new developments in the primal dual column generation technique abstract the optimal solutions of the restricted master problems typically leads to an unstable behavior of the standard column generation technique and consequently originates an unnecessarily large number of iterations of the method to overcome this drawback variations of the standard approach use interior points of the dual feasible set instead of optimal solutions in this paper we focus on a variation known as the primal dual column generation technique which uses a primal dual interior point method to obtain well centered non optimal solutions of the restricted master problems we show that the method converges to an optimal solution of the master problem even though non optimal solutions are used in the course of the procedure also computational experiments are presented using linear relaxed reformulations of three classical integer programming problems the cutting stock problem the vehicle routing problem with time windows and the capacitated lot sizing problem with setup times the numerical results indicate that the appropriate use of a primal dual interior point method within the column generation technique contributes to a reduction of the number of iterations as well as the running times on average furthermore the results show that the larger the instance the better the relative performance of the primal dual column generation technique

the fleet size and mix problem for capacitated arc routing abstract there have been several attempts to solve the capacitated arc routing problem with m vehicles starting their tours from a central node the objective has been to minimize the total distance travelled in the problem treated here we also have the fixed costs of the vehicles included in the objective function a set of vehicle capacities with their respective costs are used thus the objective function becomes a combination of fixed and variable costs the solution procedure consists of four phases in the first phase a chinese or rural postman problem is solved depending on whether all or some of the arcs in the network demand service with the objective of minimizing the total distance travelled it results in a tour called the giant tour in the second phase the giant tour is partitioned into single vehicle subtours feasible with respect to the constraints a new network is constructed with the node set corresponding to the arcs of the giant tour and with the arc set consisting of the subtours of the giant tour the arc costs include both the fixed and variable costs of the subtours the third phase consists of solving the shortest path problem on this new network to result in the least cost set of subtours represented on the new network in the last phase a postprocessor is applied to the solution to improve it the procedure is repeated for different giant tours to improve the final solution the problem is extended to the case where there can be upper bounds on the number of vehicles with given capacities using a branch and bound method extension to directed networks is given some computational results are reported

an exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts this paper presents a new exact algorithm for the capacitated vehicle routing problem cvrp based on the set partitioning formulation with additional cuts that correspond to capacity and clique inequalities the exact algorithm uses a bounding procedure that finds a near optimal dual solution of the lp relaxation of the resulting mathematical formulation by combining three dual ascent heuristics the first dual heuristic is based on the q route relaxation of the set partitioning formulation of the cvrp the second one combines lagrangean relaxation pricing and cut generation the third attempts to close the duality gap left by the first two procedures using a classical pricing and cut generation technique the final dual solution is used to generate a reduced problem containing only the routes whose reduced costs are smaller than the gap between an upper bound and the lower bound achieved the resulting problem is solved by an integer programming solver computational results over the main instances from the literature show the effectiveness of the proposed algorithm

conformity of two sociometric relations the problem of comparing two sociometric relations or measurements a andb recorded in distinct sociomatrices was originally discussed by katz and powell in the early 1950 s and hubert and baker in the late 1970 s the problem is considered again using a probabilistic model designed specifically for discrete valued network measurements the model allows for the presence of various structural tendencies such as reciprocity and differential popularity a parameter that isolates the tendency for actors to choose other actors on both relations simultaneously is introduced and estimated conditional on the presence of other parameters that reflect additional important network properties the parameter is presented as a symmetric index but is also generalized to the predictive a onb orb ona situation this approach to the problem is illustrated with the same data used by the earlier solutions and the unique nature of the two relations in the data set a received choices b perceived choices as it affects the modeling is discussed significance tests for the parameter and related parameters are described as well as an extension to more than two relations

a generic exact solver for vehicle routing and related problems major advances were recently obtained in the exact solution of vehicle routing problems vrps sophisticated branch cut and price bcp algorithms for some of the most classical vrp variants now solve many instances with up to a few hundreds of customers however adapting and reimplementing those successful algorithms for other variants can be a very demanding task this work proposes a bcp solver for a generic model that encompasses a wide class of vrps it incorporates the key elements found in the best existing vrp algorithms ng path relaxation rank 1 cuts with limited memory path enumeration and rounded capacity cuts all generalized through the new concepts of packing set and elementarity set the concepts are also used to derive a branching rule based on accumulated resource consumption and to generalize the ryan and foster branching rule extensive experiments on several variants show that the generic solver has an excellent overall performance in many problems being better than the best specific algorithms even some non vrps like bin packing vector packing and generalized assignment can be modeled and effectively solved

