an efficient hybrid multi objective particle swarm optimization with a multi objective dichotomy line search recently more research works are focused on multi objective particle swarm optimization algorithm mopso due to its ability of global and local search for solving multi objective optimization problems moops however most of existing mopsos cannot achieve satisfactory results in solution quality this paper proposes an efficient hybrid multi objective particle swarm optimization with a multi objective dichotomy line search mols named mols mopso to deal with such problem mols mopso combines an effective particle updating strategy with the local search of mols the effective particle updating strategy is used for global search to deal with premature convergence and diversity maintenance within the swarm the mols is periodically activated for fast local search to converge toward the pareto front the exploratory capabilities are enhanced more efficiently by keeping a desirable balance between global search and local search so as to ensure sufficient diversity and well distribution amongst the solutions of the non dominated fronts while retaining at the same time the convergence to the pareto optimal front comparing mols mopso with various state of the art multi objective optimization algorithms developed recently the comparative study shows the effectiveness of mols mopso which not only assures a better convergence to the pareto frontier but also illustrates a good diversity and distribution of solutions

simultaneous primal dual right hand side sensitivity analysis from a strictly complementary solution of a linear program this paper establishes theorems about the simultaneous variation of right hand sides and cost coefficients in a linear program from a strictly complementary solution some results are extensions of those that have been proven for varying the right hand side of the primal or the dual but not both other results are new in addition changes in the optimal partition and what that means in economic terms are related to the basis driven approach notably to the theory of compatibility in addition to new theorems about this relation the transition graph is extended to provide another visualization of the underlying economics

an improved strength pareto evolutionary algorithm 2 with application to the optimization of distributed generations this paper presents an improved strength pareto evolutionary algorithm 2 ispea2 which introduces a penalty factor in objective function constraints uses adaptive crossover and a mutation operator in the evolutionary process and combines simulated annealing iterative process over spea2 the testing result of ispea2 by authoritative testing functions meets the requirement of petro optimum fronts the case study result shows that the proposed algorithm provides a rapid convergence in obtaining pareto optimal solutions during the calculation process of evolution based on the fuzzy set theory ispea2 is able to solve the multi objective problems in the ieee 33 bus system and its validity and practicality are demonstrated by the utilization on dg s economic dispatch and optimal operation in the field of power industry

inventory model with fuzzy lead time and dynamic demand over finite time horizon using a multi objective genetic algorithm the real world inventory control problems are normally imprecisely defined and human interventions are often required in solving these decision making problems in this paper a realistic inventory problem with an infinite rate of replenishment over a prescribed finite but imprecise time horizon is formulated considering time dependent ramp type demand which increases with time lead time is also assumed as fuzzy in nature shortages are allowed and backlogged partially two models are considered depending upon the ordering policies of the decision maker dm the imprecise parameters are first transformed to corresponding nearest interval numbers depending upon some distance metric on fuzzy numbers and then following the interval mathematics the objective function for total profit from the planning horizon is obtained which is an interval function then interval objective decision making problem is reduced to multi objective problems using different approaches finally a fast and elitist multi objective genetic algorithm femoga is used for solving these multi objective models to find pareto optimal decisions for the dm the models are illustrated numerically as a particular case the results due to linear trended and constant demands have been presented

