optimization engineering techniques for the exact solution of np hard combinatorial optimization problems abstract the design of effective exact enumerative algorithms for finding the optimal solution of a given np hard combinatorial optimization problem whose mathematical model is given by an integer linear program is considered the commonly used approaches i e dynamic programming branch and bound branch and cut and branch and price are shortly described since the most effective algorithm to be used for finding the optimal solution of a given problem strongly depends on the specific instance to be solved then the best results are often obtained by using hybrid algorithms i e by combining different approaches according to what can be called an optimization engineering technique to illustrate the above mentioned approach the well known 0 1 knapsack problem asymmetric travelling salesman problem and 2 constraint bin packing problem are considered

best approximation in c algebras on developpe des methodes permettant d obtenir les meilleures approximations des ideaux de sous algebres et de sous espaces des c algebres

resource constrained assignment scheduling many resource constrained assignment scheduling problems can be modeled as 0 1 assignment problems with side constraints apsc unlike the well known assignment problem of linear programming apsc is np complete in this paper we define a branch and bound algorithm for solving apsc to optimality the algorithm employs a depth first polychotomous branching strategy in conjunction with a bounding procedure that utilizes subgradient optimization we also define a heuristic procedure for obtaining approximate solutions to apsc the heuristic uses subgradient optimization to guide the search for a good solution as well as to provide a bound on solution quality we present computational experience with both procedures applied to over 400 test problems the algorithm is demonstrated to be effective across three different classes of resource constrained assignment scheduling problems the heuristic generates solutions for these problems that are on average within 0 8 of optimality

semi crossed products of c algebras abstract given a c algebra u and endomorphim there is an associated nonselfadjoint operator algebra z x u called the semi crossed product of u with if is an automorphim z x u can be identified with a subalgebra of the c crossed product z x u if u is commutative and is an automorphim satisfying certain conditions z x u is an operator algebra of the type studied by arveson and josephson suppose s is a locally compact hausdorff space s s is a continuous and proper map and is the endomorphim of u c0 s given by necessary and sufficient conditions on the map are given to insure that the semi crossed product z x c0 s is i semiprime ii semisimple ii strongly semisimple

the hirsch conjecture for dual transportation polyhedra an algorithm is given that joins any pair of extreme points of a dual transportation polyhedron by a path of at most m 1 n 1 extreme edges

a relaxation column signature method for assignment problems abstract a recent computational study 7 on algorithms for assignment problems revealed that the so called modified hung rom algorithm mhra performs very well in practice the mhra is a row signature method and its effectiveness comes mainly from its capability to reduce the level by more than one unit per cycle we present an o n 3 column signature method which has the above mentioned capability the algorithm solves a sequence of relaxed transportation problems and generates strong dual feasible bases it is shown that the average number of iterations is bounded by n log n a result on balinski s strong dual feasible bases is also presented

a parallel branch and bound algorithm for solving large asymmetric traveling salesman problems a parallel branch and bound algorithm that solves the asymmetric traveling salesman problem to optimality is described the algorithm uses an assignment problem based lower bounding technique subtour elimination branching rules and a subtour patching algorithm as an upper bounding procedure the algorithm is organized around a data flow framework for parallel branch and bound the algorithm begins by converting the cost matrix to a sparser version in such a fashion as to retain the optimality of the final solution computational results are presented for three different classes of problem instances 1 matrix elements drawn from a uniform distribution of integers for instances of size 250 to 10 000 cities 2 instances of size 250 to 1000 cities that concentrate small elements in the upper left portion of the cost matrix and 3 instances of size 300 to 3000 cities that are designed to confound neighborhood search heuristics

index reduction for differential algebraic equations by substitution method abstract differential algebraic equations daes naturally arise in many applications but present numerical and analytical difficulties the index of a dae is a measure of the degree of numerical difficulty in general the higher the index is the more difficult it is to solve the dae therefore it is desirable to transform the original dae into an equivalent dae with lower index in this paper we propose an index reduction method for linear daes with constant coefficients the method is applicable to any dae having at most one derivative per equality in contrast to the other existing methods it does not introduce any additional variables exploiting a combinatorial property of degrees of minors in polynomial matrices we show that the method always reduces the index exactly by one thus the paper exhibits an application of combinatorial matrix theory to numerical analysis of daes

