a tabu search approach for the flow shop scheduling problem in this paper we propose a tabu search approach for solving the permutation flow shop scheduling problem the proposed implementation of the tabu search approach suggests simple techniques for generating neighborhoods of a given sequence and a combined scheme for intensification and diversification that has not been considered before these new features result in an implementation that improves upon previous tabu search implementations that use mechanisms of comparable simplicity also better results were obtained than those produced by a simulated annealing algorithm from the literature

a multi objective simulated annealing algorithm for scheduling in flowshops to minimize the makespan and total flowtime of jobs in this paper we consider the problem of permutation flowshop scheduling with the objectives of minimizing the makespan and total flowtime of jobs and present a multi objective simulated annealing algorithm mosa two initial sequences are obtained by using simple and fast existing heuristics supplemented by the implementation of three improvement schemes each of the two resultant sequences corresponds to a possible non dominated solution containing the minimum value of one objective function these sequences taken one at a time are given as the starting sequences to the mosa the mosa seeks to obtain non dominated solutions through the implementation of a simple probability function that attempts to generate solutions on the pareto optimal front the probability function selects probabilistically a particular objective function considering which the algorithm uncovers non dominated solutions moreover the probability function is varied in such a way that the entire objective function space is covered uniformly so as to obtain as many non dominated and well dispersed solutions as possible the parameters in the proposed mosa are determined after conducting a pilot study two variants of the proposed algorithm called mosa i and mosa ii with different parameter settings with respect to the temperature and epoch length are considered in the performance evaluation of algorithms in order to evaluate mosa i and mosa ii we have made use of 90 benchmark problems provided by taillard eur j operation res 64 1993 278 after an extensive literature survey the following flowshop multi objective scheduling algorithms have been identified as benchmark procedures a mogls multi objective genetic local search by ishibuchi and murata ieee trans syst man cybernet c appl rev 28 1998 392 b elitist non dominated sorting genetic algorithm enga by bagchi multi objective scheduling by genetic algorithms kluwer academic publishers 1999 c gpw gradual priority weighting approach by chang hsieh and lin int j prod econ 79 2002 171 and d a posteriori approach based heuristic by framinan leisten and ruiz usano eur j operation res 141 2002 559 the non dominated sets obtained from each of the existing benchmark algorithms and the proposed mosa i and mosa ii are compared and subsequently combined to obtain a net non dominated front it is found that most of the solutions in the net non dominated front are yielded by mosa i and mosa ii in addition it is noteworthy that both mosa i and mosa ii require less computational effort than the mogls enga and gpw

decomposition formulas associated with the lauricella multivariable hypergeometric functions by making use of some techniques based upon certain inverse pairs of symbolic operators the authors investigate several decomposition formulas associated with lauricella s hypergeometric functions f b r f c r and f d r in r variables in the three variable case when r 3 some of these operational representations are constructed and applied in order to derive the corresponding decomposition formulas with the help of these inverse pairs of symbolic operators a total of 15 decomposition formulas are found which are expressed as products of hypergeometric functions of the gauss and appell types

linear dynamically varying lq control of nonlinear systems over compact sets linear quadratic controllers for tracking natural and composite trajectories of nonlinear dynamical systems evoluting over compact sets are developed typically such systems exhibit complicated dynamics i e have nontrivial recurrence the controllers which use small perturbations of the nominal dynamics as input actuators are based on modeling the tracking error as a linear dynamically varying ldv system necessary and sufficient conditions for the existence of such a controller are linked to the existence of a bounded solution to a functional algebraic riccati equation fare it is shown that despite the lack of continuity of the asymptotic trajectory relative to initial conditions the cost to stabilize about the trajectory as given by the solution to the fare is continuous an ergodic theory method for solving the fare is presented furthermore it is shown that wrapping the ldv controller around the nonlinear system secures a stable tracking dynamics finally an example of controlling the henon map to follow an aperiodic orbit is presented

efficient heuristics for flowshop sequencing with the objectives of makespan and flowtime minimisation in this paper we analyse the performance of flowshop sequencing heuristics with respect to the objectives of makespan and flowtime minimisation for flowtime minimisation we propose the strategy employed by the neh heuristic to construct partial solutions results show that this approach outperforms the common fast heuristics for flowtime minimisation while performing similarly or slightly worse than others which on reward prove to be much more cpu time consuming additionally the suggested approach is well balanced with respect to makespan and flowtime minimisation based on the previous results two algorithms are proposed for the sequencing problem with multiple objectives makespan and flowtime minimisation these algorithms provide the decision maker with a set of heuristically efficient solutions such that he she may choose the most suitable sequence for a given ratio between costs associated with makespan and those assigned to flowtime computational experience shows both algorithms to perform better than the current heuristics designed for the two criteria problem

