the robustness of estimates of total indirect effects in covariance structure models estimated by maximum likelihood the large sample distribution of total indirect effects in covariance structure models in well known using monte carlo methods this study examines the applicability of the large sample theory to maximum likelihood estimates oftotal indirect effects in sample sizes of 50 100 200 400 and 800 two models are studied model 1 is a recursive model with observable variables and model 2 is a nonrecursive model with latent variables for the large sample theory to apply the results suggest that sample szes of 200 or more and 400 or more are required for models such as model 1 and model 2 respectively

the delivery man problem and cumulative matroids given a complete directed graph g v a the delivery man problem dmp consists of determining a hamiltonian circuit minimizing the sum of distances along the circuit from a given vertex v1 to every vertex of v including v1 itself there exists a number of applications of the dmp in the fields of distribution and machine scheduling the dmp is np hard the objective of this paper is to develop new theoretical results and an exact algorithm for the problem a new integer linear programming formulation is provided and results on the matroidal structure of a class of combinatorial problems are developed these are used to derive lower bounds for the dmp these bounds are embedded into an enumerative algorithm the largest problems solved to optimality with the proposed algorithm involve 60 vertices this compares favorably with previously published methods

the constrained shortest path problem with stochastic correlated link travel times abstract this paper investigates the constrained shortest path problem in a transportation network where the link travel times are assumed to be random variables defined on the basis of joint probability mass functions a 0 1 integer programming model is formulated to find the least expected travel time paths besides the flow balance and side constraints the unique link selection constraint is particularly introduced to guarantee that only an optimal path can be finally generated then a lagrangian relaxation solution approach is provided to relax the hard constraints and decompose the relaxed model into two parts an algorithmic framework integrating the sub gradient algorithm label correcting algorithm and k shortest path algorithm is designed to minimize the gap between the upper and lower bounds to find near optimal solutions an extension that considers the joint probability mass functions of link travel times varying with time is discussed we decompose the time dependent problem into three subproblems and solve it by the modified algorithmic framework computational tests are conducted on different scales of transportation networks experimental results in a large scale network indicate that the proposed algorithm can quickly find the high quality solutions with small relative gaps demonstrating the effectiveness of the proposed approaches

an analytical comparison of different formulations of the travelling sales man problem a transformation technique is proposed that permits one to derive the linear description of the imagex of a polyhedronz under an affine linear transformation from the given linear description ofz this result is used to analytically compare various formulations of the asymmetric travelling salesman problem to the standard formulation due to dantzig fulkerson and johnson which are all shown to be weaker formulations in a precise setting we also apply this transformation technique to symmetrize formulations and show in particular that the symmetrization of the standard asymmetric formulation results into the standard one for the symmetric version of the travelling salesman problem

solving the vehicle routing problem with time windows and multiple routes exactly using a pseudo polynomial model in this paper we address a variant of the vehicle routing problem called the vehicle routing problem with time windows and multiple routes it considers that a given vehicle can be assigned to more than one route per planning period we propose a new exact algorithm for this problem our algorithm is iterative and it relies on a pseudo polynomial network flow model whose nodes represent time instants and whose arcs represent feasible vehicle routes this algorithm was tested on a set of benchmark instances from the literature the computational results show that our method is able to solve more instances than the only other exact method described so far in the literature and it clearly outperforms this method in terms of computing time

state feedback control of high order stochastic nonlinear systems with siiss inverse dynamics this technical note considers a class of high order stochastic nonlinear systems with stochastic integral input to state stability siiss inverse dynamics and drift and diffusion terms depending upon the stochastic inverse dynamics and all the states a new design and analysis approach to the problem of state feedback global regulation is developed to guarantee that all the signals of the closed loop system are bounded almost surely and the states can be regulated to zero almost surely

adaptive neural network tracking control of mimo nonlinear systems with unknown dead zones and control directions in this paper adaptive neural network nn tracking control is investigated for a class of uncertain multiple input multiple output mimo nonlinear systems in triangular control structure with unknown nonsymmetric dead zones and control directions the design is based on the principle of sliding mode control and the use of nussbaum type functions in solving the problem of the completely unknown control directions it is shown that the dead zone output can be represented as a simple linear system with a static time varying gain and bounded disturbance by introducing characteristic function by utilizing the integral type lyapunov function and introducing an adaptive compensation term for the upper bound of the optimal approximation error and the dead zone disturbance the closed loop control system is proved to be semiglobally uniformly ultimately bounded with tracking errors converging to zero under the condition that the slopes of unknown dead zones are equal simulation results demonstrate the effectiveness of the approach

