goal programming for decision making an overview of the current state of the art there have been significant advances in the theory of goal programming gp in recent years particularly in the area of intelligent modelling and solution analysis the intention of this paper is to provide an overview of these developments to detail and assess the current state of the art in the subject and to highlight areas which seem promising for future research modelling techniques such as detection and restoration of pareto efficiency normalisation redundancy checking and non standard utility function modelling are overviewed the connection between gp and other multi objective programming techniques as well as a utility interpretation of gp are examined the rationality of ranking multi criteria decision making techniques and of placing gp in such a ranking is discussed

approximation of pareto optima in multiple objective shortest path problems we study methods for approximating the set of pareto optimal paths in multiple objective shortest path problems known generalizations of standard shortest path methods will compute this set but can suffer from rapidly increasing computational and storage demands as problem size increases in an effort to avoid such difficulties we develop approximation methods that can estimate the pareto optima to any required degree of accuracy the approximation methods are fully polynomial that is they operate in time and space bounded by a polynomial in problem size and accuracy of approximation the greater the accuracy the more time required to reach a solution we show how approximation methods may be applied to yield fully polynomial approximation schemes for a variety of np complete single objective problems

a gradually implicit method with deferred correction and adaptive relaxation factors for simulation to nonlinear heat transfer abstract a gradually implicit method with deferred correction gimdc and adaptive relaxation factors arfs is developed for simulation to nonlinear heat transfer with temperature dependent properties gimdc is equivalent to explicit method initially and approaches implicit method gradually the theoretical analyses of convergence error and stability indicate that the accuracy and stability of gimdc are close to implicit method if arfs are utilized to guarantee convergence a strict condition for arfs is derived gimdc is compared with pem pure explicit method nim newton iterative method for implicit solution and fem finite element method which shows that gimdc is of acceptable numerical accuracy similar to nim and 19 28 and 12 89 higher than pem and fem respectively in average and higher efficiency the numerical tests are presented which shows that using optimized arfs confined by strict condition efficiency accuracy and stability are ensured

an fptas for optimizing a class of low rank functions over a polytope we present a fully polynomial time approximation scheme fptas for optimizing a very general class of non linear functions of low rank over a polytope our approximation scheme relies on constructing an approximate pareto optimal front of the linear functions which constitute the given low rank function in contrast to existing results in the literature our approximation scheme does not require the assumption of quasi concavity on the objective function for the special case of quasi concave function minimization we give an alternative fptas which always returns a solution which is an extreme point of the polytope our technique can also be used to obtain an fptas for combinatorial optimization problems with non linear objective functions for example when the objective is a product of a fixed number of linear functions we also show that it is not possible to approximate the minimum of a general concave function over the unit hypercube to within any factor unless p np we prove this by showing a similar hardness of approximation result for supermodular function minimization a result that may be of independent interest

small approximate pareto sets for biobjective shortest paths and other problems we investigate the problem of computing a minimum set of solutions that approximates within a specified accuracy epsilon the pareto curve of a multiobjective optimization problem we show that for a broad class of biobjective problems containing many important widely studied problems such as shortest paths spanning tree matching and many others we can compute in polynomial time an epsilon pareto set that contains at most twice as many solutions as the minimum set furthermore we show that the factor of 2 is tight for these problems i e it is np hard to do better we present upper and lower bounds for three or more objectives as well as for the dual problem of computing a specified number k of solutions which provide a good approximation to the pareto curve

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

scheduling to minimize average completion time off line and on line approximation algorithms in this paper we introduce two general techniques for the design and analysis of approximation algorithms for np hard scheduling problems in which the objective is to minimize the weighted sum of the job completion times for a variety of scheduling models these techniques yield the first algorithms that are guaranteed to find schedules that have objective function value within a constant factor of the optimum in the first approach we use an optimal solution to a linear programming relaxation in order to guide a simple list scheduling rule consequently we also obtain results about the strength of the relaxation our second approach yields on line algorithms for these problems in this setting we are scheduling jobs that continually arrive to be processed and for each time t we must construct the schedule until time t without any knowledge of the jobs that will arrive afterwards our on line technique yields constant performance guarantees for a variety of scheduling environments and in some cases essentially matches the performance of our off line lp based algorithms

meta goal programming abstract in most of the goal programming gp applications reported in the literature the election of the gp variant is made in a mechanistic way by the analyst however each variant implies a different preference structure and thus it should be chosen by the decision maker moreover the final solution of the problem depends critically on the variant chosen in this paper it is assumed that the use of a combination of gp variants may reflect in many cases more precisely the actual preferences of the decision maker in this way a sensitivity analysis of the solution obtained as well as of the own model structure can be very helpful to let the decision maker clarify his her knowledge about the reality analysed this type of problem requires a more general approach that leads to a gp formulation of the initial gp model this type of meta gp approach is presented in this paper

derivation of duality in mathematical programming and optimization theory abstract consider the primal problem to minimize a function over a set of feasible solutions in euclidean space this paper derives a general dual problem directly from this primal problem it shows that the lagrangian conjugate and johri s formulations of duality in nonlinear programming the linear programming duality and the minimum norm duality principle in optimization theory are all special cases of this general duality formulation this explains the duality why two seemingly different problems provide the same answer by showing that there really is no duality but that the dual problems are just different forms of the primal problem all these results are derived in a simple intuitive unified manner

decision making based on approximate and smoothed pareto curves we consider bicriteria optimization problems and investigate the relationship between two standard approaches to solving them i computing the pareto curve and ii the so called decision maker s approach in which both criteria are combined into a single usually nonlinear objective function previous work by papadimitriou and yannakakis showed how to efficiently approximate the pareto curve for problems like shortest path spanning tree and perfect matching we wish to determine for which classes of combined objective functions the approximate pareto curve also yields an approximate solution to the decision maker s problem we show that an fptas for the pareto curve also gives an fptas for the decision maker s problem if the combined objective function is growth bounded like a quasi polynomial function if the objective function however shows exponential growth then the decision maker s problem is np hard to approximate within any polynomial factor in order to bypass these limitations of approximate decision making we turn our attention to pareto curves in the probabilistic framework of smoothed analysis we show that in a smoothed model we can efficiently generate the complete and exact pareto curve with a small failure probability if there exists an algorithm for generating the pareto curve whose worst case running time is pseudopolynomial this way we can solve the decision maker s problem w r t any non decreasing objective function for randomly perturbed instances of e g shortest path spanning tree and perfect matching

high order exponential operator splitting methods for time dependent schrodinger equations in this paper we deduce high order error bounds for exponential operator splitting methods the employed techniques are specific to linear differential equations of the form u t a u t b u t t geq 0 involving an unbounded operator a in particular evolutionary schrodinger equations with sufficiently regular initial values are included in the analysis

a classification model based on goal programming with non standard preference functions with application to the prediction of cinema going behaviour this paper presents a goal programming model that allows for the flexible handling of the two group classification problem the goal programming model is based around the concepts of non standard preference functions and penalty function modelling an extension to a generalised distance metric case is given the inclusion of multiple levels of classification based upon different levels of certainty is incorporated into the model the model is tested on a real life data set pertaining to cinema going attendance and conclusions are drawn both in the context of the methodology and of the application

