an iterative method for the skew symmetric solution and the optimal approximate solution of the matrix equation axb c in this paper an iterative method is constructed to solve the linear matrix equation axb c over skew symmetric matrix x by the iterative method the solvability of the equation axb c over skew symmetric matrix can be determined automatically when the equation axb c is consistent over skew symmetric matrix x for any skew symmetric initial iterative matrix x 1 the skew symmetric solution can be obtained within finite iterative steps in the absence of roundoff errors the unique least norm skew symmetric iterative solution of axb c can be derived when an appropriate initial iterative matrix is chosen a sufficient and necessary condition for whether the equation axb c is inconsistent is given furthermore the optimal approximate solution of axb c for a given matrix x 0 can be derived by finding the least norm skew symmetric solution of a new corresponding matrix equation email protected email protected finally several numerical examples are given to illustrate that our iterative method is effective

s step iterative methods for non symmetric in definite linear systems in this paper a class of s step methods for nonsymmetric linear systems of equations is introduced these methods are obtained from nonsymmetric generalizations of the conjugate residual method which apply to nonsymmetric definite systems s c eisenstat h c elmans and m h schultz siam j numer anal 20 1983 pp 345 357 the s step methods are derived then in a way similar to obtaining the s step conjugate gradient g e forsythe numer math 11 1968 pp 57 76 a t chronopoulos and c w gear j comput math 25 1989 pp 153 168 a t chronopoulos ph d thesis dept of computer science university of illinois urbana il 1986 it is proven that the s step methods with s geqq 2 converge for all symmetric indefinite matrices for nonsymmetric matrices with positive definite symmetric part and for a class of nonsymmetric indefinite problems the s step methods require less computational work but s 1 more vectors of main memory storage than the standard ones these

continuum and discrete models for unbalanced woven fabrics abstract the classical models used for describing the mechanical behavior of woven fabrics do not fully account for the whole set of phenomena that occur during the testing of such materials this lack of precision is mainly due to the absence of energy terms related to the microstructural properties of the fabric and in particular to the bending stiffness of the yarns the importance of the bending stiffness on the overall mechanical behavior of woven reinforcements if already essential for the complete description of balanced fabrics becomes even more important in the case of unbalanced ones in this paper it is shown that the unbalance in the bending stiffnesses of the warp and weft yarns produces macroscopic effects that are extremely visible we mention for example the asymmetric s shape of a woven interlock subjected to a bias extension test we propose to introduce a constrained micromorphic model and simultaneously a discrete model that are both able to account for i the angle variation between warp and weft tows ii the unbalance in the bending stiffness of the yarns and iii the relative slipping of the tows the introduced constrained micromorphic model is rigorously framed in the spirit of the principle of virtual work for the study of the equilibrium of continuum bodies a suitable constraint is introduced in such micromorphic model by means of lagrange multipliers in the strain energy density and the resulting constrained model is seen to be a particular second gradient one the main advantage of using such constrained micromorphic model is that the kinematical and traction boundary conditions that can be imposed on some sub portions of the boundary of the considered body take a natural and unique meaning the discrete model is set up by opportunely interconnecting euler bernoulli beams with different bending stiffnesses in the two directions by means of rotational and translational elastic springs the main strength of such discrete model is that the slipping of the tows is described in a rather realistic way suitable numerical simulations are presented for both the continuum and the discrete models and a comparison between the simulations and the experimental results is performed showing a definitely good agreement

a tabu search heuristic for deterministic two mode blockmodeling of binary network matrices two mode binary data matrices arise in a variety of social network contexts such as the attendance or non attendance of individuals at events the participation or lack of participation of groups in projects and the votes of judges on cases a popular method for analyzing such data is two mode blockmodeling based on structural equivalence where the goal is to identify partitions for the row and column objects such that the clusters of the row and column objects form blocks that are either complete all 1s or null all 0s to the greatest extent possible multiple restarts of an object relocation heuristic that seeks to minimize the number of inconsistencies i e 1s in null blocks and 0s in complete blocks with ideal block structure is the predominant approach for tackling this problem as an alternative we propose a fast and effective implementation of tabu search computational comparisons across a set of 48 large network matrices revealed that the new tabu search heuristic always provided objective function values that were better than those of the relocation heuristic when the two methods were constrained to the same amount of computation time

improvement and comparison of heuristics for solving the uncapacitated multisource weber problem the multisource weber problem is to locate simultaneouslym facilities in the euclidean plane to minimize the total transportation cost for satisfying the demand ofn fixed users each supplied from its closest facility many heuristics have been proposed for this problem as well as a few exact algorithms heuristics are needed to solve quickly large problems and to provide good initial solutions for exact algorithms we compare various heuristics i e alternative location allocation cooper 1964 projection bongartz et al 1994 tabu search brimberg and mladenovic 1996a p median plus weber hansen et al 1996 genetic search and several versions of variable neighbourhood search based on empirical tests that are reported it is found that most traditional and some recent heuristics give poor results when the number of facilities to locate is large and that variable neighbourhood search gives consistently best results on average in moderate computing time

