well structured transition systems everywhere well structured transition systems wstss are a general class of infinite state systems for which decidability results rely on the existence of a well quasi ordering between states that is compatible with the transitions in this article we provide an extensive treatment of the wsts idea and show several new results our improved definitions allow many examples of classical systems to be seen as instances of wstss

xpath satisfiability in the presence of dtds we study the satisfiability problem associated with xpath in the presence of dtds this is the problem of determining given a query p in an xpath fragment and a dtd d whether or not there exists an xml document t such that t conforms to d and the answer of p on t is nonempty we consider a variety of xpath fragments widely used in practice and investigate the impact of different xpath operators on the satisfiability analysis we first study the problem for negation free xpath fragments with and without upward axes recursion and data value joins identifying which factors lead to tractability and which to np completeness we then turn to fragments with negation but without data values establishing lower and upper bounds in the absence and in the presence of upward modalities and recursion we show that with negation the complexity ranges from pspace to exptime moreover when both data values and negation are in place we find that the complexity ranges from nexptime to undecidable furthermore we give a finer analysis of the problem for particular classes of dtds exploring the impact of various dtd constructs identifying tractable cases as well as providing the complexity in the query size alone finally we investigate the problem for xpath fragments with sibling axes exploring the impact of horizontal modalities on the satisfiability analysis

multi parameterised compositional verification of safety properties we introduce a fully automatic technique for the parameterised verification of safety properties the technique combines compositionality and completeness with support to multiple parameters and it is implemented in a tool we start with an lts based labelled transition system csp like concurrent sequential processes formalism with parallel composition and hiding operators first we equip the formalism with types and variables which enable parameterising the structure of a system and prove that the formalism remains compositional next we show how trace refinement between parameterised processes can be checked by computing structural cut offs for types this way a parameterised verification task reduces to finitely many finite state refinement checks we also provide an extension to the theory which allows for user definable universal relations this enables parameterising system topology to some extent too finally we consider the assumptions related to the approach and show that each of them is necessary for decidability

stress related topology optimization via level set approach abstract considering stress related objective or constraint functions in structural topology optimization problems is very important from both theoretical and application perspectives it has been known however that stress related topology optimization problem is challenging since several difficulties must be overcome in order to solve it effectively traditionally simp solid isotropic material with penalization method was often employed to tackle it although some remarkable achievements have been made with this computational framework there are still some issues requiring further explorations in the present work stress related topology optimization problems are investigated via a level set based approach which is a different topology optimization framework from simp numerical examples show that under appropriate problem formulations level set approach is a promising tool for stress related topology optimization problems

explicit level set based topology optimization using an exact heaviside function and consistent sensitivity analysis summary this paper presents a level set based topology optimization method based on numerically consistent sensitivity analysis the proposed method uses a direct steepest descent update of the design variables in a level set method the level set nodal values an exact heaviside formulation is used to relate the level set function to element densities the level set function is not required to be a signed distance function and reinitialization is not necessary using this approach level set based topology optimization problems can be solved consistently and multiple constraints treated simultaneously the proposed method leads to more insight in the nature of level set based topology optimization problems the level set based design parametrization can describe gray areas and numerical hinges consistency causes results to contain these numerical artifacts we demonstrate that alternative parameterizations level set based or density based regularization can be used to avoid artifacts in the final results the effectiveness of the proposed method is demonstrated using several benchmark problems the capability to treat multiple constraints shows the potential of the method furthermore due to the consistency the optimizer can run into local minima a fundamental difficulty of level set based topology optimization more advanced optimization strategies and more efficient optimizers may increase the performance in the future copyright 2012 john wiley sons ltd

supervised feature selection in graphs with path coding penalties and network flows we consider supervised learning problems where the features are embedded in a graph such as gene expressions in a gene network in this context it is of much interest to automatically select a subgraph with few connected components by exploiting prior knowledge one can indeed improve the prediction performance or obtain results that are easier to interpret regularization or penalty functions for selecting features in graphs have recently been proposed but they raise new algorithmic challenges for example they typically require solving a combinatorially hard selection problem among all connected subgraphs in this paper we propose computationally feasible strategies to select a sparse and well connected subset of features sitting on a directed acyclic graph dag we introduce structured sparsity penalties over paths on a dag called path coding penalties unlike existing regularization functions that model long range interactions between features in a graph path coding penalties are tractable the penalties and their proximal operators involve path selection problems which we efficiently solve by leveraging network flow optimization we experimentally show on synthetic image and genomic data that our approach is scalable and leads to more connected subgraphs than other regularization functions for graphs

