solving mixed integer nonlinear programs by outer approximation a wide range of optimization problems arising from engineering applications can be formulated as mixed integer nonlinear programming problems minlps duran and grossmann 1986 suggest an outer approximation scheme for solving a class of minlps that are linear in the integer variables by a finite sequence of relaxed milp master programs and nlp subproblems

exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

improvement and comparison of heuristics for solving the uncapacitated multisource weber problem the multisource weber problem is to locate simultaneouslym facilities in the euclidean plane to minimize the total transportation cost for satisfying the demand ofn fixed users each supplied from its closest facility many heuristics have been proposed for this problem as well as a few exact algorithms heuristics are needed to solve quickly large problems and to provide good initial solutions for exact algorithms we compare various heuristics i e alternative location allocation cooper 1964 projection bongartz et al 1994 tabu search brimberg and mladenovic 1996a p median plus weber hansen et al 1996 genetic search and several versions of variable neighbourhood search based on empirical tests that are reported it is found that most traditional and some recent heuristics give poor results when the number of facilities to locate is large and that variable neighbourhood search gives consistently best results on average in moderate computing time

benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

phase transitions in an exactly soluble one dimensional exclusion process we consider an exclusion process with particles injected with rate at the origin and removed with rate at the right boundary of a one dimensional chain of sites the particles are allowed to hop onto unoccupied sites to the right only for the special case of 1 the model was solved previously by derridaet al here we extend the solution to general the phase diagram obtained from our exact solution differs from the one predicted by the mean field approximation

mean field flow difference model with consideration of on ramp and off ramp abstract in this paper an extended lattice hydrodynamic model is proposed by incorporating the effects of mean field flow difference on ramp and off ramp the linear stability condition is obtained through linear stability theory and the mkdv equation is derived by using nonlinear analysis method therefore the propagation behavior of traffic jam can be described by the kink antikink soliton solution of the mkdv equation furthermore the theoretical findings are verified with the use of numerical simulation which confirms that the stability of traffic flow can be efficiently improved with the consideration of the effects of mean field flow difference on ramp and off ramp

exact solution of a cellular automaton for traffic we present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions e g cars can enter and leave a part of a highway with certain probabilities the model studied is the asymmetric exclusion process asep with simultaneous updating of all sites it is equivalent to a special case vmax 1 of the nagel schreckenberg model for highway traffic which has found many applications in real time traffic simulations the simultaneous updating induces additional strong short range correlations compared to other updating schemes the stationary state is written in terms of a matrix product solution the corresponding algebra which expresses a system size recursion relation for the weights of the configurations is quartic in contrast to previous cases in which the algebra is quadratic we derive the phase diagram and compute various properties such as density profiles two point functions and the fluctuations in the number of particles cars in the system the current and the density profiles can be mapped onto the asep with other time discrete updating procedures through use of this mapping our results also give new results for these models

exact stationary state for an asymmetric exclusion process with fully parallel dynamics the exact stationary state of an asymmetric exclusion process with fully parallel dynamics is obtained using the matrix product ansatz we give a simple derivation for the deterministic case by a physical interpretation of the dimension of the matrices we prove the stationarity via a cancellation mechanism and by making use of an explicit representation of the matrix algebra we easily find closed expressions for the correlation functions in the general probabilistic case asymptotic expressions obtained by making use of earlier results allow us to derive the exact phase diagram

extremal principle for the steady state selection in driven lattice gases with open boundaries this paper investigates the steady states of one dimensional driven lattice gases with open boundary conditions it shows how the extremal principle proposed recently by popkov and schutz can be modified to apply to more general cases monte carlo simulations are presented for a one dimensional totally asymmetric simple exclusion process with nearest neighbor repulsion under parallel update as an example the simulations enable one to guess the exact phase diagram for this particular lattice gas with deterministic bulk dynamics by fitting the data to analytic formulas which appear to be exact in the thermodynamic limit

microscopic position and structure of a shock in ca 184 we consider the time evolution of the cellular automaton ca 184 with random initial conditions we derive a partial differential equation that describes the macroscopic time evolution of the coarse grained local density and we study some solutions of this equation in particular shock solutions and rarefaction type solutions for initial step profiles in order to elucidate the emergence of the large scale hydrodynamic behaviour we define a microscopic position of a shock and find its mean velocity its diffusion coefficient and the microscopic structure of the shock as seen from this position

