conformal mapping based coordinate generation method for flows in periodic configurations abstract a conformal mapping based coordinate generation method for periodic configurations has been developed a channel of an arbitrary shape in the physical plane representing internal configurations is mapped into a straight channel in the computational plane and a wall of an arbitrary shape in the physical plane representing external configurations is mapped into a straight wall in the computational plane the parameters of the transformations have to be determined through a method of successive approximations a simple iteration scheme that converges quite rapidly even with a poor initial guess is presented solutions for different configurations are displayed to illustrate the capabilities of the method

location routing issues models and methods this paper is a survey of location routing a relatively new branch of locational analysis that takes into account vehicle routing aspects we propose a classification scheme and look at a number of problem variants both exact and heuristic algorithms are investigated finally some suggestions for future research are presented

numerical computation of the capacity of generalized condensers abstract we present a boundary integral method for numerical computation of the capacity of generalized condensers the presented method applies to a wide variety of generalized condenser geometry including the cases when the plates of the generalized condenser are bordered by piecewise smooth jordan curves or are rectilinear slits the presented method is used also to compute the harmonic measure in multiply connected domains

the numerical solution of the biharmonic equation by conformal mapping the solution to the biharmonic equation in a simply connected region omega in the plane is computed in terms of the goursat functions the boundary conditions are conformally transplanted to the disk with a numerical conformal map a linear system is obtained for the taylor coefficients of the goursat functions the coefficient matrix of the linear system can be put in the form i k where k is the discretization of a compact operator k can be thought of as the composition of a block hankel matrix with a diagonal matrix the compactness leads to clustering of eigenvalues and the hankel structure yields a matrix vector multiplication cost of o n log n thus if the conjugate gradient method is applied to the system then superlinear convergence will be obtained numerical results are given to illustrate the spectrum clustering and superlinear convergence

variable neighborhood search principles and applications abstract systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization called variable neighborhood search vns we present a basic scheme for this purpose which can easily be implemented using any local search algorithm as a subroutine its effectiveness is illustrated by solving several classical combinatorial or global optimization problems moreover several extensions are proposed for solving large problem instances using vns within the successive approximation method yields a two level vns called variable neighborhood decomposition search vnds modifying the basic scheme to explore easily valleys far from the incumbent solution yields an efficient skewed vns svns heuristic finally we show how to stabilize column generation algorithms with help of vns and discuss various ways to use vns in graph theory i e to suggest disprove or give hints on how to prove conjectures an area where metaheuristics do not appear to have been applied before

a unified solution framework for multi attribute vehicle routing problems vehicle routing attributes are extra characteristics and decisions that complement the academic problem formulations and aim to properly account for real life application needs hundreds of methods have been introduced in recent years for specific attributes but the development of a single general purpose algorithm which is both efficient and applicable to a wide family of variants remains a considerable challenge yet such a development is critical for understanding the proper impact of attributes on resolution approaches and to answer the needs of actual applications this paper contributes towards addressing these challenges with a component based design for heuristics targeting multi attribute vehicle routing problems and an efficient general purpose solver the proposed unified hybrid genetic search metaheuristic relies on problem independent unified local search genetic operators and advanced diversity management methods problem specifics are confined to a limited part of the method and are addressed by means of assignment sequencing and route evaluation components which are automatically selected and adapted and provide the fundamental operators to manage attribute specificities extensive computational experiments on 29 prominent vehicle routing variants 42 benchmark instance sets and overall 1099 instances demonstrate the remarkable performance of the method which matches or outperforms the current state of the art problem tailored algorithms thus generality does not necessarily go against efficiency for these problem classes

a parallel multi neighborhood cooperative tabu search for capacitated vehicle routing problems abstract this paper presents a parallel tabu search algorithm that utilizes several different neighborhood structures for solving the capacitated vehicle routing problem single neighborhood or neighborhood combinations are encapsulated in tabu search threads and they cooperate through a solution pool for the purpose of exploiting their joint power the computational experiments on 32 large scale benchmark instances show that the proposed method is highly effective and competitive providing new best solutions to four instances while the average deviation of all best solutions found from the collective best results reported in the literature is about 0 22 we are also able to associate the beneficial use of special neighborhoods with some test instance characteristics and uncover some sources of the collective power of multi neighborhood cooperation

superlinear convergence estimates for a conjugate gradient method for the biharmonic equation the method of muskhelishvili for solving the biharmonic equation using conformal mapping is investigated in r h chan t k delillo and m a horn siam j sci comput 18 1997 pp 1571 1582 it was shown using the hankel structure that the linear system in n i muskhelishvili some basic problems of the mathematical theory of elasticity noordhoff groningen the netherlands is the discretization of the identity plus a compact operator and therefore the conjugate gradient method will converge superlinearly estimates are given here of the superlinear convergence in the cases when the boundary curve is analytic or in a holder class