a new model to predict in vivo human knee kinematics under physiological like muscle activation although a number of approaches have attempted to model knee kinematics rarely have they been validated against in vivo data in a larger subject cohort here we assess the feasibility of four bar linkage mechanisms in addressing knee kinematics and propose a new approach that is capable of accounting for lengthening characteristics of the ligaments including possible laxity as well as the internal external rotation of the joint mr scans of the knee joints of 12 healthy volunteers were taken at flexion angles of 0 degrees 30 degrees and 90 degrees under both passive and active muscle conditions by reconstructing the surfaces at each position the accuracy of the four bar linkage mechanism was assessed for every possible combination of points within each cruciate ligament attachment area the specific set of parameters that minimized the deviation between the predictions and the in vivo pose was derived producing a mean error of 1 8 and 2 5 on the medial and 1 7 and 2 4mm on the lateral side at 30 degrees and 90 degrees flexion respectively for passive motion significantly improving on the models that did not consider internal external rotation for active flexion mean medial errors were 3 3 and 4 7 mm and lateral errors 3 4 and 4 8 mm using this best parameter set a generic predictive model was created and assessed against the known in vivo positions producing a maximum average error of 4 9 mm at 90 degrees flexion the accuracy achieved shows that kinematics may be accurately reconstructed for subject specific musculoskeletal models to allow a better understanding of the load distribution within the knee

direct comparison of measured and calculated total knee replacement force envelopes during walking in the presence of normal and abnormal gait patterns knee joint forces measured from instrumented implants provide important information for testing the validity of computational models that predict knee joint forces the purpose of this study was to validate a parametric numerical model for predicting knee joint contact forces against measurements from four subjects with instrumented tkrs during the stance phase of gait model sensitivity to abnormal gait patterns was also investigated the results demonstrated good agreement for three subjects with relatively normal gait patterns where the difference between the mean measured and calculated forces ranged from 0 05 to 0 45 body weights and the envelopes of measured and calculated forces from three walking trials overlapped the fourth subject who had a quadriceps avoidance external moment pattern initially had little overlap between the measured and calculated force envelopes when additional constraints were added tailored to the subject s gait pattern the model predictions improved to complete force envelope overlap coefficient of multiple determination analysis indicated that the shape of the measured and calculated force waveforms were similar for all subjects adjusted coefficient of multiple correlation values between 0 88 and 0 92 the parametric model was accurate in predicting both the magnitude and waveform of the contact force and the accuracy of model predictions was affected by deviations from normal gait patterns equally important the envelope of forces generated by the range of solutions substantially overlapped with the corresponding measured envelope from multiple gait trials for a given subject suggesting that the variable strategic processes of in vivo force generation are covered by the solution range of this parametric model

phased multicriteria preference finding abstract this paper considers the implications of a tendency of multicriteria decision makers to use screening ordering and choosing phases to find a preference as they reduce the set of their candidate alternatives this corresponds with increasing levels of effort and willingness to use sophisticated cognitive processes it suggests that appropriate corresponding types of measurement are those using attributes utilities and relative scores of alternatives for which standard methods are smart maut and ahp theory on the decision processes of the mind is incorporated which shows how to structure criteria trees and that relatively measured weights and scores should be synthesised using a power function tests of revised utility and relative mcdm methods and of software incorporating these ideas are reviewed they facilitate interactive refinement of scores at all points of the criteria tree and easy reduction in the number of alternatives two alternative screening phases are considered one based on scoring all the attributes together the other scoring the attributes in clusters in the structured criteria tree empirical tests confirm the value of the three phase approach but leave slightly open the question about which type of first phase is preferable

selecting the optimum portfolio using fuzzy compromise programming and sharpe s single index model different approaches besides the traditional markowitz s model have been proposed in the literature to analyze portfolio selection problems among them compromise programming cp is a suitable multiobjective programming technique which allows the handling of several objectives in those situations in which the existence of a high level of conflict between criteria does not permit the simultaneous optimization of all the considered objectives when objectives and constraints are in an imprecise environment fuzzy cp arises as a suitable solving method imprecision will be quantified by means of fuzzy numbers that represent the continuous possibility distributions for fuzzy parameters and hence place a constraint on the possible values the parameters may assume in this paper a new fuzzy compromise programming approach is proposed based on the obtaining of the minimum fuzzy distance to the fuzzy ideal solution of the portfolio selection problem once this fuzzy distance has been obtained the second step consists of finding a crisp decision vector an optimal portfolio implying a fuzzy distance to the ideal solution the more accurate as possible to the fuzzy minimum distance previously obtained

a fuzzy goal programming method with imprecise goal hierarchy two most widely used approaches to treating goals of different importance in goal programming gp are 1 weighted gp where importance of goals is modelled using weights and 2 preemptive priority gp where a goal hierarchy is specified implying infinite trade offs among goals placed in different levels of importance these approaches may be too restrictive in modelling of real life decision making problems in this paper a novel fuzzy goal programming method is proposed where the hierarchical levels of the goals are imprecisely defined the imprecise importance relations among the goals are modelled using fuzzy relations an additive achievement function is defined which takes into consideration both achievement degrees of the goals and degrees of satisfaction of the fuzzy importance relations examples are given to illustrate the proposed method

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

arbitrary order krylov deferred correction methods for differential algebraic equations in this paper a new framework for the construction of accurate and efficient numerical methods for differential algebraic equation dae initial value problems is presented the methods are based on applying spectral deferred correction techniques as preconditioners to a picard integral collocation formulation for the solution the resulting preconditioned nonlinear system is solved using newton krylov schemes such as the newton gmres method least squares based orthogonal polynomial approximations are computed using gaussian type quadratures and spectral integration is used to avoid the numerically unstable differentiation operator the resulting krylov deferred correction kdc methods are of arbitrary order of accuracy and very stable preliminary results show that these new methods are very competitive with existing dae solvers particularly when high precision is desired

combining equity and utilitarianism in a mathematical programming model we discuss the problem of combining the conflicting objectives of equity and utilitarianism for social policy making in a single mathematical programming model the definition of equity we use is the rawlsian one of maximizing the minimum utility over individuals or classes of individuals however when the disparity of utility becomes too great the objective becomes progressively utilitarian such a model is particularly applicable not only to health provision but to other areas as well building a mixed integer linear programming milp formulation of the problem raises technical issues because the objective function is nonconvex and the hypograph is not milp representable in its initial form we present a succinct formulation and show that it is sharp in the sense that its linear programming relaxation describes the convex hull of the feasible set before extra resource allocation or policy constraints are added we apply the formulation to a healthcare planning problem and show that instances of realistic size are easily solved by standard milp software this paper was accepted by dimitris bertsimas optimization

binary fuzzy goal programming goal programming is an important technique for solving many decision management problems fuzzy goal programming involves applying the fuzzy set theory to goal programming thus allowing the model to take into account the vague aspirations of a decision maker using preference based membership functions we can define the fuzzy problem through natural language terms or vague phenomena in fact decision making involves the achievement of fuzzy goals some of them are met and some not because these goals are subject to the function of environment resource constraints thus binary fuzzy goal programming is employed where the problem cannot be solved by conventional goal programming approaches this paper proposes a new idea of how to program the binary fuzzy goal programming model the binary fuzzy goal programming model can then be solved using the integer programming method finally an illustrative example is included to demonstrate the correctness and usefulness of the proposed model