generalized monte carlo significance tests summary simple monte carlo significance testing has many applications particularly in the preliminary analysis of spatial data the method requires the value of the test statistic to be ranked among a random sample of values generated according to the null hypothesis however there are situations in which a sample of values can only be conveniently generated using a markov chain initiated by the observed data so that independence is violated this paper describes two methods that overcome the problem of dependence and allow exact tests to be carried out the methods are applied to the rasch model to the finite lattice ising model and to the testing of association between spatial processes power is discussed in a simple case

a basis deficiency allowing variation of the simplex method for linear programming h one of the most important and fundamental concepts in the simplex methodology basis is restricted to being a square matrix of the order exactly equal to the number of rows of the coefficient matrix such inflexibility might have been the source of too many zero steps taken by the simplex method in solving real world linear programming problems which are usually highly degen erate to dodge this difficulty we first generalize the basis to allow the deficient case characterized as one that has columns fewer than rows of the coefficient matrix variations of the primal and dual simplex procedures are then made and used to form a two phase method based on such a basis the number of whose columns varies dynamically in the solution process generally speaking the more degenerate a problem to be handled is the fewer columns the basis will have so thii renders the possibility of efficiently solving highly degenerate problems we also provide a valuable insight into the distinctive and favorable behavior of the proposed method by reporting our computational experiments 1998 elsevier science ltd all rights reserved

separation algorithms for 0 1 knapsack polytopes valid inequalities for 0 1 knapsack polytopes often prove useful when tackling hard 0 1 linear programming problems to generate such inequalities one needs separation algorithms for them i e routines for detecting when they are violated we present new exact and heuristic separation algorithms for several classes of inequalities namely lifted cover extended cover weight and lifted pack inequalities moreover we show how to improve a recent separation algorithm for the 0 1 knapsack polytope itself extensive computational results on miplib and or library instances show the strengths and limitations of the inequalities and algorithms considered

branch and price column generation for solving huge integer programs we discuss formulations of integer programs with a huge number of variables and their solution by column generation methods i e implicit pricing of nonbasic variables to generate new columns or to prove lp optimality at a node of the branch and bound tree we present classes of models for which this approach decomposes the problem provides tighter lp relaxations and eliminates symmetry we then discuss computational issues and implementation of column generation branch and bound algorithms including special branching rules and efficient ways to solve the lp relaxation we also discuss the relationship with lagrangian duality

efficient elementary and restricted non elementary route pricing abstract column generation is involved in the current most efficient approaches to routing problems set partitioning formulations model routing problems by considering all possible routes and selecting a subset that visits all customers these formulations often produce tight lower bounds and require column generation for their pricing step the bounds in the resulting branch and price are tighter when elementary routes are considered but this approach leads to a more difficult pricing problem balancing the pricing with route relaxations has become crucial for the efficiency of the branch and price for routing problems recently the ng routes relaxation was proposed as a compromise between elementary and non elementary routes the ng routes are non elementary routes with the restriction that when following a customer the route is not allowed to visit another customer that was visited before if they belong to a dynamically computed set the larger the size of these sets the closer the ng route is to an elementary route this work presents an efficient pricing algorithm for ng routes and extends this algorithm for elementary routes therefore we address the shortest path problem with resource constraint spprc and the elementary shortest path problem with resource constraint espprc the proposed algorithm combines the decremental state space relaxation technique dssr with completion bounds we apply this algorithm for the generalized vehicle routing problem gvrp and for the capacitated vehicle routing problem cvrp demonstrating that it is able to price elementary routes for instances up to 200 customers a result that doubles the size of the espprc instances solved to date

