modeling and analysis of cross ply and angle ply laminated plates under patch loads using rbf based meshfree method and new hsdt abstract angle ply laminated plates have been examined for flexure analysis with multiquadric radial basis function mqrbf base meshfree method a new higher order shear deformation theory hsdt representing the transverse shear strain function is proposed in the displacement field proposed theory satisfies the condition of continuity and differentiability and is accurate enough to predict the results of flexure governing differential equations gdes are derived using energy principle a matlab code is developed to obtain the results for deflection and stresses of the angle ply laminated plate the flexure results for laminated plates under patch loads commonly used in general practice is obtained with proposed hsdts and meshfree method present results are validated with published results for the cross ply laminated plate and some new results are produced for different loading conditions for angle ply laminated plates in the present study eight layered symmetric cross ply laminate of equal thickness an antisymmetric cross ply laminate of equal thickness and a general angle ply laminate of equal thickness is considered the effect of the span to thickness ratio number of layers and shifting patch loads is presented

effect of boundary constraint on the frequency response of moderately thick doubly curved cross ply panels using mixed fourier solution functions abstract a hitherto unavailable analytical solution to the boundary value problem of free vibration response of shear flexible cross ply laminated doubly curved panels is presented the laminated shell theory formulation is based on the first order shear deformation theory fsdt including rotatory and surface parallel inertias the governing equations of the panel are defined by five highly coupled partial differential equations in five unknowns three displacements and two rotations the assumed solution functions for the eigen boundary value problem are selected in terms of mixed type double fourier series extensive numerical results that are presented in this study include 1 convergence characteristics of computed natural frequencies and 2 effects of length to thickness ratio radius to length ratio lamination sequence boundary constraint and shell geometry on the normalized natural frequencies of interest also numerically investigated is the highly complex interaction among bending stretching type coupling effect membrane action due to shell curvature surface parallel end constraints or lack thereof and the effects of transverse shear deformation rotatory inertias and surface parallel inertias

the steiner traveling salesman problem with online edge blockages abstract we consider the online steiner traveling salesman problem in this problem we are given an edge weighted graph g v e and a subset d v of destination vertices with the optimization goal to find a minimum weight closed tour that traverses every destination vertex of d at least once during the traversal the salesman could encounter at most k non recoverable blocked edges the edge blockages are real time meaning that the salesman knows about a blocked edge whenever it occurs we first show a lower bound on the competitive ratio and present an online optimal algorithm for the problem while this optimal algorithm has non polynomial running time we present another online polynomial time near optimal algorithm for the problem experimental results show that our online polynomial time algorithm produces solutions very close to the offline optimal solutions

traveling salesman path problems in the traveling salesman path problem we are given a set of cities traveling costs between city pairs and fixed source and destination cities the objective is to find a minimum cost path from the source to destination visiting all cities exactly once in this paper we study polyhedral and combinatorial properties of a variant we call the traveling salesman walk problem in which the objective is to find a minimum cost walk from the source to destination visiting all cities at least once we first characterize traveling salesman walk perfect graphs graphs for which the convex hull of incidence vectors of traveling salesman walks can be described by linear inequalities we show these graphs have a description by way of forbidden minors and also characterize them constructively we also address the asymmetric traveling salesman path problem atspp and give a factor o sqrt n approximation algorithm for this problem

a new class of cutting planes for the symmetric travelling salesman problem a comprehensive class of cutting planes for the symmetric travelling salesman problem tsp is proposed which contains the known comb inequalities the path inequalities and the 3 star constraints as special cases its relation to the clique tree inequalities is discussed the cutting planes are shown to be valid for a relaxed version of the tsp the travelling salesman problem on a road network and under certain conditions to define facets of the polyhedron associated with this problem

derivation of a model for symmetric lamellipodia with instantaneous cross link turnover we start with a model for the actin cytoskeleton in a symmetric lamellipodium cp oelz et al in cell adh migr 2 2 117 126 2008 which includes the description of the life cycle of chemical bonds based on age structured models based on the assumption that their average lifetime is actually small as compared to the time scale of the dynamics in which we are interested we pass after applying an appropriate scaling to a limit where this average lifetime goes to zero we obtain a gradient flow model and formulate a time step approximation scheme we use it to construct solutions analytically proving their local in time existence and present a typical numerical solution based on this scheme

a note on the undirected rural postman problem polytope this note refers to the article by g ghiani and g laporte a branch and cut algorithm for the undirected rural postman problem math program 87 2000 we show that some conditions for the facet defining property of the basic non trivial inequalities are not sufficient and that the rural postman problem polytope is more complex even when focusing on canonical inequalities only