elliptic integrals and the schwarz christoffel transformation abstract the real elliptic integrals of the first and second kind in jacobi s normal form are computed efficiently using the convolution number in conjunction with the method of frobenius for this purpose certain treatments of the laurent series are included different regions of convergence on the real axis are determined and for each one a different series is developed the real elliptic integral of the third kind is solved within a limited parameter plane by the same method the integral of the schwarz christoffel transformation is solved in the complex variable by complex convolution number algebra using the unit disk as mapping region different regions of convergence of frobenius laurent and taylor series are determined to cover the whole disk the complex evaluation of the elliptic integral of the third kind is included a schwarz christoffel formula for an infinite periodic mapping is given the solutions for exterior interior periodic and cyclic polygons are separately treated examples of several polygon mappings are presented graphically and compared with previous numerically integrated solutions the parameter problem is solved by the newton raphson method using a quotient matrix as approximation for the jacobian matrix the coordinate relations are simplified by using an overdetermined system an exact analytical jacobian matrix is computed solving leibniz derivative of the schwarz christoffel integral and results are compared with the approximate quotient matrix method

boundary fitted coordinate systems for numerical solution of partial differential equations a review a comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given some general mathematical framework and error analysis common to such coordinate systems is also included the general categories of generating systems are those based on conformal mapping orthogonal systems nearly orthogonal systems systems produced as the solution of elliptic and hyperbolic partial differential equations and systems generated algebraically by interpolation among the boundaries also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation dynamically adaptive coordinate systems coupled with the physical solution and time dependent systems that follow moving boundaries are treated references reporting experience using such coordinate systems are reviewed as well as those covering the system development

on the boundary integral formulation of the plane theory of elasticity with applications analytical aspects abstract a formulation of the plane strain problem of the theory of elasticity in stresses for simply connected domains is carried out in terms of real functions within the frame of what is known as the boundary integral method special attention is devoted to the problem of determination of the arbitrary constants appearing in the solution in view of work in progress where numerical techniques are used relying on some mathematical results formulated in the appendix simple applications concerning the first and the second fundamental problems for the circle and for the ellipse are given which show the correctness of the formulation and the necessity of recurring to numerical techniques once the geometry of the problem or the type of boundary conditions deviates from being simple following parts of the present work are devoted to the numerical treatment of the obtained system of equations as well as to the theories of thermoelasticity and thermo electromagneto elasticity

a hybrid evolutionary algorithm for the periodic location routing problem abstract the well known vehicle routing problem vrp has been studied in depth over the last decades nowadays generalizations of vrp have been developed for tactical or strategic decision levels of companies but not both the tactical extension or periodic vrp pvrp plans a set of trips over a multiperiod horizon subject to frequency constraints the strategic extension is motivated by interdependent depot location and routing decisions in most distribution systems low quality solutions are obtained if depots are located first regardless of the future routes in the location routing problem lrp location and routing decisions are tackled simultaneously here for the first time except for some conference papers the goal is to combine the pvrp and lrp into an even more realistic problem covering all decision levels the periodic lrp or plrp a hybrid evolutionary algorithm is proposed to solve large size instances of the plrp first an individual representing an assignment of customers to combinations of visit days is randomly generated the evolution operates through an evolutionary local search els on visit day assignments the algorithm is hybridized with a heuristic based on the randomized extended clarke and wright algorithm recwa to create feasible solutions and stops when a given number of iterations is reached the method is evaluated over three sets of instances and solutions are compared to the literature on particular cases such as one day horizon lrp or one depot pvrp this metaheuristic outperforms the previous methods for the plrp

a variable neighborhood search for the capacitated vehicle routing problem with two dimensional loading constraints abstract this paper addresses the capacitated vehicle routing problem with two dimensional loading constraints 2l cvrp which is a generalized capacitated vehicle routing problem in which customer demand is a set of two dimensional rectangular weighted items the objective is to design the route set of minimum cost for a homogenous fleet of vehicles starting and terminating at a central depot to serve all the customers all the items packed in one vehicle must satisfy the two dimensional orthogonal packing constraints a variable neighborhood search is proposed to address the routing aspect and a skyline heuristic is adapted to examine the loading constraints to speed up the search process an efficient data structure trie is utilized to record the loading feasibility information of routes but also to control the computational effort of the skyline spending on the same route the effectiveness of our approach is verified through experiments on widely used benchmark instances involving two distinct versions of loading constraints unrestricted and sequential versions numerical experiments show that the proposed method outperforms all existing methods and improves or matches the majority of best known solutions for both problem versions