hybrid optimization methods for time dependent sequencing problems abstract in this paper we introduce novel optimization methods for sequencing problems in which the setup times between a pair of tasks depend on the relative position of the tasks in the ordering our proposed methods rely on a hybrid approach where a constraint programming model is enhanced with two distinct relaxations one discrete relaxation based on multivalued decision diagrams and one continuous relaxation based on linear programming both relaxations are used to generate bounds and enhance constraint propagation experiments conducted on three variants of the time dependent traveling salesman problem indicate that our techniques substantially outperform general purpose methods such as mixed integer linear programming and constraint programming models

the improved lasalle type theorems for stochastic functional differential equations abstract the main aim of this paper is to improve some results obtained by mao x mao the lasalle type theorems for stochastic functional differential equations nonlinear stud 7 2000 307 328 our new theorems give better results while conditions imposed are much weaker than in the paper mentioned above for example we need only the local lipschitz condition but neither the linear growth condition nor the bounded moment condition on the solutions to guarantee the existence and uniqueness of the global solution to the underlying stochastic functional differential equation sfde under the weaker conditions imposed in this paper we establish a generalised existence and uniqueness theorem which covers a wider class of nonlinear sfdes as demonstrated by the examples discussed in this paper moreover from our improved results follow some new criteria on the stochastic asymptotic stability for sfdes

the effect of sampling error on convergence improper solutions and goodness of fit indices for maximum likelihood confirmatory factor analysis a monte carlo study assessed the effect of sampling error and model characteristics on the occurrence of nonconvergent solutions improper solutions and the distribution of goodness of fit indices in maximum likelihood confirmatory factor analysis nonconvergent and improper solutions occurred more frequently for smaller sample sizes and for models with fewer indicators of each factor effects of practical significance due to sample size the number of indicators per factor and the number of factors were found for gfi agfi and rmr whereas no practical effects were found for the probability values associated with the chi square likelihood ratio test

further results on global adaptive stabilisation for a class of uncertain stochastic nonlinear systems this paper considers the global adaptive stabilisation for a class of uncertain stochastic nonlinear systems comparing with the existing relevant literature the systems under investigation allow more serious unknowns uncertainties more importantly by remarkably reducing the dimension of dynamic compensator for system unknowns from n to 2 and considerably diminishing the overparametrisation in the existing literature this paper proposes an improved design scheme for adaptive state feedback controllers it is turned out that with the designed controller in loop all the closed loop system states are globally bounded and the original system states converge to the origin both in the sense of probability one a simulation example is also given to demonstrate the effectiveness of the theoretical results

brief paper backstepping controller design for a class of stochastic nonlinear systems with markovian switching a more general class of stochastic nonlinear systems with irreducible homogenous markovian switching are considered in this paper as preliminaries the stability criteria and the existence theorem of strong solutions are first presented by using the inequality of mathematic expectation of a lyapunov function the state feedback controller is designed by regarding markovian switching as constant such that the closed loop system has a unique solution and the equilibrium is asymptotically stable in probability in the large the output feedback controller is designed based on a quadratic plus quartic form lyapunov function such that the closed loop system has a unique solution with the equilibrium being asymptotically stable in probability in the large in the unbiased case and has a unique bounded in probability solution in the biased case

a simple and effective metaheuristic for the minimum latency problem abstract the minimum latency problem mlp is a variant of the traveling salesman problem which aims to minimize the sum of arrival times at vertices the problem arises in a number of practical applications such as logistics for relief supply scheduling and data retrieval in computer networks this paper introduces a simple metaheuristic for the mlp based on a greedy randomized approach for solution construction and iterated variable neighborhood descent with random neighborhood ordering for solution improvement extensive computational experiments on nine sets of benchmark instances involving up to 1000 customers demonstrate the good performance of the method which yields solutions of higher quality in less computational time when compared to the current best approaches from the literature optimal solutions known for problems with up to 50 customers are also systematically obtained in a fraction of seconds

