a genuinely multidimensional convective pressure flux split riemann solver for euler equations a simple inexpensive genuinely multidimensional hll type riemann solver for euler equations of gasdynamics is proposed the genuinely multidimensional formulation is based on the work of balsara 17 in the present approach the missing contact wave in the hll type solver is restored using the hll cps formulation of mandal and panwar 5 a few two dimensional standard test cases are solved to demonstrate the efficacy of the proposed solver a very simple new genuinely multidimensional hll type riemann solver for euler equations is proposed due to the use of closed form expressions for the fluxes the present method is easier to apply the contact discontinuity is restored using the hll cps formulation without the need for independently specifying its direction of evolution numerical test results demonstrate the efficacy of the present method of its ability to capture accurate solutions

a new possibilistic programming approach for solving fuzzy multiobjective assignment problem in this paper we propose a new possibilistic programming approach to solve a fuzzy multiobjective assignment problem in which the objective function coefficients are characterized by triangular possibility distributions the proposed solution approach simultaneously minimizes the best scenario the likeliest scenario and the worst scenario for the imprecise objective functions using level sets the level sets are used to define the confidence level of the fuzzy judgments of the decision maker additionally we provide a systematic framework in which the decision maker controls the search direction by updating both the membership values and aspiration levels until a set of satisfactory solutions is obtained numerical examples with dataset from realistic situations are provided to demonstrate the effectiveness of the proposed approach

an evaluation of roe s scheme generalizations for equilibrium real gas flows the extension of roe s approximate riemann solver to equilibrium real gas is analyzed by means of a general formulation allowing us to clarify the inherent nonuniqueness of the average state and the influence of the functional form of the equation of state several generalizations of roe s scheme are then reviewed and their numerical performances are discussed by computing some 2d steady hypersonic flows the flow solvers are coupled with a newly developed efficient and robust procedure for thermochemical air properties evaluation all of the tested equilibrium solvers achieve very similar results they are found of comparable numerical efficiency the higher performances being associated with vinokur s and liou s solvers it is concluded that equilibrium simulations in 2d are by no means less robust than the perfect gas ones when coupled with the proposed procedure for properties evaluation

two stage stochastic optimization problems with stochastic ordering constraints on the recourse abstract we consider two stage risk averse stochastic optimization problems with a stochastic ordering constraint on the recourse function two new characterizations of the increasing convex order relation are provided they are based on conditional expectations and on integrated quantile functions a counterpart of the lorenz function we propose two decomposition methods to solve the problems and prove their convergence our methods exploit the decomposition structure of the risk neutral two stage problems and construct successive approximations of the stochastic ordering constraints numerical results confirm the efficiency of the methods

an inexact probabilistic possibilistic optimization framework for flood management in a hybrid uncertain environment flooding is one of the leading causes of loss due to natural catastrophes and at least one third of all losses due to natural forces can be attributed to flooding flood management systems involve a variety of complexities such as multiple uncertainties dynamic variations and policy implications this paper presents an inexact probabilistic possibilistic programming with fuzzy random coefficients ipp frc model for flood management in a hybrid uncertain environment ipp frc is capable not only of tackling multiple uncertainties in the form of intervals with fuzzy random boundaries but of addressing the dynamic complexity through capacity expansion planning within a multi region multi flood level and multi option context the possibility and necessity measures used in ipp frc are suitable for risk seeking and risk averse decision making respectively a case study is used to demonstrate the applicability of the proposed methodology for facilitating flood management the results indicate that the inexact degrees of possibility and necessity would decrease with increased probabilities of occurrence implying a potential tradeoff between fulfillment of objectives and associated risks a number of decision alternatives can be obtained under different policy scenarios they are helpful for decision makers to formulate the appropriate flood management policy according to practical situations the performance of ipp frc is analyzed and compared with a possibility based fractile model

conditional stability in an inverse problem of determining a non smooth boundary an inverse problem for determining an unknown boundary is discussed we prove conditional stability of logarithmic type for unknown lipschitz boundaries under a priori assumptions the proof is based on estimation of harmonic measures

computational treatment of source terms in two equation turbulence models the source terms in turbulence models require careful treatment to obtain a stable discretization the choice between implicit and explicit treatment has to be made this can be done either on the basis of individual terms or on the basis of the exact jacobian of the source terms a comparison of both methods shows that the latter is generally applicable and superior to the first approximate method with respect to convergence speed this comes from the possibility of using the multigrid technique with the exact method whereas this is not always possible with the approximate method in principle for robustness a time step restriction for the source terms has to be introduced to prevent the turbulence quantities from becoming negative or infinitely large an approximation of the appropriate time step is calculated practical results however indicate that the time step restriction is not always necessary different two equation turbulence models are investigated confirming the generality of the approach