approximation methods for the muskhelishvili equation on smooth curves we investigate the possibility of applying approximation methods to the famous muskhelishvili equation on a simple closed smooth curve since the corresponding integral operator is not invertible the initial equation has to be corrected in a special way it is shown that the spline galerkin spline collocation and spline qualocation methods for the corrected equation are stable and the corresponding approximate solutions converge to an exact solution of the muskhelishvili equation in appropriate norms numerical experiments confirm the effectiveness of the proposed methods

order matters a variable neighborhood search for the swap body vehicle routing problem abstract this article presents investigations on the performance of standard and problem specific neighborhood operators for the swap body vehicle routing problem more specifically our work analyzes the contribution of each operator to the solution quality in addition an experimental setting is defined that can be utilized to identify promising sequences in a variable neighborhood search the experiments verify that the sequence matters since two best known solutions can be equaled and 16 out of 18 solutions can be improved with a maximal improvement of 2 25 and an average improvement of 0 70

a fast interface solver for the biharmonic dirichlet problem on polygonal domains in this paper we propose and analyze an efficient discretization scheme for the boundary reduction of the biharmonic dirichlet problem on convex polygonal domains we show that the biharmonic dirichlet problem can be reduced to the solution of a harmonic dirichlet problem and of an equation with a poincare steklov operator acting between subspaces of the trace spaces we then propose a mixed fe discretization by linear elements of this equation which admits efficient preconditioning and matrix compression resulting in the complexity log varepsilon 1 o n log qn here n is the number of degrees of freedom on the underlying boundary varepsilon 0 is an error reduction factor q 2 or q 3 for rectangular or polygonal boundaries respectively as a consequence an asymptotically optimal iterative interface solver for boundary reductions of the biharmonic dirichlet problem on convex polygonal domains is derived a numerical example confirms the theory

classical free streamline flow over a polygonal obstacle in classical kirchhoff flow an ideal incompressible fluid flows past an obstacle and around a motionless wake bounded by free streamlines since 1869 it has been known that in principle the two dimensional kirchhoff flow over a polygonal obstacle can be determined by constructing a conformal map onto a polygon in the log hodograph plane in practice however this idea has rarely been put to use except for very simple obstacles because the conformal mapping problem has been too difficult this paper presents a practical method for computing flows over arbitrary polygonal obstacles to high accuracy in a few seconds of computer time we achieve this high speed and flexibility by working with a modified schwarz christoffel integral that maps onto the flow region directly rather than onto the log hodograph polygon this integral and its associated parameter problem are treated numerically by methods developed earlier by trefethen for standard schwarz christoffel maps

on stability of approximation methods for the muskhelishvili equation we study approximation methods for the muskhelishvili integral equations on curves with comer points and establish necessary and sufficient conditions for their stability

a fractal patch test element consistency is generally checked using the patch test on an element patch of finite size this condition may in certain cases be too restrictive and disqualifies elements that appear to be convergent a method termed fractal patch test is presented in which the patch size is maintained constant while the distorted mesh is refined examples are given for four node quadrilateral elements used in plane stress and strain analysis and for plate bending elements

numerical computation of muskhelishvili s integral equation in plane elasticity based on muskhelishvili s integral equation and the schwarz christoffel integral a numerical procedure is developed for solving the stress fields on plates with emphasis on the region around crack tips the difficulties in the numerical determination of accessory parameters in the schwarz christoffel transformation are overcome by separating the improper integral into two parts a finite form of integral in a continuous region which can be integrated exactly and a definite integral free of singularity which can easily be computed numerically furthermore the difficulties in the numerical computation of the kernel function in the boundary integral equation are resolved by finding the limit of the kernel function as the source point approaches the field point some numerical results of plane stress problems are provided to demonstrate the accuracy of this approach

a perturbation based variable neighborhood search heuristic for solving the vehicle routing problem with simultaneous pickup and delivery with time limit abstract the vehicle routing problem with simultaneous pickup and delivery with time limit vrpspdtl is a variant of the basic vehicle routing problem where the vehicles serve delivery as well as pick up operations of the clients under time limit restrictions the vrpspdtl determines a set of vehicle routes originating and terminating at a central depot such that the total travel distance is minimized for this problem we propose a mixed integer mathematical optimization model and a perturbation based neighborhood search algorithm combined with the classic savings heuristic variable neighborhood search and a perturbation mechanism the numerical results show that the proposed method produces superior solutions for a number of well known benchmark problems compared to those reported in the literature and reasonably good solutions for the remaining test problems

