optimal solution of vehicle routing problems using minimum k trees we consider the problem of optimally scheduling a fleet of k vehicles to make deliveries to n customers subject to vehicle capacity constraints given a graph with n 1 nodes a k tree is defined to be a set of n k edges that span the graph we show that the vehicle routing problem can be modeled as the problem of finding a minimum cost k tree with two k edges incident on the depot and subject to some side constraints that impose vehicle capacity and the requirement that each customer be visited exactly once the side constraints are dualized to obtain a lagrangian problem that provides lower bounds in a branch and bound algorithm this algorithm has produced proven optimal solutions for a number of difficult problems including a well known problem with 100 customers and several real problems with 25 71 customers

nonstandard conserved hamiltonian structures in dissipative damped systems nonlinear generalizations of damped harmonic oscillator in this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified emden type nonlinear oscillator equation with linear forcing x xx x3 x 0 which preserves the form of the time independent integral conservative hamiltonian and the equation of motion generalizing this transformation we prove the existence of nonstandard conservative hamiltonian structure for a general class of damped nonlinear oscillators including lienard type systems further using the above hamiltonian structure for a specific example namely the generalized modified emden equation x xqx x2q 1 0 where and q are arbitrary parameters the general solution is obtained through appropriate canonical transformations we also present the conservative hamiltonian structure of the damped mathews lakshmanan oscillator equation the associated lagrangian description for all the above systems is also briefly discussed

exact solutions of the generalized lane emden equation a generalized lane emden equation with indices n is discussed which reduces to the lane emden equation proper for 2 1 1 general properties of the set of solutions of this equation are derived and exact solutions are given these include a singular solution without free integration constant for arbitrary n and for particular relations between n and among the two parameter solutions nonequivalent families of solutions of the same equation are obtained

a direct approach to finding exact invariants for one dimensional time dependent classical hamiltonians for a classical hamiltonian h 1 2 p2 v q t with an arbitrary time dependent potential v q t exact invariants that can be expressed as series in positive powers of p i q p t n 0pnfn q t are examined the method is based on direct use of the equation di dt i t i h 0 a recursion relation for the coefficients fn q t is obtained all potentials that admit an invariant quadratic in p are found and for those potentials all invariants quadratic in p are determined the feasibility of extending the analysis to find invariants that are polynomials in p of higher degree than quadratic is discussed the systems for which invariants quadratic in p have been found are transformed to autonomous systems by a canonical transformation

schrodinger equation with time dependent boundary conditions a schrodinger equation for a well potential with varying width is studied generalized canonical transformations are shown to transform the problem into a time dependent harmonic oscillator problem submitted to fixed boundary conditions this transformed problem is solved by a perturbation technique and gives the evolution of the average energy of the system according to the motion of the well motions corresponding to a renormalization or compaction group are shown to be solvable by separation of variables

analysis and solution of a nonlinear second order differential equation through rescaling and through a dynamical point of view the solutions of the equation y yy y3 0 where is a free parameter are investigated for 1 9 the equation is linearizable through an eight parameter symmetry group and is completely integrable for 1 9 only two symmetries subsist but through a dynamical description the analytical asymptotic solutions and their behavior are given according to the value of and according to the initial conditions

n dimensional equations with the maximum number of symmetry generators the authors obtain the general class of ordinary differential equations that can be reduced by a point transformation to the free particle equation and given the general form of the lie symmetry generators for these equations they apply these results to obtain the symmetry generators for the n dimensional harmonic oscillator and for a particle in a constant magnetic field

symmetry and singularity properties of second order ordinary differential equations of lie s type iii abstract we extend the work of abraham shrauner b abraham shrauner hidden symmetries and linearization of the modified painleve ince equation j math phys 34 1993 4809 4816 on the linearization of the modified painleve ince equation to a wider class of nonlinear second order ordinary differential equations invariant under the symmetries of time translation and self similarity in the process we demonstrate a remarkable connection with the parameters obtained in the singularity analysis of this class of equations

