an approximability result of the multi vehicle scheduling problem on a path with release and handling times in this paper we consider a scheduling problem of vehicles on a path g with n vertices and n 1 edges there are m identical vehicles each vertex in g has exactly one job any of the n jobs must be processed by some vehicle each job has a release time and a handling time with the edges symmetric travel times are associated the problem asks to find an optimal schedule of the m vehicles that minimizes the maximum completion time of all the jobs the problem is known to be np hard for any fixed m 2 in this paper we show that the problem with a fixed m admits a polynomial time approximation scheme our algorithm can be extended to the case where g is a tree so that a polynomial time approximation scheme is obtained if m and the number of leaves in g are fixed

branch and price algorithm for fuzzy integer programming problems with block angular structure this paper deals with fuzzy integer linear programming problems with block angular structure in which the fuzzy constraints are simplified by using possibility and necessity relations this main fuzzy problem is efficiently decomposed and is solved by a branch and price algorithm in the nodes of the branch and price tree the linear relaxation of the problem is solved by applying a column generation method also the relationship between the optimal solutions of this problem under possibility and necessity relations is derived to show the validation of the proposed algorithm some results are proved in addition the application of this algorithm is illustrated on fuzzy multicommodity flow problem for this case a new branching scheme is proposed to preserve the network structure of the subproblems which are produced in the column generation method some examples are solved and their results are compared with the previous works also the results of the proposed algorithm are reported on some large scale benchmark instances

reproducing kernel structure and sampling on time warped spaces with application to warped wavelets time warped signal spaces have received attention in the literature among the topics of particular interest are sampling of time warped signals and signal analysis using warped analysis functions including wavelets this correspondence introduces a reproducing kernel rk structure for time warped signal spaces that unifies multiple perspectives on sampling in such spaces

optimality conditions for truncated laguerre networks presents optimality conditions for truncated laguerre networks both for continuous time and for discrete time contrary to the current approach no assumption is made about the whiteness of the power spectrum of the input signal curiously the results obtained have the same form as those published for the more restrictive case where the input signal is an impulse at the time origin or white noise

a new solution algorithm for improving performance of ant colony optimization this study proposes an improved solution algorithm using ant colony optimization aco for finding global optimum for any given test functions the procedure of the aco algorithms simulates the decision making processes of ant colonies as they forage for food and is similar to other artificial intelligent techniques such as tabu search simulated annealing and genetic algorithms aco algorithms can be used as a tool for optimizing continuous and discrete mathematical functions the proposed algorithm is based on each ant searches only around the best solution of the previous iteration with b the proposed algorithm is called as acorses an abbreviation of aco reduced search space b is proposed for improving aco s solution performance to reach global optimum fairly quickly the acorses is tested on fourteen mathematical test functions taken from literature and encouraging results were obtained the performance of acorses is compared with other optimization methods the results showed that the acorses performs better than other optimization algorithms available in literature in terms of minimum values of objective functions and number of iterations

frequency warped filter banks and wavelet transforms a discrete time approach via laguerre expansion we introduce a new generation of perfect reconstruction filter banks that can be obtained from classical critically sampled filter banks by means of frequency transformations the novel filters are laguerre type iir filters that can be directly derived and designed from ordinary orthogonal or biorthogonal filter banks generalized downsampling and upsampling operators based on dispersive delay lines are the building blocks of our structures by iterating the filter banks we construct new orthogonal and complete sets of wavelets whose passbands are not octave spaced and may be designed by selecting a single parameter

optimum laguerre networks for a class of discrete time systems an analytical approach is introduced that directly yields the optimum value of the laguerre parameter b this is achieved by minimizing the mean square error between the unit sample response of the given discrete system and that of its laguerre counterpart it is shown that laguerre networks are best suited to realized systems whose exponential unit sample responses die down rapidly