the fuzzy quadratic assignment problem with penalty new models and genetic algorithm the assignment problem is to find the total costs optimal jobs assignment schedule where n jobs are allocated to n workers and each worker receives exactly just one job such that the total cost is optimal the quadratic assignment problem with penalty takes three types of costs into consideration direct cost interactive cost an penalty in this paper the fuzzy quadratic assignment problem with penalty is formulated as expected value model chance constrained programming and dependent chance programming according to various decision criteria and the crisp equivalents are given furthermore hybrid genetic algorithm is designed for solving the proposed fuzzy programming models

conformal grid generation this paper treats conformal mapping as it relates to the generation of grids to be used for flow simulation classical and contemporary mapping methods are discussed and compared in some detail numerous suggestions are included to help the reader avoid common pitfalls and the mapping methods believed most promising are identified

record breaking optimization results using the ruin and recreate principle a new optimization principle is presented solutions of problems are partly but significantly ruined and rebuilt or recreated afterwards performing this type of change frequently one can obtain astounding results for classical optimization problems the new method is particularly suited for more complex optimization problems discontinuous ones problems with hard to find admissible solutions problems with complex objectives or many constraints the method is an all purpose heuristic numerical results are given for the traveling salesman problem for the vehicle routing problem with time windows and for network optimization numerical evidence for the quality of the proposed principle is given for most of the instances of a research library of problems the ruin and recreate r r implementation achieved the best published results for many instances better or much better solutions could be found

using clustering analysis in a capacitated location routing problem abstract the location routing problem lrp appears as a combination of two difficult problems the facility location problem flp and the vehicle routing problem vrp in this work we consider a discrete lrp with two levels a set of potential capacitated distribution centres dc and a set of ordered customers in our problem we intend to determine the set of installed dcs as well as the distribution routes starting and ending at the dc the problem is also constrained with capacities on the vehicles moreover there is a homogeneous fleet of vehicles carrying a single product and each customer is visited just once as an objective we intend to minimize the routing and location costs several authors have integrated cluster analysis procedures in heuristics for lrps as a contribution to this direction in this work several hierarchical and non hierarchical clustering techniques with several proximity functions are integrated in a sequential heuristic algorithm for the above mentioned lrp model all the versions obtained using different grouping procedures were tested on a large number of instances adapted from data in the literature and the results were compared so as to obtain some guidelines concerning the choice of a suitable clustering technique

an 8 node brick finite element an 8 node brick element based on the assumed stress hybrid formulation is described with three additional stress fields the element stiffness matrix now has the required rank of 18 and the bending response is exact with rectangular elements surprisingly the 2 2 2 gauss rule suffices for all numerical integrations to satisfy the constant stress patch test

derivation and analytical investigation of three direct boundary integral equations for the fundamental biharmonic problem we derive and investigate three families of direct boundary integral equations for the solution of the plane fundamental biharmonic boundary value problem these three families are fairly general so that they as special cases encompass various known and applied equations as demonstrated by giving many references to the literature we investigate the families by analytical means for a circular boundary curve where the radius is a parameter we find for all three combinations of equations i that the solution of the equations is non unique for one or more critical radius radii and ii that this lack of uniqueness can always be removed by combining the integral equations with a suitable combination of one or more supplementary condition s we conjecture how the results obtained can or cannot be generalized to other boundary curves through the concept logarithmic capacity a few published general results about uniqueness are compared with our findings

numerical computation of schwarz christoffel transformation for simply connected unbounded domain abstract a direct numerical conformal mapping based on the modified kantorovich method is developed to transform the upper half plane onto a bounded polygon in the complex domain the accessary parameters in the schwarz christoffel formula are determined iteratively from solving a set of nonlinear equations which are in terms of the side length ratios of the polygon both pure and compound gauss jacobi quadratures are employed to evaluate the improper integrals and their first order derivatives with end point singularities in addition to the parameter determination the computational schemes for forward and inverse mapping which can be applied to the numerucal grid generation for computational fluid dynamics are also presented several examples are provided in order to demonstrate the advantage of this approach

solution of viscous internal flows on curvilinear grids generated by the schwarz christoffel transformation abstract a method is presented for combining an accurate orthogonal curvilinear coordinate generation procedure with a fast accurate and stable forward marching viscous flow solution technique to solve for the flow field in arbitrary axisymmetric ducts in this method the coordinates are generated from the plane potential flow streamlines and potential lines using the schwarz christoffel transformation with a composite finite difference formula which is valid everywhere and which treats the poles exactly by analytic integration since the coordinate streamlines approximate the actual streamlines the equations of motion for viscous compressible flow can be parabolized so as to solve for both the boundary layers and core flow in a single streamwise pass the versatility of the method is demonstrated by two examples of viscous compressible swirling flow through complex radial gas turbine passages author