the symmetric traveling salesman polytope and its graphical relaxation composition of valid inequalities the graphical relaxation of the traveling salesman problem is the relaxation obtained by requiring that the salesman visit each city at least once instead of exactly once this relaxation has already led to a better understanding of the traveling salesman polytope in cornuejols fonlupt and naddef 1985 we show here how one can compose facet inducing inequalities for the graphical traveling salesman polyhedron and obtain other facet inducing inequalities this leads to new valid inequalities for the symmetric traveling salesman polytope this paper is the first of a series of three papers on the symmetric traveling salesman polytope the next one studies the strong relationship between that polytope and its graphical relaxation and the last one applies all the theoretical developments of the two first papers to prove some new facet inducing results

halin graphs and the travelling salesman problem a halin graphh t c is obtained by embedding a treet having no nodes of degree 2 in the plane and then adding a cyclec to join the leaves oft in such a way that the resulting graph is planar these graphs are edge minimal 3 connected hamiltonian and in general have large numbers of hamilton cycles we show that for arbitrary real edge costs the travelling salesman problem can be polynomially solved for such a graph and we give an explicit linear description of the travelling salesman polytope the convex hull of the incidence vectors of the hamilton cycles for such a graph

a hybrid metaheuristic approach for the capacitated arc routing problem the capacitated arc routing problem carp is a difficult combinatorial optimization problem that has been intensively studied in the last decades we present a hybrid metaheuristic approach hma to solve this problem which incorporates an effective local refinement procedure coupling a randomized tabu thresholding procedure with an infeasible descent procedure into the memetic framework other distinguishing features of hma include a specially designed route based crossover operator for solution recombination and a distance and quality based replacement criterion for pool updating extensive experimental studies show that hma is highly scalable and is able to quickly identify either the best known results or improved best known results for almost all currently available carp benchmark instances in particular it discovers an improved best known result for 15 benchmark instances 6 classical instances and 9 large sized instances whose optima are unknown furthermore we analyze some key elements and properties of the hma carp algorithm to better understand its behavior

on the relationship between the biconnectivity augmentation and travelling salesman problems abstract a strategy for solving the traveling salesman problem is adapted to the problem of finding a biconnected subgraph of a weighted graph whose cost function satisfies the triangle inequality an approximation algorithm similar to christofides algorithm 5 for the traveling salesman problem is shown to possess the same worst case bound of 3 2 when applied to the biconnectivity augmentation problem a tight inequality is derived relating the cost of an optimal traveling salesman tour to the cost of an optimal biconnection

guided local search and its application to the traveling salesman problem abstract the traveling salesman problem tsp is one of the most famous problems in combinatorial optimization in this paper we are going to examine how the techniques of guided local search gls and fast local search fls can be applied to the problem gls sits on top of local search heuristics and has as a main aim to guide these procedures in exploring efficiently and effectively the vast search spaces of combinatorial optimization problems gls can be combined with the neighborhood reduction scheme of fls which significantly speeds up the operations of the algorithm the combination of gls and fls with tsp local search heuristics of different eiciency and effectiveness is studied in an effort to determine the dependence of gls on the underlying local search heuristic used comparisons are made with some of the best tsp heuristic algorithms and general optimization techniques which demonstrate the advantages of gls over alternative heuristic approaches suggested for the problem

a guided local search metaheuristic for the team orienteering problem in the team orienteering problem top a set of locations is given each with a score the goal is to determine a fixed number of routes limited in length that visit some locations and maximise the sum of the collected scores this paper describes an algorithm that combines different local search heuristics to solve the top guided local search gls is used to improve two of the proposed heuristics an extra heuristic is added to regularly diversify the search in order to explore more areas of the solution space the algorithm is compared with the best known heuristics of the literature and applied on a large problem set the obtained results are almost of the same quality as the results of these heuristics but the computational time is reduced significantly applying gls to solve the top appears to be a very promising technique furthermore the usefulness of exploring more areas of the solution space is clearly demonstrated

on the roles of complementary and admissible boundary constraints in fourier solutions to the boundary value problems of completely coupled r th order pdes abstract a heretofore unavailable double fourier series based approach for obtaining non separable solution to a system of completely coupled linear r th order partial differential equations with constant coefficients and subjected to general completely coupled boundary conditions has been presented the method has been successfully implemented to solve a class of hitherto unsolved boundary value problems pertaining to free and forced vibrations of arbitrarily laminated anisotropic doubly curved thin panels of rectangular planform with arbitrarily prescribed both symmetric and asymmetric with respect to the panel centerlines admissible boundary conditions and subjected to general transverse loading existing solutions such as those due to navier or levy are based on the well known method of separation of variables such solutions represent particular solutions whenever the method of separation of variables work and when these particular solution functions fortuitously satisfy the boundary conditions for derivation of the complementary solution the complementary boundary constraints are introduced through boundary discontinuities of some of the particular solution functions and their partial derivatives such discontinuities form sets of measure zero various cases of lamination geometry and dynamic response forced and free vibrations of a class of thin anisotropic laminated shells curved panels have been shown to follow from the above six sets of boundary conditions are used to illustrate the present method for the derivation of complementary solutions navier type solutions whenever available form special cases of the present general solution