an additive bounding procedure for combinatorial optimization problems we know that the effectiveness of the branch and bound algorithms proposed for the solution of combinatorial optimization problems greatly depends on the tightness of the available bounds in this paper we consider optimization problems with a linear objective function we propose an additive approach for computing lower bounds that yields an increasing sequence of values an application to the traveling salesman problem with precedence constraints is presented to exemplify the technique

a domain decomposition method for the polar factorization of vector valued mappings we prove the convergence of an overlapping domain decomposition method for the polar factorization of vector valued mappings we introduce a consistent discretization of this problem under the form of an assignment problem the domain decomposition method applied to the discrete problem does not necessarily produce the wanted discrete solution however we prove that the sequence of outputs it produces when we refine the discretization tends to the solution of the continuous problem

a combinatorial algorithm for the euler equations of incompressible flows abstract a lagrangian time discretization is introduced for the euler equations of inviscid incompressible flows using the least square projection onto the manifold of volume preserving diffeomorphisms a further discretization is performed first by splitting the physical domain into n blocks of equal volume then by approximating each volume preserving mapping involved in the time discretization by a permutation of the n blocks finally a combinatorial algorithm is obtained where the classical assignment problem has to be solved at each time step

semicrossed products of operator algebras and their c envelopes abstract let a be a unital operator algebra and let be an automorphism of a that extends to a automorphism of its c envelope c env a we introduce the isometric semicrossed product a is z and we show that c env a is z c env a z in contrast the c envelope of the familiar contractive semicrossed product a z may not equal c env a z our main tool for calculating c envelopes for semicrossed products is a new concept the relative semicrossed product of an operator algebra by an endomorphism as an application of our theory we show that if t x is the tensor algebra of a c correspondence x a and is a extendible automorphism of t x that fixes the diagonal elementwise then the contractive semicrossed product satisfies c env t x z o x z where o x denotes the cuntz pimsner algebra of x a this extends the main result of davidson and katsoulis 2010 6

index reduction of differential algebraic equations by differential dixon resultant abstract high index differential algebraic equations daes are ordinary differential equations odes with constraints and arise frequently from many mathematical models of physical phenomenons and engineering fields in this paper we generalize the idea of differential elimination with dixon resultant to polynomially nonlinear daes we propose a new algorithm for index reduction of daes and establish the notion of differential dixon resultant which can provide the differential resultant of the enlarged system of original equations to make use of structure of daes variable pencil technique is given to determine the termination of differentiation moreover we also provide a heuristic method for removing the extraneous factors from differential resultant the experimentation shows that the proposed algorithm outperforms existing ones for many examples taken from the literature

a parallel shortest augmenting path algorithm for the assignment problem abstract we describe a parallel version of the shortest augmenting path algorithm for the assignment problem while generating the initial dual solution and partial assignment in parallel does not require substantive changes in the sequential algorithm using several augmenting paths in parallel does require a new dual variable recalculation method the parallel algorithm was tested on a 14 processor butterfly plus computer on problems with up to 900 million variables the speedup obtained increases with problem size the algorithm was also embedded into a parallel branch and bound procedure for the traveling salesman problem on a directed graph which was test on the butterfly plus on problems involving up to 7 500 cities to our knowledge these are the largest assignment problems and traveling salesman problems solved so far

minimizing variation of production rates in just in time systems a survey abstract in the past several years there has been growing interest in scheduling problems where jobs are penalized both for being early and for being tardy this notable deviation from previous work in which finishing early is generally regarded as being at least as desirable as finishing on time is perceived to be the one that well captures the scheduling dimension of jit production systems a number of excellent surveys on these problems has appeared over the last four years there is however another important scheduling objective in jit production systems which is to minimize variation of rates at which processes supply their outputs these scheduling problems are for example of primary concern in the toyota jit system thus far most research efforts in this area have been focused on minimizing variation of the rate at which different products are being produced on the final multi model assembly line which itself is a supplying process we shall review the results of this research and relate them to the due date based scheduling problems extensions and open problems will also be reviewed schedules that minimize variation of the rate at which different products are being produced on the line do not necessarily minimize variation in the line demand for outputs of processes that supply it few heuristics for the problem of minimizing the variation are available and hardly anything is known on its complexity as wel as exact algorithms to tackle it we shall review a mathematical programming model of the problem and open questions that result from it