topology optimization with implicit functions and regularization summary topology optimization is formulated in terms of the nodal variables that control an implicit function description of the shape the implicit function is constrained by upper and lower bounds so that only a band of nodal variables needs to be considered in each step of the optimization the weak form of the equilibrium equation is expressed as a heaviside function of the implicit function the heaviside function is regularized to permit the evaluation of sensitivities we show that the method is a dual of the bendshe kikuchi method the method is applied both to problems of optimizing single material and

a capacity rounding algorithm for the minimum cost circulation problem a dual framework of the tardos algorithm recently e tardos gave a strongly polynomial algorithm for the minimum cost circulation problem and solved the open problem posed in 1972 by j edmonds and r m karp her algorithm runs in o m2t m n logm time wherem is the number of arcs n is the number of vertices andt m n is the time required for solving a maximum flow problem in a network withm arcs andn vertices in the present paper taking an approach that is a dual of tardos s we also give a strongly polynomial algorithm for the minimum cost circulation problem our algorithm runs in o m2s m n logm time and reduces the computational complexity wheres m n is the time required for solving a shortest path problem with a fixed origin in a network withm arcs n vertices and a nonnegative arc length function the complexity is the same as that of orlin s algorithm recently developed by efficiently implementing the edmonds karp scaling algorithm

an enhanced aggregation method for topology optimization with local stress constraints abstract by introducing a new reduction parameter into the kreisselmeier steihauser k s function this paper presents a general k s formulation providing an approximation to the feasible region restricted by active constraints the approximation is highly accurate even when the aggregation parameter takes a relatively small value numerical difficulties such as high nonlinearity and serious violation of local constraints that may be exhibited by the original k s function are thus effectively alleviated in the considered topology optimization problem the material volume is to be minimized under local von mises stress constraints imposed on all the finite elements an enhanced aggregation algorithm based on the general k s function in conjunction with a removal and re generation strategy for selecting the active constraints is then proposed to treat the stress constraints of the optimization problem numerical examples are given to demonstrate the validity of the present algorithm it is shown that the proposed method can achieve reasonable solutions with a high computational efficiency in handling large scale stress constrained topology optimization problems

a newly developed qp relaxation method for element connectivity parameterization to achieve stress based topology optimization for geometrically nonlinear structures the aim of this work is to present a novel computational approach to employ the stress based topology optimization method stom to minimize the volume subject to the locally defined stress constraints of a geometrically nonlinear structure in the framework of the element connectivity parameterization ecp method considering the locally defined stress constraints in topology optimization to is a classic and challenging engineering problem and successful optimization procedures have recently been developed using the density based to method for linear elastic structures however no study has yet considered the static failure constraint when using to for a geometrically nonlinear structure therefore the present study develops a novel computational approach for the stom for a geometrically nonlinear structure to successfully optimize a geometrically nonlinear structure the unstable element issue must be properly addressed in addition to the stress singularity issue the existence of a large number of constraints and the highly nonlinear behavior of the local stress constraints to effectively resolve these issues this research adopts the ecp method to interpolate and optimize the connectivities among solid finite elements furthermore we find that a stress singularity issue linked to the local optima issue arises in the ecp method that is different from that of the density based to by investigating the singularity behavior in detail we develop a new qp relaxation method that is suitable for the ecp method to demonstrate the improved capability of the proposed ecp method with the modified qp relaxation several two dimensional to problems are solved

a strongly polynomial algorithm to solve combinatorial linear programs khachiyan and recently karmarkar gave polynomial algorithms to solve the linear programming problem these algorithms have a small theoretical drawback namely the number of arithmetic steps depends on the size of the input numbers we present a polynomial linear programming algorithm whose number of arithmetic steps depends only on the size of the numbers in the constraint matrix but is independent of the size of the numbers in the right hand side and objective vectors in particular it gives a polynomial algorithm for the minimum cost flow and multicommodity flow problems in which the number of arithmetic steps is independent of the size of the costs and capacities the algorithm makes use of an existing polynomial linear programming algorithm the problem of whether any algorithm has a running time that is independent even of the size of the numbers in the constraint matrix remains open

polyhedra related to undirected multicommodity flows abstract let g vg eg and h vh eh be two undirected graphs and vh vg we associate with g and h the unbounded polyhedron p g h in q eg which consists of all nonegative rational valued functions vectors l on eg such that for each edge st in h the distance between s and t in the graph g whose edges eg have the lengths l is no less that 1 let h be the least positive integer k such that each vertex of p g h is 1 k integral for any g with vg vh h if such a k does not exist in other terms h is the least positive integer k such that each problem dual to a maximum undirected multicommodity flow problem with the commodity graph h has on optimal solution that is 1 k integral we prove that h can be only 1 2 4 and moreover for each k 1 2 4 we describe the class of h s with h k also results concerning extreme of cones related to feasibility multicommodity flow problems are presented