on the performance of exponential integrators for problems in magnetohydrodynamics exponential integrators have been introduced as an efficient alternative to explicit and implicit methods for integrating large stiff systems of differential equations over the past decades these methods have been studied theoretically and their performance was evaluated using a range of test problems while the results of these investigations showed that exponential integrators can provide significant computational savings the research on validating this hypothesis for large scale systems and understanding what classes of problems can particularly benefit from the use of the new techniques is in its initial stages resistive magnetohydrodynamic mhd modeling is widely used in studying large scale behavior of laboratory and astrophysical plasmas in many problems numerical solution of mhd equations is a challenging task due to the temporal stiffness of this system in the parameter regimes of interest in this paper we evaluate the performance of exponential integrators on large mhd problems and compare them to a state of the art implicit time integrator both the variable and constant time step exponential methods of epirk type are used to simulate magnetic reconnection and the kevin helmholtz instability in plasma performance of these methods which are part of the epic software package is compared to the variable time step variable order bdf scheme included in the cvode part of sundials library we study performance of the methods on parallel architectures and with respect to magnitudes of important parameters such as reynolds lundquist and prandtl numbers we find that the exponential integrators provide superior or equal performance in most circumstances and conclude that further development of exponential methods for mhd problems is warranted and can lead to significant computational advantages for large scale stiff systems of differential equations such as mhd

convergence behavior of interior point algorithms we show that most interior point algorithms for linear programming generate a solution sequence in which every limit point satisfies the strict complementarity condition these algorithms include all path following algorithms and some potential reduction algorithms the result also holds for the monotone complementarity problem if a strict complementarity solution exists in general the limit point is a solution that maximizes the number of its nonzero components among all solutions

arbitrarily high order convected scheme solution of the vlasov poisson system abstract the convected scheme cs is a forward trajectory semi lagrangian method for solution of transport equations which has been most often applied to the kinetic description of plasmas and rarefied neutral gases in its simplest form the cs propagates the solution forward in time by advecting the so called moving cells along their characteristic trajectories and by remapping them on the mesh at the end of the time step the cs is conservative positivity preserving simple to implement and it is not subject to time step restriction to maintain stability recently guclu and hitchon 2012 1 a new methodology was introduced for reducing numerical diffusion based on a modified equation analysis the remapping error was compensated by applying small corrections to the final position of the moving cells prior to remapping while the spatial accuracy was increased from 2nd to 4th order the new scheme retained the important properties of the original method and was shown to be extremely simple and efficient for constant advection problems here the cs is applied to the solution of the vlasov poisson system which describes the evolution of the velocity distribution function of a collection of charged particles subject to reciprocal coulomb interactions the vlasov equation is split into two constant advection equations one in configuration space and one in velocity space and high order time accuracy is achieved by proper composition of the operators the splitting procedure enables us to use the constant advection solver which we extend to arbitrarily high order of accuracy in time and space a new improved procedure is given which makes the calculation of the corrections straightforward focusing on periodic domains we describe a spectrally accurate scheme based on the fast fourier transform the proposed implementation is strictly conservative and positivity preserving the ability to correctly reproduce the system dynamics as well as resolving small scale features in the solution is shown in classical 1d 1v test cases both in the linear and the non linear regimes

a splitting approach for the magnetic schrodinger equation the schrodinger equation in the presence of an external electromagnetic field is an important problem in computational quantum mechanics it also provides a nice example of a differential equation whose flow can be split with benefit into three parts after presenting a splitting approach for three operators with two of them being unbounded we exemplarily prove first order convergence of lie splitting in this framework the result is then applied to the magnetic schrodinger equation which is split into its potential kinetic and advective parts the latter requires special treatment in order not to lose the conservation properties of the scheme we discuss several options numerical examples in one two and three space dimensions show that the method of characteristics coupled with a nonequispaced fast fourier transform nfft provides a fast and reliable technique for achieving mass conservation at the discrete level

an exponential type integrator for the kdv equation we introduce an exponential type time integrator for the kdv equation and prove its first order convergence in h 1 for initial data in h 3 furthermore we outline the generalization of the presented technique to a second order method