an exact algorithm for a single vehicle routing problem with time windows and multiple routes this paper describes an exact algorithm for solving a problem where the same vehicle performs several routes to serve a set of customers with time windows the motivation comes from the home delivery of perishable goods where vehicle routes are short and must be combined to form a working day a method based on an elementary shortest path algorithm with resource constraints is proposed to solve this problem the method is divided into two phases in the first phase all non dominated feasible routes are generated in the second phase some routes are selected and sequenced to form the vehicle workday computational results are reported on euclidean problems derived from benchmark instances of the classical vehicle routing problem with time windows

facets and valid inequalities for the time dependent travelling salesman problem abstract the time dependent travelling salesman problem tdtsp is a generalization of the traditional tsp where the travel cost between two cities depends on the moment of the day the arc is travelled in this paper we focus on the case where the travel time between two cities depends not only on the distance between them but also on the position of the arc in the tour we consider two formulations proposed in the literature we analyze the relationship between them and derive several families of valid inequalities and facets in addition to their theoretical properties they prove to be very effective in the context of a branch and cut algorithm

improper solutions in the analysis of covariance structures their interpretability and a comparison of alternate respecifications a monte carlo approach was employed to investigate the interpretability of improper solutions caused by sampling error in maximum likelihood confirmatory factor analysis four models were studied with two sample sizes of the overall goodness of fit indices provided by the lisrel vi program significant differences between improper and proper solutions were found only for the root mean square residual as expected indicators of the factor on which the negative uniqueness estimate occurred had biased loadings and the correlations of its factor with other factors were also biased in contrast the loadings of indicators on other factors and those factor intercorrelations did not have any bias of practical significance for initial solutions with one negative uniqueness estimate three respecifications were studied fix the uniqueness at 00 fix it at 20 or constrain the domain of the solution to be proper for alternate respecified solutions that were converged and proper the constrained solutions and uniqueness fixed at 00 solutions were equivalent the mean goodness of fit and pattern coefficient values for the original improper solutions were not meaningfully different from those obtained under the constrained and uniqueness fixed at 00 respecifications

lyapunov like techniques for stochastic stability the purpose of this paper is to study the stabilizability problem for control stochastic nonlinear systems driven by a wiener process sufficient conditions for the existence of stabilizing feedback laws that are smooth except possibly at the equilibrium point of the system are provided by means of stochastic lyapunov like techniques the notion of dynamic asymptotic stability in probability of control stochastic differential systems is introduced and the stabilization by means of dynamic controllers is studied

an analytical comparison of the lp relaxations of integer models for the k club problem abstract given an undirected graph g v e a k club is a subset of nodes that induces a subgraph with diameter at most k the k club problem is to find a maximum cardinality k club in this study we use a linear programming relaxation standpoint to compare integer formulations for the k club problem the comparisons involve formulations known from the literature and new formulations built in different variable spaces for the case k 3 we propose two enhanced compact formulations from the lp relaxation standpoint these formulations dominate all other compact formulations in the literature and are equivalent to a formulation with a non polynomial number of constraints also for k 3 we compare the relative strength of lp relaxations for all formulations examined in the study new and known from the literature based on insights obtained from the comparative study we devise a strengthened version of a recursive compact formulation in the literature for the k club problem k 1 and show how to modify one of the new formulations for the case k 3 in order to accommodate additional constraints recently proposed in the literature

the asymptotic covariance matrix of maximum likelihood estimates in factor analysis the case of nearly singular matrix of estimates of unique variances this paper is concerned with the asymptotic covariance matrix acm of maximum likelihood estimates mles of factor loadings and unique variances when one element of mles of unique variances is nearly zero i e the matrix of mles of unique variances is nearly singular in this situation standard formulas break down we give explicit formulas for the acm of mles of factor loadings and unique variances that could be used even when an element of mles of unique variances is very close to zero we also discuss an alternative approach using the augmented information matrix under a nearly singular matrix of mles of unique variances and derive the partial derivatives of the alternative constraint functions with respect to the elements of factor loadings and unique variances 2000 elsevier science inc all rights reserved ams classification 62h25 62f12