a high order time splitting method based on integral deferred correction for semi lagrangian vlasov simulations semi lagrangian schemes with various splitting methods and with different reconstruction interpolation strategies have been applied to kinetic simulations for example the order of spatial accuracy of the algorithms proposed in qiu and christlieb 2010 29 is very high as high as ninth order however the temporal error is dominated by the operator splitting error which is second order for strang splitting it is therefore important to overcome such low order splitting error in order to have numerical algorithms that achieve higher orders of accuracy in both space and time in this paper we propose to use the integral deferred correction idc method to reduce the splitting error specifically the temporal order accuracy is increased by r with each correction loop in the idc framework where r 1 2r 1 2 for coupling the first order splitting and the strang splitting respectively the proposed algorithm is applied to the vlasov poisson system the guiding center model and two dimensional incompressible flow simulations in the vorticity stream function formulation we show numerically that the idc procedure can automatically increase the order of accuracy in time we also investigate numerical stability of the proposed algorithm via performing fourier analysis to a linear model problem

knee model sensitivity to cruciate ligaments parameters a stability simulation study for a living subject abstract if the biomechanic function of the different anatomical sub structures of the knee joint was needed in physiological conditions the only possible way is a modelling approach subject specific geometries and kinematic data acquired from the same living subject were the foundations of the 3d quasi static knee model developed each cruciate ligament was modelled by means of 25 elastic springs paying attention to the anatomical twisting of the fibres the sensitivity of the model to the cross sectional area was performed during the anterior posterior tibial translations the sensitivity to all the cruciate ligaments parameters was performed during the internal external rotations the model reproduced very well the mechanical behaviour reported in literature during anterior posterior translations in particular considering 30 of the mean insertional area during the internal external tibial rotations similar behaviour of the axial torques was obtained in the three sensitivity analyses the overlapping of the ligaments was assessed at about 25 of internal axial rotation the presented model featured a good level of accuracy in combination with a low computational weight and it could provide an in vivo estimation of the role of the cruciate ligaments during the execution of daily living activities

high order operator splitting methods based on an integral deferred correction framework integral deferred correction idc methods have been shown to be an efficient way to achieve arbitrary high order accuracy and possess good stability properties in this paper we construct high order operator splitting schemes using the idc procedure to solve initial value problems ivps we present analysis to show that the idc methods can correct for both the splitting and numerical errors lifting the order of accuracy by r with each correction where r is the order of accuracy of the method used to solve the correction equation we further apply this framework to solve partial differential equations pdes numerical examples in two dimensions of linear and nonlinear initial boundary value problems are presented to demonstrate the performance of the proposed idc approach

solving multi period project selection problems with fuzzy goal programming based on topsis and a fuzzy preference relation project portfolio managers are multi objective decision makers dms who are expected to select the best mix of projects by maximizing profits and minimizing risks over a multi period planning horizon however project portfolio decisions are complex multi objective problems with a high number of projects from which a subset has to be chosen subject to various constraints and a multitude of priorities and preferences we propose a goal programming gp approach for project portfolio selection that embraces conflicting fuzzy goals with imprecise priorities a fuzzy goal with an aspiration level and a predefined membership function is defined for each objective the impreciseness in the priorities of the membership values of the fuzzy goals is modeled with fuzzy relations this leads to type ii fuzzy sets since fuzzy relations are organized between the membership values of the fuzzy goals which are themselves fuzzy sets the proposed model is based on the technique for order preference by similarity to ideal solution topsis and fuzzy preference relations topsis is used to reduce the multi objective problem into a bi objective problem the resulting bi objective problem is solved with fuzzy gp fgp the fuzzy preference relations are used to help dms express their preferences with respect to the membership values of the fuzzy goals the proposed approach is used to solve a real life problem characterized as a fuzzy multi objective project selection with multi period planning horizon mops mpph the performance of the proposed approach is compared with a competing method in the literature we show that our approach generates high quality solutions with minimal computational efforts

on equitable resource allocation problems a lexicographic minimax approach in this expository paper we review a variety of resource allocation problems in which it is desirable to allocate limited resources equitably among competing activities applications for such problems are found in diverse areas including distribution planning production planning and scheduling and emergency services location each activity is associated with a performance function representing for example the weighted shortfall of the selected activity level from a specified target a resource allocation solution is called equitable if no performance function value can be improved without either violating a constraint or degrading an already equal or worse off i e larger performance function value that is associated with a different activity a lexicographic minimax solution determines this equitable solution that is it determines the lexicographically smallest vector whose elements the performance function values are sorted in nonincreasing order the problems reviewed include large scale allocation problems with multiple knapsack resource constraints multiperiod allocation problems for storable resources and problems with substitutable resources the solution of large scale problems necessitates the design of efficient algorithms that take advantage of special mathematical structures indeed efficient algorithms for many models will be described we expect that this paper will help practitioners to formulate and solve diverse resource allocation problems and motivate researchers to explore new models and algorithmic approaches

the accuracy of joint surface models constructed from data obtained with an electromagnetic tracking device electromagnetic tracking devices are widely used in biomechanics in this article a method is evaluated to construct models of articular surfaces using an electromagnetic tracking device first the accuracy of the space tracker was examined and optimised then from several joint surfaces random points were measured and eighth degree polynomials were fitted to these measurements to check if the fit converged well plots of cross sections of the model with corresponding data points were examined the accuracy of the models was determined by comparing them with computed tomography data and by reproducibility tests all the fits converged well to the data the root mean square rms error of the models varied from 0 07 to 0 18mm and was proportional to the size and complexity of the surface this was mainly due to systematic errors made by the space tracker which were also proportional to the size and complexity of the surface

approximation of min max and min max regret versions of some combinatorial optimization problems this paper investigates for the first time in the literature the approximation of min max regret versions of classical problems like shortest path minimum spanning tree and knapsack for a constant number of scenarios we establish fully polynomial time approximation schemes for the min max versions of these problems using relationships between multi objective and min max optimization using dynamic programming and classical trimming techniques we construct a fully polynomial time approximation scheme for min max regret shortest path we also establish a fully polynomial time approximation scheme for min max regret spanning tree and prove that min max regret knapsack is not at all approximable for a non constant number of scenarios in which case min max and min max regret versions of polynomial time solvable problems usually become strongly np hard non approximability results are provided for min max regret versions of shortest path and spanning tree

a stereophotogrammetric method for measurements of ligament structure a stereophotogrammetric method is presented to reconstruct the course of a curve in the three dimensional space this method is exclusively suitable as a non destructive tool to determine the surface fiber structure of ligaments tendons and other organised collagenous structures in addition it is a convenient tool to measure the geometry of articular surfaces and other complicated surface shapes

a theoretical framework for proving accuracy results for deferred corrections general techniques are described for proving accuracy results for deferred correction solutions to differential equations these techniques apply also to computational estimates of the local discretization error the proofs avoid the necessity of demonstrating the existence of asymptotic expansions of the global error in powers of some meshsize parameter