an automata theoretic approach to the verification of distributed algorithms abstract we introduce an automata theoretic method for the verification of distributed algorithms running on ring networks in a distributed algorithm an arbitrary number of processes cooperate to achieve a common goal e g elect a leader processes have unique identifiers pids from an infinite totally ordered domain an algorithm proceeds in synchronous rounds which allow processes to exchange pids store them in registers and compare their register contents to specify correctness properties we introduce a logic that can reason about processes and pids we show that model checking distributed algorithms can be reduced to satisfiability in propositional dynamic logic with loop and converse using this reduction we provide an automata theoretic approach to proving distributed algorithms correct up to a given number of rounds overall we show that round bounded verification of distributed algorithms over rings is pspace complete provided the number of rounds is given in unary

velocity extension for the level set method and multiple eigenvalues in shape optimization in the context of structural optimization by the level set method we propose an extension of the velocity of the underlying hamilton jacobi equation the gradient method is endowed with a hilbertian structure based on the h1 sobolev space numerical results for compliance minimization and mechanism design show a strong improvement of the rate of convergence of the level set method another important application is the optimization of multiple eigenvalues

development of pareto topology optimization considering thermal loads abstract in this research we developed a level set based topology optimization with a topological derivative formulation considering thermal load thermo elasticity equations were utilized to obtain the sensitivity of the objective function after inserting a small hole in the domain total strain energy and the maximum stress in the design domain were taken as the objective functions after taking the thermal loading effect into account the total strain energy density function became a nonhomogeneous function of the strain in addition temperature variation changed hooke s law from a linear homogeneous to a linear nonhomogeneous expression including a zero order term we derived the sensitivity value of the selected objective functions with respect to a perturbation in the structural domain under mechanical and thermal loads while considering these changes in the governing equations we performed several numerical optimization problems to demonstrate the validity of the present level set based pareto topology optimization two types of examples compliance and stress minimization were solved based on the chosen objective functions furthermore in the stress minimization examples the derived formula was extended to consider thermal effects in the failure theories for pressure independent and dependent materials

relaxed most negative cycle and most positive cut canceling algorithms for minimum cost flow this paper presents two new scaling algorithms for the minimum cost network flow problem one a primal cycle canceling algorithm the other a dual cut canceling algorithm both algorithms scale a relaxed optimality parameter and create a second inner relaxation the primal algorithm uses the inner relaxation to cancel a most negative node disjoint family of cycles w r t the scaled parameter the dual algorithm uses it to cancel most positive cuts w r t the scaled parameter we show that in a network with n nodes and m arcs both algorithms need to cancel only omn objects per scaling phase furthermore we show how to efficiently implement both algorithms to yield weakly polynomial running times that are as fast as any other cycle or cut canceling algorithms our algorithms have potential practical advantages compared to some other canceling algorithms as well along the way we give a comprehensive survey of cycle and cut canceling algorithms for min cost flow we also clarify the formal duality between cycles and cuts

a mixed fem approach to stress constrained topology optimization we present an alternative topology optimization formulation capable of handling the presence of stress constraints in a straightforward fashion the main idea is to adopt a mixed finite element discretization scheme wherein not only displacements as usual but also stresses are the variables entering the formulation by doing so any stress constraint may be handled within the optimization procedure without resorting to post processing operation typical of displacement based techniques that may also cause a loss in accuracy in stress computation if no smoothing of the stress is performed two dual variational principles of hellinger reissner type are presented in continuous and discrete form that which included in a rather general topology optimization problem in the presence of stress constraints that is solved by the method of moving asymptotes int j numer meth engng 1984 24 3 359 373 extensive numerical simulations are performed and ongoing extensions outlined including the optimization of elastoplastic and incompressible media copyright 2007 john wiley sons ltd

half integrality of node capacitated multiflows and tree shaped facility locations on trees in this paper we establish a novel duality relationship between node capacitated multiflows and tree shaped facility locations we prove that the maximum value of a tree distance weighted maximum node capacitated multiflow problem is equal to the minimum value of the problem of locating subtrees in a tree and the maximum is attained by a half integral multiflow utilizing this duality we show that a half integral optimal multiflow and an optimal location can be found in strongly polynomial time these extend previously known results in the maximum free multiflow problems we also show that the set of tree distance weights is the only class having bounded fractionality in maximum node capacitated multiflow problems