branch and price algorithms for the solution of the multi trip vehicle routing problem with time windows we investigate the exact solution of the vehicle routing problem with time windows where multiple trips are allowed for the vehicles in contrast to previous works in the literature we specifically consider the case in which it is mandatory to visit all customers and there is no limitation on duration we develop two branch and price frameworks based on two set covering formulations a traditional one where columns variables represent routes that is a sequence of consecutive trips and a second one in which columns are single trips one important difficulty related to the latter is the way mutual temporal exclusion of trips can be handled it raises the issue of time discretization when solving the pricing problem our dynamic programming algorithm is based on concept of groups of labels and representative labels we provide computational results on modified small sized instances 25 customers from solomon s benchmarks in order to evaluate and compare the two methods results show that some difficult instances are out of reach for the first branch and price implementation while they are consistently solved with the second

using phantom and imaginary latent variables to parameterize constraints in linear structural models the most widely used computer programs for structural equation models analysis are the lisrel series of joreskog and sorbom the only types of constraints which may be made directly are fixing parameters at a constant value and constraining parameters to be equal rindskopf 1983 showed how these simple properties could be used to represent models with more complicated constraints namely inequality constraints on unique variances in this paper two new concepts are introduced which enable a much wider variety of constraints to be made the concepts phantom and imaginary latent variables allow fairly general equality and inequality constraints on factor loadings and structural model coefficients

a branch and cut and price algorithm for the cumulative capacitated vehicle routing problem abstract in this paper we consider the cumulative capacitated vehicle routing problem ccvrp which is a variation of the well known capacitated vehicle routing problem cvrp in this problem the traditional objective of minimizing total distance or time traveled by the vehicles is replaced by minimizing the sum of arrival times at the customers we propose a branch and cut and price algorithm for obtaining optimal solutions to the problem to the best of our knowledge this is the first published exact algorithm for the ccvrp we present computational results based on a set of standard cvrp benchmarks and investigate the effect of modifying the number of vehicles available

brief paper finite time stability and instability of stochastic nonlinear systems this paper presents a new definition of finite time stability for stochastic nonlinear systems this definition involves stability in probability and finite time attractiveness in probability an important lyapunov theorem on finite time stability for stochastic nonlinear systems is established a theorem extending the stochastic lyapunov theorem is also proved moreover an example and a lemma are presented to illustrate the scope of extension a useful inequality extended from bihari s inequality is derived which plays an important role in showing the lyapunov theorem finally a lyapunov theorem on finite time instability is proved which states that almost surely globally asymptotical stability is not equivalent to finite time stability for some stochastic systems two simulation examples are given to illustrate the theoretical analysis

state feedback h_ infty control for a class of nonlinear stochastic systems this paper discusses the h infty control problem for a class of nonlinear stochastic systems with both state and disturbance dependent noise by means of hamilton jacobi equations both infinite and finite horizon nonlinear stochastic h infty control designs are developed some results on nonlinear h infty control of deterministic systems are generalized to a stochastic setting we introduce some useful concepts such as zero state observability and zero state detectability which together with the stochastic lasalle invariance principle yield some valuable consequences in infinite horizon nonlinear stochastic h infty control

a classification of formulations for the time dependent traveling salesman problem abstract the time dependent traveling salesman problem tdtsp is a generalization of the classical traveling salesman problem where the cost of any given arc is dependent of its position in the tour the tdtsp can model several real world applications e g one machine sequencing in this paper we present a classification of formulations for the tdtsp this framework includes both new and old formulations the new formulation presented in this paper is derived from a quadratic assignment model for the tdtsp in a first step lawler s transformation procedure is used to derive an equivalent linearized version of the quadratic model in a second step a stronger formulation is obtained by tightening some constraints of the previous formulation it is shown that in terms of linear relaxations the latter formulation is either equivalent or better than other formulations already known from the literature finally we compare these formulations with other well known formulations for the classical traveling salesman problem

nonconvergence improper solutions and starting values in lisrel maximum likelihood estimation in the framework of a robustness study on maximum likelihood estimation with lisrel three types of problems are dealt with nonconvergence improper solutions and choice of starting values the purpose of the paper is to illustrate why and to what extent these problems are of importance for users of lisrel the ways in which these issues may affect the design and conclusions of robustness research is also discussed