an outer approximation algorithm for a class of mixed integer nonlinear programs an outer approximation algorithm is presented for solving mixed integer nonlinear programming problems of a particular class linearity of the integer or discrete variables and convexity of the nonlinear functions involving continuous variables are the main features in the underlying mathematical structure based on principles of decomposition outer approximation and relaxation the proposed algorithm effectively exploits the structure of the problems and consists of solving an alternating finite sequence of nonlinear programming subproblems and relaxed versions of a mixed integer linear master program convergence and optimality properties of the algorithm are presented as well as a general discussion on its implementation numerical results are reported for several example problems to illustrate the potential of the proposed algorithm for programs in the class addressed in this paper finally a theoretical comparison with generalized benders decomposition is presented on the lower bounds predicted by the relaxed master programs

alternative formulations of a combined trip generation trip distribution modal split and trip assignment model abstract the traditional four step model has been widely used in travel demand forecasting by considering trip generation trip distribution modal split and traffic assignment sequentially in a fixed order however this sequential approach suffers from the inconsistency among the level of service and flow values in each step of the procedure in the last two decades this problem has been addressed by many researchers who have sought to develop combined or integrated models that can consider travelers choice on different stages simultaneously and give consistent results in this paper alternative formulations including mathematical programming mp formulation and variational inequality vi formulations are provided for a combined travel demand model that integrates trip generation trip distribution modal split and traffic assignment using the random utility theory framework thus the proposed alternative formulations not only allow a systematic and consistent treatment of travel choice over different dimensions but also have behavioral richness qualitative properties of the formulations are also given to ensure the existence and uniqueness of the solution particularly the model is analyzed for a special but useful case where the probabilistic travel choices are assumed to be a hierarchical logit model furthermore a self adaptive goldstein levitin polyak glp projection algorithm is adopted for solving this special case

a branch and cut algorithm for the undirected traveling purchaser problem the purpose of this paper is to present a branch and cut algorithm for the undirectedtraveling purchaser problem which consists of determining a minimum cost route through a subset of markets where the cost is the sum of travel and purchase costs the problem is formulated as an integer linear program and several families of valid inequalities are derived to strengthen the linear relaxation the polyhedral structure of the formulation is analyzed and several classes of valid inequalities are proved to be facet defining a branch and cut procedure is developed and tested over four classes of randomly generated instances results show that the proposed algorithm outperforms all previous approaches and can optimally solve instances containing up to 200 markets

bifurcations for quasilinear schrodinger equations i abstract this paper is concerned with bifurcation problems for quasilinear schrodinger type equations such as the modified nonlinear schrodinger equations which have appeared as several models from mathematical physics we give a new approach for dealing with bifurcation problems of nonlinear potential operators the novelty of our approach lies in establishing multiple bifurcations without making a reduction to finite dimensional problems the finite dimensional reduction procedures that have been used in the past work for semilinear problems but are not suitable for quasilinear problems we give a unified approach requiring much less regularity of the problems as applications we provide multiple bifurcation results for the modified nonlinear schrodinger equations

solving the combined modal split and traffic assignment problem with two types of transit impedance function abstract the gradient projection gp algorithm has been shown as a successful path based algorithm for solving various traffic assignment problems in this paper the gp algorithm is adapted for solving the combined modal split and traffic assignment cmsta problem which can be viewed as an elastic demand traffic equilibrium problem edtep with two modes using the excess demand formulation of edtep the cmsta problem is reformulated and solved by a modified gp algorithm numerical results based on a real bi modal network in the city of winnipeg canada are provided to demonstrate the efficiency and robustness of the modified path based gp algorithm for solving the cmsta problem in addition the cmsta problem is investigated with two types of impedance function for the transit mode and with different degrees of dispersion for the modal split function the computational results show the modified gp algorithm outperforms the classical evan s algorithm for both types of transit impedance function and it can be as efficient as the original gp algorithm for solving the traffic assignment problem with fixed demand

competitive facility location model with concave demand abstract we consider a spatial interaction model for locating a set of new facilities that compete for customer demand with each other as well as with some pre existing facilities to capture the market expansion and the market cannibalization effects customer demand is assumed to be a concave non decreasing function of the total utility derived by each customer from the service offered by the facilities the problem is formulated as a non linear knapsack problem for which we develop a novel solution approach based on constructing an efficient piecewise linear approximation scheme for the objective function this allows us to develop exact and optimal solution approaches capable of dealing with relatively large scale instances of the model we also develop a fast heuristic algorithm for which a tight worst case error bound is established

