characterization of the critical submanifolds in quantum ensemble control landscapes the quantum control landscape is defined as the functional that maps the control variables to the expectation values of an observable over the ensemble of quantum systems analyzing the topology of such landscapes is important for understanding the origins of the increasing number of laboratory successes in the optimal control of quantum processes this paper proposes a simple scheme to compute the characteristics of the critical topology of the quantum ensemble control landscapes showing that the set of disjoint critical submanifolds one to one corresponds to a finite number of contingency tables that solely depend on the degeneracy structure of the eigenvalues of the initial system density matrix and the observable whose expectation value is to be maximized the landscape characteristics can be calculated as functions of the table entries including the dimensions and the numbers of positive and negative eigenvalues of the hessian quadratic form of each of the connected components of the critical submanifolds typical examples are given to illustrate the effectiveness of this method

a frictional contact algorithm for implicit material point method the explicit material point method mpm works successfully in modeling high frequency problems but it is very computationally expensive in simulating low frequency with small time steps or quasi static problems thus several groups have developed an implicit mpm for modeling low frequency problems recently a few attempts were undertaken to investigate the contact problems using the implicit mpm but the accuracy was dissatisfactory the contact problem is one of the saddle point problems which are usually indefinite and highly ill conditioned these features bring great challenges to the newton like methods which require the hessen matrix to be positive definite an easy implementing frictional contact algorithm is proposed for the implicit mpm which is based on an augmented lagrange formulation by employing the uzawa algorithm the condition number of the original problem is dramatically improved and the positive definiteness of the effective stiffness matrix can be reserved in addition the uzawa algorithm decouples the unknown variables and the multipliers which simplifies the solving process the resulting nonlinear equations are solved by the newton method in which the tangential matrix is assembled explicitly by using the compressed sparse row csr technique the total storage of the matrix can be greatly reduced the accuracy efficiency and robustness of the contact algorithm have been validated by the numerical studies the results obtained by the implicit mpm with the proposed contact algorithm agree well with the analytical solution the computational accuracy and efficiency are much higher than the explicit mpm the cutting simulation demonstrates the competitive advantages of the implicit mpm over the fem and the robustness of the contact algorithm

mass matrix formulation of the flip particle in cell method a refinement of flip brackbill and ruppel j comput phys 65 314 1986 is described which uses a mass matrix formulation to achieve greater accuracy and less numerical diffusion over the previous version without the refinement there is a significant dissipation of energy in modeling elastic vibrations of a solid moreover in modeling an initial flow discontinuity there are sub grid scale oscillations in the particle velocity field in the neighborhood of the discontinuity these difficulties are eliminated using the mass matrix in addition the mass matrix formulation conserves kinetic energy linear and angular momentum and is galilean invariant

bc opt a branch and cut code for mixed integer programs a branch and cut mixed integer programming system called bc opt is described incorporating most of the valid inequalities that have been used or suggested for such systems namely lifted 0 1 knapsack inequalities 0 1 gub knapsack and integer knapsack inequalities flowcover and continuous knapsack inequalities path inequalities for fixed charge network flow structure and gomory mixed integer cuts the principal development is a set of interface routines allowing these cut routines to generate cuts for new subsets or aggregations of constraints

production planning problem with sequence dependent setups as a bilevel programming problem abstract each of n products is to be processed on two machines in order to satisfy known demands in each of t periods only one product can be processed on each machine at any given time each switch from one item to another requires sequence dependent setup time the objective is to minimize the total setup time and the sum of the costs of production storage and setup we consider the problem as a bilevel mixed 0 1 integer programming problem the objective of the leader is to assign the products to the machines in order to minimize the total sequence dependent setup time while the objective of the follower is to minimize the production storage and setup cost of the machine we develop a heuristics based on tabu search for solving the problem at the end some computational results are presented

reproducing kernel particle methods for large deformation analysis of non linear structures abstract large deformation analysis of non linear elastic and inelastic structures based on reproducing kernel particle methods rkpm is presented the method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis the current formulation considers hyperelastic and elasto plastic materials since they represent path independent and path dependent material behaviors respectively in this paper a material kernel function and an rkpm material shape function are introduced for large deformation analysis the support of the rkpm material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation the essential boundary conditions are introduced by the use of a transformation method the transformation matrix is formed only once at the initial stage if the rkpm material shape functions are employed the appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions in transient problems with an explicit time integration method the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles several hyperelasticity and elasto plasticity problems are studied to demonstrate the effectiveness of the method the numerical results indicated that rkpm handles large material distortion more effectively than finite elements due to its smoother shape functions and consequently provides a higher solution accuracy under large deformation unlike the conventional finite element approach the nodal spacing irregularity in rkpm does not lead to irregular mesh shape that significantly deteriorates solution accuracy no volumetric locking is observed when applying non linear rkpm to nearly incompressible hyperelasticity and perfect plasticity problems further model adaptivity in rkpm can be accomplished simply by adding more points in the highly deformed areas without remeshing

