easy calculation of the predicted trajectories considering the respective system constraints but allows to use simple linear feedback parts in a two degree of freedom control structure moreover this formalism permits one to handle non minimum phase systems and furthermore to deal with parameter uncertainties and exogenous perturbations respective robustness analysis tools are available finally an induction drive example is discussed in detail and experimental results for this fast electro mechanical system are presented

a lower bound for weighted completion time variance we consider a single machine scheduling problem to minimize the weighted completion time variance this problem is known to be np hard we propose a heuristic and a lower bound based on job splitting and the viswanathkumar and srinivasan procedure the test on more than 2000 instances shows that this lower bound is very tight and the heuristic yields solutions very close to optimal ones since the gap between the solution given by the heuristic and the lower bound is very small

a hierarchical o n force calculation algorithm a novel code for the approximate computation of long range forces between n mutually interacting bodies is presented the code is based on a hierarchical tree of cubic cells and features mutual cell cell interactions which are calculated via a cartesian taylor expansion in a symmetric way such that total momentum is conserved the code benefits from an improved and simple multipole acceptance criterion that reduces the force error and the computational effort for n 104 the computational costs are found empirically to rise sublinearly with n for applications in stellar dynamics this is the first competitive code with complexity o n it is faster than the standard tree code by a factor of 10 or more

a fast algorithm for modeling multiple bubbles dynamics this work presents the development of a numerical strategy that combines the fast fourier transform on multipoles fftm method and the boundary element method bem to study the physics of multiple bubbles dynamics in moving boundary problems the recent fftm method can be employed to speedup the resolution of the boundary integral equation however one major drawback of the method is that its efficiency deteriorates quite significantly when the problem is spatially sparsely populated as in the case where multiple bubbles are well separated to overcome this deficiency a new version of fftm with clustering is proposed henceforth called fftm clustering the new algorithm first identifies and groups closely positioned bubbles the original fftm is then used to compute the potential contributions from the bubbles within its own group while contributions from the other separated groups are evaluated via the multipole to local expansions translations operations directly we tested the fftm clustering on several multiple bubble examples to demonstrate its effectiveness over the original fftm method and vast improvement over the standard bem the high efficiency of the fftm clustering method allows us to simulate much larger multiple bubbles dynamics problems within reasonable time some physical behaviors of the multiple bubbles are also presented in this work

minimizing weighted mean absolute deviation of job completion times from their weighted mean we address a single machine scheduling problem where the objective is to minimize the weighted mean absolute deviation of job completion times from their weighted mean this problem and its precursors aim to achieve the maximum admissible level of service equity it has been shown earlier that the unweighted version of this problem is np hard in the ordinary sense for that version a pseudo polynomial time dynamic program and a 2 approximate algorithm are available however not much except for an important solution property exists for the weighted version in this paper we establish the relationship between the optimal solution to the weighted problem and a related one in which the deviations are measured from the weighted median rather than the mean of the job completion times this generalizes the 2 approximation result mentioned above we proceed to give a pseudo polynomial time dynamic program establishing the ordinary np hardness of the problem in general we then present a fully polynomial time approximation scheme as well finally we report the findings from a limited computational study on the heuristic solution of the general problem our results specialize easily to the unweighted case they also lead to an approximation of the set of schedules that are efficient with respect to both the weighted mean absolute deviation and the weighted mean completion time

a fast algorithm for three dimensional potential fields calculation fast fourier transform on multipoles in this paper we present a fast algorithm for rapid calculation of the potential fields in three dimensions this method arises from an observation that potential evaluation using the multipole to local expansion translation operator can be expressed as a series discrete convolutions of the multipole moments with their associated spherical harmonics functions the high efficiency of the algorithm is primarily due to the use of fft algorithms to evaluate the numerous discrete convolutions we refer to it as the fast fourier transform on multipoles fftm method it is demonstrated that fftm is all accurate method it is significantly more accurate than fmm for a given order of expansion it is also shown that the algorithm has computational complexity of o na where a ranges from 1 0 to 1 3

deterministic and random single machine sequencing with variance minimization we discuss the problem of scheduling several jobs on a single machine so as to minimize the variance of the jobs completion times by exploiting the well known pooled variance formula we obtain a general formula for the change in variance due to the interchange of two specified jobs whose positions have not been fixed in the sequence this result permits us to obtain explicit optimal sequences for problems with 6 or 7 jobs and to show that schrage s conjecture on positioning the job with the third largest processing time is true for problems with up to 18 jobs we then develop a heuristic procedure based on a variance interchange formula and compare it with other known heuristic methods we also consider a problem never before examined namely the case when processing times are not known deterministically but are random variables we obtain some general results under certain assumptions on the parameters of the distributions of processing times and extend to the random situation many results applicable to the deterministic case finally we give some results for the exponential distribution of processing times