parallel high order integrators in this work we discuss a class of defect correction methods which is easily adapted to create parallel time integrators for multicore architectures and is ideally suited for developing methods which can be order adaptive in time the method is based on integral deferred correction idc which was itself motivated by spectral deferred correction by dutt greengard and rokhlin bit 40 2000 pp 241 266 the method presented here is a revised formulation of explicit idc dubbed revisionist idc ridc which can achieve p th order accuracy in wall clock time comparable to a single forward euler simulation on problems where the time to evaluate the right hand side of a system of differential equations is greater than latency costs of interprocessor communication such as in the case of the n body problem the key idea is to rewrite the defect correction framework so that after initial start up costs each correction loop can be lagged behind the previous correction loop in a manner that facilitates running the predictor and m p 1 correctors in parallel on an interval which has k steps where k gg p we prove that given an r th order runge kutta method in both the prediction and m correction loops of ridc then the method is order r times m 1 the parallelization in ridc uses a small number of cores the number of processors used is limited by the order one wants to achieve using a four core cpu it is natural to think about fourth order ridc built with forward euler or eighth order ridc constructed with second order runge kutta numerical tests on an n body simulation show that ridc methods can be significantly faster than popular runge kutta methods such as the classical fourth order runge kutta scheme in a pde setting one can imagine coupling ridc time integrators with parallel spatial evaluators thereby increasing the parallelization the ideas behind ridc extend to implicit and semi implicit idc and have high potential in this area

fuzzy goal programming a parametric approach narasimhan incorporated fuzzy set theory within goal formulation in 1980 since then much research has been performed in this field and various models for solving fuzzy goal programming have been proposed one of the well known models was proposed by tiwari et al in 1987 19 where an additive model was proposed this paper is an extension to the tiwari et al model that deals with the sum of weighted negative deviations between the desirable achievement degree and the common target here properties of the model are proposed a numerical example is also given to illustrate the approach

compromise programming non interactive calibration of utility based metrics utility functions have been used widely to support multi objective decision making expansion of a general additive utility function around the ideal results in a composite linear quadratic metric of a compromise programming problem determining the unknown parameters of the composite linear quadratic metric requires substantial interaction with the decision maker who might not always be available or capable to participate in such a process we propose a non interactive method that uses information on observed attribute levels to obtain the unknown parameters of the composite linear quadratic metric and enables forecasting and scenario analysis the method is illustrated with a small scale numerical example

bicriterion single machine scheduling with resource dependent processing times a bicriterion problem of scheduling jobs on a single machine is studied the processing time of each job is a linear decreasing function of the amount of a common discrete resource allocated to the job a solution is specified by a sequence of the jobs and a resource allocation the quality of a solution is measured by two criteria f1 and f2 the first criterion is the maximal or total weighted resource consumption and the second criterion is a regular scheduling criterion depending on the job completion times both criteria have to be minimized general schemes for the construction of the pareto set and the pareto set epsilon approximation are presented computational complexities of problems to minimize f1 subject to f 2 le k and to minimize f2 subject to f 1 le k where k is any number are studied for various functions f1 and f2 algorithms for solving these problems and for the construction of the pareto set and the pareto set epsilon approximation for the corresponding bicriterion problems are presented

an overview of techniques for solving multiobjective mathematical programs multiobjective mathematical programming has been one of the fastest growing areas of or ms during the last 15 years this paper presents some reasons for the rapidly growing increase in interest in multiobjective mathematical programming a discussion of the advantages and disadvantages of the three general approaches articulation of the decision maker s preference structure over the multiple objectives prior to during or after the optimization towards multiobjective mathematical programming a nontechnical overview of many of the specific solution techniques for multiobjective mathematical programming and a discussion of important areas for further research the overview concentrates on those techniques which require an articulation of the decision maker s preference structure either during or after the optimization since these are the areas where most of the recent research has been conducted it differs from previous overviews in that in addition to the timing of the elicited preference informa

relative measurement and the power function abstract relative measurement is considered in the context of nomology a theory that defines and relates categories of activity that arise in qualitative decision making a nomological variable is defined to correspond to the amount weight or importance of any naturally forming cluster or category of qualitative information this article shows that in general the mind measures nomological variables relatively and changes in a nomological variable relative to its current value the way the mind assesses the relationship between two related nomological variables generally should be modelled as a power function and it is appropriate to use a geometric mean to average multiple observations empirical evidence from psychophysics is shown to support these results when synthesising direct and indirect relative comparisons of nomological variables it is proven that the indirect comparisons should be given a weight that is inversely proportional to the number of relative measurements made in the indirect comparison this result is shown to be consistent with but not identical with the use of the row geometric means approach for synthesising pairwise relative comparison matrices such as in the analytical hierarchy process in the case of more than three variables other terms should be included in the synthesis the article reports on empirical research that endorses the use of nomological structuring and relative weighting of criteria trees it shows that decision makers generally prefer scoring within intervals when comparing alternatives but can also use relative measurement where there are difficulties with identifying intervals the former leads to modelling by an additive value function the latter to a power function

a highly accurate solver for stiff ordinary differential equations we introduce a solver for stiff ordinary differential equations that is based on the deferred correction scheme for the corresponding picard integral equation our solver relies on the assumption that the solution can be accurately represented by a combination of carefully selected complex exponentials the solver s accuracy and stability rely on the computation of highly accurate quadrature weights for the integration of the selected exponentials on equidistant nodes we analyze our solver stability and accuracy regions and demonstrate its fast convergence on stiff problems the solver is combined with an adaptive step size scheme employing interpolation formulas for the exponentially fitted solution

a practical weight sensitivity algorithm for goal and multiple objective programming this paper presents a weight sensitivity algorithm that can be used to investigate a portion of weight space of interest to the decision maker in a goal or multiple objective programme the preferential information required from the decision maker is an initial estimate of their starting solution with an equal weights solution being used as a default if this is not available and preference information that will define the portion of weight space on which the sensitivity analysis is to be conducted the different types of preferential information and how they are incorporated by the algorithm are discussed the output of the algorithm is a set of distinct solutions that characterise the portion of weight space searched the possible different output requirements of decision makers are detailed in the context of the algorithm the methodology is demonstrated on two examples one hypothetical and the other relating to predicting cinema going behaviour conclusions and avenues for future research are given

krylov implicit integration factor methods for spatial discretization on high dimensional unstructured meshes application to discontinuous galerkin methods abstract integration factor methods are a class of exactly linear part time discretization methods in q nie y t zhang r zhao efficient semi implicit schemes for stiff systems journal of computational physics 214 2006 521 537 a class of efficient implicit integration factor iif methods were developed for solving systems with both stiff linear and nonlinear terms arising from spatial discretization of time dependent partial differential equations pdes with linear high order terms and stiff lower order nonlinear terms the tremendous challenge in applying iif temporal discretization for pdes on high spatial dimensions is how to evaluate the matrix exponential operator efficiently for spatial discretization on unstructured meshes to solve pdes on complex geometrical domains how to efficiently apply the iif temporal discretization was open in this paper we solve this problem by applying the krylov subspace approximations to the matrix exponential operator then we apply this novel time discretization technique to discontinuous galerkin dg methods on unstructured meshes for solving reaction diffusion equations numerical examples are shown to demonstrate the accuracy efficiency and robustness of the method in resolving the stiffness of the dg spatial operator for reaction diffusion pdes application of the method to a mathematical model in pattern formation during zebrafish embryo development shall be shown

