a greedy randomized adaptive search procedure for maximum independent set an efficient randomized heuristic for a maximum independent set is presented the procedure is tested on randomly generated graphs having from 400 to 3 500 vertices and edge probabilities from 0 2 to 0 9 the heuristic can be implemented trivially in parallel and is tested on an mimd computer with 1 2 4 and 8 processors computational results indicate that the heuristic frequently finds the optimal or expected optimal solution in a fraction of the time required by implementations of simulated annealing tabu search and an exact partial enumeration method

a time indexed formulation of non preemptive single machine scheduling problems we consider the formulation of non preemptive single machine scheduling problems using time indexed variables this approach leads to very large models but gives better lower bounds than other mixed integer programming formulations we derive a variety of valid inequalities and show the role of constraint aggregation and the knapsack problem with generalised upper bound constraints as a way of generating such inequalities a cutting plane branch and bound algorithm based on these inequalities has been implemented computational experience on small problems with 20 30 jobs and various constraints and objective functions is presented

computing redundant resources for the resource constrained project scheduling problem several efficient lower bounds and time bound adjustment methods for the resource constrained project scheduling problem rcpsp have recently been proposed some of them are based on redundant resources in this paper we define redundant functions which are very useful for computing redundant resources we also describe an algorithm for computing all maximal redundant functions once all these redundant functions have been determined we have to identify those that are useful for bounding surprisingly their number is reasonable even for large resource capacities so a representative subset of them can be tabulated to be used efficiently computational results on classical rcpsp instances confirm their usefulness

optimal control of linear time varying systems via piecewise linear polynomial functions a linear time varying optimal control system with a quadratic performance index is solved by using piecewise linear polynomial functions only a small number of basis functions are needed to produce a satisfactory result and the outcome is much better than the solutions obtained by using walsh functions block pulse functions or taylor polynomial series owing to the available recursive formula the computational work is convenient and straightforward

a new lp based lower bound for the cumulative scheduling problem abstract this paper deals with the computation of lower bounds for cumulative scheduling problems based on a new linear programming formulation these lower bounds take into account how resource requirements can be satisfied simultaneously for a given resource capacity one of the main interests of this paper is that the solutions of the lp can be tabulated for a given value of resource capacity thus even if it is based on a linear programming formulation the computation of the bounds is low time consuming as confirmed by our computational results on the resource constrained project scheduling problem

an exact algorithm for the resource constrained project scheduling problem based on a new mathematical formulation in this paper we consider the project scheduling problem with resource constraints where the objective is to minimize the project makespan we present a new 0 1 linear programming formulation of the problem that requires an exponential number of variables corresponding to all feasible subsets of activities that can be simultaneously executed without violating resource or precedence constraints different relaxations of the above formulation are used to derive new lower bounds which dominate the value of the longest path on the precedence graph and are tighter than the bound proposed by stinson et al 1978 a tree search algorithm based on the above formulation that uses new lower bounds and dominance criteria is also presented computational results indicate that the exact algorithm can solve hard instances that cannot be solved by the best algorithms reported in the literature

orthogonal series approach to the sensitivity analysis of linear systems the orthogonal series expansion technique is applied for the approximate determination of sensitivity functions of linear dynamic systems as shown the present approach has two distinct advantages only a small number of coefficients need to be computed for the determination of all sensitivity functions and these coefficients are computed directly from simple equations the method is derived for single input linear systems and then extended to more general cases an illustrative example is included

a branch and bound algorithm for the resource constrained project scheduling problem a branch and bound algorithm is presented for the resource constrained project scheduling problem rcpsp given are n activities which have to be processed without preemptions during the processing period of an activity constant amounts of renewable resources are needed where the available capacity of each resource type is limited furthermore finish start precedence relations between the activities are given the objective is to determine a schedule with minimal makespan the branching scheme starts from a graph representing a set of conjunctions the classical finish start precedence constraints and disjunctions induced by the resource constraints then it either introduces disjunctive constraints between pairs of activities or places these activities in parallel concepts of immediate selection are developed in connection with this branching scheme immediate selection allows to add conjunctions as well as further disjunctions and parallelity relations computational results based on the test data of kolisch et al kolisch r sprecher a drexl a 1995 management science 41 1693 1703 and kolisch and sprecher kolisch r sprecher a 1997 psplib a project scheduling problem library ejor 96 pp 205 216 are reported