multi value microstructural descriptors for complex materials analysis of ground states we propose and analyze a multi scale and multi field description of complex materials in which we consider every material element as a system composed by q in mathbb n indistinct substructures we pay attention to the equilibrium configurations of such bodies we consider first rigid bodies with microstructure represented by means of q valued maps from the reference place to the manifold of microstructural shapes in that case just microenergetics appears then we enlarge the stage considering large strains and energies of ginzburg landau type with respect to the microstructural descriptor fields in both cases we provide conditions for semicontinuity of the relevant energies and the existence of ground states

the median tour and maximal covering tour problems formulations and heuristics abstract in this paper the authors introduce two bicriterion routing problems the median tour problem mtp and the maximal covering tour problem mctp in both problems the tour must visit only p of the n nodes on the network in addition both problems have as one of their objectives the minimization of total tour length the second objective in both problems maximizes access to the tour for the nodes not directly on it in the mtp the access objective is the minimization of the total travel distance necessary for demand at the nodes to reach their nearest stop on the tour in the mctp the access objective is to maximize the total demand within some prespecified maximal travel distance from a tour stop it is shown that the mctp may be viewed as a special case of the mtp consequently solution procedures developed for the mtp may also be employed to solve the mctp unfortunately both problems are np hard in addition the number of efficient solutions may grow exponentially with the number of nodes in the particular problem instance consequently a heuristic procedure is developed to generate a good approximation of the efficient frontier not only does this approximation provide the decision marker with insight into the magnitudes of the inherent tradeoffs between the two objectives but it also provides him or her with a set of feasible options to consider computational experience on a realistically scaled problem is provided applications of the problems include the design of mobile service delivery systems e g healthcare delivery in rural areas of developing countries bi modal transportation systems e g overnight mail delivery and distributed computer networks among others

poincare meets korn via maxwell extending korn s first inequality to incompatible tensor fields for a bounded domain r3 r3 with lipschitz boundary and some relatively open lipschitz subset t t of we prove the existence of some c 0c 0 such that equation 0 1 c t l2 r3 3 symt l2 r3 3 curlt l2 r3 3 holds for all tensor fields in h curl h curl i e for all square integrable tensor fields t r3 3t r3 3 with square integrable generalized rotation curlt r3 3 having vanishing restricted tangential trace on t t if t t 0 1 still holds at least for simply connected and for all tensor fields t h curl t h curl which are l2 l2 perpendicular to so 3 so 3 i e to all skew symmetric constant tensors here both operations curl and tangential trace are to be understood row wise for compatible tensor fields t vt v 0 1 reduces to a non standard variant of the well known korn s first inequality in r3r3 namely c v l2 r3 3 sym v l2 r3 3 for all vector fields v h1 r3 v h1 r3 for which vn vn n 1 3n 1 3 are normal at t t on the other hand identifying vector fields v h1 r3 v h1 r3 having the proper boundary conditions with skew symmetric tensor fields t 0 1 turns to poincare s inequality since 2c v l2 r3 c t l2 r3 3 curlt l2 r3 3 2 v l2 r3 therefore 0 1 may be viewed as a natural common generalization of korn s first and poincare s inequality from another point of view 0 1 states that one can omit compatibility of the tensor field t at the expense of measuring the deviation from compatibility through curl t decisive tools for this unexpected estimate are the classical korn s first inequality helmholtz decompositions for mixed boundary conditions and the maxwell estimate

facility siting and integer friendly programming abstract facility siting on networks has been accomplished with some success via integer linear programming formulations of a particular character specifically constraint expansion often brings about zero one solutions with little or no branching and bounding additionally when multi objective zero one programming problems require solution the weighting method may often be employed with some success examples of constraint expanded and multi objective problems from facility siting and from other settings are analyzed for common features

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

connecting molecular dynamics to micromorphic theory ii balance laws abstract in this paper the time evolution laws for the averaged conserved dynamical variables are derived based on a molecular dynamic model it is found that they follow exactly the balance laws in micromorphic continuum derived by eringen in a top down approach since all the mechanical variables in micromorphic theory can be obtained from an atomic model through statistical ensemble averaging and those averaged quantities satisfy the balance laws that govern the behavior of the continuum it is thus concluded that the atomic model is consistent with the continuum model and correspondence between these two models is analytically achieved

network distance characteristics that affect computational effort in p median location problems abstract in solving location models the effort expended and the quality of the solutions obtained often varies significantly from one problem instance to another our conjecture is that this is not a random occurrence but instead can be correlated with characteristics of the network upon which the model is constructed in this paper we examine a variety of approaches for generating networks for the p median model the types of networks studied include those based on euclidean inter point distances shortest paths developed from a predefined network and randomly generated distance matrices in addition to the process by which the network is constructed we consider the distribution of distances symmetry and the satisfaction of the triangle inequality all of these characteristics influence the effort required to solve the p median model we have found however that the triangle inequality has the most significant impact