optimal level schedules in mixed model multi level jit assembly systems with pegging abstract solving the level or balanced schedule problem is the most important scheduling goal for just in time production assembly systems for most industrial applications determining the optimal balanced schedule in a multi level facility is a very difficult combinatorial problem however if outputs at production levels which feed the final assembly level are dedicated or pegged to the final product into which they will be assembled then it can be shown that an efficient scheduling algorithm can be implemented to determine the optimal level schedule it can also be shown that several symmetrical properties of the pegging model can be exploited to significantly reduce the computational requirements of the problem

a lift and project cutting plane algorithm for mixed 0 1 programs we propose a cutting plane algorithm for mixed 0 1 programs based on a family of polyhedra which strengthen the usual lp relaxation we show how to generate a facet of a polyhedron in this family which is most violated by the current fractional point this cut is found through the solution of a linear program that has about twice the size of the usual lp relaxation a lifting step is used to reduce the size of the lp s needed to generate the cuts an additional strengthening step suggested by balas and jeroslow is then applied we report our computational experience with a preliminary version of the algorithm this approach is related to the work of balas on disjunctive programming the matrix cone relaxations of lovasz and schrijver and the hierarchy of relaxations of sherali and adams

a note on level schedules for mixed model assembly lines in just in time production systems this note formulates an assignment problem for obtaining optimal level schedules for mixed model assembly lines in jit production systems the problem was formulated as a quadratic integer programming problem in a recent paper by miltenburg 1989 where however only enumerative algorithms and heuristics were proposed for its solution our assignment formulation can also be extended to more general objective functions than the one used by miltenburg

cones of matrices and set functions and 0 1 optimization it has been recognized recently that to represent a polyhedron as the projection of a higher dimensional but simpler polyhedron is a powerful tool in polyhedral combinatorics a general method is developed to construct higher dimensional polyhedra or in some cases convex sets whose projection approximates the convex hull of 0 1 valued solutions of a system of linear inequalities an important feature of these approximations is that one can optimize any linear objective function over them in polynomial time in the special case of the vertex packing polytope a sequence of systems of inequalities is obtained such that the first system already includes clique odd hole odd antihole wheel and orthogonality constraints in particular for perfect and many other graphs this first system gives the vertex packing polytope for various classes of graphs including t perfect graphs it follows that the stable set polytope is the projection of a polytope with a polynomial number of facets an extension o

semisimple triangular af algebras abstract we give several necessary and sufficient conditions for a triangular af algebra to be semisimple in particular a triangular af algebra which can be written using the standard embedding infinitely often is semisimple we also give a semisimple triangular af algebra which does not have a presentation of this form if two triangular af algebras have the same peters poon wagner diagonal invariant then either both are semisimple or both are not however we give two algebras with the same diagonal invariant where one has the jacobson radical equal to the strong radical and the other does not semisimplicity can be characterized in terms of power s fundamental relation we give generalizations of these results to triangular subalgebras of groupoid c algebras it is shown that there is a unique maximal bimodule over the diagonal which does not intersect the radical using this we show that the wedderburn principal theorem does not hold for all triangular af algebras a necessary condition for the theorem to hold is that the above mentioned unique bimodule is a subalgebra

a new strongly polynomial dual network simplex algorithm this paper presents a new dual network simplex algorithm for the minimum cost network flow problem the algorithm works directly on the original capacitated network and runs in o mn m n logn logn time for the network withn nodes andm arcs this complexity is better than the complexity of orlin plotkin and tardos 1993 dual network simplex algorithm by a factor ofm n

transportation problems which can be solved by the use of hirsch paths for the dual problems balinski uses his signature method for the proof of the hirsch conjecture for dual transportation polyhedra to obtain an efficient algorithm for the assignment problem we will show how to extend this method to other primal transportation problems including transportation problems with unit demands we then prove that balinski s assignment algorithm is equivalent cycle by cycle to that of hung and rom we demonstrate that under some assumptions for our probability model a modification of the latter algorithm has an average complexity of o n2logn and present some computational results confirming this we also present results that indicate that this modification compares favorably with balinski s algorithm and other codes