classification of dantzig wolfe reformulations for binary mixed integer programming problems abstract in this note we provide a classification of dantzig wolfe reformulations for binary mixed integer programming problems we specifically focus on modeling the binary conditions in the convexification approach to the dantzig wolfe decomposition for a general binary mixed integer programming problem an extreme point of the overall problem does not necessarily correspond to an extreme point of the subproblem therefore the binary conditions cannot in general be imposed on the new master problem variables but must be imposed on the original binary variables in some cases however it is possible to impose the binary restrictions directly on the new master problem variables the issue of imposing binary conditions on the original variables versus the master problem variables has not been discussed systematically for mip problems in general in the literature and most of the research has been focused on the pure binary case the classification indicates in which cases you can and cannot impose binary conditions on the new master problem variables

an additive bounding procedure for combinatorial optimization problems we know that the effectiveness of the branch and bound algorithms proposed for the solution of combinatorial optimization problems greatly depends on the tightness of the available bounds in this paper we consider optimization problems with a linear objective function we propose an additive approach for computing lower bounds that yields an increasing sequence of values an application to the traveling salesman problem with precedence constraints is presented to exemplify the technique

a branch and cut algorithm for the multiple depot vehicle scheduling problem we consider the multiple depot vehicle scheduling problem mdvsp and propose a branch and bound algorithm for solving it that combines column generation variable fixing and cutting planes we show that the solutions of the linear relaxation of the mdvsp contain many odd cycles we derive a class of valid inequalities by extending the notion of odd cycle and describe a lifting procedure for these inequalities we prove that the lifted inequalities represent under certain conditions facets of the underlying polytope finally we present the results of a computational study comparing several strategies variable fixing cutting planes mixed branching and tree search for solving the mdvsp

entropy based algorithms for best basis selection adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals it permits efficient compression of a variety of signals such as sound and images the predefined libraries of modulated waveforms include orthogonal wavelet packets and localized trigonometric functions and have reasonably well controlled time frequency localization properties the idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost the method relies heavily on the remarkable orthogonality properties of the new libraries all expansions in a given library conserve energy and are thus comparable several cost functionals are useful one of the most attractive is shannon entropy which has a geometric interpretation in this context

discrete optimization in public rail transport many problems arising in traffic planning can be modelled and solved using discrete optimization we will focus on recent developments which were applied to large scale real world instances most railroad companies apply a hierarchically structured planning process starting with the definition of the underlying network used for transport one has to decide which infrastructural improvements are necessary usually the rail system is periodically scheduled a fundamental base of the schedule are the lines connecting several stations with a fixed frequency possible objectives for the construction of the line plan may be the minimization of the total cost or the maximization of the passengers s comfort satisfying certain regulations after the lines of the system are fixed the train schedule can be determined a criterion for the quality of a schedule is the total transit time of the passengers including the waiting time which should be minimized satisfying some operational constraints for each trip of the schedule a train consisting of a locomotive and some carriages is needed for service the assignment of rolling stock to schedule trips has to satisfy operational requirements a comprehensible objective is to minimize the total cost after all strategic and tactical planning the schedule has to be realized several external influences for example delayed trains force the dispatcher to recompute parts of the schedule on line

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

a column generation approach to the multiple depot vehicle scheduling problem we give a new formulation to the multiple depot vehicle scheduling problem as a set partitioning problem with side constraints whose continuous relaxation is amenable to be solved by column generation we show that the continuous relaxation of the set partitioning formulation provides a much tighter lower bound than the additive bound procedure previously applied to this problem we also establish that the additive bound technique cannot provide tighter bounds than those obtained by lagrangian decomposition in the framework in which it has been used so far computational results that illustrate the robustness of the combined set partitioning column generation approach are reported for problems four to five times larger than the largest problems that have been exactly solved in the literature finally we show that the gap associated with the additive bound based on the assignment and shortest path relaxations can be arbitrarily bad in the general case and as bad as 50 in the symmetric case