a level set method for structural topology optimization this paper presents a new approach to structural topology optimization we represent the structural boundary by a level set model that is embedded in a scalar function of a higher dimension such level set models are flexible in handling complex topological changes and are concise in describing the boundary shape of the structure furthermore a well founded mathematical procedure leads to a numerical algorithm that describes a structural optimization as a sequence of motions of the implicit boundaries converging to an optimum solution and satisfying specified constraints the result is a 3d topology optimization technique that demonstrates outstanding flexibility of handling topological changes fidelity of boundary representation and degree of automation we have implemented the algorithm with the use of several robust and efficient numerical techniques of level set methods the benefit and the advantages of the proposed method are illustrated with several 2d examples that are widely used in the recent literature of topology optimization especially in the homogenization based methods

stress based shape and topology optimization with the level set method abstract this paper proposes a level set method to solve minimum stress and stress constrained shape and topology optimization problems the method solves a sub optimization problem every iteration to obtain optimal boundary velocities a p norm stress functional is used to aggregate stresses in a single constraint the shape sensitivity function is derived and a computational procedure based on a least squares interpolation approach is devised in order to compute sensitivities at the boundaries adaptive constraint scaling is used to enforce exact control of stress limits numerical results show that the method is able to solve the problem efficiently for single and multiple load cases obtaining solutions with smooth boundaries

self adjusting binary search trees the splay tree a self adjusting form of binary search tree is developed and analyzed the binary search tree is a data structure for representing tables and lists so that accessing inserting and deleting items is easy on an n node splay tree all the standard search tree operations have an amortized time bound of o log n per operation where by amortized time is meant the time per operation averaged over a worst case sequence of operations thus splay trees are as efficient as balanced trees when total running time is the measure of interest in addition for sufficiently long access sequences splay trees are as efficient to within a constant factor as static optimum search trees the efficiency of splay trees comes not from an explicit structural constraint as with balanced trees but from applying a simple restructuring heuristic called splaying whenever the tree is accessed extensions of splaying give simplified forms of two other data structures lexicographic or multidimensional search trees and link cut trees

topology optimization of continuum structures with local stress constraints we introduce an extension of current technologies for topology optimization of continuum structures which allows for treating local stress criteria we first consider relevant stress criteria for porous composite materials initially by studying the stress states of the so called rank 2 layered materials then on the basis of the theoretical study of the rank 2 microstructures we propose an empirical model that extends the power penalized stiffness model also called simp for solid isotropic microstructure with penalization for inter mediate densities in a second part solution aspects of topology problems are considered to deal with the so called singularity phenomenon of stress constraints in topology design an constraint relaxation of the stress constraints is used we describe the mathematical programming approach that is used to solve the numerical optimization problems and show results for a number of example applications 1998 john wiley sons ltd

approximation algorithms for solving the constrained arc routing problem in mixed graphs abstract given a mixed graph g with vertex set v let e and a denote the sets of edges and arcs respectively we use q and z to denote the sets of positive rational numbers and positive integers respectively for any connected mixed graph g v e a w l u with a length function w e a q and two integer functions l u e a z satisfying l e u e for each e e a we are asked to determine a minimum length tour t traversing each e e a at least l e and at most u e times this new constrained arc routing problem generalizes the mixed chinese postman problem let n v and m e a denote the number of vertices and edges including arcs respectively using network flow techniques we design a 1 1 l 0 approximation algorithm in time o n 2 m 3 log n to solve this constrained arc routing problem such that l e u e holds for each edge e e l e u e holds for each arc e a and l 0 min l e e e in addition we present two optimal combinatorial algorithms in times o n 3 and o nm 2 log n to solve this problem for the cases a and e respectively

phase field relaxation of topology optimization with local stress constraints we introduce a new relaxation scheme for structural topology optimization problems with local stress constraints based on a phase field method in the basic formulation we have a pde constrained optimization problem where the finite element and design analysis are solved simultaneously the starting point of the relaxation is a reformulation of the material problem involving linear and 0 1 constraints only the 0 1 constraints are then relaxed and approximated by a cahn hilliard type penalty in the objective functional which yields convergence of minimizers to 0 1 designs as the penalty parameter decreases to zero a major advantage of this kind of relaxation opposed to standard approaches is a uniform constraint qualification that is satisfied for any positive value of the penalization parameter the relaxation scheme yields a large scale optimization problem with a high number of linear inequality constraints we discretize the problem by finite elements and solve the arising finite dimensional programming problems by a primal dual interior point method numerical experiments for problems with local stress constraints based on different criteria indicate the success and robustness of the new approach