fast approximation schemes for boolean programming and scheduling problems related to positive convex half product we address a version of the half product problem and its restricted variant with a linear knapsack constraint for these minimization problems of boolean programming we focus on the development of fully polynomial time approximation schemes with running times that depend quadratically on the number of variables applications to various single machine scheduling problems are reported minimizing the total weighted flow time with controllable processing times minimizing the makespan with controllable release dates minimizing the total weighted flow time for two models of scheduling with rejection

flatness and quasi static state feedback in non linear delay systems two notions from the theory of non linear systems without time delays are generalized to non linear delay systems flatness and quasi static state feedback depending on the generality of the relations considered flatness properties of increasing generality are obtained flatness flatness flatness and difference differential flatness it is then shown that difference differentially flat delay systems are linearizable by a certain class of predictive quasi static state feedback i e that they are equivalent by such feedback to a linear controllable system the mathematical framework is difference differential algebra

constructing efficient solutions structure of multiobjective linear programming it is not a difficult task to find a weak pareto or pareto solution in a multiobjective linear programming molp problem the difficulty lies in finding all these solutions and representing their structure this paper develops an algorithm for solving this problem we investigate the solutions and their relationships in the objective space the algorithm determines finite number of weights each of which corresponds to a weighted sum problems by solving these problems we further obtain all weak pareto and pareto solutions of the molp and their structure in the constraint space the algorithm avoids the degeneration problem which is a major hurdle of previous works and presents an easy and clear solution structure

towards context aware tracking a flatness based automotive oriented scheme with elastic execution time and sheaf determination a context aware tracking scheme made of two main ingredients is presented firstly closed loop computations that are computed incrementally yielding anytime algorithms whose threads can be interrupted as soon as the crudest law is computed the best available result is then furnished the anytime character is also used to reach short term mid term and long term objectives secondly and dually to the previous temporal considerations a sheaf of trajectories is maintained in a long term a choice is made in this sheaf at beginning of the mid term phase depending on the external conditions hence the term contex aware tracking the chosen trajectory is then tracked in the end of the mid term phase

note a note on the minimization of mean squared deviation of completion times about a common due date this paper points out a conceptual flaw present in a recent publication it shows how the methodology can be modified to correct this flaw it also presents improved bounds to determine the nature of a given problem

positive half products and scheduling with controllable processing times we study the single machine scheduling problem with controllable job processing times to minimize a linear combination of the total weighted job completion time and the total weighted processing time compression we show that this scheduling problem is a positive half product minimization problem positive half products make up an interesting subclass of half products and are introduced in this paper to provide a conceptual framework for the problem with controllable job processing times as well as other problems this framework allows to readily derive in one fell swoop a number of results for the problem with controllable processing times from more general results obtained earlier for the half product we also present fast fully polynomial time approximation schemes for the problem with controllable processing times the schemes apply to all positive half products

convergence of the projected gradient method for quasiconvex multiobjective optimization we consider the projected gradient method for solving the problem of finding a pareto optimum of a quasiconvex multiobjective function we show convergence of the sequence generated by the algorithm to a stationary point furthermore when the components of the multiobjective function are pseudoconvex we obtain that the generated sequence converges to a weakly efficient solution

multilevel matrix multiplication and fast solution of integral equations abstract a fast multigrid approach is described for the task of calculating k x y u y dy for each x r d discretizing by an equidistant grid with n points and meshsize h and approximating the integrations to o h2s accuracy it is shown that the complexity of this calculation can be reduced from o n2 to o sn provided the kernel k is sufficiently smooth for potential type kernels the complexity is reduced to o sn log n corresponding integral equations can be solved to a similar accuracy in basically the same amount of work using a special kind of distributed relaxation in a multigrid algorithm one and two dimensional numerical tests and theoretical derivations of optimal strategies are reported the method is applicable to the task of multiplying by any matrix with appropriate smoothness properties including most types of many body interactions

relative flatness and flatness of implicit systems in this work we define the concept of relative flatness of a system with respect to a subsystem the subsystem associated to a set of outputs of a system is constructed and called here output subsystem it is shown that the relative flatness of a system with respect to the output subsystem implies the flatness of the corresponding implicit system obtained by setting these outputs to zero a sufficient condition of relative flatness based on a relative derived flag is presented based on these results a sufficient condition for the flatness of a class of nonlinear implicit systems is obtained