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

solving a real world train unit assignment problem we face a real world train unit assignment problem for an operator running trains in a regional area given a set of timetabled train trips each with a required number of passenger seats and a set of train units each with a given number of available seats the problem calls for an assignment of the train units to the trips possibly combining more than one train unit for a given trip that fulfills the seat requests with respect to analogous case studies previously faced in the literature ours is characterized by the fairly large number of distinct train unit types available in addition to the fairly large number of trips to be covered as a result although there is a wide margin of improvement over the solution used by the practitioners as our results show even only finding a solution of the same value is challenging in practice we present a successful heuristic approach based on an ilp formulation in which the seat requirement constraints are stated in a strong form derived from the description of the convex hull of the variant of the knapsack polytope arising when the sum of the variables is restricted not to exceed two computational results on real world instances are reported showing the effectiveness of the proposed approach

improved method for optimum choice of free parameter in orthogonal approximations we report on our investigations to choose a free parameter to minimize the error energy when approximating a given signal with orthogonal basis functions this method requires limited knowledge of the signal to be approximated and has a low computational cost

nonuniform fast fourier transforms using min max interpolation the fast fourier transform fft is used widely in signal processing for efficient computation of the ft of finite length signals over a set of uniformly spaced frequency locations however in many applications one requires nonuniform sampling in the frequency domain i e a nonuniform ft several papers have described fast approximations for the nonuniform ft based on interpolating an oversampled fft this paper presents an interpolation method for the nonuniform ft that is optimal in the min max sense of minimizing the worst case approximation error over all signals of unit norm the proposed method easily generalizes to multidimensional signals numerical results show that the min max approach provides substantially lower approximation errors than conventional interpolation methods the min max criterion is also useful for optimizing the parameters of interpolation kernels such as the kaiser bessel function

tilings of the time frequency plane construction of arbitrary orthogonal bases and fast tiling algorithms the authors consider expansions which give arbitrary orthonormal tilings of the time frequency plane these differ from the short time fourier transform wavelet transform and wavelet packets tilings in that they change over time they show how this can be achieved using time varying orthogonal tree structures which preserve orthogonality even across transitions the method is based on the construction of boundary and transition filters these allow us to construct essentially arbitrary tilings time varying modulated lapped transforms are a special case where both boundary and overlapping solutions are possible with filters obtained by modulation they present a double tree algorithm which for a given signal decides on the best binary segmentation in both time and frequency that is it is a joint optimization of time and frequency splitting the algorithm is optimal for additive cost functions e g rate distortion and results in time varying best bases the main application of which is for compression of nonstationary signals experiments on test signals are presented

dynamic siso and miso system approximations based on optimal laguerre models a general procedure based on the knowledge of the input and the output signals is proposed to approximate the prescribed linear time invariant lti systems by means of optimal laguerre models the main contribution of this paper is to apply the newton raphson s iterative technique to compute the so called optimal laguerre pole in a continuous time case or optimal time scale factor in a discrete time case and especially to show that the gradient and the hessian can be expressed analytically moreover the excitations used are not limited to the ones that ensure the orthogonality of the outputs of laguerre filters i e dirac delta or white noise as is usually done in existing methods however persistently exciting input signal s are used the proposed procedure will be directly formulated for siso systems siso systems being a special case with the number of inputs equal to one the proposed algorithm has direct applications in system identification model reduction and noisy modeling

the fixed job schedule problem with working time constraints we consider a generalization of the fixed job schedule problem where a bound is imposed on the total working time of each processor it is shown that the problem is np hard but polynomially solvable in the preemptive case we introduce several lower bounds one is determined through definition of a special class of graphs for which the maximum clique problem is shown to be polynomial lower bounds and dominance criteria are exploited in a branch and bound algorithm for optimal solution of the problem the effectiveness of the algorithm is analyzed through computational experiments

an exact algorithm for multiple depot bus scheduling abstract in this paper we present an exact algorithm for solving the multiple depot bus scheduling problem the algorithm uses two well known linear programming relaxations of the problem the first a pure network flow problem is used to obtaine a dual feasible solution to the second relaxation a multi commodity network flow problem which is solved using dual simplex branch and bound is then used to obtaine the optimal integer solution this technique is then used to solve exactly problems much greater than any previously reported technique results are presented for problems with up to 600 trips and 3 depots