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

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

multi phase dynamic constraint aggregation for set partitioning type problems dynamic constraint aggregation is an iterative method that was recently introduced to speed up the linear relaxation solution process of set partitioning type problems this speed up is mostly due to the use at each iteration of an aggregated problem defined by aggregating disjoint subsets of constraints from the set partitioning model this aggregation is updated when needed to ensure the exactness of the overall approach in this paper we propose a new version of this method called the multi phase dynamic constraint aggregation method which essentially adds to the original method a partial pricing strategy that involves multiple phases this strategy helps keeping the size of the aggregated problem as small as possible yielding a faster average computation time per iteration and fewer iterations we also establish theoretical results that provide some insights explaining the success of the proposed method tests on the linear relaxation of simultaneous bus and driver scheduling problems involving up to 2 000 set partitioning constraints show that the partial pricing strategy speeds up the original method by an average factor of 4 5

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

boundary behaviors for liouville s equation in planar singular domains abstract we study asymptotic behaviors near the boundary of complete metrics of constant curvature in planar singular domains and establish an optimal estimate of these metrics by the corresponding metrics in tangent cones near isolated singular points on boundary the conformal structure plays an essential role

exact algorithms for the vehicle routing problem based on spanning tree and shortest path relaxations we consider the problem of routing vehicles stationed at a central facility depot to supply customers with known demands in such a way as to minimize the total distance travelled the problem is referred to as the vehicle routing problem vrp and is a generalization of the multiple travelling salesman problem that has many practical applications we present tree search algorithms for the exact solution of the vrp incorporating lower bounds computed from i shortest spanning k degree centre tree k dct and ii q routes the final algorithms also include problem reduction and dominance tests computational results are presented for a number of problems derived from the literature the results show that the bounds derived from the q routes are superior to those from k dct and that vrps of up to about 25 customers can be solved exactly

selected topics in column generation dantzig wolfe decomposition and column generation devised for linear programs is a success story in large scale integer programming we outline and relate the approaches and survey mainly recent contributions not yet found in textbooks we emphasize the growing understanding of the dual point of view which has brought considerable progress to the column generation theory and practice it stimulated careful initializations sophisticated solution techniques for the restricted master problem and subproblem as well as better overall performance thus the dual perspective is an ever recurring concept in our selected topics

comparison of bundle and classical column generation when a column generation approach is applied to decomposable mixed integer programming problems it is standard to formulate and solve the master problem as a linear program seen in the dual space this results in the algorithm known in the nonlinear programming community as the cutting plane algorithm of kelley and cheney goldstein however more stable methods with better theoretical convergence rates are known and have been used as alternatives to this standard one of them is the bundle method our aim is to illustrate its differences with kelley s method in the process we review alternative stabilization techniques used in column generation comparing them from both primal and dual points of view numerical comparisons are presented for five applications cutting stock which includes bin packing vertex coloring capacitated vehicle routing multi item lot sizing and traveling salesman we also give a sketchy comparison with the volume algorithm

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

stabilized dynamic constraint aggregation for solving set partitioning problems abstract dynamic constraint aggregation dca and dual variable stabilization dvs are two methods that can reduce the negative impact of degeneracy when solving linear programs the first uses a projection to reduce the primal space whereas the second acts in the dual space in this paper we develop a new method called stabilized dynamic constraint aggregation sdca that combines dca and dvs for solving set partitioning problems it allows to fight degeneracy from both primal and dual perspectives simultaneously to assess the effectiveness of sdca we report computational results obtained for highly degenerate multi depot vehicle scheduling problem instances solved by column generation these results indicate that sdca can reduce the average computational time of the master problem by a factor of up to 7 with respect to the best of the two combined methods furthermore they show that its performance is robust with regard to increasing levels of degeneracy in test problems

interior curvature estimates and the asymptotic plateau problem in hyperbolic space we show that for a very general class of curvature functions defined in the positive cone the problem of finding a complete strictly locally convex hypersurface in h satisfying f 0 1 with a prescribed asymptotic boundary at infinity has at least one smooth solution with uniformly bounded hyperbolic principal curvatures moreover if is euclidean starshaped the solution is unique and also euclidean starshaped while if is mean convex the solution is unique we also show via a strong duality theorem that analogous results hold in de sitter space a novel feature of our approach is a global interior curvature estimate