exact solution approaches for bilevel lot sizing abstract in this paper we propose exact solution methods for a bilevel uncapacitated lot sizing problem with backlogs this is an extension of the classical uncapacitated lot sizing problem with backlogs in which two autonomous and self interested decision makers constitute a two echelon supply chain the leader buys items from the follower in order to meet external demand at lowest cost the follower also tries to minimize its costs both parties may backlog we study the leader s problem i e how to determine supply requests over time to minimize its costs in view of the possible actions of the follower we develop two mixed integer linear programming reformulations as well as cutting planes to cut off feasible but suboptimal solutions we compare the reformulations on a series of benchmark instances

fuzzy programming approach to multi objective stochastic programming problems when b i s follow joint normal distribution abstract in this paper a multi objective chance constrained programming problem has been considered when bi s are normal random variables and the constraints have a joint probability distribution the probabilistic problem is converted into an equivalent deterministic non linear programming problem then the fuzzy programming technique has been applied to obtain a compromise solution a numerical example is also presented to illustrate the methodology

s r decomposition based numerical manifold method the numerical manifold method nmm surmounting the mesh dependence has successfully solved very complicated problems involving small deformation and large movement but had few applications to large deformation and large rotation problems because the false volume expansion and other issues exist in this study it is shown that the false volume expansion in nmm can be excellently resolved by using the s r strain rotation decomposition theorem which can precisely reflect complex physical behaviors occurring in the process of large rotation and large deformation the numerical methods based on the s r decomposition theorem have been limited to the static analysis of large deformations to remove this limitation a new formulation taking into account dynamical features is proposed based on the weak form of momentum conservation law under the framework of nmm the generalized a method is employed to discretize the temporal variables the updates of variables are described using the updated co moving coordinate system thus a new method named s r d based nmm is established the new formulation can be implemented in any other partition of unity based methods as well so as to improve the performances of such methods in the analysis of dynamic large deformations c 2016 elsevier b v all rights reserved

control landscapes for two level open quantum systems a quantum control landscape is defined as the physical objective as a function of the control variables in this paper the control landscapes for two level open quantum systems whose evolution is described by general completely positive trace preserving maps i e kraus maps are investigated in detail the objective function which is the expectation value of a target system operator is defined on the stiefel manifold representing the space of kraus maps three practically important properties of the objective function are found a the absence of local maxima or minima i e false traps b the existence of multi dimensional sub manifolds of optimal solutions corresponding to the global maximum and minimum and c the connectivity of each level set all of the critical values and their associated critical sub manifolds are explicitly found for any initial system state away from the absolute extrema there are no local maxima or minima and only saddles may exist whose number and the explicit structure of the corresponding critical sub manifolds are determined by the initial system state there are no saddles for pure initial states one saddle for a completely mixed initial state and two saddles for partially mixed initial states in general the landscape analysis of critical points and optimal manifolds is relevant to explain the relative ease of obtaining good optimal control outcomes in the laboratory even in the presence of the environment

economic lot sizing an o n log n algorithm that runs in linear time in the wagner whitin case we consider the n period economic lot sizing problem where the cost coefficients are not restricted in sign in their seminal paper h m wagner and t m whitin proposed an o n2 algorithm for the special case of this problem where the marginal production costs are equal in all periods and the unit holding costs are nonnegative it is well known that their approach can also be used to solve the general problem without affecting the complexity of the algorithm in this paper we present an algorithm to solve the economic lot sizing problem in o n log n time and we show how the wagner whitin case can even be solved in linear time our algorithm can easily be explained by a geometrical interpretation and the time bounds are obtained without the use of any complicated data structure furthermore we show how wagner and whitin s and our algorithm are related to algorithms that solve the dual of the simple plant location formulation of the economic lot sizing problem