spline galerkin methods for the sherman lauricella equation on contours with corners spline galerkin approximation methods for the sherman lauricella integral equation on simple closed piecewise smooth contours are studied and necessary and sufficient conditions for their stability are obtained it is shown that the method under consideration is stable if and only if certain operators associated with the corner points of the contour are invertible numerical experiments demonstrate a good convergence of the spline galerkin methods and validate theoretical results moreover it is shown that if all corners of the contour have opening angles located in interval 0 1 pi 1 9 pi then the corresponding galerkin method based on splines of order 0 1 or 2 is always stable these results are in strong contrast with the behavior of the nystrom method which has a number of instability angles in the interval mentioned

mellin convolution operators in bessel potential spaces abstract mellin convolution equations acting in bessel potential spaces are considered the study is based upon two results the first one concerns the interaction of mellin convolutions and bessel potential operators bpos in contrast to the fourier convolutions bpos and mellin convolutions do not commute and we derive an explicit formula for the corresponding commutator in the case of mellin convolutions with meromorphic symbols these results are used in the lifting of the mellin convolution operators acting on bessel potential spaces up to operators on lebesgue spaces the operators arising belong to an algebra generated by mellin and fourier convolutions acting on l p spaces fredholm conditions and index formulae for such operators have been obtained earlier by one of the authors and are employed here the results of the present work have numerous applications in boundary value problems for partial differential equations in particular for equations in domains with angular points

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

solving theodorsen s integral equation for conformal maps with the fast fourier transform and various nonlinear iterative methods we investigate several iterative methods for the numerical solution of theodorsen s integral equation the discretization of which is either based on trigonometric polynomials or function families with known attenuation factors all our methods require simultaneous evaluations of a conjugate periodic function at each step and allow us to apply the fast fourier transform for this in particular we discuss the nonlinear jor iteration the nonlinear sor iteration a nonlinear second order euler iteration the nonlinear chebyshev semi iterative method and its cyclic variant under special symmetry conditions for the region to be mapped onto we establish local convergence in the case of discretization by trigonometric interpolation and give simple formulas for the optimal parameters e g the underrelaxation factor and the asymptotic convergence factor weaker related results for the general non symmetric case are presented too practically our methods extend the range of application of theodorsen s method and improve its effectiveness strikingly

sequential and parallel large neighborhood search algorithms for the periodic location routing problem we propose a large neighborhood search lns algorithm to solve the periodic location routing problem plrp the plrp combines location and routing decisions over a planning horizon in which customers require visits according to a given frequency and the specific visit days can be chosen we use parallelization strategies that can exploit the availability of multiple processors the computational results show that the algorithms obtain better results than previous solution methods on a set of standard benchmark instances from the literature

on the stability of the nystrom method for the muskhelishvili equation on contours with corners the stability of the nystrom method for the muskhelishvili equation on piecewise smooth simple contours is studied it is shown that in the space l 2 the method is stable if and only if certain operators a j from an algebra of toeplitz operators are invertible the operators a j depend on the parameters of the equation considered on the opening angles j of the corner points j and on parameters of the approximation method mentioned numerical experiments show that there are opening angles where the operators a j are noninvertible therefore for contours with such corners the method under consideration is not stable otherwise the method is always stable numerical examples show an excellent convergence of the method

a variable neighborhood search heuristic for periodic routing problems the aim of this paper is to propose a new heuristic for the periodic vehicle routing problem pvrp without time windows the pvrp extends the classical vehicle routing problem vrp to a planning horizon of several days each customer requires a certain number of visits within this time horizon while there is some flexibility on the exact days of the visits hence one has to choose the visit days for each customer and to solve a vrp for each day our method is based on variable neighborhood search vns computational results are presented that show that our approach is competitive and even outperforms existing solution procedures proposed in the literature also considered is the special case of a single vehicle i e the periodic traveling salesman problem ptsp it is shown that slight changes of the proposed vns procedure is also competitive for the ptsp

new optimization heuristics in a former paper we introduced a very effective new general purpose optimization principle we compared this method which we called threshold accepting ta with the well known simulated annealing sa method for discrete optimization the empirical results demonstrated the superiority of the ta algorithm in further experiments with the ta principle we discovered two new powerful optimization heuristics the great deluge algorithm gda and the record to record travel rrt these algorithms resemble in their structure the formerly studied ta and the sa method the differences lie in their acceptance rules for worse intermediate solutions both the gda and the rrt are essentially one parameter algorithms i e for the achievement of best possible performance a good choice is necessary only for a single parameter this is in contrast for instance to the classical as algorithm where it is necessary to choose carefully a certain sequence of parameters the so called annealing schedule the quality of the computational results obtained so far by rrt and gda shows that the new algorithms behave equally well as ta and thus a fortiori better than sa