lie point symmetries and exact solutions of quasilinear differential equations with critical exponents abstract we consider a general class of quasilinear ordinary differential equations which contains in particular the lane emden equation the liouville equation the poisson boltzmann equation equations involving the radial forms of the laplace p laplace and the k hessian operators the lie point symmetry group of these equations is calculated then the corresponding noether symmetries are found and used to obtain first integrals and exact solutions of the equations with critical exponents

a nonlocal connection between certain linear and nonlinear ordinary differential equations oscillators we explore a nonlocal connection between certain linear and nonlinear ordinary differential equations odes representing physically important oscillator systems and identify a class of integrable nonlinear odes of any order we also devise a method to derive explicit general solutions of the nonlinear odes interestingly many well known integrable models can be accommodated into our scheme and our procedure thereby provides further understanding of these models

symmetries of nonlinear differential equations and linearisation a non linear ordinary differential equation is linearisable if it possesses sl 3 r symmetry the conditions under which the abelian two dimensional subalgebras of sl 3 r are sufficient for linearisation are established

a first integral for a class of time dependent anharmonic oscillators with multiple anharmonicities the integrability of the equation q f t q2 g t q3 h t q4 j t q5 is considered particular cases of this equation arise in the study of charged plasma in an axially symmetric magnetic field and in shear free spherically symmetric gravitational fields in general relativity the above equation with only a quadratic term arises in the study of shear free fluids in general a krasinski j math phys 30 433 1989 the equation with a cubic term is applicable when there is an electromagnetic field in special cases we reduce the solution to a quadrature that has solutions in terms of elliptic integrals a lie point symmetry analysis is performed and the different cases that arise are considered for the existence of a symmetry

finite point transformations and linearisation of x f t x the usefulness of finite point transformations is emphasised as a systematic tool for studying the eventual linearisation of ordinary second order differential equations

computational experience with exterior point algorithms for the transportation problem an experimental computational study to compare the classical primal simplex algorithm and the exterior point algorithms for the transportation problem tp is presented totally four algorithms are compared on uniformly randomly generated test problems the results are very encouraging for one of the competitive algorithms in particular a dual forest exterior point algorithm is on average up to 4 5 times faster than network simplex algorithm on tps of size 300x300 and for all classes this result leads into corresponding savings in computational time from the computational performance we conclude that as the problem size increases exterior point algorithm get relatively faster

on the general solution for the modified emden type equation in this paper we demonstrate that the modified equation of emden type mee is integrable either explicitly or by quadrature for any value of and we also prove that the mee possesses appropriate time independent hamiltonian functions for the full range of parameters and in addition we show that the mee is intimately connected with two well known nonlinear models namely the equation of force free duffing type oscillator and the two dimensional lotka volterra equation and thus the complete integrability of the latter two models can also be understood in terms of the mee

autonomous self similar ordinary differential equations and the painleve connection we demonstrate an intimate connection between nonlinear higher order ordinary differential equations possessing the two symmetries of autonomy and self similarity and the leading order behaviour and resonances determined in the application of the painleve test similar behaviour is seen for systems of first order differential equations several examples illustrate the theory in an integrable case of the abc system the singularity analysis reveals a positive and a negative resonance and the method of leading order behaviour leads naturally to a laurent expansion containing both

a generalization of the lane emden equation abstract we consider a class of second order initial value problems which includes the well known lane emden equation from astrophysics as a special case local existence global existence and uniqueness of solutions are proven

a nonlocal connection between certain linear and nonlinear ordinary differential equations extension to coupled equations identifying integrable coupled nonlinear ordinary differential equations odes of dissipative type and deducing their general solutions are some of the challenging tasks in nonlinear dynamics in this paper we undertake these problems and unearth two classes of integrable coupled nonlinear odes of arbitrary order to achieve these goals we introduce suitable nonlocal transformations in certain linear odes and generate the coupled nonlinear odes in particular we show that the problem of solving these classes of coupled nonlinear odes of any order effectively reduces to solving a single first order nonlinear ode we then describe a procedure to derive explicit general solutions for the identified integrable coupled odes when the above mentioned first order nonlinear ode reduces to a bernoulli equation the equations which we generate and solve include the two coupled versions of modified emden equations in second order coupled versions of chazy equations in third order and their variants higher d