solving the resource constrained project scheduling problem using filter and fan approach the resource constrained project scheduling problem is a notoriously difficult problem in combinatorial optimization for which extensive investigation has been devoted to the development of efficient algorithms to find optimal or near optimal solutions this paper proposes a new heuristic algorithm for this problem based on filter and fan method incorporated with a local search exploring in the defined neighborhood space in the algorithm the local search is used to generate a starting solution as well as to re optimize the best schedules produced by the filter and fan method the filter and fan is itself a local search procedure that generates compound moves in a tree search fashion computational results applied on a standard set of 2040 benchmark problems from the literature demonstrate the effectiveness of the approach

general formulation for the numerical solution of optimal control problems a new improved computational method for a class of optimal control problems is presented the state and the costate adjoint variables are approximated using a set of basis functions a method similar to a variational virtual work approach with weighing coefficients is used to transform the canonical equations into a set of algebraic equations the method allows approximating functions that need not satisfy the initial conditions a priori a lagrange multiplier technique is used to enforce the terminal conditions this enlarges the space from which the approximating functions can be chosen orthogonal polynomials are used to obtain a set of simultaneous equations with fewer non zero entries such a sparse system results in substantial computational economy two examples a time invariant system and a time varying system with quadratic performance index are solved using three different sets of orthogonal polynomials and the power series to demonstrate the feasibility and efficiency of this method

analysis and optimal control of time varying linear systems via block pulse functions succinct and clear sighted operational properties of block pulse functions are fully applied to the analysis and optimal control of time varying linear systems with quadratic performance index piecewise constant solutions equally distributed which are simple in form and convenient for use or implementation are consequently obtained another advantage of this method is that any positive integer can be chosen as the number of sub intervals whereas in the case of walsh function approximation the choice can only be made from 2 4 8 16 32 and so on the algorithms developed in the paper are illustrated by appropriate examples

an algorithm for solving the job shop problem in this paper we propose a branch and bound method for solving the job shop problem it is based on one machine scheduling problems and is made more efficient by several propositions which limit the search tree by using immediate selections it solved for the first time the famous 10 10 job shop problem proposed by muth and thompson in 1963

skeletons from the treecode closet abstract we consider treecodes n body programs which use a tree data structure from the standpoint of their worst case behavior that is we derive upper bounds on the largest possible errors that are introduced into a calculation by use of various multipole acceptability criteria mac we find that the conventional barnes hut mac can introduce potentially unbounded errors unless 3 and that this behavior while rare is demonstrable in astrophysically reasonable examples we consider two other macs closely related to the bh mac while they do not admit the same unbounded errors they nevertheless require extraordinary amounts of cpu time to guarantee modest levels of accuracy we derive new error bounds based on some additional easily computed moments of the mass distribution these error bounds form the basis for four new macs which can be used to limit the absolute or relative error introduced by each multipole evaluation or with the introduction of some additional data structures the absolute or rms error in the final acceleration of each particle using the sum squares mac to analytically place a 1 bound on the rms error in a series of test models we find that it significantly outperforms the 0 65 bh mac in terms of both accuracy mean rms and maximum error and performance floating point operation count

a greedy randomized adaptive search procedure for the two partition problem we present a greedy randomized adaptive search procedure grasp for the network 2 partition problem the heuristic is empirically compared with the kernighan lin k l method on a wide range of instances the grasp approach dominates k l with respect to solution value on a large percentage of the instances tested the ability of grasp to find optimal solutions is assessed by comparing its performance with a general purpose mixed integer programming package

a new approach for modeling and solving set packing problems in recent years the unconstrained quadratic binary program has emerged as a unified modeling and solution framework for a variety of combinatorial optimization problems experience reported in the literature with several problem classes has demonstrated that this unified approach works surprisingly well in terms of solution quality and computational times often rivaling and sometimes surpassing special purpose methods in this paper we report on the application of this unified framework to set packing problems with a variety of coefficient distributions computational experience is reported illustrating the attractiveness of the approach in particular our results highlight both the effectiveness and robustness of our approach across a wide array of test problems

a sharp error estimate for the fast gauss transform we report an error estimate of the multi dimensional fast gauss transform fgt which is much sharper than that previously reported in the literature an application to the karhunen loeve decomposition in the three dimensional physical space is also presented that shows savings of three orders of magnitude in time and memory compared to a direct solver