non properly embedded h planes in mathbb h 2 times mathbb r for any h in 0 frac 1 2 we construct complete non proper stable simply connected surfaces embedded in mathbb h 2 times mathbb r with constant mean curvature h

computational study of a column generation algorithm for bin packing and cutting stock problems this paper reports on our attempt to design an efficient exact algorithm based on column generation for the cutting stock problem the main focus of the research is to study the extend to which standard branch and bound enhancement features such as variable fixing the tightening of the formulation with cutting planes early branching and rounding heuristics can be usefully incorporated in a branch and price algorithm we review and compare lower bounds for the cutting stock problem we propose a pseudo polynomial heuristic we discuss the implementation of the important features of the integer programming column generation algorithm and in particular the implementation of the branching scheme our computational results demonstrate the efficiency of the resulting algorithm for various classes of bin packing and cutting stock problems

an efficient transformation of the generalized vehicle routing problem abstract the generalized vehicle routing problem gvrp is the problem of designing optimal delivery or collection routes subject to capacity restrictions from a given depot to a number of predefined mutually exclusive and exhaustive clusters in this paper we describe an efficient transformation of the gvrp into a capacitated arc routing problem carp for which an exact algorithm and several approximate procedures are reported in literature it constitutes the only known approach for solving the gvrp

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

logit models and logistic regressions for social networks i an introduction to markov graphs and p spanning nearly sixty years of research statistical network analysis has passed through at least two generations of researchers and models beginning in the late 1930 s the first generation of research dealt with the distribution of various network statistics under a variety of null models the second generation beginning in the 1970 s and continuing into the 1980 s concerned models usually for probabilities of relational ties among very small subsets of actors in which various simple substantive tendencies were parameterized much of this research most of which utilized log linear models first appeared in applied statistics publications

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

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

new route relaxation and pricing strategies for the vehicle routing problem in this paper we describe an effective exact method for solving both the capacitated vehicle routing problem cvrp and the vehicle routing problem with time windows vrptw that improves the method proposed by baldacci et al baldacci r n christofides a mingozzi 2008 an exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts math programming115 2 351 385 for the cvrp the proposed algorithm is based on the set partitioning sp formulation of the problem we introduce a new route relaxation called ng route used by different dual ascent heuristics to find near optimal dual solutions of the lp relaxation of the sp model we describe a column and cut generation algorithm strengthened by valid inequalities that uses a new strategy for solving the pricing problem the new ng route relaxation and the different dual solutions achieved allow us to generate a reduced sp problem containing all routes of any optimal solution that is finally solved by an integer programming solver the proposed method solves four of the five open solomon s vrptw instances and significantly improves the running times of state of the art algorithms for both vrptw and cvrp

dynamic constraint and variable aggregation in column generation abstract starting from the improved primal simplex ips decomposition introduced by elhallaoui et al 2011 to tackle degeneracy in general linear programs we introduce and discuss the mathematical foundations of improved column generation decompositions icg that are better than the standard column generation decomposition when degeneracy is an issue we also present an improved dynamic constraint aggregation idca which is a specialization of icg to efficiently solve set partitioning problems we show that idca improves the dynamic constraint aggregation dca and the multiphase dynamic constraint aggregation mpdca algorithms elhallaoui et al 2005 2010 that not only reduce degeneracy but also profit from it to efficiently solve set partitioning problems idca solves at each iteration a complementary problem cp to obtain a group of variables that can be aggregated or pivoted into the basis to bypass degenerate pivots and decrease the objective value and to obtain more central dual solutions to generate new columns our numerical results show reduction factors in the solution times exceeding 10 for idca compared to a state of the art standard column generation solver

global smoothness for a singular monge ampere equation abstract the global c n 2 regularity for the graph of solutions to a singular monge ampere equation was established in 7 this equation arises in the study of hyperbolic affine spheres and is singular at the boundary a compatibility condition for higher regularity was found in 7 in this paper we verify the compatibility condition and obtain the global c regularity in the even dimensional case

the dirichlet problem for nonlinear second order elliptic equations ii complex monge ampere and uniformaly elliptic equations on considere le probleme de dirichlet pour des equations elliptiques non lineaires d ordre 2 pour une fonction reelle dans un domaine borne de r n a frontiere lisse