a linear decision based approximation approach to stochastic programming stochastic optimization especially multistage models is well known to be computationally excruciating moreover such models require exact specifications of the probability distributions of the underlying uncertainties which are often unavailable in this paper we propose tractable methods of addressing a general class of multistage stochastic optimization problems which assume only limited information of the distributions of the underlying uncertainties such as known mean support and covariance one basic idea of our methods is to approximate the recourse decisions via decision rules we first examine linear decision rules in detail and show that even for problems with complete recourse linear decision rules can be inadequate and even lead to infeasible instances hence we propose several new decision rules that improve upon linear decision rules while keeping the approximate models computationally tractable specifically our approximate models are in the forms of the so called second order cone soc programs which could be solved efficiently both in theory and in practice we also present computational evidence indicating that our approach is a viable alternative and possibly advantageous to existing stochastic optimization solution techniques in solving a two stage stochastic optimization problem with complete recourse

real time forecasting and daily operation of a multireservoir system during floods by linear quadratic gaussian control the problem of short term daily operation of a multireservoir system during floods is examined the problem is how to use all available real time information to solve the tactical problem of regulating reservoirs to minimize the expected value of flood damage during a relatively short operating horizon and to do so consistently with the long term operating strategy a state space mathematical model is presented for short term forecasting of river flows and description of the dynamics of a multireservoir system the model includes reduced order state space unit hydrographs to forecast storm runoff from effective rainfall and state space representations of linear flood routing the optimization problem is solved in the framework of discrete time linear quadratic gaussian lqg control lqg control is a computationally efficient and flexible method of solving the large dimensional optimization problems associated with the solution of the tactical problem of short term operation of reservoirs for application of the lqg control methodology the system must be represented in state space form with quadratic cost functions subject to linear equality constraints given by the state transition equations the scheme was found to be suitable for operation under moderate flood conditions when capacity constraints are not likely to become binding the methodology has been applied and tested in a real world case

risk decision making method using interval numbers and its application based on the prospect value with multiple reference points a risk decision making method with multiple reference points is proposed two reference points and three reference points are set in the prospect theory two weighting optimization models are established two cases are applied to illustrate the importance of multiple reference points a multi attribute risk decision making problem using interval numbers is studied based on the prospect theory a decision making process often involves various reference standards resulting from different decision making mentalities and contexts to solve these kinds of decision making problems we propose a risk decision making method with multiple reference points for both static and dynamic situations first the guidelines for setting reference points under both static and dynamic conditions are provided based on the nature of the decision making problem second both expected values and positive ideal points for alternatives are set for the static decision making strategy and three reference points are provided for the dynamic strategy including expected values positive ideal points and the development status of alternatives according to the guidelines third characterization techniques used to solve prospect values of decision making alternatives are proposed for both static and dynamic decision making problems then a detailed analysis is provided in terms of weighting functions and prospect values in addition two optimization models using the attribute weight and multi stage weight are established by considering the sensitivity of these two weights to the decision making problem with the aim of maximizing the differentiation degree of alternatives on that basis a ranking analysis is provided for the alternatives finally the proposed method is applied to two cases including supplier selection of key components for large aircraft and an emergency event to illustrate the application and feasibility of the method

interactive multiobjective fuzzy random linear programming maximization of possibility and probability this paper considers multiobjective linear programming problems with fuzzy random variables coefficients a new decision making model is proposed to maximize both possibility and probability which is based on possibilistic programming and stochastic programming an interactive algorithm is constructed to obtain a satisficing solution satisfying at least weak pareto optimality

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

possibilistic linear programming a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem in this paper we review some fuzzy linear programming methods and techniques from a practical point of view in the rst part the general history and the approach of fuzzy mathematical programming are introduced using a numerical example some models of fuzzy linear programming are described in the second part of the paper fuzzy mathematical programming approaches are compared to stochastic programming ones the advantages and disadvantages of fuzzy mathematical programming approaches are exemplied in the setting of an optimal portfolio selection problem finally some newly developed ideas and techniques in fuzzy mathematical programming are briey reviewed c 2000 elsevier science b v all rights reserved

grid adaptation using chimera composite overlapping meshes the objective of this paper is to perform grid adaptation using composite over lapping meshes in regions of large gradient to capture the salient features accurately during computation the chimera grid scheme a multiple overset mesh technique is used in combination with a navier stokes solver the numerical solution is first converged to a steady state based on an initial coarse mesh solution adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high gradient region but without requiring the mesh boundaries to join in any special way communications through boundary interfaces between those separated grids are carried out using tri linear interpolation applications to the euler equations for shock reflections and to a shock wave boundary layer interaction problem are tested with the present method the salient features are well resolved