on not first not last conditions in disjunctive scheduling abstract this paper is concerned with the development of constraint propagation techniques for the characterization of feasible solutions in disjunctive scheduling in disjunctive scheduling a set of uninterruptible tasks is to be performed on a set of resources each task has a release date a deadline and a fixed processing time each resource can handle only one task at a time some of these propagation techniques are implemented by rules that deduce either mandatory or forbidden sequences between tasks or sets of tasks for instance certain rules indicate whether a given task must or cannot be performed before or after a set of other competing tasks we focus our attention on the latter problem known as the not first not last nf nl problem the genericity of propagation rules is a question of major importance it induces that the result of the overall propagation must not depend on the order in which the inference rules are applied hence one must search for completeness in the time windows narrowing in order to ensure the convergence of the propagation towards a unique fix point an efficient algorithm is proposed it guarantees the completeness of time windows narrowing due to nf nl conditions it has been integrated in a branch and bound procedure to solve job shop instances it has also been tested within several lower bounding procedures computational results are reported and the power and complementarity of nf nl rules with other classical inference rules are discussed

a linear programming and constraint propagation based lower bound for the rcpsp abstract a new destructive lower bound for the resource constrained project scheduling problem rcpsp is presented given are n activities which have to be processed without preemptions during the processing period of an activity constant amounts of renewable resources are needed where the available capacity of each resource type is limited furthermore finish start precedence relations between the activities are given the objective is to determine a schedule with minimal makespan the lower bound calculations are based on two methods for proving infeasibility of a given threshold value t for the makespan the first uses constraint propagation techniques while the second is based on a linear programming formulation a column generation procedure is presented for the linear programming formulation and computational results are reported for an algorithm combining both concepts

lower bounds for resource constrained project scheduling problems abstract a destructive lower bound for the multi mode resource constrained project scheduling problem with minimal and maximal time lags is presented given are n activities which may be processed in different modes without preemptions during processing certain amounts of renewable and non renewable resources are needed where the available capacity of each resource type is limited furthermore minimal and maximal time lags between the activities are given the objective is to determine a schedule with minimal makespan the lower bound calculations are based on two methods for proving infeasibility of a given threshold value t for the makespan the first uses constraint propagation techniques while the second is based on a linear programming formulation which is solved by a column generation procedure computational results are reported for several test instances of the multi mode problem with and without time lags and the single mode version with time lags

constrained multi project plannings problems a lagrangean decomposition approach abstract this paper describes a lagragean decomposition technique for solving multi project planning problems with resource constraints and alternative modes of performing each activity in the projects the decompsition can be useful in several ways from one side it provides bounds on the optimum so that the quality of approximate solutions can be evaluated furthermore in the context of branch and bound algorithms it can be used for more effective fathoming of the tree nodes finally in the modelling perspective the la grangean optimal multipliers can provide insights to project managers as prices for assigning the resources to different projects

a method for the cutting stock problem with different qualities abstract an operations research project at a swedish company is reported the project deals with the problem of allocating wood products with different quality requirements to be cut from wooden boards which in turn consists of a number of quality zones a major difficulty is the existence of distinct time limits since the cross cutting of the boards is done in a real time process in this paper we derive a mathematical model which includes a set packing problem that accurately describes the real world problem this problem is then solved using a combination of lagrangean relaxation and subgradient optimization numerical results for practical problems are reported the results indicate a valid model and satisfactory efficiency of the proposed solution procedure

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

decomposing combinatorial auctions and set packing problems combinatorial auctions allow bidders to bid on bundles of items rather than just on single items the winner determination problem in combinatorial auctions is the problem of determining the allocation of items to bidders such that the sum of the accepted bid prices is maximized this problem is equivalent to the well known maximum weight set packing problem even though these problems are np hard in general they can be solved in polynomial time on instances whose associated item graphs have bounded treewidth called structured item graphs however the tractability of determining whether for a given problem instance a structured item graph of fixed treewidth exists and if so computing one efficiently was an open problem in this article we solve this problem by proving that deciding the existence of structured item graphs is computationally intractable even for treewidth 3 motivated by this unfavorable complexity result we investigate other structural restrictions and we show that the notion of hypertree decomposition a well studied measure of hypergraph cyclicity turns out to be most useful here indeed we show that the winner determination problem is solvable in polynomial time on instances whose dual auction hypergraphs have bounded hypertree width our solution method is based on encoding winner determination via a constraint satisfaction optimization problem and on exhibiting an algorithm to solve this latter problem efficiently for such structurally restricted instances the class of tractable instances identified by our approach while being efficiently recognizable properly contains the class of instances having a structured item graph moreover on the larger class our method solves winner determination with the same asymptotic complexity as the best algorithm proposed in the literature for the subclass of structured item graphs hypertree decompositions can equally profitably be applied to the maximum weight independent set problem which is the dual problem of maximum weight set packing