a particle method for history dependent materials abstract a broad class of engineering problems including penetration impact and large rotations of solid bodies causes severe numerical problems for these problems the constitutive equations are history dependent so material points must be followed this is difficult to implement in a eulerian scheme on the other hand purely lagrangian methods typically result in severe mesh distortion and the consequence is ill conditioning of the element stiffness matrix leading to mesh lockup or entanglement remeshing prevents the lockup and tangling but then interpolation must be performed for history dependent variables a process which can introduce errors proposed here is an extension of the particle in cell method in which particles are interpreted to be material points that are followed through the complete loading process a fixed eulerian grid provides the means for determining a spatial gradient because the grid can also be interpreted as an updated lagrangian frame the usual convection term in the acceleration associated with eulerian formulations does not appear with the use of maps between material points and the grid the advantages of both eulerian and lagrangian schemes are utilized so that mesh tangling is avoided while material variables are tracked through the complete deformation history example solutions in two dimensions are given to illustrate the robustness of the proposed convection algorithm and to show that typical elastic behavior can be reproduced also it is shown that impact with no slip is handled without any special algorithm for bodies governed by elasticity and strain hardening plasticity

lagrangian versus eulerian integration errors abstract the possibility to use a lagrangian frame to solve problems with large time steps was successfully explored previously by the authors for the solution of homogeneous incompressible fluids and also for solving multi fluid problems idelsohn et al 2012 2014 2013 the strategy used by the authors was named particle finite element method second generation pfem 2 the objective of this paper is to demonstrate in which circumstances the use of a lagrangian frame with particles is more accurate than a classical eulerian finite element method and when large time steps and or coarse meshes may be used

imposition of essential boundary conditions in the material point method summary there is increasing interest in the material point method mpm as a means of modelling solid mechanics problems in which very large deformations occur e g in the study of landslides and metal forming however some aspects vital to wider use of the method have to date been ignored in particular methods for imposing essential boundary conditions in the case where the problem domain boundary does not coincide with the background grid element edges in this paper we develop a simple procedure originally devised for standard finite elements for the imposition of essential boundary conditions to the mpm expanding its capabilities to boundaries of any inclination to the authors knowledge this is the first time that a method has been proposed that allows arbitrary dirichlet boundary conditions zero and non zero values at any inclination to be imposed in the mpm the method presented in this paper is different from other mpm boundary approximation approaches in that i the boundaries are independent of the background mesh ii artificially stiff regions of material points are avoided and iii the method does not rely on spurious mirroring of the problem domain to imposed symmetry the main contribution of this work is equally applicable to standard finite elements and the mpm this article is protected by copyright all rights reserved

single item lot sizing with non decreasing capacities we consider the single item lot sizing problem with capacities that are non decreasing over time when the cost function is i non speculative or wagner whitin for instance constant unit production costs and non negative unit holding costs and ii the production set up costs are non increasing over time it is known that the minimum cost lot sizing problem is polynomially solvable using dynamic programming when the capacities are non decreasing we derive a compact mixed integer programming reformulation whose linear programming relaxation solves the lot sizing problem to optimality when the objective function satisfies i and ii the formulation is based on mixing set relaxations and reduces to the known convex hull of solutions when the capacities are constant over time we illustrate the use and potential effectiveness of this improved lp formulation on a few test instances including instances with and without wagner whitin costs and with both non decreasing and arbitrary capacities over time

uncapacitated lot sizing with backlogging the convex hull an explicit description of the convex hull of solutions to the uncapacitated lot sizing problem with backlogging in its natural space of production setup inventory and backlogging variables has been an open question for many years in this paper we identify valid inequalities that subsume all previously known valid inequalities for this problem we show that these inequalities are enough to describe the convex hull of solutions we give polynomial separation algorithms for some special cases finally we report a summary of computational experiments with our inequalities that illustrates their effectiveness

lot size models with back logging strong reformulations and cutting planes we examine mixed integer programming reformulations of the uncapacitated lot sizing problem with backlogging first we consider the effect of using a standard reformulation technique for fixed charge network flow problems which involves the introduction of new variables leading to a known plant location reformulation and a shortest path reformulation each of these reformulations is strong in the sense that its linear programming relaxation solves the lot sizing problem secondly we attempt to treat the problem in the space of the original variables we give an implicit description of the convex hull of solutions and show how the problem of finding a violated cutting plane can be solved as a linear program we also describe a family of strong valid inequalities which can be generated rapidly by a heuristic and which have proved effective in a cut generation algorithm the efficiency of both the shortest path formulation and the cutting plane algorithm have been tested on a series of multi item capacitated lot sizing problems with backlogging near optimal solutions have been found to problems with 8 periods and up to 100 times

