a note on the selection of benders cuts a new cut selection criterion for benders cuts is proposed and computationally analyzed the results show that the new criterion is more robust and often considerably faster than the standard ones

the traveling salesman problem an overview of exact and approximate algorithms in this paper some of the main known algorithms for the traveling salesman problem are surveyed the paper is organized as follows 1 definition 2 applications 3 complexity analysis 4 exact algorithms 5 heuristic algorithms 6 conclusion

entropy formula for random transformations we exhibit random strange attractors with random sinai bowen ruelle measures for the composition of independent random diffeomorphisms

formulations and benders decomposition algorithms for multidepot salesmen problems with load balancing this paper describes new models and exact solution algorithms for the fixed destination multidepot salesmen problem defined on a graph with n nodes where the number of nodes each salesman is to visit is restricted to be in a predefined range such problems arise when the time to visit a node takes considerably longer as compared to the time of travel between nodes in which case the number of nodes visited in a salesman s tour is the determinant of their load the new models are novel multicommodity flow formulations with o n 2 binary variables which is contrary to the existing formulations for the same and similar problems that typically include o n 3 binary variables the paper also describes benders decomposition algorithms based on the new formulations for solving the problem exactly results of the computational experiments on instances derived from tsplib show that some of the proposed algorithms perform remarkably well in cases where formulations solved by a state of the art optimization code fail to yield optimal solutions within reasonable computation time

a nonlinear programming algorithm based on non coercive penalty functions we consider first the differentiable nonlinear programming problem and study the asymptotic behavior of methods based on a family of penalty functions that approximate asymptotically the usual exact penalty function we associate two parameters to these functions one is used to control the slope and the other controls the deviation from the exact penalty we propose a method that does not change the slope for feasible iterates and show that for problems satisfying the mangasarian fromovitz constraint qualification all iterates will remain feasible after a finite number of iterations the same results are obtained for non smooth convex problems under a slater qualification condition

mahler measure and entropy for commuting automorphisms of compact groups we compute the joint entropy ofd commuting automorphisms of a compact metrizable group letr d u 1 1 d 1 1 be the ring of laurent polynomials ind commuting variables andm be anr d module then the dual groupx m ofm is compact and multiplication onm by each of thed variables corresponds to an action m of d by automorphisms ofx m every action of d by automorphisms of a compact abelian group arises this way iff r d our main formula shows that the topological entropy of alpha r d left langle f right rangle is given by h left alpha r d left langle f right rangle right log m left f right int limits 0 1 ldots int limits 0 1 log left f left e 2 pi it 1 ldots e 2 pi it d right right dt 1 ldots dt d where m f is the mahler measure off this reduces to the classical result for toral automorphisms via jensen s formula while the entropy of a single automorphism of a compact group is always the logarithm of an algebraic integer this no longer seems to hold for joint entropy of commuting automorphisms since values such as 7 3 4 2 occur if p is a non principal prime ideal we show h left alpha r d p right 0 using an analogue of the yuzvinskii thomas addition formula we computeh m for arbitraryr d modulesm and then the joint entropy for an action of d on a not necessarily abelian compact group using a result of boyd we characterize those m which have completely positive entropy in terms of the prime ideals associated tom and show this condition implies that m is mixing of all orders we also establish an analogue of berg s theorem proving that if m has finite entropy then haar measure is the unique measure of maximal entropy if and only if m has completely positive entropy finally we show that for expansive actions the growth rate of the number of periodic points equals the topological entropy

nonlinear augmented lagrangian and duality theory in this paper a unified framework of a nonlinear augmented lagrangian dual problem is investigated for the primal problem of minimizing an extended real valued function by virtue of a nonlinear augmenting penalty function our framework is more general than the ones in the literature in the sense that our nonlinear augmenting penalty function is defined on an open set and that our assumptions are presented in terms of a substitution of the dual variable so our scheme includes barrier penalty functions and the weak peak at zero property as special cases by assuming that the increment of the nonlinear augmenting penalty function with respect to the penalty parameter satisfies a generalized peak at zero property necessary and sufficient conditions for the zero duality gap property are established and the existence of an exact penalty representation is obtained

a node current based 2 index formulation for the fixed destination multi depot travelling salesman problem abstract the travelling salesman problem forms a basis for many optimisation problems in logistics finance and engineering several variants exist to accommodate for different problem types in this paper we discuss the fixed destination multi depot travelling salesman problem where several salesmen will start from different depots and they are required to return to the depot they originated from we propose a novel formulation for this problem using 2 index binary variables and node currents and compare it to other 2 index formulations from the literature this novel formulation requires less binary variables and continuous variables to formulate a problem resulting in lower computation times using a large benchmark the effectiveness of the new formulation is demonstrated