the painleve test hidden symmetries and the equation y yy ky3 0 for general values of the parameter k the equation y yy ky3 0 can be reduced to quadrature via a lie algebraic approach either direct or through hidden symmetries for specific values of k mostly in 1 9 1 8 the solution can be expressed in parametric form for these values of k the equation passes the weak painleve test for some other values of k the equation passes the painleve test but the solution cannot in general be expressed parametrically

exact solutions of coupled lienard type nonlinear systems using factorization technique general solutions of nonlinear ordinary differential equations odes are in general difficult to find although powerful integrability techniques exist in the literature for this purpose it has been shown that in some scalar cases particular solutions may be found with little effort if it is possible to factorize the equation in terms of first order differential operators in our present study we use this factorization technique to address the problem of finding solutions of a system of general two coupled lienard type nonlinear differential equations we describe a generic algorithm to identify specific classes of lienard type systems for which solutions may be found we demonstrate this method by identifying a class of two coupled equations for which the particular solution can be found by solving a bernoulli equation this class of equations include coupled generalization of the modified emden equation we further deduce the general solution of a class of coupled odes using the factorization proced

nonlocal symmetries of a class of scalar and coupled nonlinear ordinary differential equations of any order in this paper we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations odes of arbitrary order related to linear odes through nonlocal relations the procedure makes use of the lie point symmetries of the linear odes and the nonlocal connection to deduce the nonlocal symmetries of the corresponding nonlinear odes using these nonlocal symmetries we obtain reduction transformations and reduced equations to specific examples we find that the reduced equations can be explicitly integrated to deduce the general solutions for these cases we also extend this procedure to coupled higher order nonlinear odes with specific reference to second order nonlinear odes

maximal subalgebra associated with a first integral of a system possessing sl 3 r algebra conventionally the symmetries of a dynamical system are used to determine the first integrals associated with the system in this paper the reverse procedure is adopted for one dimensional systems possessing sl 3 r symmetry the equivalence of such systems enables the free particle equation to be used as a vehicle it is observed that for three particular first integrals each gives rise to a triplet of generators having isomorphic algebras it is then shown how the knowledge of a first integral and its associated triplet enables one to obtain the remaining integrals and triplets

a nonlocal connection between certain linear and nonlinear ordinary differential equations part ii complex nonlinear oscillators in this paper we present a method to identify integrable complex nonlinear oscillator systems and construct their solutions for this purpose we introduce two types of nonlocal transformations which relate specific classes of nonlinear complex ordinary differential equations odes with complex linear odes thereby proving the integrability of the former we also show how to construct the solutions using the two types of nonlocal transformations with several physically interesting cases as examples

dynamics of a completely integrable n coupled lienard type nonlinear oscillator we present a system of n coupled lienard type nonlinear oscillators which is completely integrable and possesses n time independent and n time dependent explicit integrals in a special case it becomes maximally superintegrable and admits 2n 1 time independent integrals the results are illustrated for the n 2 and arbitrary number cases general explicit periodic with frequency independent of amplitude and quasi periodic solutions as well as decaying type frontlike solutions are presented depending on the signs and magnitudes of the system parameters though the system is of a nonlinear damped type our investigations show that it possesses a hamiltonian structure and that under a contact transformation it is transformable to a system of uncoupled harmonic oscillators

ordinary differential equations invariant under translation in the independent variable and rescaling the lagrangian formulation abstract the lagrangian formulation of the class of general second order ordinary differential equations invariant under translation in the independent variable and rescaling is presented the differential equations arising from this analysis are analysed using the painleve test the well known differential equation y y y k y 3 0 is a unique member of this class when k 3 since it is linearisable by a point transformation a wider subset is shown to be linearisable by means of a nonlocal transformation