the general routing problem polyhedron facets from the rpp and gtsp polyhedra in this paper we study the polyhedron associated with the general routing problem grp this problem first introduced by orloff in 1974 is a generalization of both the rural postman problem rpp and the graphical traveling salesman problem gtsp and thus is np hard we describe a formulation of the problem such that from every non trivial facet inducing inequality for the rpp and gtsp polyhedra we obtain facet inducing inequalities for the grp polyhedron we describe a new family of facet inducing inequalities for the grp the honeycomb constraints which seem to be very useful for solving grp and rpp instances finally new classes of facets obtained by composition of facet inducing inequalities are presented

a polyhedral approach to the rural postman problem abstract in this paper we study the polyhedron associated with the rural postman problem rpp because the rpp is np hard we cannot expect to find a complete description of the rural postman polyhedron of a general graph but a partial knowledge of such a description frequently proves to be useful for both theoretical and computational purposes we have tried to characterize the facial structure of this unbounded full dimensional polyhedron sets of valid inequalities inducing facets have been studied as well as their use in a cutting plane algorithm the application of this algorithm to a set of rpp instances taken from the literature and two instances of larger size taken from a real world graph is described all these instances were solved to optimality

odd minimum cut sets and b matchings we show that the determination of a minimum cut set of odd cardinality in a graph with even and odd vertices can be dealt with by a minor modification of the polynomially bounded algorithm of gomory and hu for multi terminal networks we connect this problem to the problem of identifying a matching or blossom constraint that chops off a point which is not contained in the convex hull of matchings or proving that no such inequality exists both the b matching problems without and with upper bounds are considered we discuss how the results of this paper can be used in conjunction with commercial lp packages lo solve b matching problems

the traveling salesman problem on a graph and some related integer polyhedra given a graphg n e and a length functionl e the graphical traveling salesman problem is that of finding a minimum length cycle goingat least once through each node ofg this formulation has advantages over the traditional formulation where each node must be visited exactly once we give some facet inducing inequalities of the convex hull of the solutions to that problem in particular the so called comb inequalities of grotschel and padberg are generalized some related integer polyhedra are also investigated finally an efficient algorithm is given wheng is a series parallel graph

frequency response of a moderately thick antisymmetric cross ply cylindrical panel using mixed type of fourier solution functions abstract a hitherto unavailable analytical solution to the boundary value problem of the free vibration response of shear flexible antisymmetric cross ply laminated cylindrical panels is presented the laminated shell theory formulation is based on the first order shear deformation theory fsdt including rotatory and surface parallel inertias the governing equations of the panel are defined by five highly coupled partial differential equations in five unknowns three displacements and two rotations the assumed solution functions for the eigen boundary value problem are selected in terms of mixed type double fourier series numerical results presented for parametric effects such as length to thickness ratio and radius to thickness ratio should serve as a bench mark for future comparison a four node shear flexible finite element is selected to compare the results with the present solution

the steiner travelling salesman problem with correlated costs the steiner travelling salesman problem stsp is a variant of the tsp that is suitable for instances defined on road networks we consider an extension of the stsp in which the road traversal costs are both stochastic and correlated this happens for example when vehicles are prone to delays due to rush hours road works or accidents following the work of markowitz on portfolio selection we model this problem as a bi objective mean variance problem then we show how to approximate the efficient frontier via integer programming we also show how to exploit certain special structures in the correlation matrices computational results indicate that our approach is viable for instances with up to 100 nodes it turns out that minimum variance tours can look rather different from minimum expected cost tours

a cutting plane algorithm for the general routing problem the general routing problem grp is the problem of finding a minimum cost route for a single vehicle subject to the condition that the vehicle visits certain vertices and edges of a network it contains the rural postman problem chinese postman problem and graphical travelling salesman problem as special cases we describe a cutting plane algorithm for the grp based on facet inducing inequalities and show that it is capable of providing very strong lower bounds and in most cases optimal solutions

the rural postman problem with deadline classes vehicle routing problems with general time windows are extremely difficult to solve however the time windows in a particular problem may have a special structure which can be exploited we consider a single vehicle arc routing problem in which the arcs are partitioned into deadline classes it is shown that a cutting plane approach works well for this problem

a cutting plane procedure for the travelling salesman problem on road networks abstract a cutting plane algorithm for the exact solution of the symmetric travelling salesman problem tsp is proposed the real tours on a usually incomplete road network which are in general non hamiltonian are characterized directly by an integer linear programming model the algorithm generates special cutting planes for this model computational results for real road networks with up to 292 visiting places are reported as well as for classical problems of the literature with up to 120 cities some of the latter problems have been solved for the first time with a pure cutting plane approach