accelerating the convergence of spectral deferred correction methods in the recent paper by dutt greengard and rokhlin a variant of deferred or defect correction methods is presented which couples gaussian quadrature with the picard integral equation formulation of the initial value ordinary differential equation the resulting spectral deferred correction sdc methods have been shown to possess favorable accuracy and stability properties even for versions with very high order of accuracy in this paper we show that for linear problems the iterations in the sdc algorithm are equivalent to constructing a preconditioned neumann series expansion for the solution of the standard collocation discretization of the ode this observation is used to accelerate the convergence of sdc using the gmres krylov subspace method for nonlinear problems the gmres acceleration is coupled with a linear implicit approach stability and accuracy analyses show the accelerated scheme provides an improvement in the accuracy efficiency and stability of the original sdc approach furthermore preliminary numerical experiments show that accelerating the convergence of sdc methods can effectively eliminate the order reduction previously observed for stiff ode systems

the finite helical axis of the knee joint a non invasive in vivo study using fast pc mri an understanding of the in vivo knee joint kinematics is critical for the further improvement and validation of knee joint models and for the development of better surgical and rehabilitative protocols unfortunately most studies exploring the finite helical axis fha tend to produce excellent qualitative results but quantitative results are often lacking thus the purpose of this study was to non invasively and in vivo quantify the tibiofemoral fha in a relatively large normal population during volitional knee extension using fast pc mri to report the data relative to consistent coordinate systems making it available for modeling input experimental comparison and for device design to determine the variability of the fha to investigate the screw home mechanism and to test the hypothesis that knee joint kinematics are independent of gender intra and inter subject repeatability was excellent the intra inter subject repeatability of the fha orientation in the frontal and axial planes was 1 8 3 3 and 3 7 6 0 of the average value respectively at the beginning of extension the fha was directed laterally and slightly superiorly and at the end of extension it was directed in the lateral inferior direction indicative of the screw home mechanism the fha location was not fixed during extension there was small but significant differences in all fha parameters between genders and normalizing positional data relative to epicondylar width helped to reduce this difference the data obtained in the current study forms an excellent base for future knee joint modeling and clinical studies

convergence and order reduction of runge kutta schemes applied to evolutionary problems in partial differential equations we address the question of convergence of fully discrete runge kutta approximations we prove that under certain conditions the order in time of the fully discrete scheme equals the conventional order of the runge kutta formula being used however these conditions which are necessary for the result to hold are not natural as a result in many problems the order in time will be strictly smaller than the conventional one a phenomenon called order reduction this phenomenon is extensively discussed both analytically and numerically as distinct from earlier contributions we here treat explicit runge kutta schemes although our results are valid for both parabolic and hyperbolic problems the examples we present are therefore taken from the hyperbolic field as it is in this area that explicit discretizations are most appealing

a general framework for designing approximation schemes for combinatorial optimization problems with many objectives combined into one in this paper we present a general framework for designing approximation schemes for combinatorial optimization problems in which the objective function is a combination of more than one function examples of such problems include those in which the objective function is a product or ratio of two linear functions parallel machine scheduling problems with the makespan objective robust versions of weighted multiobjective optimization problems and assortment optimization problems with logit choice models the main idea behind our approximation schemes is the construction of an approximate pareto optimal frontier of the functions that constitute the given objective using this idea we give the first fully polynomial time approximation schemes for the max min resource allocation problem with a fixed number of agents combinatorial optimization problems in which the objective function is the sum of a fixed number of ratios of linear functions or the product of a fixed number of linear functions and assor

implied constraints and a unified theory of duality in linear and nonlinear programming abstract a unified theory of duality in linear and nonlinear programming can be easily derived from the perspective of implied constraints that is constraints implied by the given constraints of the problem the key idea is to construct special types of implied constraints which will bound the objective function this simple idea motivates a complete concise and clear development of a unified theory of duality which seeks the tightest bound on the primal objective function the derivation is intuitive and geometric and leads to a more general formulation of duality in nonlinear programming than the formulations known so far duality theorems are shown to hold for this formulation in general to solve the dual the set of implied constraints on the primal objective function needs to be generated a duality gap exists if this set is only partially generated in a dual formulation this is implicity the case in formulations such as the lagrangian and surrogate duality in linear programming this set can be generated linearly resulting in the constraints of the dual problem this formulation is also equivalent to a special conjugate function the conjugate function approach to duality is formulated more for the perturbations in the parameters of the problem and has not developed this fact

multi choice goal programming with utility functions abstract goal programming gp has been and still is the most widely used technique for solving multiple criteria decision problems and multiple objective decision problems by finding a set of satisfying solutions however the major limitation of goal programming is that can only use aspiration levels with scalar value for solving multiple objective problems in order to solve this problem multi choice goal programming mcgp was proposed by chang 2007a following the idea of mcgp this study proposes a new concept of level achieving in the utility functions to replace the aspiration level with scalar value in classical gp and mcgp for multiple objective problems according to this idea it is possible to use the skill of mcgp with utility functions to solve multi objective problems the major contribution of using the utility functions of mcgp is that they can be used as measuring instruments to help decision makers make the best appropriate policy corresponding to their goals with the highest level of utility achieved in addition the above properties can improve the practical utility of mcgp in solving more real world decision management problems

a general structure of achievement function for a goal programming model abstract a key element of a goal programming model is the achievement function that is the function that measures the degree of minimisation of the unwanted deviation variables of the goals considered in the model the three oldest and still most widely used forms of achievement functions are the following archimedean lexicographic and minmax while they are the most common other newer versions can offer theoretical and practical advantages these newer forms will be analytically described and interpreted in utility terms throughout this paper the presentation will end with a very general structure which encompasses as particular cases basically all the achievement functions proposed in the literature

an arbitrary order fully implicit hybrid kinetic solver for linear radiative transport using integral deferred correction abstract in this work we describe the implementation of an arbitrarily high order hybrid solver for linear kinetic radiative transport equations the hybrid method is derived from a splitting of the radiative flux into free streaming and collisional components to which high and low resolution discrete ordinates methods are applied respectively arbitrarily high orders of accuracy with respect to time and space are attained by combining an integral deferred correction idc time integration scheme constructed with implicit euler substepping on radau ii right biased nodes with an upwind discontinuous galerkin dg spatial discretization on uniform cartesian meshes numerical experiments are used to demonstrate that the aforementioned idc methods can be constructed such that they are unconditionally stable l stable to within machine precision asymptotic analysis is used to show that such idc methods also preserve the diffusion limit of the underlying transport equation on the semi discrete level in the sense that the semi discrete transport system under an implicit idc discretization recovers the same idc discretization of the limiting diffusion equation convergence results in one spatial dimension are provided and it is found that while the hybrid method exhibits convergence stagnation and order reduction in certain scenarios the overall accuracy of the hybrid approximation is comparable to a standard discrete ordinates approximation in many cases numerical results for two test problems in two spatial dimensions are given to compare the computational efficiency of the hybrid method against a standard discrete ordinates method and to compare the efficiency of space time discretizations of different orders of accuracy the results indicate that a properly chosen hybrid discrete ordinates method can be more efficient than a standard discrete ordinates method by a factor of between 2 and 8 when idc timestepping methods are used further among the first third and fifth order space time discretizations considered here the first order method is the least efficient and the third order method is the most efficient