layer potentials for elastostatics and hydrostatics in curvilinear polygonal domains the symbolic calculus of pseudodifferential operators of mellin type is applied to study layer potentials on a plane domain q whose boundary 9q is a curvilinear polygon a singularity type is a zero of the determinant of the matrix of symbols of the mellin operators and can be used to calculate the bad values of p for which the system is not fredholm on lp 9q using the method of layer potentials we study the singularity types of the system of elastostatics lu uau au vdivu 0 in a plane domain q whose boundary 9k2 is a curvilinear polygon here u 0 and u a oo when a oo the system is the stokes system of hydrostatics for the traction double layer potential we show that all singularity types in the strip 0 re z i lie in the interval 1 1 so that the system of integral equations is a fredholm operator of index 0 on lp aq for all p 2 p oo the explicit dependence of the singularity types on a and the interior angles 0 of aq is calculated the singularity type of each corner is independent of a if the corner is nonconvex introduction recently there has been considerable interest in using layer potentials to solve lp boundary value problems for elliptic operators and systems on a lipschitz domain q in r for the systems of elastostatics dkv and hydrostatics fkv dahlberg fabes kenig and verchota have used rellich type identities to prove that the double layer potential integral equations yield a fredholm operator of index 0 on l 2 q for p 2 only limited information is available on the boundary integral equations for general lipschitz domains in rn the general problem of the notion of symbol on the boundary of a general lipschitz domain is still very much open in this paper we treat a very special case a curvilinear polygonal domain in r in this 2 dimensional case a precise symbolic calculus of pseudodifferential operators of mellin type is available we show that certain double layer boundary integral equations yield operators which for all p 2 p 00 are received by the editors december 14 1988 1980 mathematics subject classification 1985 revision primary 35j25 45e05 research partially supported by the italian cnr 1990 american mathematical society 0002 9947 90 1 00 25 per page

new insertion and postoptimization procedures for the traveling salesman problem this paper describes a new insertion procedure and a new postoptimization routine for the traveling salesman problem the combination of the two methods results in an efficient algorithm genius which outperforms known alternative heuristics in terms of solution quality and computing time

conformal mapping based coordinate generation method for channel flows abstract a conformal mapping based coordinate generation method for channel type configurations has been developed a channel of an arbitrary shape in the physical plane is mapped into a straight channel in the computational plane the parameters of the transformation have to be determined through a method of successive approximations a simple iteration scheme that converges quite rapidly even with a poor initial guess is presented solutions for different configurations are displayed to illustrate the capabilities of the method results of the tests show higher order accuracy of the method in the case of curved channels

conformal mappings for internal viscous flow problems abstract isolated occlusions in a straight channel or pipe can be described analytically in a fashion that allows efficient accurate computation of nonlinear flow fields through conformal transformations

the evaluation of the conjugate function of a periodic spline on a uniform mesh abstract we present an o n log n algorithm for the simultaneous evaluation at all n points of a uniform mesh of a function conjugate to a periodic spline the algorithm is based on the attenuation factor theory and makes use of the fft it can be applied to other function classes with known attenuation factors also for the approximation by functions conjugate to splines of odd degree we state several optimality criterions and error bounds

heuristic algorithms for the 2 period balanced travelling salesman problem in euclidean graphs in the 2 period travelling salesman problem some nodes called double nodes are visited in both of two periods while the remaining ones called single nodes are visited in either one of the periods in this paper we study the case in which a balance constraint is also introduced we require that the difference between the number of visited nodes in the two periods must be below a fixed threshold moreover we suppose that distances between nodes are euclidean the problem is np hard and exact methods now available appear inadequate here we propose three heuristics computational experiences and a comparison between the algorithms are also given

variable neighbourhood structures for cycle location problems abstract variable neighbourhood search is a metaheuristic used mainly to tackle combinatorial optimization problems its performance depends on having a good variable neighbourhood structure that is a sequence of neighbourhoods that are ideally pairwise disjoint and contain feasible solutions further and further from a given feasible solution this article defines a variable neighbourhood structure with these properties that is new for cycle location problems it find bounds for the neighbourhood sizes and shows how to iterate over then when the cycle is a circuit it tests the structure and iteration method using variable neighbourhood search on a range of median cycle problems and finds a neighbourhood size beyond which there is on average no benefit in applying local search this neighbourhood size is found not to depend on problem size or bound on circuit length