a polyhedral approach to the asymmetric traveling salesman problem several branch and bound algorithms for the exact solution of the asymmetric traveling salesman problem atsp based on the assignment problem ap relaxation have been proposed in the literature these algorithms perform very well for some instances e g those with uniformly random integer costs but very poorly for others the aim of this paper is to evaluate the effectiveness of a branch and cut algorithm exploiting atsp specific facet defining cuts to be used to attack hard instances that cannot be solved by the ap based procedures from the literature we present new separation algorithms for some classes of facet defining cuts and a new variable pricing technique for dealing with highly degenerate primal lp problems a branch and cut algorithm based on these new results is designed and evaluated through computational analysis on several classes of both random and real world instances the outcome of the research is that on hard instances the branch and cut algorithm clearly outperforms the best ap based algorithms from the literature

technical note a polynomial simplex method for the assignment problem we present a polynomial primal simplex algorithm for the assignment problem for n n assignment problem with integer cost coefficients the algorithm generates at most n3 ln bases prior to reach the optimal basis where is the difference in objective value between an initial extreme point and the optimal extreme point

efficient index reduction algorithm for large scale systems of differential algebraic equations in many mathematical models of physical phenomenons and engineering fields such as electrical circuits or mechanical multibody systems which generate the differential algebraic equations daes systems naturally in general the feature of daes is a sparse large scale system of fully nonlinear and high index to make use of its sparsity this paper provides a simple and efficient algorithm for index reduction of large scale daes system we exploit the shortest augmenting path algorithm for finding maximum value transversal mvt as well as block triangular forms btfs we also present the extended signature matrix method with the block fixed point iteration and its complexity results furthermore a range of nontrivial problems are demonstrated by our algorithm

a unified framework for primal dual methods in minimum cost network flow problems we introduce a broad class of algorithms for finding a minimum cost flow in a capacitated network the algorithms are of the primal dual type they maintain primal feasibility with respect to capacity constraints while trying to satisfy the conservation of flow equation at each node by means of a wide variety of procedures based on flow augmentation price adjustment and ascent of a dual functional the manner in which these procedures are combined is flexible thereby allowing the construction of algorithms that can be tailored to the problem at hand for maximum effectiveness particular attention is given to methods that incorporate features from classical relaxation procedures experimental codes based on these methods outperform by a substantial margin the fastest available primal dual and primal simplex codes on standard benchmark problems

pryce pre analysis adapted to some dae solvers abstract the ode solver hbt 12 5 of order 12 t nguyen ba h hao h yagoub r vaillancourt one step 5 stage hermite birkho taylor ode solver of order 12 appl math comput 211 2009 313 328 doi 10 1016 j amc 2009 01 043 which combines a taylor series method of order 9 with a runge kutta method of order 4 is expanded into the dae solver hbt 12 5dae of order 12 dormand prince s dp 8 7 13m is also expanded into the dae solver dp 8 7 dae pryce structural pre analysis extended odes and ode first order forms are adapted to these dae solvers with a stepsize control based on local error estimators and a modified pryce algorithm to advance integration hbt 12 5dae uses only the first nine derivatives of the unknown variables as opposed to the first 12 derivatives used by the taylor series method t12dae of order 12 numerical results show the advantage of hbt 12 5dae over t12dae dp 8 7 dae and other known dae solvers

varietes de modules extremales de faisceaux semi stables sur ℙ 2 ℂ soient r c1 c2 des entiers avec r 1 et m r c1 c2 la variete de modules des faisceaux algebriques semi stables sur 2 de rang r et de classes de chern c1 c2 on dit que m r c1 c2 est extremale si dim m r c1 c2 0 et dim m r c1 c2 1 0 on se donne ici une description de certaines de ces varietes dites de faible hauteur si m r c1 c2 est de faible hauteur il existe des fibres exceptionnels e g f et des entiers q h n tels que tout faisceau semi stable e de rang r et de classes de chern c1 c2 sur 2 soit isomorphe au conoyau d un morphisme injectif de faisceaux f g q f h e n on considere l espace vectoriel w hom g q f h e n et l action evidente du groupe algebrique g aut g q f h aut e n sur w on definit une notion de semi stabilite pour l action de ce groupe en general non reductif et on montre qu en associant a un morphisme semi stable f le faisceau coker f on definit un morphisme w ss m r c1 c2 ou w ss est l ouvert g invariant des points semi stables qui est un bon quotient de m r c 1 c2 par g