accelerating t sne using tree based algorithms the paper investigates the acceleration of t sne an embedding technique that is commonly used for the visualization of high dimensional data in scatter plots using two tree based algorithms in particular the paper develops variants of the barnes hut algorithm and of the dual tree algorithm that approximate the gradient used for learning t sne embeddings in o n log n our experiments show that the resulting algorithms substantially accelerate t sne and that they make it possible to learn embeddings of data sets with millions of objects somewhat counterintuitively the barnes hut variant of t sne appears to outperform the dual tree variant

the operational matrices of integration and differentiation for the fourier sine cosine and exponential series for the fourier sine cosine series basis vector varphi t and the fourier exponential series basis vector psi t a linear nonsingular transfor marion t is determined such that psi t t varphi t this result is then used to show that the operational matrices of integration p and q for varphi t and psi t respectively are related by the expression tp qt analogous results are derived for the corresponding operational matrices of differentiation d and r general expressions are derived for t p q d and r

a branch price and cut algorithm for multi mode resource leveling abstract we propose a new mixed integer programming formulation and solution algorithm for a multi mode resource constrained project scheduling problem with availability constraints calendars and the objective to minimize the resource availability cost our model exploits the problem structure and has an exponential number of variables which necessitates a column generation approach the linear programming relaxation is strengthened by adding valid inequalities that need to be carefully separated in order to show the desired effect integer optimal solutions are obtained by an exact state of the art branch price and cut algorithm classical time indexed mixed integer programming formulations for similar problems quite often fail already on instances with only 30 jobs depending on the network complexity and the total freedom of arranging jobs a reason is the typically very weak linear programming relaxation our model can be interpreted as a non trivial dantzig wolfe reformulation of a time indexed formulation in particular for larger instances our reformulation gives significantly tighter dual bounds enabling us to optimally solve instances with 50 multi mode jobs this outperforms the classical formulation by far

application of legendre series to the optimal control of integrodifferential equations this paper extends the application of shifted legendre series expansions to integrodifferential systems with quadratic performance index based on the shifted legendre series a directly computational formulation for evaluating the optimal control and trajectory is developed the formulation is straightforward and convenient for digital computation an example is given to demonstrate the applicability of the proposed method

on a paper by christofides et al for solving the multiple resource constrained single project scheduling problem abstract in a recently published article in ejor christofides et al cat present a depth first search branch and bound solution procedure for the multiple resource constrained single project scheduling problem while there are many important contributions in this paper we show by counterexample that if the branching strategy described by the authors is used the optimal solution might not result computational experience on a set of test problems appearing in the open literature is reported both with the original branching strategy suggested by the authors and a modified branching strategy that we propose the modified strategy guarantees the determination of the optimal solution in all instances of the problem at the expense of an increase in node evaluations and average cpu time computational results using the revised procedure and a hybrid breadth first search procedure also investigated by cat are reported

a random activity network generator exact and heuristic procedures are often developed to obtain optimal and near optimal solutions to decision problems modeled as activity networks testing the accuracy and efficiency of these procedures requires the use of activity networks with various sizes structures and parameters the size of the network is determined by its number of nodes and arcs where the structure is chosen from the set of all structures for the specified network size the network parameters depend on the nature of the decision problem often it is desirable for test problems to be generated at random from the space of all feasible networks this paper deals with the problem of generating the size and structure of the network at random from the space of all feasible networks it develops a theory which guarantees the randomness of the network structure the theory is the basis for two methods one can be used to generate dense networks where the other is used to generate nondense networks the methods which are practical a