relaxations for two level multi item lot sizing problems we consider several variants of the two level lot sizing problem with one item at the upper level facing dependent demand and multiple items or clients at the lower level facing independent demands we first show that under a natural cost assumption it is sufficient to optimize over a stock dominant relaxation we further study the polyhedral structure of a strong relaxation of this problem involving only initial inventory variables and setup variables we consider several variants uncapacitated at both levels with or without start up costs uncapacitated at the upper level and constant capacity at the lower level constant capacity at both levels we finally demonstrate how the strong formulations described improve our ability to solve instances with up to several dozens of periods and a few hundred products

an extended validation of the last generation of particle finite element method for free surface flows in this paper a new generation of the particle method known as particle finite element method pfem which combines convective particle movement and a fixed mesh resolution is applied to free surface flows this interesting variant previously described in the literature as pfem 2 is able to use larger time steps when compared to other similar numerical tools which implies shorter computational times while maintaining the accuracy of the computation pfem 2 has already been extended to free surface problems being the main topic of this paper a deep validation of this methodology for a wider range of flows to accomplish this task different improved versions of discontinuous and continuous enriched basis functions for the pressure field have been developed to capture the free surface dynamics without artificial diffusion or undesired numerical effects when different density ratios are involved a collection of problems has been carefully selected such that a wide variety of froude numbers density ratios and dominant dissipative cases are reported with the intention of presenting a general methodology not restricted to a particular range of parameters and capable of using large time steps the results of the different free surface problems solved which include rayleigh taylor instability sloshing problems viscous standing waves and the dam break problem are compared to well validated numerical alternatives or experimental measurements obtaining accurate approximations for such complex flows

a multi level non linear multi objective decision making under fuzziness this paper studies a three level non linear multi objective decision making tln modm problem with linear or non linear constraints and in which the objective function at every level are non linear functions which are to be maximized this paper makes an extension work of abo sinna j operat res soc india opsearch 38 5 2001 484 495 which deal with a bi level non linear multi objective decision making problem under fuzziness the three level programming tlp problem whether from the stand point of the three planner stackelberg behavior or from the interactive organizational behavior is a very practical problem and encountered frequently in actual practice this paper proposes a three planner multi objective decision making model and solution method for solving this problem this method uses the concepts of tolerance membership function and multi objective optimization at each level to develop a fuzzy max min decision model for generating pareto optimal satisfactory solution for tln modm problem the first level decision maker fldm specifies his her objective functions and decisions with possible tolerances which are described by membership functions of fuzzy set theory then the second level decision maker sldm specifies his her objective functions and decisions in the view of the fldm with possible tolerances which are described by membership functions of fuzzy set theory finally the third level decision maker tldm uses the preference information for the fldm and sldm to solves his her problem subject to the two upper level decision makers restrictions an illustrative numerical example is given to demonstrate the obtained results

stackelberg solutions for fuzzy random two level linear programming through probability maximization with possibility this paper considers stackelberg solutions for decision making problems in hierarchical organizations under fuzzy random environments taking into account vagueness of judgments of decision makers fuzzy goals are introduced into the formulated fuzzy random two level linear programming problems on the basis of the possibility and necessity measures that each objective function fulfills the corresponding fuzzy goal together with the introduction of probability maximization criterion in stochastic programming we propose new two level fuzzy random decision making models which maximize the probabilities that the degrees of possibility and necessity are greater than or equal to certain values through the proposed models it is shown that the original two level linear programming problems with fuzzy random variables can be transformed into deterministic two level linear fractional programming problems for the transformed problems extended concepts of stackelberg solutions are defined and computational methods are also presented a numerical example is provided to illustrate the proposed methods

control landscapes for open system quantum operations the reliable realization of control operations is a key component of quantum information applications in practice meeting this goal is very demanding for open quantum systems this paper investigates the landscape defined as the fidelity j between the desired and achieved quantum operations with an open system the goal is to maximize j as a functional of the control variables we specify the complete set of critical points of the landscape function in the so called kinematic picture an associated hessian analysis of the landscape reveals that upon the satisfaction of a particular controllability criterion the critical topology is dependent on the particular environment but no false traps i e suboptimal solutions exist thus a gradient type search algorithm should not be hindered in searching for the ultimate optimal solution with such controllable systems moreover the maximal fidelity is proven to coincide with uhlmann s fidelity between the environmental initial states associated with the achieved and desired quantum operations which provides a generalization of uhlmann s theorem in terms of kraus maps