fast solver for plane potential problems with mixed boundary conditions abstract the present paper proposes a new fast algorithm for plane potential problems on simply connected domains with mixed boundary conditions dirichlet and von neumann conditions are given on complementary parts of the boundary the method is based on the solution of a corresponding riemann hilbert problem in terms of cauchy integrals they can be computed efficiently and accurately by means of fast fourier transforms once the problem has been transformed conformally onto a standard domain and singularities have been extracted analytically

a new ilp based refinement heuristic for vehicle routing problems in this paper we address the distance constrained capacitated vehicle routing problem dcvrp where k minimum cost routes through a central depot have to be constructed so as to cover all customers while satisfying for each route both a capacity and a total distance travelled limit

an exact method for the capacitated location routing problem the capacitated location routing problem lrp consists of opening one or more depots on a given set of a priori defined depot locations and designing for each opened depot a number of routes in order to supply the demands of a given set of customers with each depot are associated a fixed cost for opening it and a capacity that limits the quantity that can be delivered to the customers the objective is to minimize the sum of the fixed costs for opening the depots and the costs of the routes operated from the depots this paper describes a new exact method for solving the lrp based on a set partitioning like formulation of the problem the lower bounds produced by different bounding procedures based on dynamic programming and dual ascent methods are used by an algorithm that decomposes the lrp into a limited set of multicapacitated depot vehicle routing problems mcdvrps computational results on benchmark instances from the literature show that the proposed method outperforms the current best known exact methods both for the quality of the lower bounds achieved and the number and the dimensions of the instances solved to optimality

a hybrid differential evolution algorithm to vehicle routing problem with fuzzy demands in this paper the vehicle routing problem with fuzzy demands vrpfd is considered and a fuzzy chance constrained program model is designed based on fuzzy credibility theory then stochastic simulation and differential evolution algorithm are integrated to design a hybrid intelligent algorithm to solve the fuzzy chance constrained program model moreover the influence of the dispatcher preference index on the final objective of the problem is discussed using stochastic simulation and the best value of the dispatcher preference index is obtained

using greedy clustering method to solve capacitated location routing problem with fuzzy demands abstract in this paper the capacitated location routing problem with fuzzy demands clrp fd is considered in clrp fd facility location problem flp and vehicle routing problem vrp are observed simultaneously indeed the vehicles and the depots have a predefined capacity to serve the customers that have fuzzy demands to model this problem a fuzzy chance constrained programming model of that is designed based upon the fuzzy credibility theory to solve this problem a greedy clustering method gcm including the stochastic simulation is proposed to obtain the best value of the dispatcher preference index of the model and to analyze its influence on the final solution numerical experiments are carried out finally to show the performance of the greedy clustering method associated results are compared with the lower bound of the solutions

a hybrid intelligent algorithm for portfolio selection problem with fuzzy returns portfolio selection theory with fuzzy returns has been well developed and widely applied within the framework of credibility theory several fuzzy portfolio selection models have been proposed such as mean variance model entropy optimization model chance constrained programming model and so on in order to solve these nonlinear optimization models a hybrid intelligent algorithm is designed by integrating simulated annealing algorithm neural network and fuzzy simulation techniques where the neural network is used to approximate the expected value and variance for fuzzy returns and the fuzzy simulation is used to generate the training data for neural network since these models are used to be solved by genetic algorithm some comparisons between the hybrid intelligent algorithm and genetic algorithm are given in terms of numerical examples which imply that the hybrid intelligent algorithm is robust and more effective in particular it reduces the running time significantly for large size problems

the patch test for elements the main purpose of this paper is to emphasize the necessity of convergence tests in general and the patch test in particular following a brief introduction the patch test is described with examples this it is hoped will help to remove any lingering misunderstanding of this very useful convergence test some positive contributions of the test in the formulation and improvement of elements are also discussed

schwarz christoffel mappings a general approach abstract a general method is developed for constructing equations of the schwarz christoffel type these equations define conformal transformations between regions of the complex plane each of whose boundaries may consist of straight or continuously curved line segments and corners the more familiar types of schwarz christoffel equations are rederived and some new types are obtained

an engineers defence of the patch test this convergence criterion is proved for any legalizable finite element formulation i e any model for which a conforming displacement version is possible using the same nodal variables engineers may therefore take control of and responsibility for convergence for most of the elements in service today stummel s counter example is explained as a technical misunderstanding due to inadequate documentation of the patch test it is suggested without proof that the test properly applied is universal provided that it is always combined with an adequate test of stability