a variational principle for free semigroup actions abstract in this paper we introduce a notion of measure theoretical entropy for a finitely generated free semigroup action and establish a variational principle when the semigroup is generated by continuous self maps on a compact metric space and has finite topological entropy in the case of semigroups generated by ruelle expanding maps we prove the existence of equilibrium states and describe some of their properties of independent interest are the different ways we will present to compute the metric entropy and a characterization of the stationary measures

entropy and the variational principle for actions of sofic groups recently lewis bowen introduced a notion of entropy for measure preserving actions of a countable sofic group on a standard probability space admitting a generating partition with finite entropy by applying an operator algebra perspective we develop a more general approach to sofic entropy which produces both measure and topological dynamical invariants and we establish the variational principle in this context in the case of residually finite groups we use the variational principle to compute the topological entropy of principal algebraic actions whose defining group ring element is invertible in the full group c algebra

integer linear programming formulations of multiple salesman problems and its variations in this paper we extend the classical multiple traveling salesman problem mtsp by imposing a minimal number of nodes that a traveler must visit as a side condition we consider single and multidepot cases and propose integer linear programming formulations for both with new bounding and subtour elimination constraints we show that several variations of the multiple salesman problem can be modeled in a similar manner computational analysis shows that the solution of the multidepot mtsp with the proposed formulation is significantly superior to previous approaches

fuglede kadison determinants and entropy for actions of discrete amenable groups consider a discrete group t and an element in the integral group ring zt then t acts from the left on the discrete additive group zt ztf by automorphisms of groups dualizing we obtain a left t action on the compact pontrjagin dual group xf zt ztf by continuous automorphisms of groups by definition xf is a closed subshift of s1 1 for measurable or topological actions of amenable groups a good entropy theory is available ow m thus from now on let t be a finitely generated discrete amenable group we are interested in determining the topological entropy hf of the t action on xf it agrees with the measure theoretic entropy of the t action on xf equipped with its haar probability measure in their paper fk from 1952 fuglede and kadison introduced a determinant for units in finite factor von neumann algebras more recently l ck has general ized their theory to nonunits and to group von neumann algebras which are not necessarily factors l2 he needed this to define l2 torsion for general covering spaces the von neumann algebra a t of the amenable group t is a certain completion of cr and hence we may consider the fuglede kadison l ck determinant detjvr of we refer to section 6 for the definition of a log strong f0lner sequence it is known that finitely generated virtually nilpotent groups have log strong f0lner sequences our main result is

gibbs measures for fibred systems abstract we consider a topological dynamical system t y y on a metric space y which forms a fibre bundle over another dynamical system if t is fibrewise expanding and exact along fibres and if is a holder continuous function we prove the existence of a system of conditional measures called a family of gibbs measures where the jacobian is determined by this theorem reduces to ruelle s perron frobenius theorem when the base of the fibred system consists of a single point the method of proof does not use any form of symbolic representation we also study continuity properties of a family of gibbs measures over the base and give applications to the equilibrium theory of higher dimensional complex dynamics

smoothing approximation to l1 exact penalty function for inequality constrained optimization abstract in this paper we propose a method to smooth l 1 exact penalty function for inequality constrained optimization it is shown that an approximate global solution of the original problem can be obtained by searching a global solution of the smoothed penalty problem under some mild conditions the method based on our smoothing function is shown to be globally convergent some numerical examples are given to illustrate the applicability of the present smoothing method

mathematical formulations for a 1 full truckload pickup and delivery problem abstract we address a generalization of the asymmetric traveling salesman problem where routes have to be constructed to satisfy customer requests which either involve the pickup or delivery of a single commodity a vehicle is to be routed such that the demand and the supply of the customers is satisfied under the objective to minimize the total distance traveled the commodities which are collected from the pickup customers can be used to accommodate the demand of the delivery customers in this paper we present three mathematical formulations for this problem class and apply branch and cut algorithms to optimally solve the model formulations for two of the models we derive benders cuts based on the classical and the generalized benders decomposition finally we analyze the different mathematical formulations and associated solution approaches on well known data sets from the literature

correlation spectrum of quenched and annealed equilibrium states for random expanding maps we show that the integrated transfer operators for positively weighted independent identically distributed smooth expanding systems give rise to annealed equilibrium states for a new variational principle the unique annealed equilibrium state coincides with the unique annealed gibbs state using work of ruelle 1990 and fried 1995 on generalised fredholm determinants for transfer operators we prove that the discrete spectrum of the transfer operators coincides with the correlation spectrum of these invariant measures yielding exponential decay of correlations and with the poles of an annealed zeta function defined also for complex weights a modified integrated transfer operator is introduced which describes the relativised quenched states studied e g by kifer 1992 and conditions including srb ensuring coincidence of quenched and annealed states are given for small random perturbations we obtain stability results on the quenched and annealed measures and spectra by applying perturbative results of young and the author 1993