faster scaling algorithms for network problems this paper presents algorithms for the assignment problem the transportation problem and the minimum cost flow problem of operations research the algorithms find a minimum cost solution yet run in time close to the best known bounds for the corresponding problems without costs for example the assignment problem equivalently minimum cost matching in a bipartite graph can be solved in o sqrt nm log nn time where n m and n denote the number of vertices number of edges and largest magnitude of a cost costs are assumed to be integral the algorithms work by scaling as in the work of goldberg and tarjan in each scaled problem an approximate optimum solution is found rather than an exact optimum

topology optimization of continuum structures with stress constraints and uncertainties in loading summary topology optimization using stress constraints and considering uncertainties is a serious challenge since a reliability problem has to be solved for each stress constraint for each element in the mesh in this paper an alternative way of solving this problem is employed where uncertainty quantification is performed through the first order perturbation approach with proper validation by monte carlo simulation uncertainties are considered in the loading magnitude and direction the minimum volume problem subjected to local stress constraints is formulated as a robust problem where the stress constraints are written as a weighted average between their expected value and standard deviation the augmented lagrangian method is used for handling the large set of local stress constraints whereas a gradient based algorithm is used for handling the bounding constraints it is shown that even in the presence of small uncertainties in loading direction different topologies are obtained when compared to a deterministic approach the effect of correlation between uncertainties in loading magnitude and direction on optimal topologies is also studied where the main observed result is loss of symmetry in optimal topologies this article is protected by copyright all rights reserved

topology optimization using a reaction diffusion equation abstract this paper presents a structural topology optimization method based on a reaction diffusion equation in our approach the design sensitivity for the topology optimization is directly employed as the reaction term of the reaction diffusion equation the distribution of material properties in the design domain is interpolated as the density field which is the solution of the reaction diffusion equation so free generation of new holes is allowed without the use of the topological gradient method our proposed method is intuitive and its implementation is simple compared with optimization methods using the level set method or phase field model the evolution of the density field is based on the implicit finite element method as numerical examples compliance minimization problems of cantilever beams and force maximization problems of magnetic actuators are presented to demonstrate the method s effectiveness and utility

topology optimization with local stress constraint based on level set evolution via reaction diffusion abstract this work focuses the structural topology optimization problem of mass minimization subject to local stress constraints to this aim two related issues are addressed the first one is the successful strategy used to define local stress constraints by means of an augmented lagrangian approach the second and main contribution of the present paper is the use of a reaction diffusion equation to guide via evolution of a level set the design optimization sequence the advantages of this strategy are twofold firstly it allows the creation of new holes during the optimization process a significant feature for a true topological optimization method secondly reinitialization steps usually found in classical hamilton jacobi based evolution are eliminated with a significant improvement in convergence ease a set of benchmark examples in two dimensions are presented numerical results show the efficiency of the algorithm to create new holes identify stress concentrations and to provide stable optimization sequences converging to local minima defined by stress saturated designs

topological derivative based topology optimization of structures subject to drucker prager stress constraints abstract an algorithm for topology optimization of elastic structures under plane stress subject to the drucker prager stress constraint is presented the algorithm is based on the use of the topological derivative of the associated objective functional in conjunction with a level set representation of the structure domain in this context a penalty functional is proposed to enforce the point wise stress constraint and a closed formula for its topological derivative is derived the resulting algorithm is of remarkably simple computational implementation it does not require post processing procedures of any kind and features only a minimal number of user defined algorithmic parameters this is in sharp contrast with current procedures for topological structural optimization with local stress constraints the effectiveness and efficiency of the algorithm presented here are demonstrated by means of numerical examples the examples show in particular that it can easily handle structural optimization problems with underlying materials featuring strong asymmetry in their tensile and compressive yield strengths

on the computational behavior of a polynomial time network flow algorithm a variation on the edmonds karp scaling approach to the minimum cost network flow problem is examined this algorithm which scales costs rather than right hand sides also runs in polynomial time large scale computational experiments indicate that the computational behavior of such scaling algorithms may be much better than had been presumed within several distributions of square dense capacitated transportation problems a cost scaling code scale exhibits linear growth in average execution time with the number of edges while two network simplex codes rnet and gnet exhibit greater than linear growth our experiments reveal that median and mean execution times are predictable with surprising accuracy for all of the three codes and all three distributions from which test problems were generated moreover for fixed problem size individual execution times appear to behave as though they are approximately lognormally distributed with constant variance the experiments also reveal sensitivity of the parameters in the models and in the models themselves to variations in the distribution of problems this argues for caution in the interpretation of such computational studies beyond the realm in which the computations were performed