projective cutting planes given a polytope mathcal p an interior point x in mathcal p and a direction d in mathbb r n the projection of x along d asks to find the maximum step length t such that

optimal boundary regularity for nonlinear singular elliptic equations abstract in this paper we prove the optimal boundary regularity under natural structural conditions for a large class of nonlinear elliptic equations with singular terms near the boundary by a careful construction of super and sub solutions we obtain precise growth estimates for solutions at the boundary and reduce the boundary regularity to the interior one by a rescaling argument

dynamic aggregation of set partitioning constraints in column generation column generation is often used to solve problems involving set partitioning constraints such as vehicle routing and crew scheduling problems when these constraints are in large numbers and the columns have on average more than 8 12 nonzero elements column generation often becomes inefficient because solving the master problem requires very long solution times at each iteration due to high degeneracy to overcome this difficulty we introduce a dynamic constraint aggregation method that reduces the number of set partitioning constraints in the master problem by aggregating some of them according to an equivalence relation to guarantee optimality this equivalence relation is updated dynamically throughout the solution process tests on the linear relaxation of the simultaneous vehicle and crew scheduling problem in urban mass transit show that this method significantly reduces the size of the master problem degeneracy and solution times especially for larger problems in fact for an instance involving 1 600 set partitioning constraints the master problem solution time is reduced by a factor of 8

hypersurfaces of constant mean curvature in hyperbolic space with prescribed asymptotic boundary at infinity in this paper we study the problem of finding smooth complete hypersurfaces of constant mean curvature in hyperbolic space with a prescribed asymptotic boundary at infinity our main results are proved by deriving a priori global gradient estimates based on the classical maximum principle for elliptic equations

on the dirichlet problem for minimal graphs in hyperbolic space soit r n n 2 un domaine borne on etudie le probleme de dirichlet suivant f f i f j f ij 1 df 2 n f 0 dans f 0 dans f 0 sur on considere le comportement a la frontiere de la solution

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

pseudolikelihood estimation for social networks abstract interest in log linear modeling for social network data has grown steadily since holland and leinhardt 1981 proposed their p 1 model that model was designed for a single binary relationship directed graph representing interactions between individuals it assumed that interactions between pairs of individuals are mutually independent subsequent work has extended the model in various ways including block modeling and the case of dependence between pairs of individuals in empirical work it would often be desirable to fit a wide variety of these models as the differences in predictions or goodness of fit are likely to provide insights into the data this has not been common practice however because estimation for some of the models has been difficult and the maximum likelihood schemes developed for others involve different computer programs not always available in standard packages the focus of this article is on a general estimation technique that maximizes the pseudolikelihood the pro

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

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

asymptotic behavior of area minimizing currents in hyperbolic space on etudie le comportement asymptotique des courants localement rectifiables minimisant l aire dans un espace hyperbolique on considere l aspect theorie de la mesure geometrique et l aspect equation aux derivees partielles

complete surfaces of constant mean curvature 1 in the hyperbolic 3 space in the study of minimal surfaces in the euclidean 3 space the weierstrass representation plays an important role bryant br showed that an analogue of the weierstrass representation formula holds for surfaces of constant mean curvature i in the hyperbolic 3 space x3 in this article we abbreviate the term constant mean curvature i as cmc 1 like minimal surfaces in the euclidean space the hyperbolic gauss map of cmc 1 surfaces is defined as a holomorphic map to c u oo however in contrast to the euclidean case the hyperbolic gauss map of a cmc 1 surface may not be extended across the ends even if the total gaussian curvature is finite we call a complete cmc 1 surface whose gauss map can be extended across all of its ends a cmc 1 surface of regular ends in this article we produce an explicit tool to construct cmc 1 surfaces of regular ends in section 2 we show that such surfaces are constructed by solving some ordinary differential equations with regular singularity in our cmc 1 category ossermann s inequality is not expected and the cohn vossen inequality is the best possible one we show in section 4 that the equality of the cohn vossen inequality never holds for complete cmc 1 surfaces in xh3 in section 5 we give a necessary and sufficient condition that a regular end of a cmc 1 surface be embedded in section 6 we classify complete cmc 1 surfaces of genus 0 with two regular ends our classification contains new examples furthermore in section 7 we construct several new cmc 1 surfaces with regular embedded ends each of these examples has a nontrivial deformation which is mentioned in section 3 it should be remarked that our construction does not work for surfaces with irregular ends but there is another construction by perturbing minimal surfaces in the euclidean 3 space the authors constructed cmc 1 surfaces all of whose ends are irregular see uy1