risk averse two stage stochastic linear programming modeling and decomposition we formulate a risk averse two stage stochastic linear programming problem in which unresolved uncertainty remains after the second stage the objective function is formulated as a composition of conditional risk measures we analyze properties of the problem and derive necessary and sufficient optimality conditions next we construct a new decomposition method for solving the problem that exploits the composite structure of the objective function we illustrate its performance on a portfolio optimization problem

a possibilistic programming approach for closed loop supply chain network design under uncertainty the design of closed loop supply chain networks has attracted more attention in recent years according to business and environmental factors the significance of accounting for uncertainty and risk in such networks spurs an interest to develop appropriate decision making tools to cope with uncertain and imprecise parameters in closed loop supply chain network design problems this paper proposes a bi objective possibilistic mixed integer programming model to deal with such issues the proposed model integrates the network design decisions in both forward and reverse supply chain networks and also incorporates the strategic network design decisions along with tactical material flow ones to avoid the sub optimalities led from separated design in both parts to solve the proposed possibilistic optimization model an interactive fuzzy solution approach is developed by combining a number of efficient solution approaches from the recent literature numerical experiments are conducted to demonstrate the significance and applicability of the developed possibilistic model as well as the usefulness of the proposed solution approach

interactive fuzzy random two level linear programming based on level sets and fractile criterion optimization in this paper assuming cooperative behavior of the decision makers two level linear programming problems under fuzzy random environments are considered by introducing a level sets of fuzzy random variables and defining an a stochastic two level linear programming problem for guaranteeing the degree of realization of the problem through a new decision making model proposed based on the fractile criterion optimization model considering fuzzy goals the a stochastic two level programming problem can be equivalently transformed into a deterministic problem interactive fuzzy programming to derive a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented an illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method

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

an interval parameter fuzzy nonlinear optimization model for stream water quality management under uncertainty planning for water quality management systems is complicated by a variety of uncertainties and nonlinearities where difficulties in formulating and solving the resulting inexact nonlinear optimization problems exist with the purpose of tackling such difficulties this paper presents the development of an interval fuzzy nonlinear programming ifnp model for water quality management under uncertainty methods of interval and fuzzy programming were integrated within a general framework to address uncertainties in the left and right hand sides of the nonlinear constraints uncertainties in water quality pollutant loading and the system objective were reflected through the developed ifnp model the method of piecewise linearization was developed for dealing with the nonlinearity of the objective function a case study for water quality management planning in the changsha section of the xiangjiang river was then conducted for demonstrating applicability of the developed ifnp model the results demonstrated that the accuracy of solutions through linearized method normally rises positively with the increase of linearization levels it was also indicated that the proposed linearization method was effective in dealing with ifnp problems uncertainties can be communicated into optimization process and generate reliable solutions for decision variables and objectives the decision alternatives can be obtained by adjusting different combinations of the decision variables within their solution intervals it also suggested that the linearized method should be used under detailed error analysis in tackling ifnp problems

a new flux splitting scheme a new flux splitting scheme is proposed the scheme is remarkably simple and yet its accuracy rivals and in some cases surpasses that of roe s solver in the euler and navier stokes solutions carried out in this study the scheme is robust and converges as fast as the roe splitting we propose an appropriately defined cell face advection mach number using values from the two straddling cells via associated characteristic speeds this interface mach number is then used to determine the upwind extrapolation for the convective quantities accordingly the name of the scheme is coined as the advection upstream splitting method ausm we also introduce a new pressure splitting which is shown to behave successfully yielding much smoother results than other existing pressure splittings of particular interest is the supersonic blunt body problem in which the roe scheme gives anomalous solutions the ausm produces correct solutions without difficulty for a wide range of flow conditions as well as grids

multigrid and defect correction for the steady navier stokes equations theoretical and experimental convergence results are presented for nonlinear multigrid and iterative defect correction applied to finite volume discretizations of the full steady 2d compressible navier stokes equations iterative defect correction is introduced for circumventing the difficulty in solving navier stokes equations discretized with a second or higher order accurate convective part by fourier analysis applied to a model equation an optimal choice is made for the operator to be inverted in the defect correction iteration as a smoothing technique for the multigrid method collective symmetric point gauss seidel relaxation is applied with as the basic solution technique exact newton iteration applied to a continuously differentiable first order upwind discretization of the full navier stokes equations for non smooth flow problems the convergence results obtained are already competitive with those of well established navier stokes methods for smooth flow problems the present method performs better than any standard method here first order discretization error accuracy is attained in a single multigrid cycle and second order accuracy in only one defect correction cycle the method contributes to the state of the art in efficiently computing compressible viscous flows

a multicut algorithm for two stage stochastic linear programs outer linearization methods such as van slyke and wets s l shaped method for stochastic linear programs generally apply a single cut on the nonlinear objective at each major iteration the structure of stochastic programs allows for several cuts to be placed at once this paper describes a multicut algorithm to carry out this procedure it presents experimental and theoretical justification for reductions in major iterations