consolidated optimization algorithm for resource constrained project scheduling problems abstract resource constrained project scheduling problems rcpsps represent an important class of practical problems over the years many optimization algorithms for solving them have been proposed with their performances evaluated using well established test instances with various levels of complexity while it is desirable to obtain a high quality solution and fast rate of convergence from an optimization algorithm no single one performs well across the entire space of instances furthermore even for a given algorithm the optimal choice of its operators and control parameters may vary from one problem to another to deal with this issue we present a generic framework for solving rcpsps in which various meta heuristics each with multiple search operators are self adaptively used during the search process and more emphasis is placed on the better performing algorithms and their underlying search operators to further improve the rate of convergence and introduce good quality solutions into the population earlier a local search approach is introduced the experimental results clearly indicate the capability of the proposed algorithm to attain high quality results using a small population compared with several state of the art algorithms the proposed one delivers the best solutions for problems with 30 and 60 activities and is very competitive for those involving 120 activities

solutions of convolution integral and fredholm integral equations via double fourier series double fourier series are developed to approximate the solutions of the convolution integral and fredholm integral equations properties of fourier series are first briefly presented and the operational matrix of integration together with the product operational matrix is utilized to reduce the computation of integral equations to a set of simultaneous linear algebraic equations the method is computationally very attractive and applications are demonstrated through illustrative examples

path relinking for unconstrained binary quadratic programming abstract this paper presents two path relinking algorithms to solve the unconstrained binary quadratic programming ubqp problem one is based on a greedy strategy to generate the relinking path from the initial solution to the guiding solution and the other operates in a random way we show extensive computational results on five sets of benchmarks including 31 large random ubqp instances and 103 structured instances derived from the maxcut problem comparisons with several state of the art algorithms demonstrate the efficacy of our proposed algorithms in terms of both solution quality and computational efficiency it is noteworthy that both algorithms are able to improve the previous best known results for almost 40 percent of the 103 maxcut instances

multi manifold discriminant isomap for visualization and classification isomap aims to recover the intrinsic geometric structure of manifold by preserving geodesic distances between all pairs of data points however it is an unsupervised dimensionality reduction method usually using class label information can increase the discriminating capability hence a new supervised isomap is proposed in this paper dubbed multi manifold discriminant isomap mmd isomap first data points are partitioned into different manifolds according to their class label information then mmd isomap aims at seeking an optimal nonlinear subspace to preserve the geometrical structure of each manifold according to the isomap criterion meanwhile to enhance the discriminating capability by maximizing the distances between data points of different manifolds finally the corresponding optimization problem is solved by using a majorization algorithm furthermore two new numerical metrics are designed to measure the performance of dimensionality reduction method in both visualization and classification experiments mmd isomap achieves improved performance over many state of the art methods preserve the geometrical structure and enhance the discriminating capability smacof algorithm is introduced to solve the optimization problem two metrics are designed to evaluate dimensionality reduction methods experiments show the effectiveness of the method in visualization and classification

linear programming based algorithms for preemptive and non preemptive rcpsp abstract in this paper the rcpsp resource constrained project scheduling problem is solved using a linear programming model each activity may or may not be preemptive each variable is associated to a subset of independent activities antichains the properties of the model are first investigated in particular conditions are given that allow a solution of the linear program to be a feasible schedule from these properties an algorithm based on neighbourhood search is derived one neighbour solution is obtained through one simplex pivoting if this pivoting preserves feasibility methods to get out of local minima are provided the solving methods are tested on the psplib instances in a preemptive setting and prove efficient they are used when preemption is forbidden with less success and this difference is discussed

analysis and optimal control of time varying systems via chebyshev polynomials abstract the operational properties of the forward and backward integration and the product of chebyshev polynomials are derived these properties are applied to the analysis and optimal control of time varying linear systems by the approximation of time functions by truncated chebyshev series due to the unique property of the chebyshev polynomials excellent results are obtained as demonstrated by examples

grasp for set packing problems abstract the principles of the greedy randomized adaptative search procedure grasp metaheuristic are instantiated for the set packing problem we investigated several construction phases and evaluated improvements based on advanced strategies these improvements include a self tuning procedure using reactive grasp an intensification procedure using path relinking and a procedure involving the diversification of the selection using a learning process two sets of various numerical instances were used to perform the computational experiments the first set contains randomly generated instances while the second includes instances relating to real problems in railway planning no metaheuristic has previously been applied to this combinatorial problem consequently we have discussed grasp s performances both in relation to lower upper bounds and to the results obtained with cplex when such results are available our analysis based on the average performances observed shows the impact of the suggested strategies and indicates the configuration that produces the best results