a hybrid genetic algorithm for estimating the optimal time scale of linear systems approximations using laguerre models we deal with the problem of finding the optimal time scale of the truncated laguerre series using numerical search techniques we develop a hybrid genetic algorithm ga to search the nonlinear multimodal squared error function that results from least squares approximations of the impulse response of causal linear time invariant stable systems the hybrid ga incorporates a newton raphson nr local optimizer for fast convergence to the global minimum point the proposed method competes favorably with the pure ga in solution accuracy the number of function evaluations being the same and with an established gradient directed optimization algorithm in number of function evaluations the solution accuracy being the same

wavelet based representations for a class of self similar signals with application to fractal modulation a potentially important family of self similar signals based upon a deterministic scale invariance characterization is introduced these signals which are referred to as dy homogeneous signals because they generalize the well known homogeneous functions have highly convenient representations in terms of orthonormal wavelet bases in particular wavelet representations can be exploited to construct orthonormal self similar bases for these signals the spectral and fractal characteristics of dy homogeneous signals make them appealing candidates for use in a number of applications as one potential example their use in a communications based context is considered specifically a strategy for embedding information into a dy homogeneous waveform on multiple time scales is developed this multirate modulation strategy called fractal modulation is potentially well suited for use with noisy channels of simultaneously unknown duration and bandwidth

the coding gain of multiplexed wavelet transforms evangelista 1994 1993 introduced the multiplexed wavelet transform mwt and pointed out its potential applications to the analysis synthesis processing and coding of pseudo periodic signals such as voiced speech and music coders based on the mwt have been shown to outperform the conventional subband coders when a reliable pitch parameter can be extracted from data in this paper we investigate the effects of uniform quantization of the mwt coefficients we compare the performance of the new coders with that of wt block dct and klt coders in terms of the coding gain achieved when optimal bit allocation schemes are adopted

heuristic algorithms for the multiple depot vehicle scheduling problem we consider the np hard multiple depot vehicle scheduling problem in which a given set of time tabled trips have to be assigned to vehicles stationed at different depots so as to minimize the number of vehicles used and the overall operational cost the problem arises in the management of transportation companies in this paper some structural properties of the problem are studied and used to design a new polynomial time heuristic algorithm which always guarantees the use of the minimum number of vehicles several effective refining procedures are also proposed extensive computational results on test problems involving up to 1 000 trips and 10 depots are reported showing that the new approach always produces very tight approximate solutions in small computing times and outperforms other heuristics from the literature

discrete frequency warped wavelets theory and applications we extend the definition of dyadic wavelets to include frequency warped wavelets the new wavelets are generated and the transform computed in discrete time by alternating the laguerre transform with perfect reconstruction filterbanks this scheme provides the unique implementation of orthogonal or biorthogonal warped wavelets by means of rational transfer functions we show that the discrete time warped wavelets lead to well defined continuous time wavelet bases satisfying a warped form of the two scale equation the shape of the wavelets is not invariant by translation rather the wavelet translates are obtained from one another by allpass filtering we show that the phase of the delay element is asymptotically a fractal a feature of the warped wavelet transform is that the cut off frequencies of the wavelets may be arbitrarily assigned while preserving a dyadic structure the new transform provides an arbitrary tiling of the time frequency plane which can be designed by selecting as little as a single parameter this feature is particularly desirable in cochlear and perceptual models of speech and music where accurate bandwidth selection is an issue as our examples show by defining pitch synchronous wavelets based on warped wavelets the analysis of transients and denoising of inharmonic pseudo periodic signals is greatly enhanced

unitary equivalence a new twist on signal processing unitary similarity transformations furnish a powerful vehicle for generating infinite generic classes of signal analysis and processing tools based on concepts different from time frequency and scale implementation of these new tools involves simply preprocessing the signal by a unitary transformation performing standard processing on the transformed signal and then in some cases transforming the resulting output the resulting unitarily equivalent systems can focus on the critical signal characteristics in large classes of signals and hence prove useful for representing and processing signals that are not well matched by current techniques as specific examples of this procedure we generalize linear time invariant systems orthonormal basis and frame decompositions and joint time frequency and time scale distributions these applications illustrate the utility of the unitary equivalence concept for uniting seemingly disparate approaches proposed in the literature