the asymmetric exclusion process comparison of update procedures the asymmetric exclusion process asep has attracted a lot of interest not only because of its many applications e g in the context of the kinetics of biopolymerization and traffic flow theory but also because it is a paradigmatic model for nonequilibrium systems here we study the asep for different types of updates namely random sequential sequential sublattice parallel and parallel in order to compare the effects of the different update procedures on the properties of the stationary state we use large scale monte carlo simulations and analytical methods especially the so called matrix product ansatz mpa we present in detail the exact solution for the model with sublattice parallel and sequential updates using the mpa for the case of parallel update which is important for applications like traffic flow theory we determine the phase diagram the current and density profiles based on monte carlo simulations we furthermore suggest an mpa for that case and derive the corresponding matrix algebra

a cellular automaton model for two lane traffic we present some long time limit properties of a cellular automaton that models traffic of cars on a infinite two lane road this model called tl184 is a natural generalization of the cellular automaton classified as 184 by wolfram to be abbreviated by ca184 and studied before as a model for one lane traffic tl184 models cars motions on each lane by particles that interact via the ca184 rules and cars lane changes by a possibility for particles to flip from one ca184 to another we calculate the infinite time limit of the particle current in tl184 starting from a translation invariant measure and use this result to show how the possibility of lane changes may enhance the current of cars in tl184 compared to that in a corresponding model of two non interacting one lane roads we provide examples which demonstrate that even though the rules that regulate lane changes are completely symmetric the system does not evolve to an equipartition of cars among both lanes from a given initially asymmetric distribution moreover the asymptotic car velocities and currents may be different on different lanes we also show that for a particular class of initial distributions the asymptotic car density on a lane may be a non monotonic function of the initial car density on this lane finally we derive the current density relation for an extended continuous time version of tl184 with asymmetric lane changing rules

invariant measures and convergence properties for cellular automaton 184 and related processes our results concern long time limit properties of a deterministic dynamics that is common for a wide class of processes that have been studied so far during at least last two decades the most widely known process from this class is a cellular automaton that acquired number 184 in the classification of s wolfram this ca 184 is being intensively used to model vehicular traffic however our results are mainly derived with help of another process that offers a helpful insight into the studied dynamics it is a so called ballistic annihilation model abbreviated by ba ba is a model for chemical reaction a b inert in ba a and b type particles move in opposite directions with velocities 1 and 1 respectively and annihilate upon collisions certain results concerning ba and ca 184 are also formulated in terms of another process known as a model of surface growth sg for short the surface shape in this process behaves as the integrated profile of particle distribution in ca 184

simultaneous estimation of the origin destination matrices and the parameters of a nested logit model in a combined network equilibrium model abstract this paper deals with the inverse problem of a type of traffic equilibrium models with combined modes this problem consists of obtaining a parametrization of the equilibrium model from a set of observations of the outputs for the model the inputs for the model are an origin destination o d trip matrix for the various alternatives that have been considered and a set of parameters for a nested logit model used as a demand model this model has been formulated by using a new approach called the calibration and demand adjustment model cdam based on bilevel programming which simultaneously estimates an o d matrix and the parameters for the nested logit model in this paper the cdam properties are studied and it is proved the cdam solution exists this paper develops a heuristic column paths hyperpaths generation algorithm for the cdam this algorithm iterates between the network equilibrium problem and that which is used to obtain a set of paths when equilibrium is attained and the cdam is restricted to the set of previously generated columns the so called restricted cdam the restricted cdam is formulated as a single level model under certain hypotheses and it furnishes a solution upon which to base a new estimation of the o d matrix and the vector of parameters the computational tests on the algorithm have been carried out using data from a multi modal network in madrid

the computation of the worst conditional expectation abstract recent advances in risk theory identify risk as a measure related to the tail of a probability distribution function since it represents the worst outcomes of the random variable measures like value at risk var conditional var expected shortfall and so on have become familiar operational tools for many financial applications in this paper one of these measures the worst conditional expectation with threshold of a discrete random variable z shortly wce z is considered it has been found that its computation can be formulated as a fractional integer programming problem with a single linear constraint but its complexity is np hard therefore it must be solved by implicit enumeration due to its similarity with the knapsack problem it has been found that a good upper bound and a sharp data structure allow the implementation of a branch bound that is able to solve realistic size problems in less than one hundredth of a second