the general coupled matrix equations over generalized bisymmetric matrices abstract in the present paper by extending the idea of conjugate gradient cg method we construct an iterative method to solve the general coupled matrix equations j 1 p a ij x j b ij m i i 1 2 p including the generalized coupled lyapunov and sylvester matrix equations as special cases over generalized bisymmetric matrix group x 1 x 2 x p by using the iterative method the solvability of the general coupled matrix equations over generalized bisymmetric matrix group can be determined in the absence of roundoff errors when the general coupled matrix equations are consistent over generalized bisymmetric matrices a generalized bisymmetric solution group can be obtained within finite iteration steps in the absence of roundoff errors the least frobenius norm generalized bisymmetric solution group of the general coupled matrix equations can be derived when an appropriate initial iterative matrix group is chosen in addition the optimal approximation generalized bisymmetric solution group to a given matrix group x 1 x 2 x p in frobenius norm can be obtained by finding the least frobenius norm generalized bisymmetric solution group of new general coupled matrix equations the numerical results indicate that the iterative method works quite well in practice

a genetic algorithm for the p median problem with pos neg weights let a connected undirected graph g v e be given in the classical p median problem we want to find a set x containing p points in g such that the sum of weighted distances from x to all vertices in v is minimized we consider the semi obnoxious case where every vertex has either a positive or negative weight in this case we have two different objective functions the sum of the minimum weighted distances from x to all vertices and the sum of the weighted minimum distances in this paper we propose a genetic algorithm for both problems computational results are compared with a previously investigated variable neighborhood search algorithm

on the unified dispersion problem efficient formulations and exact algorithms abstract facility dispersion problems involve placing a number of facilities as far apart from each other as possible four different criteria of facility dispersal have been proposed in the literature erkut neuman 1991 despite their formal differences these four classic dispersion objectives can be expressed in a unified model called the partial sum dispersion model lei church 2013 in this paper we focus on the unweighted partial sum dispersion problem and introduce an efficient formulation for this generalized dispersion problem based on a construct by ogryczak and tamir 2003 we also present a fast branch and bound based exact algorithm

the minimization of matrix logarithms on a fundamental property of the unitary polar factor we show that the unitary factor up in the polar decomposition of a nonsingular matrix z uph is a minimizer for both log q z and sym log q z over the unitary matrices q u n for any given invertible matrix z cn n for any unitarily invariant norm and any n we prove that up is the unique matrix with this property to minimize all these norms simultaneously as important tools we use a generalized bernstein trace inequality and the theory of majorization

neighborhood search heuristics for the uncapacitated facility location problem abstract the uncapacitated facility location problem is one of choosing sites among a set of candidates in which facilities can be located so that the demands of a given set of clients are satisfied at minimum costs applications of neighborhood search methods to this problem have not been reported in the literature in this paper we first describe and compare several neighborhood structures used by local search to solve this problem we then describe neighborhood search heuristics based on tabu search and complete local search with memory to solve large instances of the uncapacitated facility location problem our computational experiments show that on medium sized problem instances both these heuristics return solutions with costs within 0 075 of the optimal with execution times that are often several orders of magnitude less than those required by exact algorithms on large sized instances the heuristics generate low cost solutions quite fast and terminate with solutions whose costs are within 0 0345 of each other

the directional p median problem definition complexity and algorithms an instance of a p median problem gives n demand points the objective is to locate p supply points in order to minimize the total distance of the demand points to their nearest supply point p median is polynomially solvable in one dimension but np hard in two or more dimensions when either the euclidean or the rectilinear distance measure is used in this paper we treat the p median problem under a new distance measure the directional rectilinear distance which requires the assigned supply point for a given demand point to lie above and to the right of it in a previous work we showed that the directional p median problem is polynomially solvable in one dimension we give here an improved solution through reformulating the problem as a special case of the constrained shortest path problem we have previously proven that the problem is np complete in two or more dimensions we present here an efficient heuristic to solve it compared to the robust teitz and bart heuristic our heuristic enjoys substantial speedup while sacrificing little in terms of solution quality making it an ideal choice for real world applications with thousands of demand points

fast primal and dual heuristics for the p median location problem a greedy type heuristic is presented for the p median problem and computational results for problems having up to 400 vertices are shown we describe a dual heuristic procedure for the p median based on erlenkotter s heuristic 1978 for the uncapacitated facility location problem a primal dual heuristic that generates a primal solution based on a good dual solution is also presented for both procedures computational experience relative to the same set of large size test problems is reported finally the results obtained from all procedures are compared with the bounds and corresponding computing times provided by other available heuristics for the p median location problem

solving the p median problem with pos neg weights by variable neighborhood search and some results for special cases the p median problem with positive and negative weights has been introduced by burkard and krarup computing 60 1998 193 in this paper we discuss some special cases of this problem on trees and propose a variable neighborhood search procedure for general networks which is in fact a modification of the one proposed by hansen and mladenovic locat sci 5 1997 207 for the p median we also compare the results with those obtained by a tabu search procedure