on the undirected rural postman problem tight bounds based on a new formulation the rural postman problem rpp is a classic edge routing problem a mathematical programming formulation of the rpp that differs fundamentally from those in the literature was introduced but not tested computationally by garfinkel and webb 1999 a rudimentary algorithm that yields lower bounds via cutting planes and upper bounds via heuristics is developed and tested for a variation of that formulation computational results are encouraging especially in terms of the relatively small number of added inequalities needed to get good lower bounds and the fact that the vast majority of these have efficient exact separation procedures note that a first algorithm based on this new formulation is computationally competitive allowing the possibility of far more efficient and complex future realizations

new results on the mixed general routing problem in this paper we deal with the polyhedral description and the resolution of the mixed general routing problem this problem in which the service activity occurs both at some of the nodes and at some of the arcs and edges of a mixed graph contains a large number of important arc and node routing problems as special cases here a large family of facet defining inequalities the honeycomb inequalities is described furthermore a cutting plane algorithm for this problem that incorporates new separation procedures for the k c regular path bridge and honeycomb inequalities is presented branch and bound is invoked when the final solution of the cutting plane procedure is fractional extensive computational experiments over different sets of instances are included

two phased hybrid local search for the periodic capacitated arc routing problem the periodic capacitated arc routing problem pcarp is a challenging general model with important applications the pcarp has two hierarchical optimization objectives a primary objective of minimizing the number of vehicles fv and a secondary objective of minimizing the total cost fc in this paper we propose an effective two phased hybrid local search hls algorithm for the pcarp the first phase makes a particular effort to optimize the primary objective while the second phase seeks to further optimize both objectives by using the resulting number of vehicles of the first phase as an upper bound to prune the search space for both phases combined local search heuristics are devised to ensure an effective exploration of the search space experimental results on 63 benchmark instances demonstrate that hls performs remarkably well both in terms of computational efficiency and solution quality in particular hls discovers 44 improved best known values new upper bounds for the total cost objective fc while attaining all the known optimal values regarding the objective of the number of vehicles fv to our knowledge this is the first pcarp algorithm reaching such a performance key components of hls are analyzed to better understand their contributions to the overall performance

toward solving the steiner travelling salesman problem on urban road maps using the branch decomposition of graphs the steiner travelling salesman problem stsp is an important issue in intelligent transportation systems and has various practical applications such as travelling and parcel delivery in this study we consider the stsp in real world road maps i e given a road map with a set of service points or intersections selection of the representative vertices of a graph g to determine a closed route so a vehicle can visit each service point at least once with the minimum cost it has been theoretically proved that the stsp and its ancestor travelling salesman problem are np hard however it has been empirically demonstrated that they can be solved efficiently on planar graphs with small branchwidths therefore we propose a branch decomposition based extraction algorithm for the stsp in planar graphs our algorithm can solve the stsp in a planar graph g with a time complexity of 2o bw g no 1 where bw g is the branchwidth of g in the case of planar graphs with a small branchwidth our algorithm performs efficiently we evaluated our algorithm by applying it to real world urban road maps which demonstrated the suitability of our method for real world applications

sensitivity of the response of moderately thick cross ply doubly curved panels to lamination and boundary constraint i theory abstract hitherto unavailable analytical solutions to the boundary value problem of moderately thick general cross ply laminated doubly curved panels of rectangular planform subjected to various boundary conditions are presented the five highly coupled second order linear partial differential equations that characterize the deformation of such laminates are solved in part i of the paper using a recently developed double fourier series based approach together with the ss1 ss2 and ss4 types of simply supported and c4 type of clamped boundary conditions prescribed at all four edges the issues of derivation of the linear algebraic equations arising from these boundary conditions together with an efficient method of solving the complete system of linear algebraic equations convergence characteristics and other numerical results are addressed in the accompanying part ii of this investigation

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

solving the prize collecting rural postman problem abstract in this work we present an algorithm for solving the prize collecting rural postman problem this problem was recently defined and is a generalization of other arc routing problems like for instance the rural postman problem the main difference is that there are no required edges instead there is a profit function on the edges that must be taken into account only the first time that an edge is traversed the problem is modeled as a linear integer program where the system has an exponential number of inequalities we propose a solution algorithm where iteratively we solve relaxed models with a small number of inequalities that provide upper bounds and we propose exact separation procedures for generating violated cuts when possible we also propose a simple heuristic to generate feasible solutions that provide lower bounds at each iteration we use a two phase method with different solvers at each phase despite the difficulty of the problem the numerical results from a series of computational experiments with various types of instances assess the good behavior of the algorithm in particular 75 of the instances were optimally solved with the lp relaxation of the model the remaining instances were optimally solved on a second phase most of them in small computation times