a class of globally convergent optimization methods based on conservative convex separable approximations this paper deals with a certain class of optimization methods based on conservative convex separable approximations ccsa for solving inequality constrained nonlinear programming problems each generated iteration point is a feasible solution with lower objective value than the previous one and it is proved that the sequence of iteration points converges toward the set of karush kuhn tucker points a major advantage of ccsa methods is that they can be applied to problems with a very large number of variables say 104 105 even if the hessian matrices of the objective and constraint functions are dense

logit choice models for interactive attributes abstract in multi attribute decision making madm the choice of a decision maker dm is often the result of an interplay between the dm s unique attitude the utilities specific to the dm for the attributes and the degree of positive or negative interaction among the attributes based on this conglomeration of information we introduce a few choice models to give the probabilities for different possible choices of a dm more specifically the conventional multinomial logit mnl model is extended to consider the interaction among the attributes and also the dm s unique attitudinal character the usefulness of the proposed models is illustrated in a real world application

phase transitions in a cellular automaton model of a highway on ramp we introduce a lattice gas model for the merging of two single lane automobile highways the merging rules for traffic on the two lanes are deterministic but the inflow on both lanes is stochastic analysing the stationary distribution of this stochastic cellular automaton we find a discontinuous phase transition from a free flow phase which depends on the initial state of the road to a jammed phase where all memory of the initial state is lost inside the jammed phase we identify dynamical phase transitions in the approach to stationarity each dynamical phase is characterized by a fixed number of relaxation cycles which is decreasing as one moves deeper into the jammed phase in each cycle step the number of desperate drivers who force their way onto the main road when they reach the end of the on ramp increases until stationarity

time dependent correlation functions in a one dimensional asymmetric exclusion process we study a one dimensional anisotropic exclusion process describing particles injected at the origin moving to the right on a chain of l sites and being removed at the right boundary we construct the steady state and compute the density profile exact expressions for all equal time n point density correlation functions and the time dependent two point function in the steady state as functions of the injection and absorption rates we determine the phase diagram of the model and compare our results with predictions from dynamical scaling and discuss some conjectures for other exclusion models

the maximum capture problem with random utilities problem formulation and algorithms abstract a model for the optimal location of new facilities in a competitive market is introduced under the hypothesis that customers behavior can be modeled by random utility functions it means that the company that wished to locate uses a random utility model to forecast the market share of a location therefore the company cannot forecast the behavior of every customer in a deterministic fashion but is able to embed him by a probability distribution three formulations are proposed to compute upper bounds of the objective function and compared in a numerical simulation a branch and bound method is developed and tested on examples with up to 50 potential locations and a variable neighborhood search heuristic is proposed to solve larger instances

outer approximation and submodular cuts for maximum capture facility location problems with random utilities abstract we consider a family of competitive facility location problems in which a newcomer company enters the market and has to decide where to locate a set of new facilities so as to maximize its market share the multinomial logit model is used to estimate the captured customer demand we propose a first branch and cut approach for this family of difficult mixed integer non linear problems our approach combines two types of cutting planes that exploit particular properties of the objective function the first one are the outer approximation cuts and the second one are the submodular cuts the approach is computationally evaluated on three datasets from the recent literature the obtained results show that our new branch and cut drastically outperforms state of the art exact approaches both in terms of the computing times and in terms of the number of instances solved to optimality

ramp induced transitions in traffic dynamics we present the analytical results of ramp effects in asymmetric simple exclusion processes both on ramp and off ramp are included in between the two open boundaries the ramps can be taken as the nontrivial boundaries to trigger the phase transitions exact phase diagrams are obtained analytically in the full parameter space we find that the order of the two ramps is crucial when the on ramp is placed after the off ramp along the traffic direction there are only four distinct phases free free free free free jam free jam jam and jam jam jam the other four phases from naive expectation cannot be realized i e jam free free jam jam free jam free jam and free jam free are all absent the free flow will not follow the congestion when the on ramp is placed before the off ramp we observe an interesting phase jam max free the bottleneck emerges as the flow in between the two ramps saturates to its maximum we further show that the roadway configuration is equivalent to a nonstandard intersection applications to a traffic rotary are discussed