the design of reverse distribution networks models and solution procedures abstract reverse distribution or the management of product return flows induced by various forms of reuse of products and materials has received growing attention throughout this decade in this paper we discuss reverse distribution and propose a mathematical programming model for a version of this problem due to the complexity of the proposed model we introduce a heuristic solution methodology for this problem the solution methodology complements a heuristic concentration procedure where sub problems with reduced sets of decision variables are iteratively solved to optimality based on the solutions from the sub problems a final concentration set of potential facility sites is constructed and this problem is solved to optimality the potential facility sites are then expanded in a greedy fashion to obtain the final solution this heuristic expansion was also performed using the solution found with a greedy heuristic to provide a short list of potential facility sites computational tests demonstrate a great deal of promise for this solution method as high quality solutions are obtained while expending modest computational effort

an iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation axb c an iteration method is constructed to solve the linear matrix equation axb c over symmetric x by this iteration method the solvability of the equation axb c over symmetric x can be determined automatically when the equation axb c is consistent over symmetric x its solution can be obtained within finite iteration steps and its least norm symmetric solution can be obtained by choosing a special kind of initial iteration matrix furthermore its optimal approximation solution to a given matrix can be derived by finding the least norm symmetric solution of a new matrix equation axb c finally numerical examples are given for finding the symmetric solution and the optimal approximation symmetric solution of the matrix equation axb c

aggregation error bounds for a class of location models many location models involve distances and demand points in their objective function in urban contexts there can be millions of demand points this leads to demand point aggregation which produces error we identify a general model structure that includes most such location models and present a means of obtaining error bounds for all models with this structure the error bounds suggest how to do the demand point aggregation so as to keep the error small

a gamma heuristic for the p median problem heuristic concentration hc is a two stage metaheuristic that can be applied to a wide variety of combinatorial problems it is particularly suited to location problems in which the number of facilities is given in advance in such settings the first stage of hc repeatedly applies some random start interchange or other heuristic to produce a number of alternative facility configurations a subset of the best of these alternatives is collected and the union of the facility sites in them is called a concentration set cs among the component elements of the cs are likely to be included those sites which are members of the optimal solution in earlier studies the second stage of hc has consisted of an exact procedure to extract the best possible solution from the cs in this paper we demonstrate for the p median problem the use of two sequentially active heuristics in the second stage of hc that is we offer two additional layers of heuristics to improve solutions which are found in the first stage of hc thus we are describing a variant of the hc metaheuristic consisting of three layers of heuristics which are utilized in sequence we propose for this procedure the name of gamma heuristic

survey invariant representations of discrete time periodic systems the correspondence between periodic and time invariant systems can take a variety of forms the purpose of this survey paper is to present a complete and clear picture on time invariant representations for discrete time periodic systems the core of the treatment evolves around the concept of periodic transfer function

an overview of representative problems in location research we present a survey of over 50 representative problems in location research our goal is not to review all variants of different location models or to describe solution results but rather to provide a broad overview of major location problems that have been studied indicating briefly how they are formulated and how they relate to one another we review standard problems such as median center and warehouse location problems as well as less traditional location problems which have emerged in recent years our primary focus is on problems for which operations research type models have been developed most of the problems we review have been formulated as optimization problems

a parametric periodic lyapunov equation with application in semi global stabilization of discrete time periodic systems subject to actuator saturation this paper is concerned with semi global stabilization of discrete time linear periodic systems subject to actuator saturation provided that the open loop characteristic multipliers are within the closed unit circle a low gain feedback design approach is proposed to solve the problem by state feedback our approach is based on the solution to a parametric discrete time periodic lyapunov equation the proposed approaches not only generalize the corresponding results for time invariant systems to periodic systems but also reveal some important intrinsic properties of this class of periodic matrix equations a numerical example is worked out to illustrate the effectiveness of the proposed approaches

cluster analysis and mathematical programming given a set of entities cluster analysis aims at finding subsets called clusters which are homogeneous and or well separated as many types of clustering and criteria for homogeneity or separation are of interest this is a vast field a survey is given from a mathematical programming viewpoint steps of a clustering study types of clustering and criteria are discussed then algorithms for hierarchical partitioning sequential and additive clustering are studied emphasis is on solution methods i e dynamic programming graph theoretical algorithms branch and bound cutting planes column generation and heuristics

a note on solving large p median problems abstract in a previous paper we presented a tree search algorithm for the p median problem the problem of locating p facilities medians on a network which was based upon la grangean relaxation and subgradient optimisation that algorithm solved optimally problems with an arbitrary number of medians and having up to 200 vertices in this note we show that it is possible to enhance that algorithm to solve optimally problems having up to 900 vertices using the cray 1s computer

lagrangean heuristics for location problems abstract in this paper we present a framework for developing lagrangean heuristics heuristics based upon lagrangean relaxation and subgradient optimisation with respect to location problems computational results are given for four different location problems p median uncapacitated warehouse location capacitated warehouse location and capacitated warehouse location with single source constraints these results indicate that the framework presented in this paper is robust i e it gives good quality solutions for each of these different location problems