global regulation for a class of stochastic high order nonlinear systems with multiple unknown control directions this paper concerns the global regulation for a class of stochastic high order nonlinear systems which admit more general system form than the existing works for details except for the serious sy

determinants of standard errors of mles in confirmatory factor analysis this paper studies changes of standard errors se of the normal distribution based maximum likelihood estimates mle for confirmatory factor models as model parameters vary using logical analysis simplified formulas and numerical verification monotonic relationships between ses and factor loadings as well as unique variances are found conditions under which monotonic relationships do not exist are also identified such functional relationships allow researchers to better understand the problem when significant factor loading estimates are expected but not obtained and vice versa what will affect the likelihood for heywood cases negative unique variance estimates is also explicit through these relationships empirical findings in the literature are discussed using the obtained results

practical output feedback risk sensitive control for stochastic nonlinear systems with stable zero dynamics this paper addresses the design problem of practical or satisfaction output feedback controls for stochastic strict feedback nonlinear systems in observer canonical form with stable zero dynamics under long term average tracking risk sensitive cost criteria the cost function adopted here is of the quadratic integral type usually encountered in practice rather than the quartic integral one used to avoid difficulty in control design and performance analysis of the closed loop system a sequence of coordinate diffeomorphisms is introduced to separate the zero dynamics from the entire system so that the transformed system has an appropriate form suitable for integrator backstepping design for any given risk sensitivity parameter and desired cost value by using the integrator backstepping methodology an output feedback control is constructively designed such that a the closed loop system is bounded in probability and b the long term average risk sensitive cost is upper bounded by the desired value in addition this paper does not require the uniform boundedness of the gain functions of the system noise furthermore an example is given to show the effectiveness of the theory

universal fuzzy models and universal fuzzy controllers for stochastic nonaffine nonlinear systems this paper investigates the universal fuzzy model and universal fuzzy controller problems for stochastic nonaffine nonlinear systems the underlying mechanism of stochastic fuzzy logic is first discussed and a stochastic generalized fuzzy model with new stochastic fuzzy rule base is then given based on their function approximation capability these kinds of stochastic generalized fuzzy models are shown to be universal fuzzy models for stochastic nonaffine nonlinear systems under some sufficient conditions an approach to stabilization controller design for stochastic nonaffine nonlinear systems is then developed through their stochastic generalized takagi sugeno t s fuzzy approximation models then the results of universal fuzzy controllers for two classes of stochastic nonlinear systems along with constructive procedures to obtain the universal fuzzy controllers are also provided respectively finally a numerical example is presented to illustrate the effectiveness of the proposed approach

a 2n constraint formulation for the capacitated minimal spanning tree problem in this paper we present a new formulation for the capacitated minimal spanning tree cmst problem one advantage of the new formulation is that it is more compact in the number of constraints than a well known formulation additionally we show that the linear programming relaxation of both formulations produces optimal solutions with the same cost we present a brief discussion concerning valid inequalities for the cmst which are directly derived from the new formulation we show that some of the new inequalities are not dominated by some sets of facet inducing inequalities for the cmst we derive some lagrangian relaxation based methods from the new formulation and present computational evidence showing that reasonable improvements on the original linear programming bounds can be obtained if these methods are strengthened by the use of cutting planes the reported computational results indicate that one of the methods presented in this paper dominates in most of the cases the previous best methods reported in the literature the most significant improvements are obtained in the instances with the root in the corner

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

observer based adaptive fuzzy tracking control of mimo stochastic nonlinear systems with unknown control directions and unknown dead zones in this paper an adaptive fuzzy backstepping output feedback tracking control approach is proposed for a class of multi input and multi output mimo stochastic nonlinear systems the mimo stochastic nonlinear systems under study are assumed to possess unstructured uncertainties unknown dead zones and unknown control directions by using a linear state transformation the unknown control coefficients and the unknown slopes characteristic of the dead zones are lumped together and the original system is transformed to a new system on which the control design becomes feasible fuzzy logic systems are used to approximate the unstructured uncertainties and a fuzzy state observer is designed to estimate the unmeasured states by introducing a special nussbaum gain function into the backstepping control design a stable adaptive fuzzy output feedback tracking control scheme is developed the main features of the proposed adaptive control approach are that it can guarantee the stability of the closed loop system and the tracking errors converge to a small neighborhood of zero moreover it can solve the problems of unknown control direction unknown dead zone and unmeasured states simultaneously two simulation examples are provided to show the effectiveness of the proposed approach