c operator systems and crossed products abstract the purpose of this paper is to introduce a consistent notion of universal and reduced crossed products by actions and coactions of groups on operator systems and operator spaces in particular we shall put emphasis to reveal the full power of the universal properties of the universal crossed products it turns out to make things consistent one has to perform the constructions in some bigger categories which allow the right framework for studying the universal properties and which are stable under the construction of crossed products even for non discrete groups in the case of operator systems this larger category is what we call a c operator system i e a selfadjoint subspace x of some b h which contains a c algebra a such that a x x x a in the case of operator spaces the larger category is given by what we call c operator bimodules we introduce the notion of crossed products in these categories and show that the classical imai takai and katayama duality theorems for crossed products by group co actions on c algebras extend to our notion of crossed products by c operator systems and c operator bimodules

perturbation theory for groups and lattices abstract a generalization of a theorem of dan voiculescu on perturbations of separable c algebras is proved this is applied to solve two problems relating to the perturbation theory of unitary group representations and of commutative subspace lattices the latter generalizes a theorem of niels toft andersen on compact perturbations of nests

weak existence for the semigeostrophic equations formulated as a coupled monge ampere transport problem hoskins s semigeostrophic equations are reformulated as a coupled monge ampere transport problem b j hoskins quart j royal met soc 97 1971 pp 139 153 existence of global weak solutions is obtained for this formulation

index reduction in differential algebraic equations using dummy derivatives a new index reduction algorithm for daes is developed in the usual manner parts of the dae are differentiated analytically and appended to the original system for each additional equation a derivative is selected to be replaced by a new algebraic variable called a dummy derivative the resulting augmented system is at most index 1 but no longer overdetermined the dummy derivatives are not subject to discretization their purpose is to annihilate part of the dynamics in the dae leaving only what corresponds to the dynamics of a state space form no constraint stabilization is necessary in the subsequent numerical treatment numerical tests indicate that the method yields results with an accuracy comparable to that obtained for the corresponding state space ode

lower bounds for nonlinear assignment problems using many body interactions abstract this paper concerns lower bounding techniques for the general adic assignment problem the nonlinear objective function is linearized by the introduction of additional variables and constraints thus yielding a mixed integer linear programming formulation of the problem the concept of many body interactions is introduced to strengthen this formulation and incorporated in a modified formulation obtained by lifting the original representation to a higher dimensional space this process involves two steps i addition of new variables and constraints and ii incorporation of the new variables in the objective function if this lifting process is repeated times on an adic assignment problem along with the incorporation of higher order interactions it results in the mixed integer formulation of an equivalent adic assignment problem the incorporation of many body interactions in the higher dimensional formulation improves its degeneracy properties and is also critical to the derivation of decomposition methods for the solution of these large scale mathematical programs in the higher dimensional space it is shown that a lower bound to the optimal solution of the corresponding linear programming relaxation can be obtained by dualizing a subset of constraints in this formulation and solving o n 2 1 linear assignment problems whose coefficients depend on the dual values moreover it is proved that the optimal solution to the lp relaxation is obtained if we use the optimal duals for the solution of the linear assignment problems this concept of many body interactions could be applied in designing algorithms for the solution of formulations obtained by lifting general milp s we illustrate all these concepts on the quadratic assignment problems with these decomposition bounds we have found the provably optimal solutions of two unsolved qap s of size 32 and have also improved upon existing lower bounds for other qap s

an infeasible exterior point simplex algorithm for assignment problems the so called modified hung rom algorithm based upon theoretical considerations of hirsch paths seems to be one of the most efficient algorithms for assignment problems since any two basic feasible solutions to a linear problem can always be connected with a short simplex path passing through the infeasible region development of algorithms based upon theoretical considerations on infeasible paths seems to be of great practical interest this paper presents an algorithm of this kind for assignment problems

isotonic median regression a linear programming approach the isotonic median regression problem arises in statistics it is known that the isotonic median regression problem with respect to a complete order may be solved by a pool adjacent violators algorithm in this paper we show that this algorithm is a dual method for solving a linear programming formulation of the problem the linear programming approach provides additional insight into the algorithm as well as a simple proof of its validity we also analyze the computational complexity of the algorithm and discuss its significance from the standpoint of linear programming theory

implementation and testing of a primal dual algorithm for the assignment problem state of the art computational results have shown that primal simplex algorithms are more efficient than primal dual algorithms for general minimum cost network flow problems there is however some controversy concerning their relative merits for solving assignment problems this paper presents a detailed development for a computationally efficient primal dual algorithm and extensive computational comparisons to primal simplex algorithms