validation of a three dimensional model of the knee three dimensional mathematical models of the tibio femoral joint require input of the geometry of articulating surfaces and ligament insertions and the mechanical properties of cartilage and ligaments this paper describes a validation of a knee model through a direct specimen related comparison between the knee model and the kinematics of four knee joint specimens from which the geometry data were used as input of the model the knee model is quasi static and is based on equilibrium of forces and moments the stiffness properties of the ligaments and articular cartilage were estimated on the basis of data reported in the literature the so called reference strains in the ligament bundles for the joint in extension were determined by using an optimization procedure minimizing the difference between the kinematics of the model and the kinematics of experimentally obtained flexion motions with an internally or an externally rotated tibia f 3 nm load a reasonable to good agreement between the model and the experimental kinematics could be obtained for internal external rotation laxity and the coupled translations and varu valgus rotation the disparity between model and experiment varied from knee to knee average deviations ranging from close to zero to 8 internal rotation deviation and from 5 mm posterior to 3 mm anterior position deviation the average anterior posterior laxities at both 20 and 90 flexion were within the variations reported in the literature although for each individual joint with some underestimation or overestimation it was concluded that the optimization procedure compensated for the lack of menisci and capsular structures by higher prestrains thereby overestimating the ligament forces despite the gross simplifica tions relative to the complex anatomy of the knee the present knee model can realistically simulate the passive motion characteristics of the human knee joint copyright 0 1996 elsevier science ltd

a subject specific finite element musculoskeletal framework for mechanics analysis of a total knee replacement abstract concurrent use of finite element fe and musculoskeletal ms modeling techniques is capable of considering the interactions between prosthetic mechanics and subject dynamics after a total knee replacement tkr surgery is performed however it still has not been performed in terms of favorable prediction accuracy and systematic experimental validation in this study we presented a methodology to develop a subject specific fe ms model of a human right lower extremity including the interactions among the subject specific ms model the knee joint model with ligament bundles and the deformable fe prosthesis model in order to evaluate its accuracy the fe ms model was compared with a traditional hinge constraint ms model and experimentally verified over a gait cycle both models achieved good temporal agreement between the predicted muscle force and the electromyography results though the magnitude on models is different a higher predicted accuracy quantified by the root mean square error rmse and the squared pearson correlation coefficient r2 was found in the fe ms model rmse 177 2 n r2 0 90 when compared with the ms model rmse 224 1 n r2 0 81 on the total tibiofemoral contact force the contact mechanics including the contact area pressure and stress were synchronously simulated and the maximum contact pressure 22 06 mpa occurred on the medial side of the tibial insert without exceeding the yield strength of the ultra high molecular weight polyethylene 24 79 mpa the approach outlines an accurate knee joint biomechanics analysis and provides an effective method of applying individualized prosthesis design and verification in tkr

hybrid methods for radiation transport using diagonally implicit runge kutta and space time discontinuous galerkin time integration abstract in this work we describe extensions of a hybrid method for time dependent linear kinetic radiation transport problems to high order time integration schemes of the diagonally implicit runge kutta dirk and space time discontinuous galerkin stdg types the hybrid methods are constructed by splitting the radiation flux into collided and uncollided components to which low and high resolution discrete ordinates approximations are applied the efficiency of hybrid methods constructed using dirk stdg integral deferred correction idc and implicit euler schemes is compared using a test problem in one dimensional slab geometry containing material discontinuities it is observed that i higher order methods are more efficient than the implicit euler method often by an order of magnitude or more ii third order methods yield solutions of a given error in roughly half the time of the second order method of the same type and iii for a given order of accuracy it is found that the most efficient class of time integration scheme is stdg followed by dirk with idc the least efficient for the test problem considered two test problems in two dimensional xy geometry are used to compare the computational efficiency of hybrid and standard discrete ordinates methods constructed with dirk and stdg integrators we observe that replacing a standard discrete ordinates method using an angular quadrature of order n with a hybrid discrete ordinates method using angular quadratures of order 2n and n 2 for the uncollided and collided fluxes respectively usually reduces overall solution time by a factor of 2 or more while simultaneously reducing the resulting solution error by a factor of 2 or more for the test problems considered

the nonlinear programming method of wilson han and powell with an augmented lagrangian type line search function the paper represents an outcome of an extensive comparative study of nonlinear optimization algorithms this study indicates that quadratic approximation methods which are characterized by solving a sequence of quadratic subproblems recursively belong to the most efficient and reliable nonlinear programming algorithms available at present the purpose of this paper is to analyse the theoretical convergence properties and to investigate the numerical performance in more detail in part 1 the exactl 1 penalty function of han and powell is replaced by a differentiable augmented lagrange function for the line search computation to the able to prove the global convergence and to show that the steplength one is chosen in the neighbourhood of a solution in part 2 the quadratic subproblem is exchanged by a linear least squares problem to improve the efficiency and to test the dependence of the performance from different solution methods for the quadratic or least squares subproblems

towards equitable distributions via proportional equity constraints we propose a new approach to the formulation of models for solving problems of equitable distribution equity is achieved by the use of proportional equity constraints which require that each recipient must receive ashare of the total distribution which falls within a prespecified range the algorithmic implications of this new approach are illustrated using two mathematical models we consider the problem of maximizing total flow in a multiterminal network with proportional equity constraints an efficient algorithm for solving this problem is provided as a further application we show that the introduction of such constraints still permits easy solutions for the linear knapsack problem

approximation algorithms for the set covering and vertex cover problems we propose a heuristic that delivers in o n 3 steps a solution for the set covering problem the value of which does not exceed the maximum number of sets covering an element times the optimal value

a non interactive elicitation method for non linear multiattribute utility functions theory and application to agricultural economics practical implementation of multiattribute utility theory is limited partly for the lack of operative methods to elicit the parameters of the multiattribute utility function particularly when this function is not linear as a consequence most studies are restricted to linear specifications which are easier to estimate and to interpret we propose an indirect method to elicit the parameters of a non linear utility function to be compatible with the observed behaviour of decision makers rather than with their answers to direct surveys the idea rests on approaching the parameter estimation problem as a dual of the decision problem by making the observed decisions to be compatible with a rational decision making process

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

the effect of connective tissue material uncertainties on knee joint mechanics under isolated loading conditions although variability in connective tissue parameters is widely reported and recognized systematic examination of the effect of such parametric uncertainties on predictions derived from a full anatomical joint model is lacking as such a sensitivity analysis was performed to consider the behavior of a three dimensional non linear finite element knee model with connective tissue material parameters that varied within a given interval the model included the coupled mechanics of the tibio femoral and patello femoral degrees of freedom seven primary connective tissues modeled as non linear continua articular cartilages described by a linear elastic model and menisci modeled as transverse isotropic elastic materials were included in this study a multi factorial global sensitivity analysis is proposed which can detect the contribution of influential material parameters while maintaining the potential effect of parametric interactions to illustrate the effect of material uncertainties on model predictions exemplar loading conditions reported in a number of isolated experimental paradigms were used our findings illustrated that the inclusion of material uncertainties in a coupled tibio femoral and patello femoral model reveals biomechanical interactions that otherwise would remain unknown for example our analysis revealed that the effect of anterior cruciate ligament parameter variations on the patello femoral kinematic and kinetic response sensitivities was significantly larger over a range of flexion angles when compared to variations associated with material parameters of tissues intrinsic to the patello femoral joint we argue that the systematic sensitivity framework presented herein will help identify key material uncertainties that merit further research and provide insight on those uncertainties that may not be as relative to a given response