self avoiding walks on diluted lattices near the percolation threshold using the node link picture of the infinite cluster near the percolation threshold a crossover of the critical behaviour of the self avoiding walks on the random lattice near the percolation threshold or just above threshold is suggested and a scaling function of this crossover is proposed the author compares the result of this qualitative argument with a monte carlo simulation result

a unification in the theory of linearization of second order nonlinear ordinary differential equations in this letter we introduce a new generalized linearizing transformation glt for second order nonlinear ordinary differential equations snodes the well known invertible point ipt and non point transformations npt can be derived as sub cases of the glt a wider class of nonlinear odes that cannot be linearized through npt and ipt can be linearized by this glt we also illustrate how to construct glts and to identify the form of the linearizable equations and propose a procedure to derive the general solution from this glt for the snodes we demonstrate the theory with two examples which are of contemporary interest

the generalized damped cubic equation integrability and general solution the nonlinear ordinary differential equation of the form u f1u f2u f3u3 o representing a generalized damped cubic equation is fully analysed the author finds the general expression for f2 in terms of f1 and f3 that renders the equation integrable also he shows that if f2 satisfies the above mentioned condition the former nonlinear differential equation can always be reduced through adequate changes of variable to the second painleve transcendent

self avoiding walks on lattices with a long range correlated disorder the author considers self avoiding walks saw on the dilute lattices on which the correlation function of the probability of occupied bonds sites obeys a power law r a for large separation r the saw is studied by a renormalisation group expansion in epsilon 4 d and delta 4 a the author finds the extended harris criterion for n 0 n vector model or saw is that the disorder is irrelevant if av 2 0 which does not depend on the relation between a and d if the disorder is relevant the saw has a new fixed point which has a correlation length exponent nu 2 a

solutions of an equation that lead to solutions of a modified emden equation and a coupled korteweg devries equation in a recent paper moreira res rep if ufrj 83 25 universidade federal do rio de janeiro inst de fisica cidade univ ilha do fundao rio de janeiro brazil obtained a nonlinear second order differential equation that leads to the first integral of a modified emden equation he also obtained two particular solutions of his equation this paper completely integrates moreira s equation and uses it to get a class of solutions of a coupled korteweg devries kdv equation recently studied by guha ray bagchi and sinha j math phys 27 2558 1986

a subpath ejection method for the vehicle routing problem generically ejection chains are methods conceived to allow solution transformations to be efficiently carried out by modifying a variable number of their components at each step of a local search algorithm we consider a subpath ejection chain method for the vehicle routing problem vrp under capacity and route length restrictions the method undertakes the identification of a substructure named the flower reference structure which besides coordinating moves during an ejection chain construction allows the creation of neighborhood structures with interesting combinatorial characteristics specifically we base the method on a fundamental property of creating alternating paths and cycles during an ejection chain construction a new algorithm based on a tabu search framework is proposed and computational results on a set of academic and real world problems indicate that the algorithm may be a good alternative to the best heuristic algorithms for the vrp

generalised symmetries of some nonlinear finite dimensional systems an approach based on the theorem that every variational symmetry of a variational problem is also a symmetry of the euler lagrange equation has been applied to find the generalised symmetries for the generalised henon heiles system a system possessing non polynomial type potential and a super integrable system the constants of motion of these systems have also been found

on the properties of a variant of the riccati system of equations a variant of the generalized riccati system of equations is considered it is shown that for 2n 3 the system admits a bilagrangian description and the dynamics has a node at the origin whereas for much smaller than a critical value the dynamics is periodic the origin being a centre it is found that the solution changes from being periodic to aperiodic at a critical point which is independent of the initial conditions this behaviour is explained by finding a scaling argument via which the phase trajectories corresponding to different initial conditions collapse onto a single universal orbit numerical evidence for the transition is shown further using a perturbative renormalization group argument it is conjectured that the oscillator exhibits isochronous oscillations the correctness of the conjecture is established numerically