on the error propagation of semi lagrange and fourier methods for advection problems in this paper we study the error propagation of numerical schemes for the advection equation in the case where high precision is desired the numerical methods considered are based on the fast fourier transform polynomial interpolation semi lagrangian methods using a lagrange or spline interpolation and a discontinuous galerkin semi lagrangian approach which is conservative and has to store more than a single value per cell we demonstrate by carrying out numerical experiments that the worst case error estimates given in the literature provide a good explanation for the error propagation of the interpolation based semi lagrangian methods for the discontinuous galerkin semi lagrangian method however we find that the characteristic property of semi lagrangian error estimates namely the fact that the error increases proportionally to the number of time steps is not observed we provide an explanation for this behavior and conduct numerical simulations that corroborate the different qualitative features of the error in the two respective types of semi lagrangian methods the method based on the fast fourier transform is exact but due to round off errors susceptible to a linear increase of the error in the number of time steps we show how to modify the cooley tukey algorithm in order to obtain an error growth that is proportional to the square root of the number of time steps finally we show for a simple model that our conclusions hold true if the advection solver is used as part of a splitting scheme

generalized integrating factor methods for stiff pdes the integrating factor if method for numerical integration of stiff nonlinear pdes has the disadvantage of producing large error coefficients when the linear term has large norm we propose a generalization of the if method and in particular construct multistep type methods with several orders of magnitude improved accuracy we also consider exponential time differencing etd methods and point out connections with a particular application of the commutator free lie group methods we present a new fourth order etdrk method with improved accuracy the methods considered are compared in several numerical examples

a finite element code for the simulation of one dimensional vlasov plasmas i theory abstract the galerkin method is used to obtain a finite element solution to the vlasov poisson equations over the two dimensional x v phase plane using bilinear element shape functions a set of linear equations for updated values of the distribution function is obtained in which time dependent and time independent coefficients are separated to reduce the computation involved the noise levels are low and the energy conservation good the finite element approach offers certain advantages over alternative methods in applications to problems in plasma physics in particular the flexibility in using elements of different size allows problems in which regions of the plasma are characterized by often widely differing scale lengths to be treated efficiently

a novel strategy of pareto optimal solution searching in multi objective particle swarm optimization mopso in multi objective particle swarm optimization mopso algorithms finding the global optimal particle gbest for each particle of the swarm from a set of non dominated solutions is very difficult yet an important problem for attaining convergence and diversity of solutions first a new pareto optimal solution searching algorithm for finding the gbest in mopso is introduced in this paper which can compromise global and local searching based on the process of evolution the algorithm is implemented and is compared with another algorithm which uses the sigma method for finding gbest on a set of well designed test functions finally the multi objective optimal regulation of cascade reservoirs is successfully solved by the proposed algorithm

fourth order symplectic integration abstract in this paper we present an explicit fourth order method for the integration of hamilton s equations this method preserves the property that the time evolution of such a system yields a canonical transformation from the initial conditions to the final state that is the integration step is an explicit symplectic map although the result is first derived for a specific type of hamiltonian it is shown to be quite general in particular the results can be applied to any lie group

exponential time differencing for stiff systems we develop a class of numerical methods for stiff systems based on the method of exponential time differencing we describe schemes with second and higher order accuracy introduce new runge kutta versions of these schemes and extend the method to show how it may be applied to systems whose linear part is nondiagonal we test the method against other common schemes including integrating factor and linearly implicit methods and show how it is more accurate in a number of applications we apply the method to both dissipative and dispersive partial differential equations after illustrating its behavior using forced ordinary differential equations with stiff linear parts

simultaneous data perturbations and analytic center convergence the central path is an infinitely smooth parameterization of the nonnegative real line and its convergence properties have been investigated since the mid 1980s however the central path followed by an infeasible interior point method relies on three parameters instead of one and hence is a surface instead of a path the additional parameters are included to allow for simultaneous perturbations in the cost vectors and right hand side vectors this paper provides a detailed analysis of the perturbed central path that is followed by infeasible interior point methods and we characterize when such a path converges we develop a set hausdorff convergence property and show that the central paths impose an equivalence relation on the set of admissible cost vectors we conclude with a technique to test for convergence under arbitrary simultaneous data perturbations