nonlocal and localized analyses of conditional mean transient flow in bounded randomly heterogeneous porous media 1 we consider the numerical prediction of transient flow in bounded randomly heterogeneous porous media driven by random sources initial heads and boundary conditions without resorting to monte carlo simulation after applying the laplace transform to the governing stochastic flow equations we derive exact nonlocal integro differential equations for the mean and variance covariance of transformed head and flux conditioned on measured values of log conductivity y ln k approximating these conditional moment equations recursively to second order in the standard deviation y of y we solve them by finite elements for superimposed mean uniform and convergent flows in a two dimensional domain an alternative conditional mean solution is obtained through localization of the exact moment expressions the nonlocal and localized solutions are obtained using a highly efficient parallel algorithm and inverted numerically back into the time domain a comparison with monte carlo simulations demonstrates that the moment solutions are remarkably accurate for strongly heterogeneous media with y2 as large as 4 the nonlocal solution is only slightly more accurate than the much simpler localized solution but the latter does not yield information about predictive uncertainty the accuracy of each solution improves markedly with conditioning a preliminary comparison of computational efficiency suggests that both the nonlocal and localized solutions for mean head and its variance require significantly less computer time than is required for monte carlo statistics to stabilize when the same direct matrix solver is used for all three we do not presently know how using iterative solvers would have affected this conclusion this is true whether the laplace inversion and monte carlo simulations are conducted sequentially or in parallel on multiple processors and regardless of problem size the underlying exact and recursive moment equations as well as the proposed computational algorithm are valid in both two and three dimensions only the numerical implementation of our algorithm is two dimensional

an approximation approach for representing s shaped membership functions in general to formulate a fuzzy linear programming problem with n s shaped utility membership functions traditional methods require n or more extra binary variables because s shaped curves are neither convex nor concave in all places adding binary variables does not improve the bound of the linear programming relaxation on the contrary added binary variables increase the computational burden in the solution process if problems get large therefore a formulation without binary variables should be more efficient accordingly this study proposes a piecewise linear approach to formulate an s shaped membership function mf without adding any extra binary variables which improves the efficiency of fuzzy linear programming in solving decision management problems with s shaped mfs finally a computational experiment is provided to demonstrate the superiority of the proposed models an illustrative example is also provided to show the usefulness of the proposed method

selecting the cp metric a risk aversion approach abstract through a linkage between arrow s risk theory and compromise programming we obtain a reliable specification of the metric defining the compromise distance from a point to the ideal point in the n attribute space

compromise solution by mcdm methods a comparative analysis of vikor and topsis the multiple criteria decision making mcdm methods vikor and topsis are based on an aggregating function representing closeness to the ideal which originated in the compromise programming method in vikor linear normalization and in topsis vector normalization is used to eliminate the units of criterion functions the vikor method of compromise ranking determines a compromise solution providing a maximum group utility for the majority and a minimum of an individual regret for the opponent the topsis method determines a solution with the shortest distance to the ideal solution and the greatest distance from the negative ideal solution but it does not consider the relative importance of these distances a comparative analysis of these two methods is illustrated with a numerical example showing their similarity and some differences 2003 elsevier b v all rights reserved

use of distraction loading to estimate subject specific knee ligament slack lengths abstract knee ligaments guide and restrain joint motion and their properties influence joint mechanics inverse modeling schemes have been used to estimate specimen specific ligament properties where external joint forces are assumed to balance with internal ligament and contact forces this study simplifies this assumption by adjusting experimental loads to remove internal contact forces the purpose of this study was to use novel experimental loading in an inverse modeling scheme to estimate ligament slack lengths perform validation using additional loading scenarios and evaluate sensitivity to the applied loading joint kinematics and kinetics were experimentally measured for a set of load cases an optimization scheme used a specimen specific forward kinematics model to estimate ligament slack lengths by minimizing the residual between model and experimentally measured kinetics the calibrated model was used for a form of validation by evaluating non optimized load cases additionally uncertainty analysis related kinetic errors to previously reported kinematic errors the six dof tibial reactions realized rms errors less than 23 n and 0 75 nm for optimized load cases and 33 n and 2 25 nm for the non optimized load cases the uncertainty analysis which was performed using the optimized load cases showed average kinetic rms errors less than 26 n and 0 45 nm the model s recruitment patterns were similar to those found in clinical and cadaveric studies this study demonstrated that experimental distraction loading can be used in an inverse modeling scheme to estimate ligament slack lengths with a forward kinematics model

design optimization of a total knee replacement for improved constraint and flexion kinematics total knee replacement tkr constraint and flexion range of motion can be limiting factors in terms of kinematics performance and cause for revision these characteristics are closely related to the shape of the implant components no previous studies have used a rigorous and systematic design optimization method to determine the optimal shape of tkr components previous studies have failed to define a quantifiable objective function for optimization have not used any optimization algorithms and have only considered a limited design space 4 or less design variables this study addresses these limitations and determines the optimum shape of the femoral component and ultra high molecular weight polyethylene uhmwpe insert in terms of kinematics the constraint characteristics with respect to those of the natural knee the importance of the posterior cruciate ligament and the flexion range of motion were all considered the kinematics optimized design featured small femoral radii of curvature in the frontal and sagittal planes but asymmetric with slightly larger radii of curvature for the lateral condyle this condyle was also less conforming than the medial side compared to a commercially available tkr design the kinematics performance based on constraint and flexion range of motion was improved by 81 with constraint characteristics generally closer to those of the natural knee and a 12 6 increase in the flexion range of motion up to 143 the results yielded a new tkr design while demonstrating the feasibility of design optimization in tkr design

a method for solving fuzzy goal programming problems based on minmax approach abstract narasimhan incorporated fuzzy set theory within goal programming formulation in 1980 since then numerous research has been carried out in this field one of the well known models for solving fuzzy goal programming problems was proposed by hannan in 1981 in this paper the conventional minmax approach in goal programming is applied to solve fuzzy goal programming problems it is proved that the proposed model is an extension to hannan model that deals with unbalanced triangular linear membership functions in addition it is shown that the new model is equivalent to a model proposed in 1991 by yang et al moreover a weighted model of the new approach is introduced and is compared with kim and whang s model presented in 1998 a numerical example is given to demonstrate the validity and strengths of the new models

a spectral deferred correction method for incompressible flow with variable viscosity abstract this paper presents a semi implicit spectral deferred correction sdc method for incompressible navier stokes problems with variable viscosity and time dependent boundary conditions the proposed method integrates elements of velocity and pressure correction schemes which yields a simpler pressure handling and a smaller splitting error than the sdpc method of minion and saye j comput phys 375 797 822 2018 combined with the discontinuous galerkin spectral element method for spatial discretization it can in theory reach arbitrary order of accuracy in time and space numerical experiments in three space dimensions demonstrate up to order 12 in time and 17 in space for constant as well as varying solution dependent viscosity compared to sdpc the present method yields a substantial improvement of accuracy and robustness against order reduction caused by time dependent boundary conditions

a hybrid heuristic algorithm for the open pit mining operational planning problem this paper deals with the open pit mining operational planning problem with dynamic truck allocation the objective is to optimize mineral extraction in the mines by minimizing the number of mining trucks used to meet production goals and quality requirements according to the literature this problem is np hard so a heuristic strategy is justified we present a hybrid algorithm that combines characteristics of two metaheuristics greedy randomized adaptive search procedures and general variable neighborhood search the proposed algorithm was tested using a set of real data problems and the results were validated by running the cplex optimizer with the same data this solver used a mixed integer programming model also developed in this work the computational experiments show that the proposed algorithm is very competitive finding near optimal solutions with a gap of less than 1 in most instances demanding short computing times