nonlocal symmetries and integrable ordinary differential equations x 3xx x3 0 and its generalizations the equation x 3xx x3 0 is well known in many areas of mathematics and physics it possesses the algebra sl 3 r of lie point symmetries hence is equivalent to the equation for a free particle and both left and right painleve series we investigate two higher dimensional analogs in terms of their symmetry and singularity structures we find a drastic reduction in symmetry and a loss of some of the singularity properties from the nonlocal symmetries we are able to determine the complete symmetry group as being represented by a five dimensional abelian algebra

unusual lienard type nonlinear oscillator a lienard type nonlinear oscillator of the form x kxx k2 9 x3 lambda1x 0 which may also be considered as a generalized emden type equation is shown to possess unusual nonlinear dynamical properties it is shown to admit explicit nonisolated periodic orbits of conservative hamiltonian type for lambda1 0 these periodic orbits exhibit the unexpected property that the frequency of oscillations is completely independent of amplitude and continues to remain as that of the linear harmonic oscillator this is completely contrary to the standard characteristic property of nonlinear oscillators interestingly the system though appears deceptively a dissipative type for lambda1 or 0 does admit a conserved hamiltonian description where the characteristic decay time is also independent of the amplitude the results also show that the criterion for conservative hamiltonian system in terms of divergence of flow function needs to be generalized

factorization of a class of almost linear second order differential equations a general type of almost linear second order differential equations which are directly related to several interesting physical problems is characterized the solutions of these equations are obtained using the factorization technique and their non autonomous invariants are also found by means of scale transformations

quasi lie schemes and emden fowler equations the recently developed theory of quasi lie schemes is studied and applied to investigate several equations of emden type and a scheme to deal with them and some of their generalizations is given as a first result we obtain t dependent constants of the motion for particular instances of emden equations by means of some of their particular solutions previously known results are recovered from this new perspective some t dependent constants of the motion for equations of emden type satisfying certain conditions are recovered finally new exact particular solutions are given for certain cases of emden equations

invertible point transformations painleve analysis and anharmonic oscillators the techniques of an invertible point transformation and the painleve analysis can be used to construct integrable ordinary differential equations the authors compare both techniques for anharmonic oscillators

lagrangian formalism for nonlinear second order riccati systems one dimensional integrability and two dimensional superintegrability the existence of a lagrangian description for the second order riccati equation is analyzed and the results are applied to the study of two different nonlinear systems both related with the generalized riccati equation the lagrangians are non natural and the forces are not derivable from a potential the constant value e of a preserved energy function can be used as an appropriate parameter for characterizing the behavior of the solutions of these two systems in the second part the existence of two dimensional versions endowed with superintegrability is proved the explicit expressions of the additional integrals are obtained in both cases finally it is proved that the orbits of the second system that represents a nonlinear oscillator can be considered as nonlinear lissajous figures

where two fractals meet the scaling of a self avoiding walk on a percolation cluster the scaling properties of self avoiding walks on a d dimensional diluted lattice at the percolation threshold are analyzed by a field theoretical renormalization group approach to this end we reconsider the model of y meir and a b harris phys rev lett 63 2819 1989 and argue that via renormalization its multifractal properties are directly accessible while the former first order perturbation did not agree with the results of other methods our analytic result gives an accurate description of the available mc and exact enumeration data in a wide range of dimensions 2 ensuremath leqslant d ensuremath leqslant 6

hidden symmetries and linearization of the modified painleve ince equation the linearization and hidden symmetries of the modified painleve ince equation y yy y3 0 where and are constants are presented the linearization of this equation by a nonlocal transformation yields a damped stable or growing unstable harmonic oscillator equation for 0 hidden symmetries are analyzed by transforming the modified painleve ince equation to a third order ordinary differential equation ode which in general is invariant under a three parameter group by a riccati transformation a type i hidden symmetry is found of a second order ode found from the third order ode where a symmetry is lost in the reduction of order by the non normal subgroup invariants a type ii hidden symmetry occurs in the third order ode because the symmetries of a second order ode reduced from the third order ode by another set of normal subgroup invariants are increased