multi depot vehicle scheduling problems with time windows and waiting costs the multi depot vehicle scheduling problem with time windows mdvsptw consists of scheduling a fleet of vehicles to cover a set of tasks at minimum cost each task is restricted to begin within a prescribed time interval and vehicles are supplied by different depots the problem is formulated as an integer nonlinear multi commodity network flow model with time variables and is solved using a column generation approach embedded in a branch and bound framework this paper breaks new ground by considering costs on exact waiting times between two consecutive tasks instead of minimal waiting times this new and more realistic cost structure gives rise to a nonlinear objective function in the model optimal and heuristic versions of the algorithm have been extensively tested on randomly generated urban bus scheduling problem ubsp and freight transport scheduling problem ftsp the results show that such a general solution methodology outperforms specialized algorithms when minimal waiting costs are used and can efficiently treat the case with exact waiting costs

system identification using laguerre models the traditional approach of expanding transfer functions and noise models in the delay operator to obtain linear in the parameters predictor models leads to approximations of very high order in cases of rapid sampling and or dispersion in time constants by using prior information about the time constants of the system more appropriate expansions related to laguerre networks are introduced and analyzed it is shown that the model order can be reduced compared to arx fir ar modeling by using laguerre models furthermore the numerical accuracy of the corresponding linear regression estimation problem is improved by a suitable choice of the laguerre parameter consistency error bounds persistence of excitation conditions and asymptotic statistical properties are investigated this analysis is based on the result that the covariance matrix of the regression vector of a laguerre model has a toeplitz structure

an optimal expansion of volterra models using independent kautz bases for each kernel dimension a new solution for the problem of selecting poles of the two parameter kautz functions in volterra models is proposed in general a large number of parameters are required to represent the volterra kernels although this difficulty can be overcome by describing each kernel using a basis of orthonormal functions such as the kautz basis this representation has a wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a non linear static mapping represented by the volterra series the resulting wiener volterra model can be truncated into fewer terms if the kautz functions are properly designed the underlying problem is how to select the arbitrary complex poles that fully parametrize these functions this problem has been approached in previous research by minimizing an upper bound for the error resulting from the truncation of the kernel expansion the present paper goes even further in that each multidimensional kernel is decomposed into a set of independent kautz bases each of which is parametrized by an individual pair of conjugate kautz poles intended to represent the dominant dynamic of the kernel along a particular dimension an analytical solution for one of the kautz parameters valid for volterra models of any order is derived a simulated example is presented to illustrate these theoretical results the same approach is then used to model a real non linear magnetic levitation system with oscillatory behaviour

brief paper choice of free parameters in expansions of discrete time volterra models using kautz functions this work tackles the problem of modeling nonlinear systems using volterra models based on kautz functions the drawback of requiring a large number of parameters in the representation of these models can be circumvented by describing every kernel using an orthonormal basis of functions such as the kautz basis the resulting model so called wiener volterra model can be truncated into a few terms if the kautz functions are properly designed the underlying problem is how to select the free design complex poles that fully parameterize these functions a solution to this problem has been provided in the literature for linear systems which can be represented by first order volterra models a generalization of such strategy focusing on volterra models of any order is presented in this paper this problem is solved by minimizing an upper bound for the error resulting from the truncation of the kernel expansion into a finite number of functions the aim is to minimize the number of two parameter kautz functions associated with a given series truncation error thus reducing the complexity of the resulting finite dimensional representation the main result is the derivation of an analytical solution for a sub optimal expansion of the volterra kernels using a set of kautz functions

pertinent choice of parameters for discrete kautz approximation kautz functions have received much attention in the recent mathematical modeling and identification literature these functions which involve free parameters can approximate efficiently signals with strong oscillatory behavior we consider here the choice of the free parameters in discrete two parameter kautz approximation using a key relationship between kautz and laguerre expansions we derive an upper bound for the quadratic truncation error minimization of this upper bound yields pertinent parameters whose computation then requires reduced knowledge of the function to be modeled