the p median problem a survey of metaheuristic approaches the p median problem is one of the basic models in discrete location theory as with most location problems it is classified as np hard and so heuristic methods are usually used to solve it metaheuristics are frameworks for building heuristics in this survey we examine the p median with the aim of providing an overview on advances in solving it using recent procedures based on metaheuristic rules

generating conjugate directions for arbitrary matrices by matrix equations ii abstract our previous paper 1 is continued here the matrix equation form of the reverse hestenes stiefel type recursion scheme for generaing a conjugate vector pairs is elaborated the notations of the previous paper are kept

a dynamic programming heuristic for the p median problem a new heuristic algorithm is proposed for the p median problem the heuristic restricts the size of the state space of a dynamic programming algorithm the approach may be viewed as an extension of the myopic or greedy adding algorithm for the p median model the approach allows planners to identify a large number of solutions all of which perform well with respect to the p median objective of minimizing the demand weighted average distance between customer locations and the nearest of the p selected facilities in addition the results indicate regions in which it is desirable to locate facilities computational results from three test problems are discussed

advanced greedy randomized adaptive search procedure for the obnoxious p median problem abstract the obnoxious p median problem consists in selecting a subset of p facilities from a given set of possible locations in such a way that the sum of the distances between each customer and its nearest facility is maximized the problem is np hard and can be formulated as an integer linear program it was introduced in the 1990s and a branch and cut method coupled with a tabu search has been recently proposed in this paper we propose a heuristic method based on the greedy randomized adaptive search procedure grasp methodology for finding approximate solutions to this optimization problem in particular we consider an advanced grasp design in which a filtering mechanism avoids applying the local search method to low quality constructed solutions empirical results indicate that the proposed implementation compares favorably to previous methods this fact is confirmed with non parametric statistical tests

an iterative algorithm for the reflexive solutions of the generalized coupled sylvester matrix equations and its optimal approximation abstract the generalized coupled sylvester matrix equations ay zb cy zd e f with unknown matrices y z are encountered in many systems and control applications also these matrix equations have several applications relating to the problem of computing stable eigendecompositions of matrix pencils in this work we construct an iterative algorithm to solve the generalized coupled sylvester matrix equations over reflexive matrices y z and when the matrix equations are consistent for any initial matrix pair y 0 z 0 a reflexive solution pair can be obtained within finite iteration steps in the absence of roundoff errors and the least frobenius norm reflexive solution pair can be obtained by choosing a special kind of initial matrix pair also we obtain the optimal approximation reflexive solution pair to a given matrix pair y z in the reflexive solution pair set of the generalized coupled sylvester matrix equations ay zb cy zd e f moreover several numerical examples are given to show the efficiency of the presented iterative algorithm

connecting molecular dynamics to micromorphic theory i instantaneous and averaged mechanical variables abstract this is the first part of an effort to connect molecular dynamics to a well established continuum theory micromorphic theory this effort includes two parts mechanical variables and balance laws in this paper the physical picture of micromorphic theory is introduced a geometric model of an atomic system is presented the microscopic expressions of all the instantaneous mechanical variables in micromorphic theory are derived and related to atomic coordinates and velocities and the corresponding continuum field quantities are obtained through statistical ensemble average the link between the two thoroughly different models is analytically established

computational study of large scale p median problems given a directed graph g v a the p median problem consists of determining p nodes the median nodes minimizing the total distance from the other nodes of the graph we present a branch and cut and price algorithm yielding provably good solutions for instances with v 3795 key ingredients of the algorithm are a delayed column and row generation technique exploiting the special structure of the formulation to solve the lp relaxation and cutting planes to strengthen the formulation and limit the size of the enumeration tree

the p q active uncapacitated facility location problem investigation of the solution space and an lp fitting heuristic abstract the p q active uncapacitated facility location problem is the problem of locating p facilities on n possible sites each serving at least q of the m clients at the minimum cost the problem is an extension of the uncapacitated facility location problem ufl where constraints on the number of facilities and their minimum activity have been added a use of this formulation could be the opening of p new schools where each must have at least q pupils p q active is np hard like the ufl in this paper we present a thorough investigation of the p q active ufl and propose a heuristic solution method different geometric and random cost problem instances are considered experiments show that 60 of the problems can be solved to optimality just by solving the corresponding lp relaxation using a simple local search heuristic the remaining geometric problems are solved with an average gap of 0 1 to a lower bound found by lp relaxation an effort is put into isolating problem types that are hard to solve problems with low p p q close to m combined with clustered clients or a low variation in the facility opening cost are most likely to give results worse than average gaps up to 8 are observed in the worst cases