a fuzzy approach for bi level integer non linear programming problem abstract bi level programming a tool for modeling decentralized decisions consists of the objective of the leader at its first level and that is of the follower at the second level integer programming deals with the mathematical programming problems in which some or all the variables are to be integer this paper studies a bi level integer non linear programming problem with linear or non linear constraints and in which the non linear objective function at each level are to maximized the bi level integer non linear programming bli nlp problem can be thought as a static version of the stackelberg strategy which is used leader follower game in which a stackelberg strategy is used by the leader or the higher level decision maker hldm given the rational reaction of the follower or the lower level decision maker lldm this paper proposes a two planner integer model and a solution method for solving this problem this method uses the concept of tolerance membership function and the branch and bound technique to develop a fuzzy max min decision model for generating pareto optimal solution for this problem an illustrative numerical example is given to demonstrate the obtained results

on finding compromise solutions in multicriteria problems using the fuzzy min operator abstract this paper presents an application of fuzzy approaches to the linear vectormaximum problem it shows that using the fuzzy min operator together with linear as well as special nonlinear membership functions the obtained solutions are always compromise solutions of the original multicriteria problem

modelling practical lot sizing problems as mixed integer programs in spite of the remarkable improvements in the quality of general purpose mixed integer programming software the effective solution of a variety of lot sizing problems depends crucially on the development of tight formulations for the special problem features occurring in practice after reviewing some of the basic preprocessing techniques for handling safety stocks and multilevel problems we discuss a variety of aspects arising particularly in small and large bucket time period models such as start ups changeovers minimum batch sizes choice of one or two set ups per period etc a set of applications is described that contains one or more of these special features and some indicative computational results are presented finally to show another technique that is useful a slightly different supply chain application is presented for which the a priori addition of some simple mixed integer inequalities based on aggregation leads to important improvements in the results

elasto plastic analysis of reinforced soils using mesh free method in this paper the application of the mesh free method mfm for the elasto plastic analysis of reinforced soils is studied for the first time the applied mesh free method is called the radial point interpolation method rpim in mfm unlike the finite element method fem there is no need of mesh in the traditional sense and the shape functions are based on nodes in the present study the reinforced soil is divided into three separate parts of soil reinforcements and interface layers the displacement field in each part is constructed by rpim the final system of equations is derived by the substitution of the displacement field into the weak form of the governing equation the elasto plastic behaviors of soil reinforcements and interface layers are considered there is also the ability of slippage modeling between the soil and reinforcement based on the derived equations a computer code has been developed and its validity investigated by solving some examples at the end of the paper

the discontinuous galerkin material point method for variational hyperelastic plastic solids abstract the discontinuous galerkin material point method dgmpm presented in renaud et al 2018 14 is based on the discretization of a solid domain by means of particles in a background mesh owing to the employment of the discontinuous galerkin approximation on the grid the weak form of a hyperbolic system involves fluxes that are computed at cell interfaces by means of an approximate riemann solver combining these fluxes with the projection of the updated solution from the nodes to the particles originally used in the particle in cell method allows a significative reduction of the numerical oscillations that pollute the classical mpm solutions although the dgmpm exhibits very promising aspects such as the control of the time stepping renaud et al 2020 43 or the ability to locally increase the approximation order in an arbitrary grid the method first needs to be tested in its early version on problems involving a more complex wave content it is then proposed in this paper to couple the dgmpm with variational integrators of hyperelastic plastic constitutive models the genericity provided for dealing with rate independent or rate dependent plasticity as well as the possibility to easily extend the dgmpm to thermomechanical problems makes this class of integrators appealing the approach is here illustrated on numerical examples for which comparisons are shown with the finite element and the material point methods as well as a one dimensional exact solution in the linearized geometrical limit

a probabilistic bi level linear multi objective programming problem to supply chain planning abstract bi level programming a tool for modeling decentralized decisions consists of the objective s of the leader at its first level and that is of the follower at the second level three level programming results when second level is itself a bi level programming by extending this idea it is possible to define multi level programs with any number of levels in most of the real life problems in mathematical programming the parameters are considered as random variables the branch of mathematical programming which deals with the theory and methods for the solution of conditional extremum problems under incomplete information about the random parameters is called stochastic programming supply chain planning problems are concerned with synchronizing and optimizing multiple activities involved in the enterprise from the start of the process such as procurement of the raw materials through a series of process operations to the end such as distribution of the final product to customers enterprise wide supply chain planning problems naturally exhibit a multi level decision network structure where for example one level may correspond to a local plant control scheduling planning problem and another level to a corresponding plant wide planning network problem such a multi level decision network structure can be mathematically represented by using multi level programming principles in this paper we consider a probabilistic bi level linear multi objective programming problem and its application in enterprise wide supply chain planning problem where 1 market demand 2 production capacity of each plant and 3 resource available to all plants for each product are random variables and the constraints may consist of joint probability distributions or not this probabilistic model is first converted into an equivalent deterministic model in each level to which fuzzy programming technique is applied to solve the multi objective nonlinear programming problem to obtain a compromise solution