ray projection for optimizing polytopes with prohibitively many constraints in set covering column generation a recurrent task in mathematical programming consists of optimizing polytopes with prohibitively many constraints e g the primal polytope in cutting planes methods or the dual polytope in column generation cg we present a method to optimize such polytopes using the following intersection sub problem given ray mathbf r in mathbb z n r zn find the maximum t ge 0 t 0 such that t mathbf r t r is feasible we interpret mathbf 0 n rightarrow mathbf r 0n r as a direction of growth from the origin mathbf 0 n 0n t mathbf r t r is the intersection point between mathbf 0 n rightarrow mathbf r 0n r and the polytope boundary to ease the exposition the first part of the paper is devoted to the general context of a primal or dual polytope with rational data such that i the intersection sub problem can be effectively solved in practice for input rays mathbf r in mathbb z n r zn and ii mathbf 0 n 0n is feasible by iterating over such rays mathbf r r our method produces a sequence of feasible solutions t mathbf r t r that we prove to be finitely convergent from section 3 on we focus on dual polytopes in cg formulations typically if the cg separation sub problem can be solved by dynamic programming dp so can be the intersection sub problem the proposed integer ray method irm only uses integer rays and so the intersection sub problem can be solved using a dp scheme based on states indexed by integer ray values we show that under such conditions the intersection sub problem can be even easier than the cg sub problem especially when no other integer data is available to index states in dp i e if the cg sub problem input consists of fractional or large range values as such the irm can tackle scaled instances with large range weights of capacitated problems that seem prohibitively hard for classical cg this is confirmed by numerical experiments on various capacitated set covering problems capacitated arc routing cutting stock and other three versions of elastic cutting stock i e a problem class that includes variable size bin packing

density and spectrum of minimal submanifolds in space forms let varphi m m rightarrow n n be a minimal proper immersion in an ambient space suitably close to a space form mathbb n n k of curvature k le 0 in this paper we are interested in the relation between the density function theta r of m and the spectrum of its laplace beltrami operator in particular we prove that if theta r has subexponential growth when k 0 or sub polynomial growth k 0 along a sequence then the spectrum of m m is the same as that of the space form mathbb n m k notably the result applies to anderson s smooth solutions of plateau s problem at infinity on the hyperbolic space independently of their boundary regularity we also give a simple condition on the second fundamental form that ensures m to have finite density in particular we show that minimal submanifolds with finite total curvature in the hyperbolic space also have finite density

renormalized area and properly embedded minimal surfaces in hyperbolic 3 manifolds we study the renormalized area functional mathcal a in the ads cft correspondence specifically for properly embedded minimal surfaces in convex cocompact hyperbolic 3 manifolds and somewhat more broadly poincare einstein spaces our main results include an explicit formula for the renormalized area of such a minimal surface y as an integral of local geometric quantities as well as formulae for the first and second variations of mathcal a which are given by integrals of global quantities over the asymptotic boundary loop of y all of these formulae are also obtained for a broader class of nonminimal surfaces the proper setting for the study of this functional when the ambient space is hyperbolic requires an understanding of the moduli space of all properly embedded minimal surfaces with smoothly embedded asymptotic boundary we show that this moduli space is a smooth banach manifold and develop a mathbb z valued degree theory for the natural map taking a minimal surface to its boundary curve we characterize the nondegenerate critical points of mathcal a for minimal surfaces in mathbb h 3 and finally discuss the relationship of mathcal a to the willmore functional