results concerning interval linear systems with multiple right hand sides and the interval matrix equation ax b this note tries to study different solution sets of the interval linear matrix equation ax b where a is a known square interval matrix of dimension mxm b is a rectangular interval matrix of dimension mxn while the unknown matrix x is also of dimension mxn firstly we show that shary s results for interval linear systems with a single right hand side vector cannot be simply generalized to the case of interval linear systems of the form ax b secondly we give some analytical characterizations of the ae solution sets of this interval matrix equation we use a linear programming method in order to find the interval hull matrix on the other hand we propose the use of an interval gaussian elimination to find an enclosure for the united solution set of this matrix equation since the lu decomposition of a is needed only once numerical examples have also been given

heuristic concentration two stage solution construction abstract by utilizing information from multiple runs of an interchange heuristic we construct a new solution that is generally better than the best local optimum previously found this new two stage approach to combinatorial optimization is demonstrated in the context of the p median problem two layers of optimization are superimposed the first layer is a conventional heuristic the second is a heuristic or exact procedure which draws on the concentrated solution set generated by the initial heuristic the intention is to provide an alternative heuristic procedure which when dealing with large problems has a higher probability of producing optimal solutions than existing methods the procedure is fairly general and appears to be applicable to combinatorial problems in a number of contexts

an efficient tabu search procedure for the p median problem abstract in this paper we present a new solution heuristic for the p median problem the algorithm is based on tabu search principles and uses short term and long term memory as well as strategic oscillation and random tabu list sizes our proposed procedure is compared with two other move heuristics a well known interchange heuristic and a recent hybrid heuristic in computational tests on networks ranging in size up to 500 nodes the new heuristic is found to be superior with respect to the quality of solutions produced

a branch and price algorithm for the capacitated facility location problem the capacitated facility location problem cflp is a well known combinatorial optimization problem with applications in distribution and production planning it consists in selecting plant sites from a finite set of potential sites and in allocating customer demands in such a way as to minimize operating and transportation costs a number of solution approaches based on lagrangean relaxation and subgradient optimization has been proposed for this problem subgradient optimization does not provide a primal fractional optimal solution to the corresponding master problem however in order to compute optimal solutions to large or difficult problem instances by means of a branch and bound procedure information about such a primal fractional solution can be advantageous in this paper a stabilized column generation method is therefore employed in order to solve a corresponding master problem exactly the column generation procedure is then employed within a branch and price algorithm for computing optimal solutions to the cflp computational results are reported for a set of larger and difficult problem instances

an efficient algorithm based on lanczos type of bcr to solve constrained quadratic inverse eigenvalue problems abstract this paper proposes the lanczos type of biconjugate residual bcr algorithm for solving the quadratic inverse eigenvalue problem l 2 x 2 l 1 x l 0 x 0 where l 2 l 1 and l 0 should be partially bisymmetric under a prescribed submatrix constraint an analysis reveals that the algorithm obtains the solutions of the constrained quadratic inverse eigenvalue problem in finitely many steps in the absence of round off errors finally numerical results are performed to confirm the analysis and to illustrate the efficiency of the proposed algorithm

general local search methods abstract this paper is a tutorial introduction to three recent yet widely used general heuristics simulated annealing tabu search and genetic algorithms a relatively precise description and an example of application are provided for each of the methods as well as a tentative evaluation and comparison from a pragmatic point of view

a new local search for continuous location problems this paper presents a new local search approach for solving continuous location problems the main idea is to exploit the relation between the continuous model and its discrete counterpart a local search is first conducted in the continuous space until a local optimum is reached it then switches to a discrete space that represents a discretisation of the continuous model to find an improved solution from there the process continues switching between the two problem formulations until no further improvement can be found in either thus we may view the procedure as a new adaption of formulation space search the local search is applied to the multi source weber problem where encouraging results are obtained this local search is also embedded within variable neighbourhood search producing excellent results

infinitesimal elastic plastic cosserat micropolar theory modelling and global existence in the rate independent case in this article we investigate the regularizing properties of generalized continua of cosserat micropolar type in the elasto plastic case we propose an extension of classical infinitesimal elasto plasticity to include consistently non dissipative micropolar effects it is shown that the new model is thermodynamically admissible and allows for a unique global in time solution of the corresponding rate independent initial boundary value problem the method of choice is the yosida approximation and a passage to the limit

generating conjugate directions for arbitrary matrices by matrix equations i abstract recursive methods for generating conjugate directions with respect to an arbitrary matrix are investigated there are three basic techniques to achieve this aim i minimizing a quadratic form ii generation by projections and iii use of matrix equations these techniques are equivalent to each other however the third one is stressed in this paper because of its versatility among matrix equation forms hestenes stiefel type recursions and lanczos type recursions are mentioned where the recursion matrices are bidiagonal matrices in the simple case with respect to the choice of recursion matrices direct and reverse methods are introduced the recursion matrices may have lower and upper triangular forms in the direct case and they may be lower and upper hessenberg matrices in the reverse case the recursion matrices chosen here are as simple as possible actually they have no more nonzero elements than that of a bidiagonal matrix consequently the storage of four vectors suffices to perform the recursions in all cases it is shown that restructuring the bidiagonal matrices makes it possible to avoid zero divisors for the hestenses stiefel type schemes