cluster structure near the percolation threshold derives exact relations that allow one to describe unambiguously and quantitatively the structure of clusters near the percolation threshold pc in particular the author proves the relations p dpij dp lambda ij where p is the bond density pij is the pair connectedness function and lambda ij is the average number of cutting bonds between i and j from this relation it follows that the average number of cutting bonds between two points separated by a distance of the order of the connectedness length xi diverges as mod p pc mod 1 the remaining multiply connected bonds in the percolating backbone which lump together in blobs diverge with a dimensionality dependent exponent he also shows that in the cell renormalisation group of reynolds et al 1978 1980 the thermal eigenvalue is simply related to the average number of cutting bonds in the spanning cluster he discusses a percolation model in which the blobs can be controlled by varying a parameter and study the influence on the critical exponents

relaxed tours and path ejections for the traveling salesman problem abstract we describe an edge based ejection chain method to generate compound neighborhood structures for the traveling salesman problem tsp these neighborhood structures enclose a special substructure which is not necessarily a hamiltonian tour instead the neighborhood components are linked together to compose successive levels of an ejection chain and coordinated by a suitable reference structure to generate compound moves with outstanding proprieties more precisely such a substructure can be viewed as a relaxed tour which allows solution transformations to be obtained without preserving the hamiltonian property at each step furthermore in the ejection chain process the generation of substructures produces a variety of alternating paths for the selection of subsequent ejection moves as well as for the choice of the corresponding trial moves finally we propose two algorithmic variants a preliminary and a full subpath ejection chain method p sec and f sec based on this type of compound neighborhood design both variants are guided by a simple tabu search mechanism computational results on 67 tsplib problems show that both the preliminary and the full methods find optimal and near optimal solutions very quickly frequently outperforming the best heuristic procedures for the tsp in addition the full method generally dominates the best alternative tsp procedures

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

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

generalizations of noether s theorem in classical mechanics in this paper a review is presented of various approaches to the generalization of the version of noether s theorem which is presented in most textbooks on classical mechanics its motivation is the controversy still persisting around the possible scope of a noether type theorem allowing for velocity dependent transformations our analysis is centered around the one factor common to all known treatments namely the structure of the related first integral we first discuss the most general framework in which a function of the above mentioned structure constitutes a first integral of a given lagrangian system and show that one cannot really talk about an interrelationship between symmetries and first integrals there we then compare different proposed generalizations of noether s theorem by describing the nature of the restrictions which characterize them when they are situated within the broadest framework we prove a seemingly new equivalence result between the two main approaches that of invaria

properties of second order ordinary differential equations invariant under time translation and self similar transformation the general form of a second order ordinary differential equation invariant under time translation and self similarity is obtained together with its solution in parametric form next two representatives of two different families of such equations are studied in terms of rescaled phase space variables the first example has a simple physical interpretation and its limit cycle properties and period are easily derived similar results are found for the second example but the physical interpretation is less obvious the invariant equations are used as a basis to study the asymptotic behavior of related noninvariant equations thereby underlining the critical value nature of the parameters for which a self similar solution sss exists

group classification of a family of second order differential equations abstract we find the group of equivalence transformations for equations of the form y a x y f y where a and f are arbitrary functions we then give a complete group classification of this family of equations using a direct method of analysis together with the equivalence transformations

on the local analytic integrability for a generalized damped nonlinear oscillator equation we consider the general damped nonlinear oscillator x y y a1x a2xn 1 a3x2n 1 y a4 a5xn where ai are real parameters for i 1 2 3 4 5 and n is an integer we note that these class of lienard differential systems include a large number of physically important nonlinear oscillators we provide a complete and rigorous characterization of these systems that admit a local analytic first integral in a neighborhood of the origin