bifurcation to infinitely many sinks this paper considers one parameter families of diffeomorphisms ft in two dimensions which have a curve of dissipative saddle periodic pointspt i e ftn pt pt and detdftn pt 1 the family is also assumed to create new homoclinic intersections of the stable and unstable manifolds ofpt as the parameter varies throught0 gavirlov and silnikov proved that if the new homoclinic intersections are created nondegenerately att0 then there is an infinite cascade of periodic sinks i e there are parameter valuestn accumulating att0 for which there is a sink of periodn gs2 sect 4 we show that this result is true for real analytic diffeomorphisms even if the homoclinic intersection is created degenerately we give computer evidence to show that this latter result is probably applicable to the henon map fora near 1 392 andb equal 0 3

a tabu search and a genetic algorithm for solving a bicriteria general job shop scheduling problem this paper deals with a general job shop scheduling problem with multiple constraints coming from printing and boarding industry the objective is the minimization of two criteria the makespan and the maximum lateness and we are interested in finding an approximation of the pareto frontier we propose a fast and elitist genetic algorithm based on nsga ii for solving the problem the initial population of this algorithm is either randomly generated or partially generated by using a tabu search algorithm that minimizes a linear combination of the two criteria both the genetic and the tabu search algorithms are tested on benchmark instances from flexible job shop literature and computational results show the interest of both methods to obtain an efficient and effective resolution method

structural stability of linear dynamically varying ldv controllers abstract ldv systems are linear systems with parameters varying according to a nonlinear dynamical system this paper examines the robust stability of such systems in the face of perturbations of the nonlinear system three classes of perturbations are examined differentiable functions lipschitz continuous functions and continuous functions it is found that in the first two cases the system remains stable whereas if the perturbations are among continuous functions the closed loop may not be asymptotically stable but instead is asymptotically bounded with the diameter of the residual set bounded by a function that is continuous in the size of the perturbation it is also shown that in the case of differential perturbations the resulting optimal ldv controller is continuous in the size of the perturbation an example is presented that illustrates the continuity of the variation of the controller in the case of a nonstructurally stable dynamical system

new solution methods for single machine bicriteria scheduling problem minimization of average flowtime and number of tardy jobs we consider the bicriteria scheduling problem of minimizing the number of tardy jobs and average flowtime on a single machine this problem which is known to be np hard is important in practice as the former criterion conveys the customer s position and the latter reflects the manufacturer s perspective in the supply chain we propose four new heuristics to solve this multiobjective scheduling problem two of these heuristics are constructive algorithms based on beam search methodology the other two are metaheuristic approaches using a genetic algorithm and tabu search our computational experiments indicate that the proposed beam search heuristics find efficient schedules optimally in most cases and perform better than the existing heuristics in the literature

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

nonlinear tracking over compact sets with linear dynamically varying boldmath h infty control linear dynamically varying h infty controllers are developed for tracking natural trajectories of a broad class of nonlinear systems defined over compact sets it is shown that the existence of a suboptimal h infty controller is related to the existence of a bounded solution to a functional algebraic riccati equation even though nonlinear systems running over compact sets could exhibit sensitive dependence on initial conditions the riccati solution is continuous in the suboptimal case but it may be discontinuous in the optimal case

two machine flow shop scheduling with two criteria maximum earliness and makespan abstract in this study we address the problem of minimizing makespan and maximum earliness simultaneously in a two machine flow shop environment we develop a branch and bound procedure that generates all efficient solutions with respect to two criteria we propose several lower and upper bounding schemes to enhance the efficiency of the algorithm we also propose a heuristic procedure that generates approximate efficient solutions our computational results reveal that the branch and bound procedure is capable of solving problems with up to 25 jobs and the heuristic procedure produces approximate efficient solutions that are very close to exact efficient solutions in very small computation times

some reduction and transformation formulas for the appell hypergeometric function f2 abstract an integral representation of the appell series f 2 1 2 1 2 x y is used here to obtain several finite sum expansions in terms of the less cumbersome hypergeometric functions 2f1 and 3f2 in the case when the parameters 1 2 1 and 2 are all positive integers some of our results may be seen as a generalization of the finite sum expansions of the appell series f 1 obtained by cuyt et al j comput appl math 5 1999 213 219 other important consequences as well as potential applications of our results are discussed and a listing of some useful reduction and transformation formulas is provided