crossed products of operator algebras applications of takai duality abstract let g be a partially ordered abelian group with haar measure let a g be a dynamical system and let a be the associated semicrossed product using takai duality we establish a stable isomorphism a s a k g ad g where k g denotes the compact operators in the csl algebra alg l g and denotes the right regular representation of g we also show that there exists a complete lattice isomorphism between the invariant ideals of a and the ad invariant ideals of a k g using takai duality we also continue our study of the radical for the crossed product of an operator algebra and we solve open problems stemming from the earlier work of the authors among others we show that the crossed product of a radical operator algebra by a compact abelian group is a radical operator algebra we also show that the permanence of semisimplicity fails for crossed products by r a final section of the paper is devoted to the study of radically tight dynamical systems i e dynamical systems a g for which the identity rad a g rad a g persists a broad class of such dynamical systems is identified

a survey for the quadratic assignment problem the quadratic assignment problem qap one of the most difficult problems in the np hard class models many real life problems in several areas such as facilities location parallel and distributed computing and combinatorial data analysis combinatorial optimization problems such as the traveling salesman problem maximal clique and graph partitioning can be formulated as a qap in this paper we present some of the most important qap formulations and classify them according to their mathematical sources we also present a discussion on the theoretical resources used to define lower bounds for exact and heuristic algorithms we then give a detailed discussion of the progress made in both exact and heuristic solution methods including those formulated according to metaheuristic strategies finally we analyze the contributions brought about by the study of different approaches

active set algorithms for isotonic regression a unifying framework in this and subsequent papers we will show that several algorithms for the isotonic regression problem may be viewed as active set methods the active set approach provides a unifying framework for studying algorithms for isotonic regression simplifies the exposition of existing algorithms and leads to several new efficient algorithms we also investigate the computational complexity of several algorithms

the ideal structure of certain nonselfadjoint operator algebras soit x un systeme dynamique localement compact et z x co x la sous algebre close en norme du produit croise zx co x engendre par les puissances non negatives de dans le cas homeomorphisme on determine la structure ideale de ces algebres dans le cas ou agit librement

isomorphisms between topological conjugacy algebras a family of algebras which we call topological conjugacy algebras is associated with each proper continuous map on a locally compact hausdorff space assume that i xi xi is a continuous proper map on a locally compact hausdorff space xi for i 1 2 we show that the dynamical systems x1 1 and x2 2 are conjugate if and only if some topological conjugacy algebra of x1 1 is isomorphic as an algebra to some topological conjugacy algebra of x2 2 this implies as a corollary the complete classification of the semicrossed products c0 x z which was previously considered by arveson and josephson 3 peters 19 hadwin and hoover 8 and power 21 we also obtain a complete classification of all semicrossed products of the form a d z where a d denotes the disc algebra and d d a continuous map which is analytic on the interior in this case a surprising dichotomy appears in the classification scheme which depends on the fixed point set of we also classify more general semicrossed products of uniform algebras

one processor scheduling with symmetric earliness and tardiness penalties we consider one processor scheduling problems having the following form tasks t1 t2 tn are given with each ti having a specified length li and a preferred starting time ai or equivalently a preferred completion time bi the tasks are to be scheduled nonpreemptively i e a task cannot be split on a single processor to begin as close to their preferred starting times as possible we examine two different cost measures for such schedules the sum of the absolute discrepancies from the preferred starting times and the maximum such discrepancy for the first of these we show that the problem of finding minimum cost schedules is np complete however we give an efficient algorithm that finds minimum cost schedules whenever the tasks either all have the same length or are required to be executed in a given fixed sequence for the second cost measure we give an efficient algorithm that finds minimum cost schedules in general with no constraints on the ordering or lengths of the tasks

efficient dual simplex algorithms for the assignment problem efficient algorithms based upon balinski s signature method are described for solving then n assignment problem these algorithms are special variants of the dual simplex method and are shown to have computational bounds of o n3 variants for solving sparse assignment problems withm arcs that require o m space and o mn n2 logn time in the worst case are also presented