compromise programming a utility based linear quadratic composite metric from the trade off between achievement and balanced non corner solutions abstract in this paper compromise programming cp is viewed as the maximization of the decision maker s additive utility function whose arguments are the criteria under consideration subject to an efficient frontier of criteria and the non negativity constraints in a deterministic context this is equivalent to minimizing the difference distance between utility at the ideal point and utility at a frontier point on the criteria map a meaningful statement as minimizing distances to the utopia is the ethos of compromise programming by taylor expansion of utility around the ideal point the distance to the utopia becomes the weighted sum of linear and quadratic cp distances which gives us the composite metric while the linear terms pursue achievement the quadratic ones pursue balanced non corner solutions because some decision makers fear imbalance while others prefer large achievements even to the detriment of balance the paper defines an aversion to imbalance ratio so that the composite linear quadratic metric should conform to this ratio depending on the decision maker s preferences and attitudes as the problem of selecting an appropriate metric is an ongoing issue in cp the paper is a contribution to theory and practice for the sole purpose of suggesting industrial applications an example is developed

geometric integrators for odes geometric integration is the numerical integration of a differential equation while preserving one or more of its geometric properties exactly i e to within round off error many of these geometric properties are of crucial importance in physical applications preservation of energy momentum angular momentum phase space volume symmetries time reversal symmetry symplectic structure and dissipation are examples in this paper we present a survey of geometric numerical integration methods for ordinary differential equations our aim has been to make the review of use for both the novice and the more experienced practitioner interested in the new developments and directions of the past decade to this end the reader who is interested in reading up on detailed technicalities will be provided with numerous signposts to the relevant literature

strongly agree or strongly disagree in linear classifiers such as the support vector machine svm a score is associated with each feature and objects are assigned to classes based on the linear combination of the scores and the values of the features inspired by discrete psychometric scales which measure the extent to which a factor is in agreement with a statement we propose the discrete level support vector machine dilsvm where the feature scores can only take on a discrete number of values defined by the so called feature rating levels the dilsvm classifier benefits from interpretability and it has visual appeal since it can be represented as a collection of likert scales one for each feature where we rate the level of agreement with the positive class to construct the dilsvm classifier we propose a mixed integer linear programming approach as well as a collection of strategies to reduce computational cost our numerical experiments show that the three point and the five point dilsvm classifiers have comparable accuracy to the svm with a substantial gain in interpretability and visual appeal but also in sparsity thanks to the appropriate choice of the feature rating levels

integral deferred correction methods constructed with high order runge kutta integrators spectral deferred correction sdc methods for solving ordinary differential equations odes were introduced by dutt greengard and rokhlin 2000 it was shown in that paper that sdc methods can achieve arbitrary high order accuracy and possess nice stability properties their sdc methods are constructed with low order integrators such as forward euler or backward euler and are able to handle stiff and non stiff terms in the odes in this paper we use high order runge kutta rk integrators to construct a family of related methods which we refer to as integral deferred correction idc methods the distribution of quadrature nodes is assumed to be uniform and the corresponding local error analysis is given the smoothness of the error vector associated with an idc method measured by the discrete sobolev norm is a crucial tool in our analysis the expected order of accuracy is demonstrated through several numerical examples superior numerical stability and accuracy regions are observed when high order rk integrators are used to construct idc methods

grid adaptation and non iterative defect correction for improved accuracy of numerical solutions of pdes in this work we present a computational approach for improving the order of accuracy of a given finite difference method for solution of linear and nonlinear hyperbolic partial differential equations the methodology consists of analysis of leading order terms in the discretization error of any given finite difference method leading to a modified version of the original partial differential equation singular perturbations of this modified equation are regularized using an adaptive grid distribution and a non iterative defect correction method is used to eliminate the leading order regular perturbation terms in the modified equation implementation of this approach on a low order finite difference scheme not only results in an increase in its order of accuracy but also results in an improvement in its numerical stability due to the regularization of singular perturbations the proposed approach is applied to four different canonical problems including the numerical solution of 1 liouville equation 2 inviscid burgers equation 3 nonlinear reaction advection equation and 4 a system of hyperbolic pdes when compared to exact solutions the numerical results demonstrate the ability of this method in both boosting the accuracy of finite difference schemes up to the desired order and also providing a fully stable numerical solution

incorporating additional meta objectives into the extended lexicographic goal programming framework this paper introduces two new meta objectives into the extended goal programming framework the first meta objective is the number of unmet goals and the second is a measure of closeness to the pairwise comparisons given by the decision maker these complement the original two meta objectives of the weighted sum of deviations and the maximal weighted deviation to provide a flexible four meta objective framework lexicographic and non lexicographic representations of the framework are developed an example relating to transportation is solved in both the lexicographic and non lexicographic forms weight sensitivity analysis is applied to the meta weight parameters for the non lexicographic case in order to find a range of available distinct solutions

high order multi implicit spectral deferred correction methods for problems of reactive flow models for reacting flow are typically based on advection diffusion reaction a d r partial differential equations many practical cases correspond to situations where the relevant time scales associated with each of the three sub processes can be widely different leading to disparate time step requirements for robust and accurate time integration in particular interesting regimes in combustion correspond to systems in which diffusion and reaction are much faster processes than advection the numerical strategy introduced in this paper is a general procedure to account for this time scale disparity the proposed methods are high order multi implicit generalizations of spectral deferred correction methods misdc methods constructed for the temporal integration of a d r equations spectral deferred correction methods compute a high order approximation to the solution of a differential equation by using a simple low order numerical method to solve a series of correction equations each of which increases the order of accuracy of the approximation the key feature of misdc methods is their flexibility in handling several sub processes implicitly but independently while avoiding the splitting errors present in traditional operator splitting methods and also allowing for different time steps for each process the stability accuracy and efficiency of misdc methods are first analyzed using a linear model problem and the results are compared to semi implicit spectral deferred correction methods furthermore numerical tests on simplified reacting flows demonstrate the expected convergence rates for misdc methods of orders three four and five the gain in efficiency by independently controlling the sub process time steps is illustrated for nonlinear problems where reaction and diffusion are much stiffer than advection although the paper focuses on this specific time scales ordering the generalization to any ordering combination is straightforward

conservative multi implicit spectral deferred correction methods for reacting gas dynamics in most models of reacting gas dynamics the characteristic time scales of chemical reactions are much shorter than the hydrodynamic and diffusive time scales rendering the reaction part of the model equations stiff moreover non linear forcings may introduce into the solutions sharp gradients or shocks the robust behavior and correct propagation of which require the use of specialized spatial discretization procedures this study presents high order conservative methods for the temporal integration of model equations of reacting flows by means of a method of lines discretization on the flux difference form of the equations these methods compute approximations to the cell averaged or finite volume solution the temporal discretization is based on a multi implicit generalization of spectral deferred correction methods the advection term is integrated explicitly and the diffusion and reaction terms are treated implicitly but independently with the splitting errors reduced via the spectral deferred correction procedure to reduce computational cost different time steps may be used to integrate processes with widely differing time scales numerical results show that the conservative nature of the methods allows a robust representation of discontinuities and sharp gradients the results also demonstrate the expected convergence rates for the methods of orders three four and five for smooth problems