polyhedra for lot sizing with wagner whitin costs we examine the single item lot sizing problem with wagner whitin costs over ann period horizon i e pt ht pt 1 fort 1 n 1 wherept ht are the unit production and storage costs in periodt respectively so it always pays to produce as late as possible

linear programming extended formulations for the single item lot sizing problem with backlogging and constant capacity recently several authors 8 10 have argued for the use of extended formulations to tighten production planning models in this work we present two linear programming extended formulations of the constant capacity lot sizing problem with backlogging the first one applies to the problem with a general cost function and has o n3 variables and constraints this improves on the more straightforward o n4 florian and klein 2 type formulation the second one applies when the costs satisfy the wagner whitin property but it has o n2 variables and o n3 constraints as a by product we positively answer an open question of miller and wolsey 4 about the tightness of an extended formulation for the continuous mixing set

control landscapes for observable preparation with open quantum systems a quantum control landscape is defined as the observable as a function al of the system control variables such landscapes were introduced to provide a basis to understand the increasing number of successful experiments controlling quantum dynamics phenomena this paper extends the concept to encompass the broader context of the environment having an influence for the case that the open system dynamics are fully controllable it is shown that the control landscape for open systems can be lifted to the analysis of an equivalent auxiliary landscape of a closed composite system that contains the environmental interactions this inherent connection can be analyzed to provide relevant information about the topology of the original open system landscape application to the optimization of an observable expectation value reveals the same landscape simplicity observed in former studies on closed systems in particular no false suboptimal traps exist in the system control landscape when seeking to optimize an observable even in the presence of complex environments moreover a quantitative study of the control landscape of a system interacting with a thermal environment shows that the enhanced controllability attainable with open dynamics significantly broadens the range of the achievable observable values over the control landscape

feedback control of quantum state reduction feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement we formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for the filter we explore the use of stochastic lyapunov techniques for the design of feedback controllers for quantum spin systems and demonstrate the possibility of stabilizing one outcome of a quantum measurement with unit probability

axisymmetric form of the material point method with applications to upsetting and taylor impact problems abstract the material point method is an evolution of particle in cell methods which utilize two meshes one a material or lagrangian mesh defined over material of the body under consideration and the second a spatial or eulerian mesh defined over the computational domain although meshes are used they have none of the negative aspects normally associated with conventional eulerian or lagrangian approaches the advantages of both the eulerian and lagrangian methods are achieved by using the appropriate frame for each aspect of the computation with a mapping between the two meshes that is performed at each step in the loading process the numerical dissipation normally displayed by an eulerian method because of advection is avoided by using a lagrangian step the mesh distortion associated with the lagrangian method is prevented by mapping to a user controlled mesh furthermore explicit material points can be tracked through the process of deformation thereby alleviating the need to map history variables as a consequence problems which have caused severe numerical difficulties with conventional methods are handled fairly routinely examples of such problems are the upsetting of billets and the taylor problem of cylinders impacting a rigid wall numerical solutions to these problems are obtained with the material point method and where possible comparisons with experimental data and existing numerical solutions are presented

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

solving mixed integer programming problems using automatic reformulation in this paper we describe computational experience in solving mixed 0 1 programming problems using strong valid inequalities as cutting planes in particular we report on the solution to optimality of 18 medium to large size problems including production planning problems with setup costs and capacity constraints multilevel distribution planning problems drainage and heating system design problems and electricity generator scheduling problems the solution approach uses the theory of strong valid inequalities that we developed in a series of earlier papers here we report specifically on the implementation of an experimental system mpsarx which consists of the sciconic mathematical programming system and an automatic reformulation executor arx that use this theory and on the results obtained with this system

the material point method in large strain engineering problems abstract the material point method is a variant of the finite element method formulated in an arbitrary lagrangian eulerian description of motion two kinds of spatial discretization are utilized in the method the motion of material points representing subregions of the analysed continuum is traced against a background of the computational element mesh the mesh can be chosen arbitrarily so that the main disadvantage of the finite element method related to mesh distortion is avoided application of the method to some large strain industrial problems as granular flow in a silo as well as geomechanical and plastic forming problems are shown