hierarchical gtm constructing localized nonlinear projection manifolds in a principled way it has been argued that a single two dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets and therefore a hierarchical visualization system is desirable in this paper we extend an existing locally linear hierarchical visualization system phivis in several directions 1 we allow for nonlinear projection manifolds the basic building block is the generative topographic mapping gtm 2 we introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree general training equations are derived regardless of the position of the model in the tree 3 using tools from differential geometry we derive expressions for local directional curvatures of the projection manifold like phivis our system is statistically principled and is built interactively in a top down fashion using the em algorithm it enables the user to interactively highlight those data in the ancestor visualization plots which are captured by a child model we also incorporate into our system a hierarchical locally selective representation of magnification factors and directional curvatures of the projection manifolds such information is important for further refinement of the hierarchical visualization plot as well as for controlling the amount of regularization imposed on the local models we demonstrate the principle of the approach on a toy data set and apply our system to two more complex 12 and 18 dimensional data sets

analysis of linear time varying systems and bilinear systems via fourier series a method for finding an approximate solution of linear time varying systems and bilinear systems via fourier series is proposed properties of fourier series are first briefly presented and the operational matrix for integration together with the product operational matrix are utilized to reduce the dynamical equation of a linear time varying system or bilinear system to a set of simultaneous linear algebraic equations illustrative examples are also given

a new error estimate of the fast gauss transform the fast gauss transform of l greengard and j strain siam j sci statist comput 12 1991 pp 79 94 reduces the computational complexity of the evaluation of the sum of n gaussians at m points in d dimensional space from cal o mn to cal o m n floating point operations in this note we provide numerical evidence that the error estimate of lemma 2 1 in siam j sci statist comput 12 1991 pp 79 94 is erroneous and then proceed to calculate a replacement error estimate for the fast gauss transform incorporating an improved upper bound for hermite functions

project scheduling under partially renewable resource constraints we consider a generalization of the classical resource constrained project scheduling problem we introduce so called partially renewable resources by assuming for each resource a capacity on subsets of periods the concept of partially renewable resources is a fundamental tool in order to make e g timetabling and shift scheduling aspects amenable to project scheduling in addition partially renewable resources serve to model complicated labor regulations furthermore they cover traditional renewable and nonrenewable resource constraints as special cases we consider makespan minimization as objective for the exact solution of the problem we employ a basic enumeration scheme in order to speed up convergence we formulate bounds which take into account future resource consumption of partially renewable resources moreover we generalize the serial scheduling scheme in order to get fast approximation methods a rigorous assessment of the procedures is provided by solving progen instances generated under a full factorial test design besides the well known problem parameters we employ additionally three parameters which control the generation of partially renewable resources

an effective approach to the optimal control problem for time varying linear systems via taylor series the taylor series is used for the solution of the optimal control problem for time varying linear systems instead of solving the state transition matrix from the state equation with a terminal condition the present approach first transforms the terminal condition into an initial condition and then solves the initial value problem to find the transition matrix this approach leads lo a recursive algebraic formulation for the transition matrix and only an inverse matrix of small dimension 2n 2n appears in this formulation thus a closed loop control law is obtained without solving the non linear riccati equation and the matrix to be inverted has only small dimension 2n 2n the present approach is of great interest because of its simplicity and numerical stability

geodesic distance based fuzzy c medoid clustering searching for central points in graphs and high dimensional data clustering high dimensional data and identifying central nodes in a graph are complex and computationally expensive tasks we utilize k nn graph of high dimensional data as efficient representation of the hidden structure of the clustering problem initial cluster centers are determined by graph centrality measures cluster centers are fine tuned by minimizing fuzzy weighted geodesic distances the shortest path based representation is parallel to the concept of transitive closure therefore our algorithm is capable to cluster networks or even more complex and abstract objects based on their partially known pairwise similarities the algorithm is proven to be effective to identify senior researchers in a co author network central cities in topographical data and clusters of documents represented by high dimensional feature vectors