fourier solution to higher order theory based laminated shell boundary value problem a complete i e particular as well as complementary fourier solution to the boundary value problem of static response under transverse load of a general cross ply thick doubly curved panel of rectangular planform is presented a boundary discontinuous double fourier series approach is used to solve a system of five partial differential equations generated by a higher order shear deformation theory based shell analysis with the ss2 type of simply supported boundary condition prescribed at all four edges unlike the conventional navier and levy type approaches which can only provide particular solutions the present method is general enough to provide the complete particular as well as the complementary solution for any arbitrary combination of admissible boundary conditions with almost equal ease the numerical accuracy of the solution is ascertained by studying the convergence characteristics of deflections and moments of cross ply spherical panels and also by comparison with the available first order shear deformation theory and classical lamination theory based analytical solutions hitherto unavailable important numerical results presented include sensitivity of the predicted response quantities of interest to lamination boundary constraint and thickness and curvature effects as well as their interactions

a branch and cut algorithm for the profitable windy rural postman problem abstract in this paper we study the profitable windy rural postman problem this is an arc routing problem with profits defined on a windy graph in which there is a profit associated with some of the edges of the graph consisting of finding a route maximizing the difference between the total profit collected and the total cost this problem generalizes the rural postman problem and other well known arc routing problems and has real life applications mainly in snow removal operations we propose here a formulation for the problem and study its associated polyhedron several families of facet inducing inequalities are described and used in the design of a branch and cut procedure the algorithm has been tested on a large set of benchmark instances and compared with other existing algorithms the results obtained show that the branch and cut algorithm is able to solve large sized instances optimally in reasonable computing times

static analysis of moderately thick finite antisymmetric angle ply cylindrical panels and shells abstract the analytical exact in the limit or strong or differential form of solutions to the bench mark problems of i axisymmetric angle ply circular cylindrical panels of rectangular planform and ii circumferentially complete circular cylindrical shells subjected to transverse load and with ss2 type simply supported boundary conditions prescribed at the edges are presented the problems investigated which were hitherto thought to be incapable of admitting analytical solutions have been solved utilizing a recently developed novel boundary discontinuous double fourier series approach for three kinematic relations which are extensions of those due to sanders love and donnell to the first order shear deformation theory fsdt numerical results presented for two layer square antisymmetric angle ply panels which demonstrate good convergence and show the effects of fiber orientation and thickness on the static response of these panels should serve as baseline solutions in the context of fsdt for future comparison with various approximate weak forms of solutions with either local e g finite element methods or global supports e g raleigh ritz galerkin

hamiltonian path and symmetric travelling salesman polytopes we introduce a projective approach for studying symmetric travelling salesman polytopes stsps thesymmetric travelling salesman polytope stsp v resp hamiltonian path polytope hp v is the convex hull of incidence vectors of all hamiltonian cycles resp paths on the complete undirected graph with node setv for any nodeh v hp v is aprojection of stsp v h we show that hp v and stsp v h are isomorphic and hp v is of full dimension minus one by this projective approach we obtain generalclique lifting results all based on simple conditions for deriving large new classes of stsp facets these results apply to all known non trivial stsp facets and generalize clique lifting results of maurras 1975 grotschel and padberg 1979 and naddef and rinaldi 1988

solving the hierarchical chinese postman problem as a rural postman problem abstract in the undirected hierarchical chinese postman problem hcpp the edges of a graph are partitioned into clusters and must be serviced while respecting a hierarchy or precedence relation between clusters two objectives are considered a hierarchical objective and a makespan objective in this article a transformation of the hcpp into an equivalent rural postman problem rpp is presented the hcpp is solved optimally for both objectives by applying an exact branch and cut rpp algorithm to the transformed problem two heuristics based on the rpp algorithm are also described and assessed computationally

the hierarchical mixed rural postman problem polyhedral analysis and a branch and cut algorithm abstract the hierarchical mixed rural postman problem is defined on a mixed graph where arcs and edges that require a service are divided into clusters that have to be serviced in a hierarchical order the problem generalizes the mixed rural postman problem and thus is np hard in this paper we provide a polyhedral analysis of the problem and propose a branch and cut algorithm for its solution based on the introduced classes of valid inequalities extensive computational experiments are reported on benchmark instances the exact approach allows to find the optimal solutions in less than 1 hour for instances with up to 999 vertices 2678 links and five clusters

improved lower bounds and exact algorithm for the capacitated arc routing problem in the capacitated arc routing problem carp a subset of the edges of an undirected graph has to be serviced at least cost by a fleet of identical vehicles in such a way that the total demand of the edges serviced by each vehicle does not exceed its capacity this paper describes a new lower bounding method for the carp based on a set partitioning like formulation of the problem with additional cuts this method uses cut and column generation to solve different relaxations of the problem and a new dynamic programming method for generating routes an exact algorithm based on the new lower bounds was also implemented to assess their effectiveness computational results over a large set of classical benchmark instances show that the proposed method improves most of the best known lower bounds for the open instances and can solve several of these for the first time