continuum and discrete models for structures including quasi inextensible elasticae with a view to the design and modeling of composite reinforcements abstract inspired by some composite fiber reinforcements used in aeronautical engineering and by the need of conceiving new metamaterials some discrete models including quasi inextensible elasticae are considered a class of continuum models approximately describing the macroscopic mechanical behavior of introduced structures is then heuristically proposed some of these continuum models can be regarded as a special kind of second gradient elastic media in which the higher gradient elasticity is conferred by the flexural stiffnesses of elasticae constituting the microscopic lattice the discrete models are studied by means of suitably tailored numerical codes designed to avoid numerical instabilities and locking and a comparison of discrete versus continuum models is attempted the obtained results show that the theory of generalized continua may be useful in some engineering applications and it plays a relevant role in the mechanics of woven composites the introduced discrete and continuum models are used to describe the so called bias extension test on woven fabrics and it is shown that a good choice to correctly reproduce the targeted phenomenology is to use a second gradient continuum theory however as discussed throughout the paper in the context of rigorous micro macro identification procedures there still remain many open problems to be solved especially when dealing with systems subjected to particular constraints such as inextensibility

heuristic algorithms for siting alternative fuel stations using the flow refueling location model abstract this paper presents three heuristic algorithms that solve for the optimal locations for refueling stations for alternative fuels such as hydrogen ethanol biodiesel natural gas or electricity the flow refueling location model frlm locates refueling stations to maximize the flow that can be refueled with a given number of facilities the frlm uses path based demands and because of the limitations imposed by the driving range of vehicles longer paths require combinations of more than one station to refuel round trip travel a mixed integer linear programming milp version of the model has been formulated and published and could be used to obtain an optimal solution however because of the need for combinations of stations to satisfy demands a realistic problem with a moderate size network and a reasonable number of candidate sites would be impractical to generate and solve with milp methods in this research heuristic algorithms specifically the greedy adding greedy adding with substitution and genetic algorithm are developed and applied to solve the frlm problem these algorithms are shown to be effective and efficient in solving complex frlm problems for case study purposes the heuristic algorithms are applied to locate hydrogen refueling stations in the state of florida

technical communique model reduction of periodic systems a lifting approach this note furthers existing results on the model reduction of stable periodic systems it utilizes for that matter a lifting technique to potentially attain less conservative error bounds

dynamics of cluster structures in a financial market network abstract in the course of recent fifteen years the network analysis has become a powerful tool for studying financial markets in this work we analyze stock markets of the usa and sweden we study cluster structures of a market network constructed from a correlation matrix of returns of the stocks traded in each of these markets such cluster structures are obtained by means of the p median problem pmp whose objective is to maximize the total correlation between a set of stocks called medians of size p and other stocks every cluster structure is an undirected disconnected weighted graph in which every connected component cluster is a star or a tree with one central node called a median and several leaf nodes connected with the median by weighted edges our main observation is that in non crisis periods of time cluster structures change more chaotically while during crises they show more stable behavior and fewer changes thus an increasing stability of a market graph cluster structure obtained via the pmp could be used as an indicator of a coming crisis

the volume algorithm producing primal solutions with a subgradient method we present an extension to the subgradient algorithm to produce primal as well as dual solutions it can be seen as a fast way to carry out an approximation of dantzig wolfe decomposition this gives a fast method for producing approximations for large scale linear programs it is based on a new theorem in linear programming duality we present successful experience with linear programs coming from set partitioning set covering max cut and plant location

heuristic concentration and tabu search a head to head comparison earlier this year two papers applying the metaheuristics tabu search ts and heuristic concentration hc to the p median problem were published in consecutive volumes of this journal here we apply the method of hc to some of the data sets which were used for computational experience in the paper on ts for these examples which we regard as being of a particularly challenging character hc discovers the superior solution superior to ts in about 95 of the cases and where the optimal solution is known the optimal solution in about 80 of the cases no general conclusion on the relative times for the two approaches can be drawn

existence of minimizers for a finite strain micromorphic elastic solid we investigate geometrically exact generalized continua of micromorphic type in the sense of eringen the two field problem for the macrodeformation and the affine microdeformation p gl 3 r in the quasistatic conservative load case is investigated in a variational form depending on material constants two existence theorems in sobolev spaces are given for the resulting nonlinear boundary value problems these results comprise existence results for the micro incompressible case p sl 3 r and the cosserat micropolar case p so 3 r in order to treat external loads a new condition called bounded external work has to be included which overcomes the conditional coercivity of the formulation the possible lack of coercivity is related to fracture of the micromorphic solid the mathematical analysis uses an extended korn first inequality the methods of choice are the direct methods of the calculus of variations