a characterization of completeness of blockability relations with respect to unanimity this paper gives a characterization of completeness of blockability relations on simple games it is verified in this paper that the blockability relation on a simple game is complete if and only if the simple game is s unanimous for some coalition s in n

iterated filter banks with rational rate changes connection with discrete wavelet transforms some properties of two band filter banks with rational rate changes rational filter banks are first reviewed focusing then on iterated rational filter banks compactly supported limit functions are obtained in the same manner as previously done for dyadic schemes allowing a characterization of such filter banks these functions are carefully studied and the properties they share with the dyadic case are highlighted they are experimentally observed to verify a shift property strictly verified in the dyadic ease up to an error which can be made arbitrarily small when their regularity increases in this case the high pass outputs of an iterated filter bank can be very close to samples of a discrete wavelet transform with the same rational dilation factor straightforward extension of the formalism of multiresolution analysis is also made finally it is shown that if one is ready to put up with the loss of the shift property rational iterated filter banks can be used in the same manner as if they were dyadic filter banks with the advantage that rational dilation factors can be chosen closer to 1

heuristic approaches for solving transit vehicle scheduling problem with route and fueling time constraints abstract electric bus scheduling problem can be defined as vehicle scheduling problem with route and fueling time constraints vsprftc every vehicle s travel miles route time after charging is limited thus the vehicle must be recharged after taking several trips and the minimal charging time fueling time must be satisfied a multiple ant colony algorithm aca was presented to solve vsprftc based on aca used to solve traveling salesman problem tsp a new metaheuristic approach inspired by the foraging behavior of real colonies of ants the vsprftc considered in this paper minimizes a multiple hierarchical objective function the first objective is to minimize the number of tours or vehicles and the second is to minimize the total deadhead time new improvement of aca as well as detailed operating steps was provided on the basis of former algorithm then in order to settle contradiction between accelerating convergence and avoiding prematurity or stagnation improvement on route construction rule and pheromone updating rule was adopted a group feasible trip sets blocks had been produced after the process of applying aca in dealing with the fueling time constraint a bipartite graphic model and its optimization algorithm are developed for trip set connecting in a hub and spoke network system to minimize the number of vehicle required the maximum matching of the bipartite graph is obtained by calculating the maximum inflow with the ford fulkerson algorithm at last an example was analyzed to demonstrate the correctness of the application of this algorithm it proved to be more efficient and robust in solving this problem

optimality conditions for truncated kautz networks with two periodically repeating complex conjugate poles presents optimality conditions for the approximation of a siso system by a truncated kautz network with two repeating complex conjugate poles both the continuous and the discrete time cases are discussed the author approaches the problem in a system approximation framework and he does not assume that the input signal is white or an impulse the results obtained generalize the results already known for truncated laguerre networks

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

on the determination of the optimal pole position of laguerre filters as is known in the literature at each stationary point of the squared error se curve of a laguerre filter at least one of a pair of certain laguerre coefficients weights vanishes the author describes a very efficient way to compute the derivatives of each one of these coefficients with respect to the pole position of the laguerre filter the knowledge of these derivatives makes possible the computation of high order approximations to the coefficients in question such as truncated taylor series and pade approximants the zeros of these approximations are usually good estimates of the location of the stationary points of the se curve nearer to the center of the approximation in this way the position of these stationary points in particular local minima can be estimated without resorting to a numerical search algorithm both continuous time and discrete time laguerre filters are discussed excited either by an impulse or by an arbitrary signal the authors illustrate the main results of the paper with a numerical example

comb and multiplexed wavelet transforms and their applications to signal processing as an extension of wavelet theory new wavelet bases that are discrete in nature and suitable for the analysis and synthesis of pseudo periodic digital signals are introduced by means of these bases the signal is represented in terms of a periodic trend and aperiodic fluctuations at several scales in the frequency domain the periodic trend lies in bands that are centered on the harmonics while the fluctuations are distributed in several sidebands properties of comb and multiplexed wavelet transforms are examined and the concepts applied to the analysis of real life signals in one dimension the new transforms have interesting applications to speech and music signal processing their extension to two dimensions may be useful for the analysis of pseudo periodic images