finding minimum cost circulations by canceling negative cycles a classical algorithm for finding a minimum cost circulation consists of repeatedly finding a residual cycle of negative cost and canceling it by pushing enough flow around the cycle to saturate an arc we show that a judicious choice of cycles for canceling leads to a polynomial bound on the number of iterations in this algorithm this gives a very simple strongly polynomial algorithm that uses no scaling a variant of the algorithm that uses dynamic trees runs in o nm log n min log nc m log n time on a network of n vertices m arcs and arc costs of maximum absolute value c this bound is comparable to those of the fastest previously known algorithms

fibonacci heaps and their uses in improved network optimization algorithms in this paper we develop a new data structure for implementing heaps priority queues our structure fibonacci heaps abbreviated f heaps extends the binomial queues proposed by vuillemin and studied further by brown f heaps support arbitrary deletion from an n item heap in o log n amortized time and all other standard heap operations in o 1 amortized time using f heaps we are able to obtain improved running times for several network optimization algorithms in particular we obtain the following worst case bounds where n is the number of vertices and m the number of edges in the problem graph o n log n m for the single source shortest path problem with nonnegative edge lengths improved from o m log m n 2 n o n 2 log n nm for the all pairs shortest path problem improved from o nm log m n 2 n o n 2 log n nm for the assignment problem weighted bipartite matching improved from o nm log m n 2 n o m m n for the minimum spanning tree problem improved from o m log log m n 2 n where m n min i u log i n m n note that m n log n if m n of these results the improved bound for minimum spanning trees is the most striking although all the results give asymptotic improvements for graphs of appropriate densities

minimum cost multiflows in undirected networks letn g t c a be a network whereg is an undirected graph t is a distinguished subset of its vertices calledterminals and each edgee ofg has nonnegative integer valuedcapacity c e andcost a e theminimum cost maximum multi commodity flow problem studied in this paper is to find ac admissible multiflowf ing such that i f is allowed to contain partial flows connecting any pairs of terminals ii the total value off is as large as possible and iii the total cost off is as small as possible subject to ii this generalizes on one hand the undirected version of the classical minimum cost maximum flow problem when t 2 and on the other hand the problem of finding a maximum fractional packing oft paths whena 0 lovasz and cherkassky independently proved that the latter has a half integral optimal solution

maximum network flows with concave gains this paper deals with a generalized maximum flow problem with concave gains which is a nonlinear network optimization problem optimality conditions and an algorithm for this problem are presented the optimality conditions are extended from the corresponding results for the linear gain case the algorithm is based on the scaled piecewise linear approximation and on the fat path algorithm described by goldberg plotkin and tardos for linear gain cases the proposed algorithm solves a problem with piecewise linear concave gains faster than the naive solution by adding parallel arcs

stress based topology optimization of continuum structures under uncertainties abstract this work addresses the use of the topology optimization approach to the design of continuum structures with failure constraints under the hypothesis of uncertainties in the spatial distribution of young s modulus to this end the first order perturbation approach is used to model the response of the structure and the midpoint discretization technique is used to represent the random field the objective is the minimization of the amount of material used in the design subjected to local stress constraints under uncertainties the probability of failure is bounded by the one sided chebychev inequality since the exact probability distribution function of the stress constraints is not known in advance the effective probability of failure of the obtained optimal designs is validated with the use of the monte carlo simulation approach indicating that the probability of failures of the topologies obtained with the stochastic approach is within the bounds provided by the one sided chebychev inequality the optimization problem is solved by means of the augmented lagrangian method in order to address the large number of constraints associated to this kind of formulation it is shown that the correlation length and the number of standard deviations considered in the formulation play an important role in both the obtained topology and effective probability of failure

dynamic trees as search trees via euler tours applied to the network simplex algorithm thedynamic tree is an abstract data type that allows the maintenance of a collection of trees subject to joining by adding edges linking and splitting by deleting edges cutting while at the same time allowing reporting of certain combinations of vertex or edge values for many applications of dynamic trees values must be combined along paths for other applications values must be combined over entire trees for the latter situation an idea used originally in parallel graph algorithms to represent trees by euler tours leads to a simple implementation with a time of o logn per tree operation wheren is the number of tree vertices we apply this representation to the implementation of two versions of the network simplex algorithm resulting in a time of o logn per pivot wheren is the number of vertices in the problem network