effective heuristics for multiproduct partial shipment models motivated by real applications we consider the problem of shipping products to multiple customers from limited inventory after formulating the optimization problems under different restrictions on partial shipments we find that commercially available packages applied directly are unsatisfactory as are simple greedy approaches we develop a scheme of heuristics that enables the user to select a good balance between computation time and effectiveness a detailed computational study of one and two period industrial sized problems indicates that these heuristics are computationally practical and generate solutions that are on average within 34 of the optimum

an iterative algorithm for discrete periodic lyapunov matrix equations abstract in this paper a novel iterative algorithm with a tuning parameter is developed to solve the forward discrete periodic lyapunov matrix equation associated with discrete time linear periodic systems an important feature of the proposed algorithm is that the information in the current and the last steps is used to update the iterative sequence the convergence rate of the algorithm can be significantly improved by choosing a proper tuning parameter it is shown that the sequence generated by this algorithm with zero initial conditions monotonically converges to the unique positive definite solution of the periodic lyapunov matrix equation if the tuning parameter is within the interval 0 1 in addition a necessary and sufficient convergence condition is given for the proposed algorithm in terms of the roots of a set of polynomial equations also a method to choose the optimal parameter is developed such that the algorithm has the fastest convergence rate finally numerical examples are provided to illustrate the effectiveness of the proposed algorithm

quasi gradient based inversion free iterative algorithm for solving a class of the nonlinear matrix equations abstract inspired by the gradient based and inversion free iterations a new quasi gradient based inversion free iterative algorithm is proposed for solving the nonlinear matrix equation x a t x n a i the convergence proof of the suggested algorithm is given several matrix norm inequalities are established to depict the convergence properties of this algorithm three numerical examples are given to illustrate the effectiveness of the suggested algorithms

periodic lyapunov equations some applications and new algorithms the discrete time periodic lyapunov equation has several important applications in the analysis and design of linear periodic control systems specific applications considered are the solution of state and output feedback optimal periodic control problems the stabilization by periodic state feedback and the square root balancing of discrete time periodic systems efficient and numerically reliable algorithms based on the periodic schur decomposition are proposed for the solution of periodic lyapunov equations the proposed algorithms are extensions of the direct solution methods for standard discrete time lyapunov equations for the case of indefinite as well as non negative definite solution

on korn s first inequality with non constant coefficients in this paper we prove a korn type inequality with non constant coefficients which arises from applications in elasto plasticity at large deformations more precisely let r 3 be a bounded lipschitz domain and let be a smooth part of the boundary with non vanishing two dimensional lebesgue measure define and let be given with det f p x 0 moreover suppose that rot then clearly this result generalizes the classical korn s first inequality which is just our result with f p 11 with slight modifications we are also able to treat forms of the type

numerical approximation of incremental infinitesimal gradient plasticity we investigate a representative model of continuum infinitesimal gradient plasticity the formulation is an extension of classical rate independent infinitesimal plasticity based on the additive decomposition of the symmetric strain tensor into elastic and plastic parts it is assumed that dislocation processes contribute to the storage of energy in the material whereby the curl of the plastic distortion appears in the thermodynamic potential and leads to an additional nonlocal backstress tensor the formulation is cast into a numerical framework by a saddle point approximation of the corresponding minimization problem in each incremental loading step this allows one to reformulate the nonlocal dissipation inequality to a point wise flow rule and yields a solution scheme which is a direct extension of the standard approach in classical plasticity our numerical results show the regularizing effects of the additional physically motivated terms copyright 2008 john wiley sons ltd

periodic conjugate direction algorithm for symmetric periodic solutions of general coupled periodic matrix equations abstract analysis and design of linear periodic control systems are closely related to the periodic matrix equations the conjugate direction cd method is a famous iterative algorithm to find the solution to nonsymmetric linear systems a x b in this work a new method based on the cd method is proposed for computing the symmetric periodic solutions x 1 x 2 x and y 1 y 2 y of general coupled periodic matrix equations s 0 1 a i s x i s b i s c i s y i s d i s m i s 0 1 e i s x i s f i s g i s y i s h i s n i for i 1 2 the key idea of the scheme is to extend the cd method by means of kronecker product and vectorization operator in order to assess the convergence properties of the method some theoretical results are given finally two numerical examples are included to illustrate the efficiency and effectiveness of the method

meta heuristic approaches with memory and evolution for a multi product production distribution system design problem we consider a multi product two stage production distribution system design problem pdsd where a fixed number of capacitated distribution centers are to be located with respect to capacitated suppliers plants and retail locations customers while minimizing the total costs in the system we present a mixed integer problem formulation that facilitates the development of efficient heuristic procedures we provide meta heuristic procedures including a population based scatter search with path relinking and trajectory based local and tabu search for the solution of the problem we also develop efficient construction heuristics and transshipment heuristics that are incorporated into the heuristic procedures for the solution of subproblems we present extensive computational results that show the high performance of the solution approaches we obtain smaller than 1 0 average optimality gaps with acceptable runtimes even for relatively large problems the computational results also demonstrate the effectiveness of the construction and transshipment heuristics that impact the solution quality and overall runtimes