interactive random fuzzy two level programming through possibility based probability model this paper considers interactive decision making methods for random fuzzy two level linear programming problems assuming that the decision makers concern about the probabilities that their own objective function values are smaller than or equal to certain target values fuzzy goals of the decision makers for the probabilities are introduced then the possibility based probability model to maximize the degrees of possibility with respect to the attained probability is considered interactive fuzzy nonlinear programming to obtain 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 demonstrates the feasibility and efficiency of the proposed method

characterization of the critical sets of quantum unitary control landscapes this work considers various families of quantum control landscapes i e objective functions for optimal control for obtaining target unitary transformations as the general solution of the controlled schrodinger equation we examine the critical point structure of the kinematic landscapes j f u u w a 2 and j p u a 4 tr aa w u 2 defined on the unitary group u h of a finite dimensional hilbert space h the parameter operator a e h is allowed to be completely arbitrary yielding an objective function that measures the difference in the actions of u and the target w on a subspace of state space namely the column space of a the analysis of this function includes a description of the structure of the critical sets of these kinematic landscapes and characterization of the critical points as maxima minima and saddles in addition we consider the question of whether these landscapes are morse bott functions on u h landscapes based on the intrinsic geodesic distance on u h and the projective unitary group pu h are also considered these results are then used to deduce properties of the critical set of the corresponding dynamical landscapes

improved convected particle domain interpolation method for coupled dynamic analysis of fully saturated porous media involving large deformation abstract based on the u p form governing equations and the convected particle domain interpolation technique the improved convected particle domain interpolation based material point method ccpdi is developed in this paper for the coupled dynamic and contact analysis of fully saturated porous media involving large deformation the numerical artifact noises due to material points crossing computational grid boundaries that usually occur in large deformation are eliminated by using the smoother interpolation functions presented in the convected particle domain interpolation technique the discrete equations are derived in the framework of the generalized interpolation material point method the boundary load tracking algorithm and a modified contact algorithm are proposed based on the definition of particle domains to apply accurately the surface loads on the motive boundaries and to capture correctly the contact time behaviors in large deformation problems respectively simulations of several representative one and two dimensional problems are presented to demonstrate the accuracy and effectiveness of the proposed methods compared to those obtained by using the coupling material point method and or finite element method the simulation results illustrate that the proposed ccpdi method can be successfully used in simulating the large deformation coupled dynamic responses of the solid skeleton and fluid phase in fully saturated porous media and the large deformation impact between solid and saturated porous bodies

a viscoplastic approach to model the flow of granular solids the flow of granular solids within rigid walls is modeled using continuum mechanics the problem is represented as a viscoplastic flow in which the discontinuity function is taken as in previous works by gray and stiles while the flow rule is modeled by the von mises criterion the resulting model is incompressible and based on non associated viscoplasticity the apparent viscosity results in a non linear function of the second invariant of the symmetric rate of deformation tensor and of the pressure friction cohesion and fluidity of the granular model are taken into account the constitutive model has been implemented assuming steady state in which the granular material flows under a critical state incompressible behavior discretization of the problem has been carried out by finite elements with direct iteration techniques to solve the non linear system of equations the model has been applied to the massive flow of granular material stored in vertical silos and hoppers with axisymmetric or planar shape comparisons with experimental tests performed by other authors are presented together with parametric investigations to identify the main variables affecting the response

strange an interactive method for multi objective linear programming under uncertainty abstract in the field of investment planning within a time horizon problems typically involve multiple objectives and basic data are uncertain in a large number of cases these decision problems can be written as linear programming problems in which time dependent uncertainties affect the coefficients and the right hand side of constraints given the possibility of defining plausible scenarios on basic data discrete sets of such coefficients are given each with its subjective probability of occurrence the corresponding structure is then characteristic for multi objective stochastic linear programming moslp in the paper an interactive procedure is described to obtain a best compromise for such a moslp problem this algorithm called strange extends the stem method to take the random aspects into account it involves in particular the concepts of stochastic programming with recourse in its interactive steps the efficiency projection techniques are used to provide the decision maker with detailed graphical information on efficient solution families as an illustration of the successive steps a didactic example is solved in some detail and the results of a case study in energy planning are given

logic optimality for multi objective optimization pareto dominance is one of the most basic concepts in multi objective optimization however it is inefficient when the number of objectives is large because in this case it leads to an unmanageable number of pareto solutions in order to solve this problem a new concept of logic dominance is defined by considering the number of improved objectives and the quantity of improvement simultaneously where probabilistic logic is applied to measure the quantity of improvement based on logic dominance the corresponding logic nondominated solution is defined as a feasible solution which is not dominated by other ones based on this new relationship and it is proved that each logic nondominated solution is also a pareto solution essentially logic dominance is an extension of pareto dominance since there are already several extensions for pareto dominance some comparisons are given in terms of numerical examples which indicates that logic dominance is more efficient as an application of logic dominance a house choice problem with five objectives is considered