specification and thermodynamical properties of semigroup actions in the present paper we study the thermodynamical properties of finitely generated continuous subgroup actions we propose a notion of topological entropy and pressure functions that do not depend on the growth rate of the semigroup and introduce strong and orbital specification properties under which the semigroup actions have positive topological entropy and all points are entropy points moreover we study the convergence and lipschitz regularity of the pressure function and obtain relations between topological entropy and exponential growth rate of periodic points in the context of semigroups of expanding maps obtaining a partial extension of the results obtained by ruelle for d actions d ruelle trans am math soc 187 237 251 1973 the specification properties for semigroup actions and the corresponding one for its generators and the action of push forward maps are also discussed

entropie geometrique des feuilletages on definit et on etudie l entropie geometrique d un feuilletage generalisant directement l entropie topologique d un flot

on smoothing exact penalty functions for convex constrained optimization a quadratic smoothing approximation to nondifferentiable exact penalty functions for convex constrained optimization is proposed and its properties are established the smoothing approximation is used as the basis of an algorithm for solving problems with i embedded network structures and ii nonlinear minimax problems extensive numerical results with large scale problems illustrate the efficiency of this approach

tubularity and asymptotic convergence of penalty trajectories in convex programming in this paper we give a sufficient condition for the asymptotic convergence of penalty trajectories in convex programming with multiple solutions we show that for a wide class of penalty methods the associated optimal trajectory converges to a particular solution of the original problem characterized through a minimization selection principle our main assumption for this convergence result is that all the functions involved in the convex program are tubular this new notion of regularity weaker than that of quasianalyticity is defined and studied in detail

asymptotic analysis for penalty and barrier methods in convex and linear programming we consider a wide class of penalty and barrier methods for convex programming which includes a number of specific functions proposed in the literature we provide a systematic way to generate penalty and barrier functions in this class and we analyze the existence of primal and dual optimal paths generated by these penalty methods as well as their convergence to the primal and dual optimal sets for linear programming we prove that these optimal paths converge to single points

integer programming formulations of vehicle routing problems abstract various mathematical formulations are available for situations represented by vehicle routing problems the assignment based integer programming formulations of these problems are more common and easy to understand such formulations are discussed in this paper and a much simpler formulation for the vechicle routing problem is presented for the case when all the vehicles have the same load capacity and maximum allowable cost per route

accelerating benders decomposition algorithmic enhancement and model selection criteria this paper proposes methodology for improving the performance of benders decomposition when applied to mixed integer programs it introduces a new technique for accelerating the convergence of the algorithm and theory for distinguishing good model formulations of a problem that has distinct but equivalent mixed integer programming representations the acceleration technique is based upon selecting judiciously from the alternate optima of the benders subproblem to generate strong or pareto optimal cuts this methodology also applies to a much broader class of optimization algorithms that includes dantzig wolfe decomposition for linear and nonlinear programs and related cutting plane type algorithms that arise in resource directive and price decomposition when specialized to network location problems this cut generation technique leads to very efficient algorithms that exploit the underlying structure of these models in discussing the proper formulation of mixed integer programs we suggest criteri

an artificial fish swarm algorithm based hyperbolic augmented lagrangian method this paper aims to present a hyperbolic augmented lagrangian hal framework with guaranteed convergence to an e global minimizer of a constrained nonlinear optimization problem the bound constrained subproblems that emerge at each iteration k of the framework are solved by an improved artificial fish swarm algorithm convergence to an e k global minimizer of the hal function is guaranteed with probability one where e k e as k preliminary numerical experiments show that the proposed paradigm compares favorably with other penalty type methods

combinatorial benders cuts for assembly line balancing problems with setups abstract the classical assembly line balancing problem consists of assigning assembly work to workstations in the presence of setup times that depend on the sequence of tasks assigned to each workstation the problem becomes more complicated given that two interdependent problems namely assignment and sequencing must be solved simultaneously the hierarchical nature of these two problems also suggest a natural decomposition of the problem this paper adopts such an approach and describes an exact algorithm based on benders decomposition to solve both simple and mixed model assembly line balancing problems with setups the algorithm is tested on a set of benchmark instances and numerically compared against a mixed integer linear programming formulation of the problem solved using a commercial optimizer

multi objective vehicle routing problems routing problems such as the traveling salesman problem and the vehicle routing problem are widely studied both because of their classic academic appeal and their numerous real life applications similarly the field of multi objective optimization is attracting more and more attention notably because it offers new opportunities for defining problems this article surveys the existing research related to multi objective optimization in routing problems it examines routing problems in terms of their definitions their objectives and the multi objective algorithms proposed for solving them