subset row inequalities applied to the vehicle routing problem with time windows this paper presents a branch and cut and price algorithm for the vehicle routing problem with time windows the standard dantzig wolfe decomposition of the arc flow formulation leads to a set partitioning problem as the master problem and an elementary shortest path problem with resource constraints as the pricing problem we introduce the subset row inequalities which are chvatal gomory rank 1 cuts based on a subset of the constraints in the master problem applying a subset row inequality in the master problem increases the complexity of the label setting algorithm used to solve the pricing problem because an additional resource is added for each inequality we propose a modified dominance criterion that makes it possible to dominate more labels by exploiting the step like structure of the objective function of the pricing problem computational experiments have been performed on the solomon benchmarks where we were able to close several instances the results show that applying subset row inequalities in the master problem significantly improves the lower bound and in many cases makes it possible to prove optimality in the root node

branch price and cut for the mixed capacitated general routing problem with time windows abstract the mixed capacitated general routing problem with time windows mcgrptw is defined over a mixed graph for which some nodes arcs and edges have strictly positive demand and must be serviced the problem consists of determining a set of least cost vehicle routes that satisfy this requirement while respecting pre specified time windows and without exceeding the vehicle capacity in this work we transform the mcgrptw into an equivalent node routing problem over a directed graph thus we solve the equivalent problem by using a branch price and cut algorithm which relies on some effective techniques introduced in the field computational experiments over instances derived from the capacitated arc routing problem with time windows and from the mixed capacitated general routing problem are presented the article also describes experiments over benchmark instances

constrained monte carlo maximum likelihood for dependent data maximum likelihood estimates mles in autologistic models and other exponential family models for dependent data can be calculated with markov chain monte carlo methods the metropolis algorithm or the gibbs sampler which simulate ergodic markov chains having equilibrium distributions in the model from one realization of such a markov chain a monte carlo approximant to the whole likelihood function can be constructed the parameter value if any maximizing this function approximates the mle

row reduced column generation for degenerate master problems abstract column generation for solving linear programs with a huge number of variables alternates between solving a master problem and a pricing subproblem to add variables to the master problem as needed the method is known to often suffer from degeneracy in the master problem inspired by recent advances in coping with degeneracy in the primal simplex method we propose a row reduced column generation method that may take advantage of degenerate solutions the idea is to reduce the number of constraints to the number of strictly positive basic variables in the current master problem solution the advantage of this row reduction is a smaller working basis and thus a faster re optimization of the master problem this comes at the expense of a more involved pricing subproblem itself eventually solved by column generation that needs to generate weighted subsets of variables that are said compatible with the row reduction if possible such a subset of variables gives rise to a strict improvement in the objective function value if the weighted combination of the reduced costs is negative we thus state as a by product a necessary and sufficient optimality condition for linear programming this methodological paper generalizes the improved primal simplex and dynamic constraints aggregation methods on highly degenerate linear programs recent computational experiments with these two algorithms show that the row reduction of a problem might have a large impact on the solution time we conclude with a few algorithmic and implementation issues

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

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

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

a new branch and cut algorithm for the capacitated vehicle routing problem we present a new branch and cut algorithm for the capacitated vehicle routing problem cvrp the algorithm uses a variety of cutting planes including capacity framed capacity generalized capacity strengthened comb multistar partial multistar extended hypotour inequalities and classical gomory mixed integer cuts for each of these classes of inequalities we describe our separation algorithms in detail also we describe the other important ingredients of our branch and cut algorithm such as the branching rules the node selection strategy and the cut pool management computational results for a large number of instances show that the new algorithm is competitive in particular we solve three instances b n50 k8 b n66 k9 and b n78 k10 of augerat to optimality for the first time

erratum on the dirichlet problem for minimal graphs in hyperbolic space r n 0 that can be identified with the asymptotic infinity of hn 1 let nn 1 hn 1 be a closed embedded n 1 dimensional submanifold then there exists a complete absolutely area minimizing integral n current asymptotic to nn 1 at infinity see for example 1 2 it was also noted in 1 2 that in the case n 6 currents obtained are smoothly embedded complete hypersurfaces in the case n 7 as in the euclidean case there can be a singular set of hausdorff dimension at most n 7