optimization search effort over the control landscapes for open quantum systems with kraus map evolution a quantum control landscape is defined as the expectation value of a target observable as a function of the control variables in this work control landscapes for open quantum systems governed by kraus map evolution are analyzed kraus maps are used as the controls transforming an initial density matrix i into a final density matrix to maximize the expectation value of the observable the absence of suboptimal local maxima for the relevant control landscapes is numerically illustrated the dependence of the optimization search effort is analyzed in terms of the dimension of the system n the initial state i and the target observable it is found that if the number of nonzero eigenvalues in i remains constant the search effort does not exhibit any significant dependence on n if i has no zero eigenvalues then the computational complexity and the required search effort rise with n the dimension of the top manifold i e the set of kraus operators that maximizes the objective is found to positively correlate with the optimization search efficiency under the assumption of full controllability incoherent control modeled by kraus maps is found to be more efficient in reaching the same value of the objective than coherent control modeled by unitary maps numerical simulations are also performed for control landscapes with linear constraints on the available kraus maps and suboptimal maxima are not revealed for these landscapes

an energy consistent material point method for dynamic finite deformation plasticity energy consistency for the material point method mpm is examined for thermodynamically consistent hyperelastic plastic materials it is shown that mpm can be formulated with implicit three field variational finite element algorithms which dissipate energy and conserve momentum for that class of material models with a consistent mass matrix the resulting overall numerical method inherits the energy dissipative and momentum conserving properties of the mesh solution thus the proposed mpm algorithm satisfies by construction a time discrete form of the second law of thermodynamics properties of the method are illustrated in numerical examples

a stabilized finite point method for analysis of fluid mechanics problems in this paper a meshless procedure termed the finite point method for solving convection diffusion and fluid flow type problems is presented the method is based on the use of a weighted least square interpolation procedure together with point collocation for evaluating the approximation integrals special emphasis is given to the stabilization of the convective terms and the neumann boundary condition which has been found to be essential to obtain accurate results some examples of application to diffusive and convective transport and compressible flow problems using quadratic fp interpolations are presented

projections of the capacitated network loading problem abstract consider an undirected network and a set of commodities with specified demands between various pairs of nodes of the network given two types of capacitated facilities that can be installed loaded for arc dependent costs we have to determine the integer number of facilities to load on each arc in order to send the required flow of all commodities at minimum total cost we present a natural mixed integer programming formulation of the problem and then consider its single commodity and multicommodity versions we develop equivalent formulations in a lower dimensional space by projecting out the flow variables and study the polyhedral properties of the corresponding projection cones our results strengthen an existing result for multicommodity flow problems we also characterize several classes of facet defining inequalities for this lower dimensional polyhedron and conclude by identifying some open problems and future research directions

an algorithm based on particle swarm optimization for multiobjective bilevel linear problems improved mopso for multiobjective at the upper level bilevel linear problems a hybrid scheme for the selection of the global best particles is proposed an adaptive mutation is also introduced the incorporation of these mechanisms led to significantly better results this paper presents an improved multiple objective particle swarm optimization mopso algorithm to solve bilevel linear programming problems with multiple objective functions at the upper level the algorithm aims to produce a good approximation of the entire pareto front of the problem we have previously designed a mopso algorithm for the same class of problems in which several techniques for the global best selection were tested including a new one the algorithm revealed a good convergence towards the pareto front but the diversity of the solutions was a drawback the algorithm we propose herein uses a hybrid strategy for the global best selection and an adaptive mutation operator the incorporation of these mechanisms led to an improved algorithm which also showed better overall performance than considering alternative options usually employed in mopso algorithms the algorithm and computational results are presented

solving multi item capacitated lot sizing problems using variable redefinition mixed integer programming models are typically not used to solve realistic sized production scheduling problems because they require exorbitant solution times we impose a useful taxonomy on production scheduling problems and develop alternative formulations for a wide variety of problems within the taxonomy the linear programming relaxation of the new models is very effective in generating bounds we show that these bounds are equal to those that could be generated using lagrangian relaxation or column generation the linear programming bounds increase in effectiveness as the problems become larger perhaps of greatest significance is that practitioners can obtain our results using only standard off the shelf codes such as lindo or mpsx 370 we report computational experience in several computing environments hardware and software on problems with up to 200 products and 10 time periods 2000 0 1 variables