global practical tracking for high order uncertain nonlinear systems with unknown control directions this paper addresses the global practical tracking problem for a class of high order uncertain nonlinear systems with unknown control directions under fairly weak conditions although the stabilization problem has been studied for the systems the tracking problem remains unsolved up to now mainly because of the essential differences between stabilization and tracking problems when control directions are unknown in this paper by introducing a novel coordinate transformation and new updating laws an approach is presented for the first time to design a continuous adaptive controller to make the tracking error prescribed arbitrarily small after a finite time and simultaneously to keep all the closed loop states bounded it is worth emphasizing that the proposed adaptive tracking control design scheme is motivated by the recent tracking works inspired by the ideas of universal control and dead zone and obtained by the approaches of nussbaum gain and adding a power integrator most importantly this paper removes the basic assumption that the control directions are precisely known in the related tracking works without additional conditions imposed on the systems and the reference signal

factor analysis with em algorithm never gives improper solutions when sample covariance and initial parameter matrices are proper rubin and thayer psychometrika 47 69 76 1982 proposed the em algorithm for exploratory and confirmatory maximum likelihood factor analysis in this paper we prove the following fact the em algorithm always gives a proper solution with positive unique variances and factor correlations with absolute values that do not exceed one when the covariance matrix to be analyzed and the initial matrices including unique variances and inter factor correlations are positive definite we further numerically demonstrate that the em algorithm yields proper solutions for the data which lead the prevailing gradient algorithms for factor analysis to produce improper solutions the numerical studies also show that in real computations with limited numerical precision rubin and thayer s psychometrika 47 69 76 1982 original formulas for confirmatory factor analysis can make factor correlation matrices asymmetric so that the em algorithm fails to converge however this problem can be overcome by using an em algorithm in which the original formulas are replaced by those guaranteeing the symmetry of factor correlation matrices or by formulas used to prove the above fact

simultaneous equation systems as moment structure models with an introduction to latent variable models abstract an introduction to latent variable covariance structure models is provided estimation and testing of such models with normal and non normal variables is reviewed and a relatively inexpensive asymptotically distribution free estimator is introduced the traditional econometric simultaneous equation system is reconceptualized as a random vector structural equation model extensions of the model to deal with latent variables and a wider variety of structural phenomena are made via the joreskog keesling wiley lisrel approach and a simpler approach due to bentler and weeks these representation systems are extended via first and second moments about the origin of measured variables explained in terms of the structural coefficients and the moments of explanatory variables citations to further literature are provided

mathematical formulations and exact algorithm for the multitrip cumulative capacitated single vehicle routing problem abstract this paper addresses the multitrip cumulative capacitated single vehicle routing problem mt ccsvrp in this problem inspired by disaster logistics a single vehicle can perform successive trips to serve a set of affected sites and minimize an emergency criterion the sum of arrival times two mixed integer linear programs a flow based model and a set partitioning model are proposed for small instances with 20 sites an exact algorithm for larger cases transforms the mt ccsvrp into a resource constrained shortest path problem where each node corresponds to one trip and the sites to visit become resources the resulting problem can be solved via an adaptation of bellman ford algorithm to a directed acyclic graph with resource constraints and a cumulative objective function seven dominance rules two upper bounds and five lower bounds speed up the procedure computational results on instances derived from classical benchmark problems for the capacitated vrp indicate that the exact algorithm outperforms a commercial mip solver on small instances and can solve cases with 40 sites to optimality

iterative aggregation and disaggregation algorithm for pseudo polynomial network flow models with side constraints this paper develops a general solution framework based on aggregation techniques to solve np hard problems that can be formulated as a circulation model with specific side constraints the size of the extended mixed integer linear programming formulation is generally pseudo polynomial to efficiently solve exactly these large scale models we propose a new iterative aggregation and disaggregation algorithm at each iteration it projects the original model onto an aggregated one producing an approximate model the process iterates to refine the current aggregated model until the opti mality is proved the computational experiments on two hard optimization problems a variant of the vehicle routing problem and the cutting stock problem show that a generic implementation of the proposed framework allows us to out perform previous known methods