highly accurate lagrangian flux calculation via algebraic quadratures on spline approximated donating regions abstract lagrangian flux through a fixed curve segment within a time interval t n t n k can be formulated as an integral at the initial time t n over a compact point set called donating region in which each particle will pass through the curve during the time interval and contribute to the flux based an explicit constructive and analytical solution of the donating region the author proposes algorithms of lagrangian flux calculation lfc as algebraic quadratures over the spline approximated donating regions this generic formulation yields high accuracies up to the 8th order both in time and space as another benefit lfc leads to a conservative semi lagrangian method whose time step size is free of the eulerian stability constraint c r 1 the high accuracy and robustness of the proposed lfc algorithms are demonstrated by various numerical tests with courant numbers ranging from 1 to 10 000 and with accuracies from the 2nd order to the 8th order lfc might also be useful in designing hybrid eulerian methods for complex geometries

sensitivity analysis in linear semi infinite programming perturbing cost and right hand side coefficients this paper analyzes the effect on the optimal value of a given linear semi infinite programming problem of the kind of perturbations which more frequently arise in practical applications those which affect the objective function and the right hand side coefficients of the constraints in particular we give formulae which express the exact value of a perturbed problem as a linear function of the perturbation

fourth order time stepping for kadomtsev petviashvili and davey stewartson equations purely dispersive partial differential equations such as the korteweg de vries equation the nonlinear schrodinger equation and higher dimensional generalizations thereof can have solutions which develop a zone of rapid modulated oscillations in the region where the corresponding dispersionless equations have shocks or blow up to numerically study such phenomena fourth order time stepping in combination with spectral methods is beneficial in resolving the steep gradients in the oscillatory region we compare the performance of several fourth order methods for the kadomtsev petviashvili and the davey stewartson equations two integrable equations in 2 1 dimensions these methods are exponential time differencing integrating factors time splitting implicit runge kutta and driscoll s composite runge kutta method the accuracy in the numerical conservation of integrals of motion is discussed

an efficient solution to multi objective control problems with lmi objectives we revisit a technique for solving multi objective control problems through affinely parameterizing the closed loop system with the youla parameterization and confining the search of the youla parameter to finite dimensional subspaces it is pretty well known how to solve such problems if the closed loop specifications are formulated in terms of the solvability of linear matrix inequalities however all approaches proposed so far suffer from a substantial inflation of size of the resulting optimization problems if improving the approximation accuracy on the basis of a novel state space approach to solving static output feedback control problems by convex optimization for a specific class of plants we reveal how the growth of the size of the optimization problems can be considerably reduced to arrive at more efficient algorithms as an additional ingredient we discuss how to use the so called mixed controller as a starting point for a genuine multi objective design in order to improve the algorithms

conservative semi lagrangian schemes for vlasov equations conservative methods for the numerical solution of the vlasov equation are developed in the context of the one dimensional splitting in the case of constant advection these methods and the traditional semi lagrangian ones are proven to be equivalent but the conservative methods offer the possibility to add adequate filters in order to ensure the positivity in the non constant advection case they present an alternative to the traditional semi lagrangian schemes which can suffer from bad mass conservation in this time splitting setting

adaptive multiresolution semi lagrangian discontinuous galerkin methods for the vlasov equations we develop adaptive numerical schemes for the vlasov equation by combining discontinuous galerkin discretisation multiresolution analysis and semi lagrangian time integration we implement a tree based structure in order to achieve adaptivity both multi wavelets and discontinuous galerkin rely on a local polynomial basis the schemes are tested and validated using vlasov poisson equations for plasma physics and astrophysics

a split step fourier discontinuous galerkin scheme for the kadomtsev petviashvili equation abstract in this paper we propose a method to solve the kadomtsev petviashvili equation based on splitting the linear part of the equation from the nonlinear part the linear part is treated using ffts while the nonlinear part is approximated using a semi lagrangian discontinuous galerkin approach of arbitrary order we demonstrate the efficiency and accuracy of the numerical method by providing a range of numerical simulations in particular we find that our approach can outperform the numerical methods considered in the literature by up to a factor of five although we focus on the kadomtsev petviashvili equation in this paper the proposed numerical scheme can be extended to a range of related models as well