transfer function matrix identification in mimo systems via shifted legendre polynomials a general algorithm is presented for the identification of the parameters in the transfer function matrix of a multi input multi output mimo system the approach adopted is that of expanding the system input and output variables in shifted legendre series the feasibility of the method lies in the generation of linear algebraic equations in the unknown parameters and initial conditions by means of an elegant operational matrix which relates shifted legendre polynomials to their integrals an example is included to illustrate the applicability of the proposed method

scheduling of design projects with uncertain number of iterations abstract a short product design cycle is critical to the success of companies in the era of time based competition the underlying design activities however are often interlinked and quite uncertain for example some activities may have to be iterated several times to meet the design criteria furthermore time critical projects suffer the risk of failure if they cannot meet established target dates generating good and robust schedules is thus critical especially under the concurrent engineering paradigm where the delay of a single task may have a domino effect on subsequent tasks and on other projects sharing designers and or resources this paper studies the scheduling of design projects with uncertain number of iterations while managing design risks a separable problem formulation that balances modeling accuracy and computation complexity is created with the goal to minimize project tardiness and risk penalties an optimization based methodology that combines lagrangian relaxation stochastic dynamic programming and ordinal optimization is developed numerical results supported by simulation demonstrate that near optimal solutions are obtained and uncertainties are effectively managed for problems of practical sizes

analysis and optimal control of time varying linear systems via shifted legendre polynomials this paper extends the application of shifted legendre polynomial expansion to time varying systems the extension is achieved through representing the product of two shifted legendre series in a new shifted legendre series with this treatment of the product of two time functions the operational properties of the shifted legendre polynomials are fully applied to the analysis and optimal control of time varying linear systems with quadratic performance index

numerical solution of fractional differential equations using the generalized block pulse operational matrix the riemann liouville fractional integral for repeated fractional integration is expanded in block pulse functions to yield the block pulse operational matrices for the fractional order integration also the generalized block pulse operational matrices of differentiation are derived based on the above results we propose a way to solve the fractional differential equations the method is computationally attractive and applications are demonstrated through illustrative examples

an effective branch and price algorithm for the preemptive resource constrained project scheduling problem based on minimal interval order enumeration in this paper we address the preemptive resource constrained project scheduling problem prcpsp prcpsp requires a partially ordered set of activities to be scheduled using limited renewable resources such that any activity can be interrupted and later resumed without penalty the objective is to minimize the project duration this paper proposes an effective branch and price algorithm for solving prcpsp based upon minimal interval order enumeration involving column generation as well as constraint propagation experiments conducted on various types of instances have given very satisfactory results our algorithm is able to solve to optimality the entire set of j30 bl and pack instances while satisfying the preemptive requirement furthermore this algorithm provides improved best known lower bounds for some of the j60 j90 and j120 instances in the non preemptive case rcpsp

a set packing model for the ground holding problem in congested networks abstract air traffic flow management atfm consists of several activities performed by control authorities in order to reduce delays due to traffic congestion ground holding decisions restrict certain flights from tacking off at the scheduled departure time if congestion is expected at the destination airport they are motivated by the fact that it is safer to hold an aircraft on the ground than in the air several integer linear programming models have been proposed to efficiently solve the ground holding problem ghp in this paper we investigate a set packing formulation of the ghp and design a branch and cut algorithm to solve the problem in high congestion scenarios i e when lack of capacity induces flights cancellation the constraint generation is carried out by heuristically solving the separation problem associated with a large class of rank inequalities this procedure exploits the special structure of the ghp s intersection graphs the computational results indicate that the proposed algorithm outperforms other algorithms in which flight cancellation has been allowed

project scheduling with resource constraints a branch and bound approach abstract this paper describes a branch and bound algorithm for project scheduling with resource constraints the algorithmis based on the idea of using disjunctive arcs for resolving conflicts that are created whenever sets of activities have to be scheduled whose total resource requirements exceed the resource availabilities in some periods four lower bounds are examined the first is a simple lower bound based on longest path computations the second and third bounds are derived from a relaxed integer programming formulation of the problem the second bound is based on the linear programming relaxation with the addition of cutting planes and the third bound is based on a lagrangean relaxation of the formulation this last relaxation involves a problem which is a generalization of the longest path computation and for which an efficient though not polynomial algorithm is given the fourth bound is based on the disjunctive arcs used to model the problem as a graph we report computational results on the performance of each bound on randomly generated problems involving up to 25 activities and 3 resources