new inequalities for the general routing problem abstract a large new class of valid inequalities is introduced for the general routing problem which properly contains the class of k c constraints these are also valid for the rural postman problem a separation algorithm is given for a subset of these inequalities which runs in polynomial time

the general routing polyhedron a unifying framework it is shown how to transform the general routing problem grp into a variant of the graphical travelling salesman problem gtsp this transformation yields a projective characterisation of the grp polyhedron using this characterisation it is shown how to convert facets of the gtsp polyhedron into valid inequalities for the grp polyhedron the resulting classes of inequalities subsume several previously published classes

lower bounds and heuristics for the windy rural postman problem in this paper we present several heuristic algorithms and a cutting plane algorithm for the windy rural postman problem this problem contains several important arc routing problems as special cases and has very interesting real life applications extensive computational experiments over different sets of instances are also presented

an exact algorithm for the capacitated arc routing problem with deadheading demand we study an extension of the capacitated arc routing problem carp called the capacitated arc routing problem with deadheading demand carpdd this problem extends the classical capacitated arc routing problem by introducing an additional capacity consumption incurred by a vehicle deadheading an edge it can be used e g to model time or distance constrained arc routing problems we show that the strongest carp lower bounds can be weak when directly applied to the carpdd and we introduce a new family of valid inequalities shown to significantly strengthen these bounds we develop an exact algorithm for the carpdd based on cut and column generation and branch and price and we report extensive computational results on a large set of benchmark instances the same exact algorithm is also tested on classical carp benchmark sets and is shown to improve upon the best known exact algorithms for the carp

space dependent adhesion forces mediated by transient elastic linkages new convergence and global existence results abstract in the first part of this work we show the convergence with respect to an asymptotic parameter e of a delayed heat equation it represents a mathematical extension of works considered previously by the authors 14 15 16 namely this is the first result involving delay operators approximating protein linkages coupled with a spatial elliptic second order operator for the sake of simplicity we choose the laplace operator although more general results could be derived the main arguments are i new energy estimates and ii a stability result extended from the previous work to this more involved context they allow to prove convergence of the delay operator to a friction term together with the laplace operator in the same asymptotic regime considered without the space dependence in 14 in a second part we extend fixed point results for the fully non linear model introduced in 16 and prove global existence in time this shows that the blow up scenario observed previously does not occur since the latter result was interpreted as a rupture of adhesion forces we discuss the possibility of bond breaking both from the analytic and numerical point of view

iterated local search and column generation to solve arc routing as a permutation set covering problem abstract we propose a method that combines column generation cg and iterated local search ils to solve the capacitated arc routing problem carp one of the goals is to integrate into the ils some of the duality information that underpins the cg paradigm the carp is expressed in a space of permutations and sub permutations sequences routes of the set of required edges for this the ils uses an exact decoder that maps any permutation s to a list of sequences routes of minimum cost servicing all edges in the order s 1 s 2 s 3 etc this permutation space is explored both by an ils process and a cg process that run in parallel and that communicate by exchanging sequences the first use of the cg paradigm in ils is the following all sequences discovered by cg are sent to the ils process that can inject them into the current ils solution the second application of cg in ils is a cg improver operator that acts on the current ils solution so as to try to improve it by running several cg iterations the first half of the paper describes the method in a general framework based on sequences permutations and set covering the second part is devoted to more specialized arc routing techniques for instance the cg convergence could be accelerated by factors of tens or even hundreds by exploiting two ideas in the dynamic programming dp pricing i avoid as much as possible to traverse edges without service and ii record only non dominated dp states using a fast access data structure mixing an array and a red black tree regarding the ils we show that the permutation level search can be substantially improved if the exact decoder is reinforced by a deterministic post decoder acting on explicit routes the general results are competitive reducing the best known gap of five instances and certain ideas could be potentially useful for other set covering or permutation problems

from delayed and constrained minimizing movements to the harmonic map heat equation abstract in the context of cell motility modelling and more particularly related to the filament based lamelipodium model 18 9 10 this work deals with a rigorous mathematical proof of convergence between solutions of two problems we start from a microscopic description of adhesions using a delayed and constrained vector valued equation with spacial diffusion and show the convergence towards the corresponding friction limit the convergence is performed with respect to the bond characteristic lifetime e whose inverse is also proportional to the stiffness of the bonds the originality of this work is the extension of gradient flow techniques to our setting namely the discrete finite difference term in the gradient flow energy is here replaced by a delay term which complicates greatly the mathematical analysis contrarily to the standard approach 2 16 compactness in time is not provided by the energy minimization process a series of past times are taken into account in our discrete energy a supplementary equation on the time derivative is obtained requiring uniform estimate with respect to e of the lagrange multiplier and provides compactness due to the non linearity induced by the constraint a specific stability estimate useful in our previous works is not at hand here numerical simulations even showed that this estimate does not hold nevertheless transposing our delay operator we succeed in proving convergence under slightly weaker hypotheses the result relies on a careful initial layer analysis extending 11 to the space dependent setting