a new heuristic method for the flow shop sequencing problem abstract a new heuristic method is presented for solving the m machine n job flow shop scheduling problem this method named spirit is composed of two phases the first finds an initial sequence using an analogy with the travelling salesman problem and the second tries to improve this solution using taboo search techniques the results of the heuristic are compared with those from other well known methods

generating efficient schedules for identical parallel machines involving flow time and tardy jobs this paper considers the problem of generating a set of efficient non dominated schedules on identical parallel machines involving total flow time and total number of tardy jobs in view of the np hard nature of this problem heuristic algorithms are proposed for its solution two evaluation methods that provide a scheme by which multiple non dominated sets can be compared are described and used to compare the performance of the proposed algorithms results of several experiments demonstrate the capability of the proposed algorithms and evaluation methodologies to address the problem at hand

on fundamental solutions for multidimensional helmholtz equation with three singular coefficients abstract the main result of the present paper is the construction of fundamental solutions for a class of multidimensional elliptic equations with three singular coefficients which could be expressed in terms of a confluent hypergeometric function of four variables in addition the order of the singularity is determined and the properties of the found fundamental solutions that are necessary for solving boundary value problems for degenerate elliptic equations of second order are found

multiple and bicriteria scheduling a literature survey abstract real life scheduling problems require the decision maker to consider a number of criteria before arriving at any decision a solution which is optimal with respect to a given criterion might be a poor candidate for some other the trade offs involved in considering several different criteria provide useful insights to the decision maker thus considering problems with more than one criterion is more relebant in the context of real life scheduling problems surprisingly research in this important field has been scarce when compared to research in single criterion scheduling in this paper we provide a detailed literature survey of multiple and bicriteria problems in scheduling we also provide a broad classification scheme for scheduling problems

performance analysis for multihop relaying channels with nakagami m fading ergodic capacity upper bounds and outage probability this paper investigates the ergodic capacity and outage probability performance of multihop relaying networks subject to independent non identically distributed nakagami m fading particularly we exploit a typical amplify and forward relaying system with an arbitrary number of cooperative intermediate relays and no direct link between the source and destination nodes in our analysis channel state information is assumed to be known only at the receiving nodes and the cooperative links may have distinct fading parameters and distinct average signal to noise ratio snr levels in this context a tight closed form upper bound expression for the ergodic capacity is derived for this firstly the moment generating function mgf of the inverse of the end to end snr is obtained in closed form then making use of this expression an upper bound for the ergodic capacity is attained thereafter we investigate the end to end outage probability performance of the multihop relaying channels in nakagami m fading by making use of the aforementioned mgf expression finally monte carlo simulation results are provided and show the tightness of the proposed bounds

genetic local search for multi objective flowshop scheduling problems this paper addresses flowshop scheduling problems with multiple performance criteria in such a way as to provide the decision maker with approximate pareto optimal solutions genetic algorithms have attracted the attention of researchers in the nineties as a promising technique for solving multi objective combinatorial optimization problems we propose a genetic local search algorithm with features such as preservation of dispersion in the population elitism and use of a parallel multi objective local search so as intensify the search in distinct regions the concept of pareto dominance is used to assign fitness to the solutions and in the local search procedure the algorithm is applied to the flowshop scheduling problem for the following two pairs of objectives i makespan and maximum tardiness ii makespan and total tardiness for instances involving two machines the algorithm is compared with branch and bound algorithms proposed in the literature for such instances and larger ones involving up to 80 jobs and 20 machines the performance of the algorithm is compared with two multi objective genetic local search algorithms proposed in the literature computational results show that the proposed algorithm yields a reasonable approximation of the pareto optimal set

complexity of single machine multi criteria scheduling problems abstract we examine the complexity of scheduling problems when more than one measure of performance is appropriate the criteria we study are maximal tardiness flowtime number of tardy jobs tardiness and the weighted counterparts of the last three measures the machine environment is restricted to a single machine complexity results are given for secondary criterion bicriteria and weighted criteria approaches for all combinations of measures of the problems examined only six remain open

applications of the operator h α β to the humbert double hypergeometric functions by making use of some techniques based upon certain new inverse pairs of symbolic operators the authors investigate several decomposition formulas associated with humbert hypergeometric functions f 1 f 2 f 3 j 1 j 2 x 1 and x 2 these operational representations are constructed and applied in order to derive the corresponding decomposition formulas with the help of these inverse pairs of symbolic operators as many as 34 decomposition formulas are found euler type integrals connected with humbert functions are also presented

symbolic operational images and decomposition formulas for hypergeometric functions based upon the classical derivative and integral operators we introduce a new operator which allows the derivation of new symbolic operational images for hypergeometric functions by means of these symbolic operational images a number of decomposition formulas involving quadruple series are then found other closely related results are also considered