a simple and unified approach to identify integrable nonlinear oscillators and systems in this paper we consider a generalized second order nonlinear ordinary differential equation ode of the form x k1xq k2 x k3x2q 1 k4xq 1 1x 0 where ki s i 1 2 3 4 1 and q are arbitrary parameters which includes several physically important nonlinear oscillators such as the simple harmonic oscillator anharmonic oscillator force free helmholtz oscillator force free duffing and duffing van der pol oscillators modified emden type equation and its hierarchy generalized duffing van der pol oscillator equation hierarchy and so on and investigate the integrability properties of this rather general equation we identify several new integrable cases for arbitrary value of the exponent q q r the q 1 and q 2 cases are analyzed in detail and the results are generalized to arbitrary q our results show that many classical integrable nonlinear oscillators can be derived as subcases of our results and significantly enlarge the list of integrable equations that exists in the contemporary literature t

a filter and fan approach to the job shop scheduling problem the job shop scheduling problem jssp is a notoriously difficult problem in combinatorial optimization extensive investigation has been devoted to developing efficient algorithms to find optimal or near optimal solutions this paper proposes a new heuristic algorithm for the jssp that effectively combines the classical shifting bottleneck procedure sbp with a dynamic and adaptive neighborhood search procedure our new search method based on a filter and fan f f procedure uses the sbp as a subroutine to generate a starting solution and to enhance the best schedules produced the f f approach is a local search procedure that generates compound moves by a strategically abbreviated form of tree search computational results carried out on a standard set of 43 benchmark problems show that our f f algorithm performs more robustly and effectively than a number of leading metaheuristic algorithms and rivals the best of these algorithms

first integrals and reduction of a class of nonlinear higher order ordinary differential equations abstract we propose a method for constructing first integrals of higher order ordinary differential equations in particular third fourth and fifth order equations of the form x n h x x n 1 x are considered the relation of the proposed method to local and nonlocal symmetries are discussed

a decision support system for a real vehicle routing problem abstract the vehicle routing problem has been widely studied in the literature mainly because of the real world logistics and transportation problems related to it in the present paper a new two stage exact approach for solving a real problem is shown along with decision making software in the first stage all the feasible routes are generated by means of an implicit enumeration algorithm afterwards an integer programming model is designed to select in the second stage the optimum routes from the set of feasible routes the integer model uses a number of 0 1 variables ranging from 2000 to 15 000 and gives optimum solutions in an average time of 60 seconds for instances up to 60 clients an interactive decision support system was also developed the system was tested with a set of real instances and in a worst case scenario up to 60 clients the routes obtained ranged from a 7 to 12 reduction in the distance travelled and from a 9 to 11 reduction in operational costs

on the capacitated vehicle routing problem we consider the vehicle routing problem in which a fixed fleet of delivery vehicles of uniform capacity must service known customer demands for a single commodity from a common depot at minimum transit cost this difficult combinatorial problem contains both the bin packing problem and the traveling salesman problem tsp as special cases and conceptually lies at the intersection of these two well studied problems the capacity constraints of the integer programming formulation of this routing model provide the link between the underlying routing and packing structures we describe a decomposition based separation methodology for the capacity constraints that takes advantage of our ability to solve small instances of the tsp efficiently specifically when standard procedures fail to separate a candidate point we attempt to decompose it into a convex combination of tsp tours if successful the tours present in this decomposition are examined for violated capacity constraints if not the farkas theorem provides a hyperplane separating the point from the tsp polytope we present some extensions of this basic concept and a general framework within which it can be applied to other combinatorial models computational results are given for an implementation within the parallel branch cut and price framework symphony

on the singularity analysis of ordinary differential equations invariant under time translation and rescaling the pt is applied to the general second and third order ordinary differential equations invariant under the two symmetries associated with time translation and rescaling in order to investigate their solvability and global integrability the effect of the two symmetries on the compatibility conditions is determined and we show that generally these conditions are automatically a consequence of the resonance condition use is made of truncated laurent series both in ascending and descending powers as an example the case of the generalized chazy equation is presented

first integrals for the modified emden equation q α t q qn 0 it is shown that the modified emden equation q t q qn 0 possesses first integrals for functions t other than kt 1 the function t is obtained explicitly in the case n 3 and parametrically for other n 2 the case n 2 is seen to be particularly difficult to solve