multiflows and disjoint paths of minimum total cost in this paper we discuss a number of recent and earlier results in the field of combinatorial optimization that concerns problems on minimum cost multiflows multicommodity flows and edge disjoint paths more precisely we deal with an undirected networkn consisting of a supply graphg a commodity graphh and nonnegative integer valued functions of capacities and costs of edges ofg and consider the problems of minimizing the total cost among i all maximum multiflows and ii all maximuminteger multiflows

stress related topology optimization of continuum structures involving multi phase materials considering stress constraints in structural topology optimization is very important from both theoretical and application perspectives most of the corresponding studies in literature however are only focused on the problems involving single phase homogenous materials in the present paper stress constrained topology optimization of continuum structures involving multi phase heterogeneous materials is investigated a level set based variational consistent solution framework is developed numerical examples are also presented and discussed to illustrate the effectiveness of the proposed approach

an extended level set method for shape and topology optimization in this paper the conventional level set methods are extended as an effective approach for shape and topology optimization by the introduction of the radial basis functions rbfs the rbf multiquadric splines are used to construct the implicit level set function with a high level of accuracy and smoothness and to discretize the original initial value problem into an interpolation problem the motion of the dynamic interfaces is thus governed by a system of coupled ordinary differential equations odes and a relatively smooth evolution can be maintained without reinitialization a practical implementation of this method is further developed for solving a class of energy based optimization problems in which approximate solution to the original hamilton jacobi equation may be justified and nucleation of new holes inside the material domain is allowed for furthermore the severe constraints on the temporal and spatial discretizations can be relaxed leading to a rapid convergence to the final design insensitive to initial guesses the normal velocities are chosen to perform steepest gradient based optimization by using shape sensitivity analysis and a bi sectioning algorithm a physically meaningful and efficient extension velocity method is also presented the proposed method is implemented in the framework of minimum compliance design and its efficiency over the existing methods is highlighted numerical examples show its accuracy convergence speed and insensitivity to initial designs in shape and topology optimization of two dimensional 2d problems that have been extensively investigated in the literature

structural optimization using sensitivity analysis and a level set method in the context of structural optimization we propose a new numerical method based on a combination of the classical shape derivative and of the level set method for front propagation we implement this method in two and three space dimensions for a model of linear or nonlinear elasticity we consider various objective functions with weight and perimeter constraints the shape derivative is computed by an adjoint method the cost of our numerical algorithm is moderate since the shape is captured on a fixed eulerian mesh although this method is not specifically designed for topology optimization it can easily handle topology changes however the resulting optimal shape is strongly dependent on the initial guess

finding minimum cost circulations by successive approximation we develop a new approach to solving minimum cost circulation problems our approach combines methods for solving the maximum flow problem with successive approximation techniques based on cost scaling we measure the accuracy of a solution by the amount that the complementary slackness conditions are violated we propose a simple minimum cost circulation algorithm one version of which runs in on3lognc time on an n vertex network with integer arc costs of absolute value at most c by incorporating sophisticated data structures into the algorithm we obtain a time bound of onm logn2 mlognc on a network with m arcs a slightly different use of our approach shows that a minimum cost circulation can be computed by solving a sequence of on lognc blocking flow problems a corollary of this result is an on2log nlognc time m processor parallel minimum cost circulation algorithm our approach also yields strongly polynomial minimum cost circulation algorithms our results provide evidence that the minimum cost circulation problem is not much harder than the maximum flow problem we believe that a suitable implementation of our method will perform extremely well in practice

reducing matching to polynomial size linear programming the question of whether the maximum weight matching problem can be reduced to a linear program of polynomial size is studied a partial answer to it is given i e it is shown that the chinese postman problem and optimum matching reduces to a sequence of o m 2 log n minimum mean cycle problems it is shown that this last problem can be formulated as a linear program of polynomial size this gives a polynomial algorithm for matching based on any polynomial method for linear programming a combinatorial algorithm for finding minimum mean cycles in undirected graphs is also given

two variable logic on data trees and xml reasoning motivated by reasoning tasks for xml languages the satisfiability problem of logics on data trees is investigated the nodes of a data tree have a label from a finite set and a data value from a possibly infinite set it is shown that satisfiability for two variable first order logic is decidable if the tree structure can be accessed only through the child and the next sibling predicates and the access to data values is restricted to equality tests from this main result decidability of satisfiability and containment for a data aware fragment of xpath and of the implication problem for unary key and inclusion constraints is concluded