extended formulations and branch and cut algorithms for the black and white traveling salesman problem in this paper we study integer linear programming models and develop branch and cut algorithms to solve the black and white traveling salesman problem bwtsp bourgeois laporte semet 2003 which is a variant of the well known traveling salesman problem tsp two strategies to model the bwtsp have been used in the literature the problem is either modeled on the original graph as tsp using a single set of binary edge variables and with additional non trivial hop and distance constraints between every pair of black nodes see ghiani laporte semat 2006 or as a sequence of constrained paths composed of white nodes connecting pairs of black nodes see muter 2015 in this paper we study and develop an intermediate approach based on the observation that it is sufficient to guarantee the required distance and hop limit of the path from a given black node to the next black node without explicitly stating which one it is thus instead of stating the two constraints after adding appropriately defined variables for each pair of black nodes they are stated for each black node only that represents the source of each path based on this idea we develop several variants of position and distance dependent reformulations together with corresponding layered graph representations branch and cut algorithms are developed for all proposed formulations and empirically compared by an extensive computational study the obtained results allow us to provide insights into individual advantages and disadvantages of the different models

algorithms for the vehicle routing and scheduling problems with time window constraints this paper considers the design and analysis of algorithms for vehicle routing and scheduling problems with time window constraints given the intrinsic difficulty of this problem class approximation methods seem to offer the most promise for practical size problems after describing a variety of heuristics we conduct an extensive computational study of their performance the problem set includes routing and scheduling environments that differ in terms of the type of data used to generate the problems the percentage of customers with time windows their tightness and positioning and the scheduling horizon we found that several heuristics performed well in different problem environments in particular an insertion type heuristic consistently gave very good results

stabilization of stochastic nonlinear systems driven by noise of unknown covariance this paper poses and solves a new problem of stochastic nonlinear disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise this is a natural stochastic counterpart of the problem of input to state stabilization in the sense of sontag 1989 our development starts with a set of new global stochastic lyapunov theorems for an exemplary class of stochastic strict feedback systems with vanishing nonlinearities where the equilibrium is preserved in the presence of noise we develop an adaptive stabilization scheme based on tuning functions that requires no a priori knowledge of a bound on the covariance next we introduce a control lyapunov function formula for stochastic disturbance attenuation finally we address optimality and solve a differential game problem with the control and the noise covariance as opposing players for strict feedback systems the resulting isaacs equation has a closed form solution

global stability and stabilization of more general stochastic nonlinear systems abstract this paper considers the global stability and stabilization of more general stochastic nonlinear systems due to the absence of the conventional assumptions e g lipschitz condition the stochastic nonlinear systems under investigation may have more than one weak solution however the most associated results are only applicable to the stochastic systems having a unique strong solution and therefore it is meaningful to refine and extend the relevant concepts and methods to the more general case in this paper the concepts of stochastic stability in the more general sense are first introduced to cover the stochastic nonlinear systems having more than one weak solution then the generalized stochastic barbashin krasovskii theorem and lasalle theorem are established which present the criterions of stochastic stability for more general stochastic nonlinear systems as one of the main contributions in this paper we rigorously prove the generalized stochastic barbashin krasovskii theorem moreover based on the generalized theorems the output feedback and state feedback stabilization are accomplished respectively for two classes of high order stochastic nonlinear systems under rather weaker assumptions comparing to the existing literature

an exact algorithm for a vehicle routing problem with time windows and multiple use of vehicles the vehicle routing problem with multiple use of vehicles is a variant of the classical vehicle routing problem it arises when each vehicle performs several routes during the workday due to strict time limits on route duration e g when perishable goods are transported the routes are defined over customers with a revenue a demand and a time window given a fixed size fleet of vehicles it might not be possible to serve all customers thus the customers must be chosen based on their associated revenue minus the traveling cost to reach them we introduce a branch and price approach to address this problem where lower bounds are computed by solving the linear programming relaxation of a set packing formulation using column generation the pricing subproblems are elementary shortest path problems with resource constraints computational results are reported on euclidean problems derived from well known benchmark instances for the vehicle routing problem with time windows