a branch and cut algorithm for the undirected rural postman problem the well known undirected rural postman problem is considered and a binary linear problem using new dominance relations is presented polyhedral properties are investigated and a branch and cut algorithm is developed extensive computational results indicate that the algorithm is capable of solving much larger instances than previously reported

the mixed general routing polyhedron in arc routing problems arps the aim is to find on a graph a minimum cost traversal satisfying some conditions related to the links of the graph due to restrictions to traverse some streets in a specified way most applications of arps must be modeled with a mixed graph although several exact algorithms have been proposed no polyhedral investigations have been done for arps on a mixed graph in this paper we deal with the mixed general routing problem which consists of finding a minimum cost traversal of a given link subset and a given vertex subset of a mixed graph a formulation is given that uses only one variable for each link edge or arc of the graph some properties of the associated polyhedron and some large families of facet inducing inequalities are described a preliminary cutting plane algorithm has produced very good lower bounds over a set of 100 randomly generated instances of the mixed rural postman problem finally applications of this study to other known routing problems are described

node edge arc routing and turn penalties multiple problems one neighborhood extension this article explores a structural neighborhood decomposition for arc routing problems in which the decisions about traversal orientations during services are made optimally as part of neighbor evaluation procedures using memory structures bidirectional dynamic programming and lower bounds we show that a large neighborhood involving classical moves on the sequences of services along with optimal orientation decisions can be searched in amortized o 1 time per move evaluation instead of o n as in previous works because of its generality and now reduced complexity this approach can be efficiently applied to several variants of arc routing problems extended into large neighborhoods such as ejection chains and integrated into two classical metaheuristics our computational experiments lead to solutions of high quality on the main benchmark sets for the capacitated arc routing problem carp the mixed capacitated general routing problem mcgrp the periodic carp the multidepot carp and the min ma

a branch and cut algorithm for the maximum benefit chinese postman problem the maximum benefit chinese postman problem mbcpp is an np hard problem that considers several benefits associated with each edge one for each time the edge is traversed with a service the objective is to find a closed walk with maximum benefit we propose an ip formulation for the undirected mbcpp and based on the description of its associated polyhedron we propose a branch and cut algorithm and present computational results on instances with up to 1 000 vertices and 3 000 edges

levy type boundary fourier analysis of thick cross ply panels with negative gaussian curvature a boundary discontinuous generalized double fourier series based solution to the problem of deformation of a finite dimensional general cross ply thick doubly curved panel with negative gaussian curvature and of rectangular planform modeled using a higher order shear deformation theory is presented this spectral method is used to solve a system of five highly coupled linear partial differential equations generated by the higher order shear deformation theory based laminated shell analysis with the simply supported of type 2 boundary condition prescribed on two opposite edges whereas the remaining two edges are subjected to the simply supported of type 3 constraint the hitherto unavailable important numerical results presented include sensitivity of the predicted response quantities of interest to shell geometry negative or positive gaussian curvature lamination and thickness effects as well as their interactions

multiple center capacitated arc routing problems a tabu search algorithm using capacitated trees abstract in the capacitated arc routing problem with multiple centers m carp the objective is to find routes starting from the given depots or centers such that each required arc is served capacity and usually additional constraints are satisfied and total travel cost is minimized in this paper we consider a heuristic transformation of the m carp into a multiple center capacitated minimum spanning tree problem with arc constraints that we call arc constrained cmst an algorithm for determining initial feasible solutions as well as an improvement procedure for this problem are described and the re translation of cmst solutions into the carp context is explained it is shown that the objective function value of the obtained carp solution is easily derived from the respective value of the corresponding heuristic cmst solution furthermore the possibility of including side constraints and the consideration of additional objective functions is discussed computations on real world benchmark problems compare the results of the tabu search and simulated annealing metastrategies embedded in the improvement procedure

levy type boundary fourier analysis of thick clamped hyperbolic paraboloidal cross ply panels an analytical solution to the problem of deformation of a finite dimensional general cross ply thick doubly curved panel with negative gaussian curvature and of rectangular planform modeled using a higher order shear deformation theory is presented a solution methodology based on a boundary discontinuous generalized double fourier series approach is used to solve a system of five highly coupled linear partial differential equations generated by the higher order shear deformation theory based laminated shell analysis with the c4 type rigidly clamped boundary condition prescribed on two opposite edges whereas the remaining two edges are subjected to the ss3 type constraint hitherto unavailable important numerical results presented include sensitivity of the predicted response quantities of interest to applied loading shell geometry negative or positive gaussian curvature edge clamping constraints and lamination and thickness effects as well as their possible interactions comparison with the