a variant of time minimizing assignment problem a time minimizing assignment problem tmap dealing with the allocation of n jobs to m n persons is considered in this paper one job is to be allocated to exactly one person and each person does at least one job all the persons start working on the jobs simultaneously if a person is to do more than one job he does them one after the other in any order the aim of the present study is to find that feasible assignment which minimizes the total time for completing all the jobs a lexi search approach is proposed to find an optimal feasible assignment

least squares completions for nonlinear differential algebraic equations a method has been proposed for numerically solving lower dimensional nonlinear higher index differential algebraic equations for which more classical methods such as backward differentiation or implicit runge kutta may not be appropriate this method is based on solving nonlinear dae derivative arrays using nonlinear singular least squares methods the theoretical foundations generality and limitations of this approach remain to be determined this paper carefully examines several key aspects of this approach the emphasis is on general results rather than specific results based on the structure of various applications

the hyperrigidity of tensor algebras of c correspondences abstract given a c correspondence x we give necessary and sufficient conditions for the tensor algebra t x to be hyperrigid in the case where x is coming from a topological graph we obtain a complete characterization

the jacobson radical for analytic crossed products we characterise the jacobson radical of an analytic crossed product c0 x z answering a question first raised by arveson and josephson in 1969 in fact we characterise the jacobson radical of analytic crossed products c0 x zd this consists of all elements whose fourier coefficients vanish on the recurrent points of the dynamical system and the first one is zero the multidimensional version requires a variation of the notion of recurrence taking into account the various degrees of freedom

signature classes of transportation polytopes signature algorithms solve certain classes of transportation problems in a number of steps bounded by the diameter of the dual polyhedron the class of problems to which signature algorithms may be applied the signature classes of the title are characterized and the monotonic hirsch conjecture is shown to hold for them in addition certain more precise results are given for different cases finally it is explained why a supposed proof of the hirsch conjecture for all transportation polytopes is incomplete and apparently irremedial

level schedules for mixed model just in time processes a mixed model manufacturing facility running under a just in time jit production system is controlled by setting the production sequence of the final assembly process this sequence is set to achieve the primary goal of an organization operating under a jit system which is to maintain a constant rate of part usage in this paper a graph theoretic approach is used to determine an optimal solution for this goal for a new nonconvex objective function furthermore it is shown that a schedule always exists such that at all times the deviation of actual production from the desired level of production for every product is never more than one unit

relaxation methods for minimum cost ordinary and generalized network flow problems we propose a new class of algorithms for linear cost network flow problems with and without gains these algorithms are based on iterative improvement of a dual cost and operate in a manner that is reminiscent of coordinate ascent and gauss seidel relaxation methods we compare our coded implementations of these methods with mature state of the art primal simplex and primal dual codes and find them to be several times faster on standard benchmark problems and faster by an order of magnitude on large randomly generated problems our experiments indicate that the speedup factor increases with problem dimension

a path following algorithm for the graph matching problem we propose a convex concave programming approach for the labeled weighted graph matching problem the convex concave programming formulation is obtained by rewriting the weighted graph matching problem as a least square problem on the set of permutation matrices and relaxing it to two different optimization problems a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices the concave relaxation has the same global minimum as the initial graph matching problem but the search for its global minimum is also a hard combinatorial problem we therefore construct an approximation of the concave problem solution by following a solution path of a convex concave problem obtained by linear interpolation of the convex and concave formulations starting from the convex relaxation this method allows to easily integrate the information on graph label similarities into the optimization problem and therefore perform labeled weighted graph matching the algorithm is compared with some of the best performing graph matching methods on four data sets simulated graphs qaplib retina vessel images and handwritten chinese characters in all cases the results are competitive with the state of the art

computing lower bounds for the quadratic assignment problem with an interior point algorithm for linear programming an example of the quadratic assignment problem qap is the facility location problem in which n facilities are assigned at minimum cost to n sites between each pair of facilities there is a given amount of flow contributing a cost equal to the product of the flow and the distance between sites to which the facilities are assigned proving optimality of qaps has been limited to instances having fewer than 20 facilities largely because known lower bounds are weak we compute lower bounds for a wide range of qaps using a linear programming based lower bound studied by z drezner 1995 on the majority of qaps tested a new best known lower bound is computed on 87 of the instances we produced the best known lower bound on several instances including some having more the 20 facilities the lower bound is tight the linear programs which can be large even for small qaps are solved with an interior point code that uses a preconditioned conjugate gradient algorithm to compute the interior point directions attempts to solve these instances using the cplex primal simplex algorithm as well as the cplex barrier primal dual interior point method were successful only for the smallest instances