a topology optimization method based on the level set method incorporating a fictitious interface energy this paper proposes a new topology optimization method which can adjust the geometrical complexity of optimal configurations using the level set method and incorporating a fictitious interface energy derived from the phase field method first a topology optimization problem is formulated based on the level set method and the method of regularizing the optimization problem by introducing fictitious interface energy is explained next the reaction diffusion equation that updates the level set function is derived and an optimization algorithm is then constructed which uses the finite element method to solve the equilibrium equations and the reaction diffusion equation when updating the level set function finally several optimum design examples are shown to confirm the validity and utility of the proposed topology optimization method

a new approach to the maximum flow problem all previously known efficient maximum flow algorithms work by finding augmenting paths either one path at a time as in the original ford and fulkerson algorithm or all shortest length augmenting paths at once using the layered network approach of dinic an alternative method based on the preflow concept of karzanov is introduced a preflow is like a flow except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out the method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths the algorithm and its analysis are simple and intuitive yet the algorithm runs as fast as any other known method on dense graphs achieving an o n 3 time bound on an n vertex graph by incorporating the dynamic tree data structure of sleator and tarjan we obtain a version of the algorithm running in o nm log n 2 m time on an n vertex m edge graph this is as fast as any known method for any graph density and faster on graphs of moderate density the algorithm also admits efficient distributed and parallel implementations a parallel implementation running in o n 2 log n time using n processors and o m space is obtained this time bound matches that of the shiloach vishkin algorithm which also uses n processors but requires o n 2 space

an isogeometrical approach to structural level set topology optimization abstract this paper aims to utilize the isogeometric analysis iga for the level set structural topology optimization the level set function is parametrized using the non uniform rational b spline nurbs basis functions in a higher dimension the same basis functions are employed for approximating the unknown deformations geometry modeling of the design domain and the level set function in this research three optimization problems including minimization of the mean compliance considering a certain amount of material minimization of weight with avoiding local stress concentration as well as minimization of weight and strain energy under local stress constraints are dealt with the sensitivity analyses for the optimization problems are carried out to obtain velocity functions on the boundaries in order to move the boundaries towards optimum the hamilton jacobi h j equation is solved using the forward euler scheme in order to illustrate the performance of the method to obtain reasonable results with smooth boundaries several numerical examples are presented and compared with well known problems in literature

note on weintraub s minimum cost circulation algorithm in 1974 weintraub management sci 21 1974 pp 87 97 published an algorithm for the minimum cost circulation problems with convex cost function in this note weintraub s algorithm is considered when applied to a minimum cost circulation problem with linear objective function it is shown that a minor variation of the algorithm runs in polynomial time the resulting algorithm although it is not strongly polynomial does not rely on scaling it is a generalization of the maximum flow algorithm due to edmonds and karp j assoc comput mach 19 1972 pp 248 264 that augments along the fattest augmenting path in the residual graph the algorithm described here is slower than the fastest minimum cost circulation algorithms known the authors interest in the algorithm is partially historical a scaling free almost polynomial time algorithm was published in 1974 and partially due to the different ideas involved

an o n 2 m n log n log n min cost flow algorithm the minimum cost flow problem is given a network with n vertices and m edges find a maximum flow of minimum cost many network problems are easily reducible to this problem a polynomial time algorithm for the problem has been known for some time but only recently a strongly polynomial algorithm was discovered in this paper an o n 2 m n log n log n algorithm is designed the previous best algorithm due to fujishige and orlin had an o m 2 m n log n log n time bound thus for dense graphs an improvement of two orders of magnitude is obtained the algorithm in this paper is based on fujishige s algorithm which is based on tardos s algorithm fujishige s algorithm consists of up to m iterations each consisting of o m log n steps each step solves a single source shortest path problem with nonnegative edge lengths this algorithm is modified in order to make an improved analysis possible the new algorithm may still consist of up to m iterations and an iteration may still consist of up to o m log n steps but it can still be shown that the total number of steps is bounded by o n 2 log n the improvement is due to a new technique that relates the time spent to the progress achieved

a level set approach for topology optimization with local stress constraints summary the purpose of this work is to present a level set based approach for the structural topology optimization problem of mass minimization submitted to local stress constraints the main contributions are threefold first the inclusion of local stress constraints by means of an augmented lagrangian approach within the level set context second the proposition of a constraint procedure that accounts for a continuous activation deactivation of a finite number of local stress constraints during the optimization sequence finally the proposition of a logarithmic scaling of the level set normal velocity as an additional regularization technique in order to improve the minimization sequence a set of benchmark tests in two dimensions achieving successful numerical results assesses the good behavior of the proposed method in these examples it is verified that the algorithm is able to identify stress concentrations and drive the design to a feasible local minimum copyright 2014 john wiley sons ltd