compact formulations of the steiner traveling salesman problem and related problems the steiner traveling salesman problem stsp is a variant of the tsp that is particularly suitable when routing on real life road networks the standard integer programming formulations of both the tsp and stsp have an exponential number of constraints on the other hand several compact formulations of the tsp i e formulations of polynomial size are known in this paper we adapt some of them to the stsp and compare them both theoretically and computationally it turns out that just by putting the best of the formulations into the cplex branch and bound solver one can solve instances with over 200 nodes we also briefly discuss the adaptation of our formulations to some related problems

a tabu search heuristic for the vehicle routing problem the purpose of this paper is to describe taburoute a new tabu search heuristic for the vehicle routing problem with capacity and route length restrictions the algorithm considers a sequence of adjacent solutions obtained by repeatedly removing a vertex from its current route and reinserting it into another route this is done by means of a generalized insertion procedure previously developed by the authors during the course of the algorithm infeasible solutions are allowed numerical tests on a set of benchmark problems indicate that tabu search out performs the best existing heuristics and taburoute often produces the best known solutions

the shortest path problem with resource constraints with k 2 loop elimination and its application to the capacitated arc routing problem abstract in many branch and price algorithms the column generation subproblem consists of computing feasible constrained paths in the capacitated arc routing problem carp elementarity constraints concerning the edges to be serviced and additional constraints resulting from the branch and bound process together impose two types of loop elimination constraints to fulfill the former constraints it is common practice to rely on a relaxation where loops are allowed in a k loop elimination approach all loops of length k and smaller are forbidden following bode and irnich 2012 for solving the carp branching on followers and non followers is the only known approach to guarantee integer solutions within branch and price however it comes at the cost of additional task 2 loop elimination constraints in this paper we show that a combined k 2 loop elimination in the shortest path subproblem can be accomplished in a computationally efficient way overall the improved branch and price often allows the computation of tighter lower bounds and integer optimal solutions for several instances from standard benchmark sets

instance specific multi objective parameter tuning based on fuzzy logic abstract finding good parameter values for meta heuristics is known as the parameter setting problem a new parameter tuning strategy called ipts is proposed that is a novel instance specific method to take the trade off between solution quality and computational time into consideration two important steps in the method are an a priori statistical analysis to identify the factors that determine heuristic performance in both quality and time for a specific type of problem and the transformation of these insights into a fuzzy inference system rule base which aims to return parameter values on the pareto front with respect to a decision maker s preference applied to the symmetric travelling salesman problem and the meta heuristic guided local search the approach is consistently faster than a traditional non instance specific parameter tuning strategy without significantly affecting solution quality optimised for speed computational times are shown to be on average 20 times faster while producing solutions of similar quality a number of interesting areas for further research are discussed

a note on finding a shortest complete cycle in an undirected graph abstract how to transform a shortest complete cycle problem into a traveling salesman problem is well known although these problems appear ill conditioned a 1 tree relaxation based traveling salesman algorithm solves them rather easily up to 150 nodes provided non optimal edges are eliminated the computational results are considerably better than known results for a linear programming approach

order picking in a rectangular warehouse a solvable case of the traveling salesman problem this paper addresses the problem of order picking in a rectangular warehouse that contains crossovers only at the ends of aisles an algorithm is presented for picking an order in minimum time the computational effort required is linear in the number of aisles the procedure has been implemented on a microcomputer a 50 aisle problem requires only about 1 minute to solve

a guided local search heuristic for the capacitated arc routing problem abstract this paper presents a new local search algorithm for the capacitated arc routing problem carp the procedure uses single vehicle moves and moves that operate on two routes both derived from a node routing context but properly adapted to work well for arc routing problems we combine the algorithm with the meta heuristic guided local search and further use the mechanisms of neighbor lists and edge marking to improve the solution quality and to save computation time experiments on standard benchmark problems from the literature show that our algorithm outperforms the existing heuristics for the carp on a set of new test problems the local search approach consistently produces high quality solutions and often detects an optimal solution within limited computation time

exploring variants of 2 opt and 3 opt for the general routing problem the general routing problem grp is the problem of finding a minimum length tour visiting a number of specified vertices and edges in an undirected graph in this paper we describe how the well known 2 opt and 3 opt local search procedures for node routing problems can be adapted to solve arc and general routing problems successfully two forms of the 2 opt and 3 opt approaches are applied to the grp the first version is similar to the conventional approach for the traveling salesman problem the second version includes a dynamic programming procedure and explores a larger neighborhood at the expense of higher running times extensive computational tests including ones on larger instances than previously reported in the arc routing literature are performed with variants of both algorithms in combination with the guided local search metaheuristic and the mechanisms of marking and neighbor lists the procedures systematically detect optimal or high quality solutions within limited computation time