output feedback stabilization of stochastic high order nonlinear systems under weaker conditions under the weaker conditions on the power order and the nonlinear functions this paper investigates the output feedback stabilization problem for a class of stochastic high order nonlinear systems based on the backstepping design method and homogeneous domination technique the closed loop system can be proved to be globally asymptotically stable in probability

the time dependent traveling salesman problem abstract a problem often considered in operations research and computational physics is the traveling salesman problem in which a traveling salesperson has to find the shortest closed tour between a given set of cities touching each city exactly once the distances between the single nodes are known to the traveling salesperson an extension of this problem is the time dependent traveling salesman problem in which these distances vary in time i will show how this more complex problem is treated with physical optimization algorithms like simulated annealing i will present results for the problem of the 127 beergardens in the area of augsburg in which i define a traffic zone in which traffic jams occur in the afternoon

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

parameterizing inequality constraints on unique variances in linear structural models current computer programs for analyzing linear structural models will apparently handle only two types of constraints fixed parameters and equality of parameters an important constraint not handled is inequality this is particularly crucial for preventing negative variance estimates in this paper a method is described for imposing several kinds of inequality constraints in models without the necessity for having computer programs which explicitly allow such constraints the examples discussed include the prevention of heywood cases extension to inequalities of parameters to be greater than a specified value and imposing ordered inequalities

backstepping controller design for nonlinear stochastic systems under a risk sensitive cost criterion this paper develops a methodology for recursive construction of optimal and near optimal controllers for strict feedback stochastic nonlinear systems under a risk sensitive cost function criterion the design procedure follows the integrator backstepping methodology and the controllers obtained guarantee any desired achievable level of long term average cost for a given risk sensitivity parameter theta furthermore they lead to closed loop system trajectories that are bounded in probability and in some cases asymptotically stable in the large these results also generalize to nonlinear systems with strongly stabilizable zero dynamics a numerical example included in the paper illustrates the analytical results

practical asymptotic stability of stochastic systems driven by levy processes and its application to control of tora systems two lyapunov type theorems are developed to investigate global practical asymptotic stability in probability for sdes driven by non vanishing levy processes which can be either affine or non a

fuzzy adaptive decentralized output feedback control for large scale nonlinear systems with dynamical uncertainties in this paper an adaptive fuzzy decentralized robust output feedback control approach is proposed for a class of large scale strict feedback nonlinear systems with the unmeasured states the large scale nonlinear systems in this paper are assumed to possess the unstructured uncertainties unmodeled dynamics and unknown high frequency gain sign fuzzy logic systems are used to approximate the unstructured uncertainties k filters are designed to estimate the unmeasured states and a dynamical signal and a special nussbaum gain function are introduced into the control design to solve the problem of unknown high frequency gain sign and dominate unmodeled uncertainties respectively based on the backstepping design and adaptive fuzzy control methods an adaptive fuzzy decentralized robust output feedback control scheme is developed it is proved that the proposed adaptive fuzzy control approach can guarantee that all the signals in the closed loop system are uniformly and ultimately bounded and the tracking errors converge to a small neighborhood of the origin the effectiveness of the proposed approach is illustrated by using simulation results

quadratic assignment problems abstract this paper surveys quadratic assignment problems qap at first several applications of this problem class are described and mathematical formulations of qaps are given then some exact solution methods and good heuristics are outlined their computational behaviour is illustrated by numerical results further recent results on the asymptotic probabilistic behaviour of qaps are outlined

exact algorithms for the equitable traveling salesman problem abstract given a weighted graph g v e the equitable traveling salesman problem etsp asks for two perfect matchings in g such that 1 the two matchings together form a hamiltonian cycle in g and 2 the absolute difference in costs between the two matchings is minimized the problem is shown to be np hard even when the graph g is complete we present two integer programming models to solve the etsp problem and compare the strength of these formulations one model is solved through branch and cut whereas the other model is solved through a branch and price framework a simple local search heuristic is also implemented we conduct computational experiments on different types of instances often derived from the tsplib it turns out that the behavior of the different approaches varies with the type of instances for small and medium sized instances branch and bound and branch and price produce comparable results however for larger instances branch and bound outperforms branch and price