signature methods for the assignment problem the signature of a dual feasible basis of the assignment problem is an n vector whose ith component is the number of nonbasic activities of type i j this paper uses signatures to describe a method for finding optimal assignments that terminates in at most n 1n 2 2 pivot steps and takes at most on3 work

on solving a variation of the assignment problem abstract geetha and nair recently proposed a variant of n n assignment problem with the objective of minimizing the total cost plus an additional supervisory cost they gave an o n 5 algorithm to solve the problem here we present an algorithm for this problem using balinski s signature method for the assignment problem at each stage the algorithm has a complexity of o m m n log n where m is the number of arcs in the problem

hyper heuristic approaches for the response time variability problem we propose two classes for the implementation of hyper heuristic algorithms the first is based on constructive heuristics whereas the second uses improvement methods within the latter class a general framework is designed for the use of local search procedures and metaheuristics as low level heuristics a dynamic scheme to guide the use of these approaches is also devised these ideas are tested on an np hard scheduling problem known as the response time variability problem rtvp an intensive computational experiment shows especially in the second class where the new best results are found the effectiveness of the proposed hyper heuristics

a competitive dual simplex method for the assignment problem where there is abundance of mystery and confusion in every direction the truth seldom remains hidden for long it s a matter of having plenty of angles to go at it from only the utterly simple crimes the simplex crimes you may say have the trick of remaining baffling sir john from michael innes the open house a sir john appleby mystery penguin books 1974

semicrossed products of simple c algebras let mathcal a alpha and mathcal b beta be c dynamical systems and assume that mathcal a is a separable simple c algebra and that and are automorphisms then the semicrossed products mathcal a times alpha mathbb z and mathcal b times beta mathbb z are isometrically isomorphic if and only if the dynamical systems mathcal a alpha and mathcal b beta are outer conjugate

mathematical programming modeling of the response time variability problem the response time variability problem rtvp is a scheduling problem that has recently been defined in the literature the rtvp has a broad range of real life applications from manufacturing to services and information technology a previous study developed a position exchange heuristic to apply to initial sequences for the rtvp and a milp mixed integer linear programming to obtain optimal solutions with a practical limit of 25 units to be scheduled this paper aims to improve the best mathematical programming model developed thus far in order to solve larger instances up to 40 units to optimality the contribution of this paper is 4 fold i larger instances can be solved to optimality by the off the shelf standard software ii the new optimal solutions of the rtvp can be used to compare the results of heuristic procedures iii the importance of modeling is demonstrated as well as the huge impact that reformulation redundant constraints and the elimination of symmetries have on the efficiency of milps is clearly established finally iv a challenge to develop a customized optimization algorithm to rival the milp solution efficiency for the rtvp is put forward

a transformed two stage method for reducing the part usage variation and a comparison of the product level and part level solutions in sequencing mixed model assembly lines abstract the minimization of the two stage variation in the mixed model sequencing problem of reducing the part level variation is transformed to product level terms the development is based on an existing simplification of the one stage part level variation a simplification of the two stage part level variation and the usage of a relationship matrix that evaluates the relevance among the product structures of various models algorithms based on these simplification and transformation are presented the transformation can be shown to be equivalent to that of bautista et al 1996 but results in a smaller empirical computational burden in minimizing the two stage variation and uses a relationship matrix that is independent of product mix changes the computational results show that the transformed two stage algorithm significantly outperforms the direct enumeration method in computation time for large problems and generally outperforms the one stage method in mean squared deviation the transformed two stage method can be used as a heuristic procedure or as an intermediate tool for another solution approach a more general sufficient condition than the existing conditions for the equivalence of the problems of minimizing the product level variation and minimizing the part level variation is also presented the computational experimentation demonstrates that there is a potential of obtaining significantly better solutions in part usage variation by directly considering the part level variation when this sufficient condition is not met

differential algebraic equations of index 1 may have an arbitrarily high structural index it is shown that the structural index of a linear differential algebraic equation dae with constant coefficients and with index 1 may be arbitrarily high contrary to a previous result from the literature this demonstrates that pantelides algorithm applied to daes of index 1 may perform an arbitrarily high number of iterations and differentiations