a new ilp based refinement heuristic for vehicle routing problems in this paper we address the distance constrained capacitated vehicle routing problem dcvrp where k minimum cost routes through a central depot have to be constructed so as to cover all customers while satisfying for each route both a capacity and a total distance travelled limit

fast computation of frequency warping transforms in this paper we introduce an analytical approach for the frequency warping transform criteria for the design of operators based on arbitrary warping maps are provided and an algorithm carrying out a fast computation is defined such operators can be used to shape the tiling of time frequency tf plane in a flexible way moreover they are designed to be inverted by the application of their adjoint operator according to the proposed model the frequency warping transform is computed by considering two additive operators the first one represents its nonuniform fourier transform approximation and the second one suppresses aliasing the first operator is fast computable by various interpolation approaches a factorization of the second operator is found for arbitrary shaped nonsmooth warping maps by properly truncating the operators involved in the factorization the computation turns out to be fast without compromising accuracy

lagrangian relaxation methods for solving the minimum fleet size multiple traveling salesman problem with time windows we consider the problem of finding the minimum number of vehicles required to visit once a set of nodes subject to time window constraints for a homogeneous fleet of vehicles located at a common depot this problem can be formulated as a network flow problem with additional time constraints the paper presents an optimal solution approach using the augmented lagrangian method two lagrangian relaxations are studied in the first one the time constraints are relaxed producing network subproblems which are easy to solve but the bound obtained is weak in the second relaxation constraints requiring that each node be visited are relaxed producing shortest path subproblems with time window constraints and integrality conditions the bound produced is always excellent numerical results for several actual school busing problems with up to 223 nodes are discussed comparisons with a set partitioning formulation solved by column generation are given

a method to compare influence of coalitions on group decision other than desirability relation abstract this paper proposes a method to compare influence of coalitions on group decision called blockability relation this relation is defined both on the set of all coalitions and on the set of all feasible coalitions examples show that this relation is definitely different from the desirability relation which have been dealt with in the literature in particular an example shows that the desirability relation is not always transitive and a proposition verifies that the blockability relation is always transitive in order to clarify the simple games on which these relations are defined and to investigate interrelationships among these simple games three types of operators called l intersection l restriction and extension respectively on simple games are defined where l is a family of all feasible coalitions it is verified that the extension of the l intersection of a simple game coincides with the restriction of the simple game

a new binary relation to compare viability of winning coalitions and its interrelationships to desirability relation and blockability relation this paper aims to propose a new type of binary relations called the viability relation defined on the set of all coalitions in a simple game for a comparison of coalition influence and to investigate its properties especially its interrelationships to the desirability relation and the blockability relation the viability relation is defined to compare coalitions based on their robustness over deviation of their members for complementing the inability of the desirability relation and the blockability relation to make a distinguishable comparison among winning coalitions it is verified in this paper that the viability relation on a simple game is always transitive and is complete if and only if the simple game is s unanimous for a coalition s examples show that there are no general inclusion relations among the desirability relation the blockability relation and the viability relation it is also verified that the viability relation and the blockability relation are complementary to each other specifically the blockability relation between two coalitions is equivalent to the inversed viability relation between the complements of the two coalitions

collusion properties of coalition values for games in characteristic function form abstract this paper provides some new properties of coalition values which are blockability value and viability value the investigated properties are related to coalition collusion within games in characteristic function form coalition proxy agreement and coalition association agreement of games in characteristic function form are defined it turns out that the sum of blockability value of two coalitions which do not have common members and one coalition is a dummy coalition does not decrease if there exists a coalition proxy agreement between these two coalitions it is also verified that the sum of blockability value of two coalitions which have no common members with coalition association agreement is equal to or less than the value with coalition proxy agreement in a convex game some propositions which show that the collusion properties of viability value are opposite to the collusion properties of blockability value are provided a new axiom relevant to coalition collusion is proposed and it is confirmed that blockability value satisfies the proposed axiom a counterexample which shows that viability value does not always satisfy the proposed axiom is given