exploring trust region method for the solution of logit based stochastic user equilibrium problem abstract in this research paper we explored using the trust region method to solve the logit based sue problem we proposed a modified trust region newton mtrn algorithm for this problem when solving the trust region sue subproblem we showed that applying the well known steihaug toint method is inappropriate since it may make the convergence rate of the major iteration very slow in the early stage of the computation to overcome this drawback a modified steihaug toint method was proposed we proved the convergence of our mtrn algorithm and showed its convergence rate is superlinear for the implication of our algorithm we proposed an important principle on how to select the basic route for each od pair we indicated that it is a crucial principle to accelerate the convergence rate of the minor iteration i e trust region subproblem solving iteration in this study other implication issues for the sue problem are also considered including the computation of the trial step and the strategy to ensure strict feasibility iteration point we compared the mtrn algorithm with the gradient projection gp algorithm on the sioux falls network some results of numerical analysis are also reported

understanding totally asymmetric simple exclusion process transport on networks generic analysis via effective rates and explicit vertices in this paper we rationalize relevant features of totally asymmetric simple exclusion processes on topologies more complex than a single segment we present a mean field framework exploiting the previously introduced notion of effective rates which we express in terms of the average particle density on explicitly introduced junction sites it allows us to construct the phase behavior as well as the current density characteristic from well known results for a linear totally asymmetric simple exclusion process segment in a very systematic and generic way we validate the approach by studying a fourfold vertex in all variations in the number of entering exiting segments and compare our predictions to simulation data generalizing the notion of particle hole symmetry to take into account the topology at a junction shows that the average particle density at the junction constitutes a relevant directly observable parameter which gives detailed insight into the transport process this is illustrated by a complete study of a simple network with figure of eight topology finally we generalize the approach to handle rate bias at a junction and discuss the surprisingly rich phenomenology of a biased figure of eight structure this example highlights that the proposed framework is generic and readily extends to other topologies

classification methods for random utility models with i i d disturbances under the most probable alternative rule in this paper random utility maximization based on maximization of correct classification of the choice decisions over a given data set is considered it is shown that if the disturbance vector in the random utility model is independent and identically distributed then preference determination based on the most probable alternative reduces to deterministic utility maximization as a consequence of the above equivalence the form of the error distribution normal weibull uniform etc plays no role in the determination of the preferred alternative parameter estimation under the most probable alternative rule is carried out using two methods the first is based on the solution of an appropriately defined system of linear inequalities and the second one is based on the function optimization of a newly proposed function whose optimum is achieved when the number of correctly classified individuals is maximized the ability to use these algorithms in the framework of pattern recognition and machine learning is pointed out simulations and a real case study involving intercity travel behavior are employed to assess the proposed methods

a comparison of linear reformulations for multinomial logit choice probabilities in facility location models abstract in the last decade several papers appeared on facility location problems that incorporate customer demand by the multinomial logit model three linear reformulations of the original non linear model have been proposed so far in this paper we discuss these models in terms of solvability we present empirical findings based on synthetic data

ballistic annihilation and deterministic surface growth a model of deterministic surface growth studied by krug and spohn a model of the annihilating reactiona b inert studied by elskens and frisch a one dimensional three color cyclic cellular automaton studied by fisch and a particular automaton that has the number 184 in the classification of wolfram can be studied via a cellular automaton with stochastic initial data called ballistic annihilation this automaton is defined by the following rules at timet 0 one particle is put at each integer point of to each particle a velocity is assigned in such a way that it may be either 1 or 1 with probabilities 1 2 independent of the velocities of the other particles as time goes on each particle moves along at the velocity assigned to it and annihilates when it collides with another particle in the present paper we compute the distribution of this automaton for each timet we then use this result to obtain the hydrodynamic limit for the surface profile from the model of deterministic surface growth mentioned above we also show the relation of this limit process to the process which we call moving local minimum of brownian motion the latter is the processb min x defined byb min min b y x 1 y x 1 for everyx whereb x x is the standard brownian motion withb 0 0

a bifurcation theorem for potential operators abstract a sufficient condition for bifurcation of real solutions of g u 0 where g r d e d e is given in terms of the crossing number of the eigenvalue perturbation of the linearization along the trivial solutions 0 this number describes how many eigenvalues leave the negative real axis wen the parameter varies from negative to positive values whereas in general only an odd crossing number entails bifurcation for potential operators in a hilbert space e a nonzero crossing number is sufficient for bifurcation the proof uses a lyapunov schmidt reduction and conley s index theory