reduction of excessive energy in the four noded membrane quadrilateral element part i linear theory compressible materials abstract the objective of the paper is to set forth in a consistent manner reasons for the appearance of excessive energy in the four noded membrane quadrilateral element and to propose a formulation leading to simple and reliable elements that are less sensitive to distortions of the geometrical shape by presenting the differential geometry emphasis is placed upon those geometrical attributes which are inherently related to the quadrilateral a modified version of the functional of hu washizu is employed for the discretization appropriate approximations for the displacements rotations are chosen and the physical meaning of the various parameters is identified a systematic procedure is followed for the approximation of stress and strain the convergence of the formulation is investigated by examining the inf sup condition and applying the patch test also results of numerical examples and comparisons with other elemental formulations are presented

stability of the nystrom method for the sherman lauricella equation the stability of the nystrom method for the sherman lauricella equation on piecewise smooth closed simple contour gamma is studied it is shown that in the space l 2 the method is stable if and only if certain operators associated with the corner points of gamma are invertible if gamma does not have corner points the method is always stable numerical experiments show the transformation of solutions when the unit circle is continuously transformed into the unit square and then into various rhombuses examples also show an excellent convergence of the method

potential flow in a semi infinite channel with multiple sub channels using the schwarz christoffel transformation abstract in this paper we consider the potential fluid flow in a semi infinite channel with multiple semi infinite sub channels using the schwarz christoffel transformation and complex potential theory the schwarz christoffel transformation contains several unknown parameters which are solely dependent on the dimensions of the region being considered and an alternative iterative mathematical technique to that found elsewhere in the literature is developed to determine these parameters using a runge kutta merson method of integration once these parameters have been determined we numerically integrate the schwarz christoffel transformation using a variable step adams method now the mapping from the region being considered to the upper half of the complex plane is complete in order to illustrate this mathematical technique we consider a semi infinite room with an inlet outlet placed on the ceiling and an outlet attached to the wall the inlet and outlet channels are normal to the surface to which they are attached and through each of these channels we have uniform flow at infinity hence the whole region is modelled by a semi infinite channel with two sub channels attached

modeling fuzzy multi period production planning and sourcing problem with credibility service levels a great deal of research has been done on production planning and sourcing problems most of which concern deterministic or stochastic demand and cost situations and single period systems in this paper we consider a new class of multi period production planning and sourcing problem with credibility service levels in which a manufacturer has a number of plants and subcontractors and has to meet the product demand according to the credibility service levels set by its customers in the proposed problem demands and costs are uncertain and assumed to be fuzzy variables with known possibility distributions the objective of the problem is to minimize the total expected cost including the expected value of the sum of the inventory holding and production cost in the planning horizon because the proposed problem is too complex to apply conventional optimization algorithms we suggest an approximation approach aa to evaluate the objective function after that two algorithms are designed to solve the proposed production planning problem the first is a pso algorithm combining the aa and the second is a hybrid pso algorithm integrating the aa neural network nn and pso finally one numerical example is provided to compare the effectiveness of the proposed two algorithms

extracting singularities of cauchy integrals a key point of a fast solver for plane potential problems with mixed boundary conditions abstract the authors 1991 proposed an algorithm for solving plane potential problems with mixed boundary conditions the method is based on a corresponding riemann hilbert problem on the unit disc onto which the problem has been transformed conformally numerically the evaluation of the solution reduces to the computation of cauchy integrals on the unit circle operating on singular functions explicit extraction and analytical integration of these singularities up to a certain order is possible by the schwarz formula the remaining integral can then be treated accurately applying fast fourier techniques where haas and brauchli 1991 focus on a more general description including computed examples this paper gives the mathematical details concerning the construction of the singular extraction functions explicit expressions for their coefficients are derived

an exact algorithm for the period routing problem this paper presents an exact algorithm for solving strategic and tactical multiperiod vehicle routing problems that can be modeled as period vehicle routing problems pvrps the pvrp is defined on a time horizon of several days and consists of assigning appropriate combinations of delivery to customers and designing a set of delivery routes for every day of the planning period the objective is to service all customers assigned to each day minimizing the overall routing cost this paper describes an integer programming formulation of the pvrp that is used to derive different lower bounds and an exact solution method computational results on test instances from the literature and on new sets of test instances show the effectiveness of the proposed method

a quadrature based approach to improving the collocation method the collocation method is a popular method for the approximate solution of boundary integral equations but typically does not achieve the high order of convergence reached by the galerkin method in appropriate negative norms in this paper a quadrature based method for improving upon the collocation method is proposed and developed in detail for a particular case that case involves operators with even symbol such as the logarithmic potential operating on 1 periodic functions a smooth spline trial space of odd degree with constant mesh spacingh 1 n and a quadrature rule with 2n points where ann point quadrature rule would be equivalent to the collocation method in this setting it is shown that a special quadrature rule which depends on the degree of the splines and the order of the operator can yield a maximum order of convergence two powers ofh higher than the collocation method