a branch first cut second approach for locomotive assignment the problem of assigning locomotives to trains consists of selecting the types and number of engines that minimize the fixed and operational locomotive costs resulting from providing sufficient power to pull trains on fixed schedules the force required to pull a train is often expressed in terms of horsepower and tonnage requirements rather than in terms of number of engines this complicates the solution process of the integer programming formulation and usually creates a large integrality gap furthermore the solution of the linearly relaxed problem is strongly fractional to obtain integer solutions we propose a novel branch and cut approach the core of the method consists of branching decisions that define on one branch the projection of the problem on a low dimensional subspace there the facets of the polyhedron describing a restricted constraint set can be easily derived we call this approach branch first cut second we first derive facets when at most two types of engines are used we then extend the branching rule to cases involving additional locomotive types we have conducted computational experiments using actual data from the canadian national railway company simulated test problems involving two or more locomotive types were solved over 1 2 and 3 day rolling horizons the cuts were successful in reducing the average integrality gap by 52 for the two type case and by 34 when more than 25 types were used furthermore the branch first cut second approach was instrumental in improving the best known solution for an almost 2 000 leg weekly problem involving 26 locomotive types it reduced the number of locomotives by 11 or 1 1 at an equivalent savings of 3 000 000 per unit additional tests on different weekly data produced almost identical results

solving a class of stochastic mixed integer programs with branch and price we begin this paper by identifying a class of stochastic mixed integer programs that have column oriented formulations suitable for solution by a branch and price algorithm b p we then survey a number of examples and use a stochastic facility location problem sflp for a detailed demonstration of the relevant modeling and solution techniques computational results with a scenario representation of uncertain costs demands and capacities show that b p can be orders of magnitude faster than solving the standard formulation by branch and bound we also demonstrate how b p can solve sflp exactly as exactly as a deterministic mixed integer program when demands and other parameters can be represented as certain types of independent random variables e g independent normal random variables with integer means and variances

new lower bounds for the symmetric travelling salesman problem in this paper new lower bounds for the symmetric travelling salesman problem are proposed and combined in additive bounding procedures efficient implementations of the algorithms are given in particular fast procedures for computing the linear programming reduced costs of the shortest spanning tree sst problem and for finding all ther sst of a given graph are presented computational results on randomly generated test problems are reported

vehicle routing problem with time windows and a limited number of vehicles abstract this paper introduces a variant of the vehicle routing problem with time windows where a limited number of vehicles is given m vrptw under this scenario a feasible solution is one that may contain either unserved customers and or relaxed time windows we provide a computable upper bound to the problem to solve the problem we propose a tabu search approach characterized by a holding list and a mechanism to force dense packing within a route we also allow time windows to be relaxed by introducing the notion of penalty for lateness in our approach customer jobs are inserted based on a hierarchical objective function that captures multiple objectives computational results on benchmark problems show that our approach yields solutions that are competitive to best published results on vrptw on m vrptw instances experiments show that our approach produces solutions that are very close to computed upper bounds moreover as the number of vehicles decreases the routes become more densely packed monotically this shows that our approach is good from both the optimality as well as stability point of view

coalition analysis with preference uncertainty in group decision support coalition analysis is extended to incorporate uncertain preference into three stability concepts general metarationality gmr symmetric metarationality smr and sequential stability seq under the paradigm of the graph model for conflict resolution as a follow up analysis in the graph model coalition analysis aims to assess whether equilibriums under individual calculations are vulnerable to coalition moves and countermoves and hence become unstable under coalition stabilities coalition analysis has been considered for transitive graph models with simple preference under four stabilities nash gmr smr and seq as well as general graph models with uncertain preference for the nash stability this paper introduces preference uncertainty into coalition stabilities under gmr smr and seq for general graph models that can be transitive or intransitive depending on the focal coalition s different attitudes towards preference uncertainty four different extensions are presented interrelationships of coalition stabilities are investigated within each extension and across the four extensions a case study is carried out to illustrate how to apply the proposed coalition stabilities