a branch and bound algorithm for the maximum capture problem with random utilities abstract the maximum capture problem with random utilities seeks to locate new facilities in a competitive market such that the captured demand of users is maximized assuming that each individual chooses among all available facilities according to the well know a random utility model namely the multinomial logit the problem is complex mostly due to its integer nonlinear objective function currently the most efficient approaches deal with this complexity by either using a nonlinear programing solver or reformulating the problem into a mixed integer linear programing milp model in this paper we show how the best milp reformulation available in the literature can be strengthened by using tighter coefficients in some inequalities we also introduce a new branch and bound algorithm based on a greedy approach for solving a relaxation of the original problem extensive computational experiments are presented benchmarking the proposed approach with other linear and non linear relaxations of the problem the computational experiments show that our proposed algorithm is competitive with all other methods as there is no method which outperforms the others in all instances we also show a large scale real instance of the problem which comes from an application in park and ride facility location where our proposed branch and bound algorithm was the most effective method for solving this type of problem

stable patterns for fourth order parabolic equations we consider fourth order parabolic equations of gradient type for the sake of simplicity the analysis is carried out for the specific equation u

maximizing a submodular function by integer programming polyhedral results for the quadratic case abstract we give a new mixed integer programming mip formulation for the quadratic cost partition problem that is derived from a mip formulation for maximizing a submodular function several classes of valid inequalities for the convex hull of the feasible solutions are derived using the valid inequalities for the node packing polyhedron facet defining conditions and separation algorithms are discussed and computational results are reported

an algorithm for the ranking of shortest paths an efficient computational implementation of a path deletion k shortest paths algorithm and a new algorithm for the same problem are presented in a path deletion k shortest paths algorithm a sequence g1 g2 gk of networks is is defined such that g1 is given network and its k th shortes path is trivially determined from the shortest path in gk in essence as soon as the shortest path in gk is determined it is excluded from gk in such a way that no new paths are formed and no more paths are deleted so far each gk two procedures are executed a shortest path algorithm and a path deletion algorithm in the presented computational implementation all the information resulting from the determination of the k th shortest path is carried throughout gk 1 gk 2 gk the new algorithm not only keeps this characteristics but also avoids the last k 1 executions of a shortest path algorithm which results in a suprising and very substantial reduction in the execution time in fact for randomly generated networks with 104 nodes and 105 arcs once the shortest the new algorithm computes the next 100 shortest paths in times of the order of 10 1 seconds to illustrate the efficiency of this algorithm comparative computational experiments are reported

traffic assignment model with fuzzy level of travel demand an efficient algorithm based on quasi logit formulas abstract the place of fuzzy concepts in traffic assignment ta models has been studied in recent literature keeping fuzzy level of travel demand in mind we propose a new ta model in which the travel costs of links are depended on their congestion from the results of such fuzzy ta model network planners are able to estimate the number of travelers on network links by using zero one variables the proposed model is transformed into a crisp mixed integer problem with respect to path flow variables in order to produce the logit flows from this problem damberg et al algorithm is modified then the level of certainty is maximized and perceived travel delays are minimized for a fixed certainty degree the obtained solution which is named the fuzzy equilibrium flow satisfies a quasi logit formula similar to ordinary expression of the logit route choice model eventually we examine the quality of different path enumeration techniques in the proposed model

a stochastic cellular automaton model for traffic flow with multiple metastable states a new stochastic cellular automaton ca model of traffic flow which includes slow to start effects and a driver s perspective is proposed by extending the burgers ca and the nagel schreckenberg ca model the flow density relation of this model shows multiple metastable branches near the transition density from free to congested traffic which form a wide scattering area in the fundamental diagram the stability of these branches and their velocity distributions are explicitly studied by numerical simulations

maximizing a class of submodular utility functions given a finite ground set n and a value vector a in mathbb r n we consider optimization problems involving maximization of a submodular set utility function of the form h s f left sum i in s a i right s subseteq n where f is a strictly concave increasing differentiable function this utility function appears frequently in combinatorial optimization problems when modeling risk aversion and decreasing marginal preferences for instance in risk averse capital budgeting under uncertainty competitive facility location and combinatorial auctions these problems can be formulated as linear mixed 0 1 programs however the standard formulation of these problems using submodular inequalities is ineffective for their solution except for very small instances in this paper we perform a polyhedral analysis of a relevant mixed integer set and by exploiting the structure of the utility function h strengthen the standard submodular formulation significantly we show the lifting problem of the submodular inequalities to be a submodular maximization problem with a special structure solvable by a greedy algorithm which leads to an easily computable strengthening by subadditive lifting of the inequalities computational experiments on expected utility maximization in capital budgeting show the effectiveness of the new formulation

a bifurcation theorem for critical points of variational problems on considere le probleme min x e f x ou e est un espace de hilbert reel r et f e r r est une fonctionnelle c 2