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

robust branch and cut and price for the capacitated vehicle routing problem the best exact algorithms for the capacitated vehicle routing problem cvrp have been based on either branch and cut or lagrangean relaxation column generation this paper presents an algorithm that combines both approaches it works over the intersection of two polytopes one associated with a traditional lagrangean relaxation over q routes the other defined by bound degree and capacity constraints this is equivalent to a linear program with exponentially many variables and constraints that can lead to lower bounds that are superior to those given by previous methods the resulting branch and cut and price algorithm can solve to optimality all instances from the literature with up to 135 vertices this more than doubles the size of the instances that can be consistently solved

calculation of polychotomous logistic regression parameters using individualized regressions summary the use of individualized logistic regression in which a series of separate simple logistic regression analyses are performed as a replacement for polychotomous logistic regression is studied the asymptotic relative efficiencies of the individual parameter estimates are observed to be generally high as are the efficiencies of predicted probability estimates and to a somewhat lesser extent joint tests of parameters from different regressions

a nested decomposition approach to a three stage two dimensional cutting stock problem we consider the cutting of rectangular order pieces into stock pieces of specified width and length the cutting process involves three stages of orthogonal guillotine cutting stock pieces are cut into sections that are cut into slits that are cut into order pieces restrictions imposed on the cutting process make the combinatorial structure of the problem more complex but limit the scope of solution space the objective of the problem is mainly to minimize waste but our model also accounts for other issues such as aging stock pieces urgent or optional orders and fixed setup costs our solution approach involves a nested decomposition of the problem and the recursive use of the column generation technique we use a column generation formulation of the problem gilmore and gomory 1965 and the cutting pattern generation subproblem is itself solved using a column generation algorithm lp based lower bounds on the minimum cost are computed and by rounding the lp solution a feasible solution and associated upper bound is obtained this approach could in principle be used in a branch and bound search to solve the problem to optimality we report computational results for industrial instances the algorithm is being used in industry as a production planning tool

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

regularity at infinity for area minimizing hypersurfaces in hyperbolic space equipped with the hyperbolic metric y z dxz dy2 a standard compactification of ih involves adding the boundary r 0 w so that i i is simply the one point compactification of the euclidean closed half space r 0 suppose 0 7 any interior singularities of m must remain in a bounded region of hyperbolic space near points of f in the euclidean topology m w f may thus be described as the graph of a function this function is the solution of an interesting partial differential equation that becomes degenerate along the part of the boundary corresponding to f the second author has recently established l a boundary higher regularity result for this equation which implies in particular that m w f is r if f is cgk for k 2 3 finally in case f bounds a star

uniqueness and regularity of proper harmonic maps introduction the purpose of this paper is to study some uniqueness and regularity properties of the dirichlet problem at infinity for proper harmonic maps between hyperbolic spaces in general if the metrics of two complete noncompact manifolds mm and n are given locally by ds2 imj gij dxzdxj and dsy en h 3 du du respectively then the energy density function of a c1 map u m n is defined by

logit models and logistic regressions for social networks iii valued relations this paper generalizes thep model for dichotomous social network data wasserman pattison 1996 to the polytomous case the generalization is achieved by transforming valued social networks into three way binary arrays this data transformation requires a modification of the hammersley clifford theorem that underpins thep class of models we demonstrate that provided that certain non observed data patterns are excluded from consideration a suitable version of the theorem can be developed we also show that the approach amounts to a model for multiple logits derived from a pseudo likelihood function estimation within this model is analogous to the separate fitting of multinomial baseline logits except that the hammersley clifford theorem requires the equating of certain parameters across logits the paper describes how to convert a valued network into a data array suitable for fitting the model and provides some illustrative empirical examples

complete minimal varieties in hyperbolic space it is a basic problem in the subject of minimal varieties to determine the class of complete minimal and area minimizing varieties m k in a given riemannian manifold n besides being of their own intrinsic interest the cases r of euclidean space and mn sn of the sphere are fundamental in understanding the local structure of minimal varieties due to the existence of tangent cones to general minimal varieties there has been much study of the complete areaminimizing varieties in these cases in particular relating to the bernstein conjecture and minimizing cones e g l2 f1 nevertheless many deep problems remain unsolved this paper is centered around the question of existence of complete areaminimizing varieties in hyperbolic space h here by way of contrast to the situation in ir n or s we find a comparatively complete solution to the problem of existence in fact the main result of this paper exhibits a wealth of complete area minimizing varieties in h in all dimensions and codimensions more precisely we have