research on quality performance conceptual design based on spea2 in order to solve the multi objective performance optimal problems spea2 is used to realize the performance design of injection molding machine the optimization objectives are constructed to maximize mould control power maximize injection quantity and minimize injection power the mathematical model is found to optimize the problem a solution is extracted to eliminate the imprecise nature of preference through the pareto optimal set based on fuzzy set theory compared with nsga ii and spea2 spea2 could acquire the pareto front with better distribution and smaller distance with the optimum solutions finally the case illustration of htg1000x3y injection molding machine is taken as an example to demonstrate that such method is effective and practical effective references could be provided to decision makers for objectives tradeoff at the performance conceptual design stage of injection molding machine

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

sensitivity analysis in linear semi infinite programming via partitions this paper provides sufficient conditions for the optimal value function of a given linear semi infinite programming lsip problem to depend linearly on the size of the perturbations when these perturbations involve either the cost coefficients or the right hand side function or both and they are sufficiently small two kinds of partitions are considered the first concerns the effective domain of the optimal value as a function of the cost coefficients and consists of maximal regions on which this value function is linear the second class of partitions considered in this paper concerns the index set of the constraints through a suitable extension of the concept of optimal partition from ordinary to lsip these partitions provide convex sets in particular segments on which the optimal value is a linear function of the size of the perturbations for the three types of perturbations considered in this paper

a semi lagrangian discontinuous galerkin method for scalar advection by incompressible flows a new conservative semi lagrangian formulation is proposed for the discretization of the scalar advection equation in flux form the approach combines the accuracy and conservation properties of the discontinuous galerkin dg method with the computational efficiency and robustness of semi lagrangian sl techniques unconditional stability in the von neumann sense is proved for the proposed discretization in the one dimensional case a monotonization technique is then introduced based on the flux corrected transport approach this yields a multi dimensional monotonic scheme for the piecewise constant component of the computed solution that is characterized by a smaller amount of numerical diffusion than standard dg methods the accuracy and stability of the method are further demonstrated by two dimensional tracer advection tests in the case of incompressible flows the comparison with results obtained by standard sl and dg methods highlights several advantages of the new technique

a particle in cell method for the simulation of plasmas based on an unconditionally stable field solver abstract we propose a new particle in cell pic method for the simulation of plasmas based on a recently developed unconditionally stable solver for the wave equation this method is not subject to a cfl restriction limiting the ratio of the time step size to the spatial step size typical of explicit methods while maintaining computational cost and code complexity comparable to such explicit schemes we describe the implementation in one and two dimensions for both electrostatic and electromagnetic cases and present the results of several standard test problems showing good agreement with theory with time step sizes much larger than allowed by typical cfl restrictions

a positivity preserving high order semi lagrangian discontinuous galerkin scheme for the vlasov poisson equations the vlasov poisson equations describe the evolution of a collisionless plasma represented through a probability density function pdf that self interacts via an electrostatic force one of the main difficulties in numerically solving this system is the severe time step restriction that arises from parts of the pdf associated with moderate to large velocities the dominant approach in the plasma physics community for removing these time step restrictions is the so called particle in cell pic method which discretizes the distribution function into a set of macro particles while the electric field is represented on a mesh several alternatives to this approach exist including fully lagrangian fully eulerian and so called semi lagrangian methods the focus of this work is the semi lagrangian approach which begins with a grid based eulerian representation of both the pdf and the electric field then evolves the pdf via lagrangian dynamics and finally projects this evolved field back onto the original eulerian mesh in particular we develop in this work a method that discretizes the 1 1 vlasov poisson system via a high order discontinuous galerkin dg method in phase space and an operator split semi lagrangian method in time second order accuracy in time is relatively easy to achieve via strang operator splitting with additional work using higher order splitting and a higher order method of characteristics we also demonstrate how to push this scheme to fourth order accuracy in time we show how to resolve all of the lagrangian dynamics in such a way that mass is exactly conserved positivity is maintained and high order accuracy is achieved the poisson equation is solved to high order via the smallest stencil local discontinuous galerkin ldg approach we test the proposed scheme on several standard test cases

an interior point approach to sensitivity analysis in degenerate linear programs we consider an interior point approach to sensitivity analysis in linear programming developed by the authors we investigate the quality of the interior point bounds under degeneracy in the case of a special type of degeneracy we show that these bounds have the same nice asymptotic relationship with the optimal partition bounds as in the nondegenerate case we prove a weaker relationship for general degenerate linear programs

convergence analysis of a discontinuous galerkin strang splitting approximation for the vlasov poisson equations a rigorous convergence analysis of the strang splitting algorithm with a discontinuous galerkin approximation in space for the vlasov poisson equations is provided it is shown that under suitable assumptions the error is of order mathcal o tau 2 h q h q tau where tau is the size of a time step h is the cell size and q the order of the discontinuous galerkin approximation in order to investigate the recurrence phenomena for approximations of higher order as well as to compare the algorithm with numerical results already available in the literature a number of numerical simulations are performed

product platform two stage quality optimization design based on multiobjective genetic algorithm product platform design pfd has been recognized as an effective means to satisfy diverse market niches while maintaining the economies of scale and scope numerous optimization based approaches have been proposed to help resolve the tradeoff between platform commonality and the ability to achieve distinct performance targets for each variant in this study we propose a two stage multiobjective optimization based platform design methodology tmopdm for solving the product family problem using a multiobjective genetic algorithm in the first stage the common product platform is identified using a nondominated sorting genetic algorithm ii nsga ii in the second stage each individual product is designed around the common platform such that the functional requirements of the product are best satisfied the design of a family of traction machine is used as an example to benchmark the effectiveness of the proposed approach against previous approachs

on the dimension of the set of rim perturbations for optimal partition invariance two new dimension results are presented for linear programs it is shown that the sum of the dimension of the optimal set and the dimension of the set of objective perturbations for which the optimal partition is invariant equals the number of variables a decoupling principle shows that the primal and dual results are additive the main result is then extended to convex quadratic programs but the dimension relationships are no longer dependent only on problem size furthermore although the decoupling principle does not extend completely the dimensions are additive as in the linear case

short term scheduling of cascade reservoirs using an immune algorithm based particle swarm optimization this paper presents a new approach for short term hydropower scheduling of reservoirs using an immune algorithm based particle swarm optimization ia pso ia pso is employed by coupling the immune information processing mechanism with the particle swarm optimization algorithm in order to achieve a better global solution with less computational effort with the ia pso technique the hydro electrical optimization model of reservoirs is formulated as a high dimensional dynamic nonlinear and stochastic global optimization problem of a multi reservoir hydropower system the purpose of the proposed methodology is to maximize total hydropower production here it is applied to a reservoir system on the qingjiang river in the yangtze watershed that consists of two reservoirs the results are compared with the results obtained through conventional operation method the dynamic programming and the standard pso algorithm from the comparative results it is found that the ia pso approach provides the most globally optimum solution at a faster convergence speed

a splitting approach for the kadomtsev petviashvili equation we consider a splitting approach for the kadomtsev petviashvili equation with periodic boundary conditions and show that the necessary interpolation procedure can be efficiently implemented the error made by this numerical scheme is compared to exponential integrators which have been shown in klein and roidot 2011 2 to perform best for stiff solutions of the kadomtsev petviashvili equation since many classic high order splitting methods do not perform well we propose a stable extrapolation method in order to construct an efficient numerical scheme of order four in addition the conservation properties and the possibility of order reduction for certain initial values for the numerical schemes under consideration are investigated