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

systems of p laplacian differential inclusions with large diffusion abstract in this paper we consider coupled systems of p laplacian differential inclusions and we prove under suitable conditions that a homogenization process occurs when diffusion parameters become arbitrarily large in fact we obtain that the attractors are continuous at infinity on l 2 l 2 topology with respect to the diffusion coefficients and the limit set is the attractor of an ordinary differential problem

dunford pettis properties hilbert spaces and projective tensor products we study complete continuity properties of operators onto 2 and prove several results in the dunford pettis theory of jb triples and their projective tensor products culminating in characterisations of the alternative dunford pettis property for e f where e and f are jb triples

weakly compact orthogonality preservers on c algebras we establish a complete description of weakly compact orthogonality preserving operators from a c algebra a or a jb algebra to a jb triple e we prove that any such operator is the sum of a series of mutually orthogonal triple homomorphisms from a to a certain peirce 2 subspace of e multiplied by a mutually orthogonal norm null sequence in e which enjoy certain operator commutativity relations

some results of the worst case analysis for flow shop scheduling abstract known approximation algorithms recommended for the permutation flow shop problem with the weighted sum of completion times have a worst case performance ratio which is unknown or known but unlimited we propose new algorithms with this ratio equal to m k k where k is the worst case performance ratio of an algorithm which solves an auxiliary k machine problem worst case analyses of other approximation algorithms for the mean completion time and the makespan criteria are also 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

heuristics for scheduling in flowshop with multiple objectives abstract most of the heuristics for flowshop scheduling aim at minimizing makespan however scheduling with multiple objectives such as that of minimizing makespan total flowtime and machine idletime is more effective in reducing the total scheduling cost in this article we first address the problem of scheduling to minimize makespan and total flowtime and propose a new heuristic algorithm a heuristic preference relation is developed as the basis for the heuristic so that only the potential job interchanges are checked for possible improvement with respect to these two objectives the proposed as well as the existing heuristics are evaluated in a large number of randomly generated large sized problems the proposed heuristic algorithm is then extended to cover the problem of scheduling to minimize makespan total flowtime and machine idletime the results of the experimental investigation of the evaluation of this heuristic algorithm and the existing heuristic in meeting these objectives are also reported it is found that both the proposed heuristics are more effective than the existing one for scheduling with multiple objectives

similarity solutions of an equation describing ice sheet dynamics this paper focuses upon the derivation of the similarity solutions of a nonlinear equation associated with a free boundary problem arising in glaciology we present a potential symmetry analysis of this second order nonlinear degenerate parabolic equation related to non newtonian ice sheet dynamics in the isothermal case a full classical and also a non classical symmetry analysis are presented after obtaining a general result connecting the thickness function of the ice sheet and the solution of the nonlinear equation without any unilateral formulation a particular example of a similarity solution to a problem formulated with cauchy boundary conditions is described this allows us to obtain several qualitative properties of the free moving boundary in the presence of an accumulation ablation function with realistic physical properties

relatively weakly open sets in closed balls of banach spaces and real jb triples of finite rank we prove that given a real jb triple x there exists a nonempty relatively weakly open subset of the closed unit ball of x with diameter less than 2 if and only if the banach space of x is isomorphic to a hilbert space moreover we give the structure of real jb triples whose banach spaces are isomorphic to hilbert spaces such real jb triples are also characterized in two different purely algebraic ways

on a doubly nonlinear parabolic obstacle problem modelling ice sheet dynamics this paper deals with the weak formulation of a free moving boundary problem arising in theoretical glaciology considering shallow ice sheet flow we present the mathematical analysis and the numerical solution of the second order nonlinear degenerate parabolic equation modelling in the isothermal case the ice sheet non newtonian dynamics an obstacle problem is then deduced and analyzed the existence of a free boundary generated by the support of the solution is proved and its location and evolution are qualitatively described by using a comparison principle and an energy method then the solutions are numerically computed with a method of characteristics and a duality algorithm to deal with the resulting variational inequalities the weak framework we introduce and its analysis both qualitative and numerical are not restricted to the simple physics of the ice sheet model we consider nor to the model dimension they can be successfully applied to more realistic and sophisticated models related to other geophysical settings

separate weak continuity of the triple product in dual real jb triples we prove that if e is a real jb triple having a predual e then e is the unique predual of e and the triple product on e is separately sigma e e continuous

on a degenerate parabolic hyperbolic system in glaciology giving rise to a free boundary the authors present and study a problem which models the evolution of the ice sheet in the laurentide they consider a one dimensional problem in 3 dimensional space which involves three parameters the ice thickness h the amount of water flux q and the accumulated ice velocity considering the mass conservation law the momentum or balance equations and introducing the special glaciology relations already described in the specialized literature they write the coupled system involving these three unknowns after some computations they are led to some coupled system of parabolic and hyperbolic nonlinear and possibly degenerate equations initial and boundary conditions are introduced which correspond to the special case of the hudson region replacing the data by piecewise constant approximations with respect to the time variable the authors then present some stationary discretized coupled system for which they define the notion of weak solution the purpose of this work is to obtain some existence result for this discretized system this is done using an iterative scheme which decouples the three equations an existence result is proved for each of these decoupled equations the first equation for the discretization of h is studied using the notion of super and subsolution and comparison principles the second equation for the discretization of q involves a maximal monotone graph and is studied first by replacing this multivalued graph by some single valued maximal monotone graph and then by passing to the limit the study of the last equation is very easy then uniform estimates are established on these approximate solutions this leads to an asymptotic result which finally proves the existence result for the original discretized system the last part is devoted to the qualitative study of the function q which must be nonnegative the authors prove the existence of a boundary layer corresponding to the boundary of the region q 0 the present work justifies earlier observations made by the second author when solving the problem numerically

multi objective sequence dependent setup times permutation flowshop a new algorithm and a comprehensive study abstract the permutation flowshop scheduling problem has been thoroughly studied in recent decades both from single objective as well as from multi objective perspectives to the best of our knowledge little has been done regarding the multi objective flowshop with pareto approach when sequence dependent setup times are considered as setup times and multi criteria problems are important in industry we must focus on this area we propose a simple yet powerful algorithm for the sequence dependent setup times flowshop problem with several criteria the presented method is referred to as restarted iterated pareto greedy or ripg and is compared against the best performing approaches from the relevant literature comprehensive computational and statistical analyses are carried out in order to demonstrate that the proposed ripg method clearly outperforms all other algorithms and as a consequence it is a state of art method for this important and practical scheduling problem

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

theory and methodology a bicriteria approach to the two machine flow shop scheduling problem in this paper we address the problem of minimizing makespan and sum of completion times simultaneously in a two machine flow shop environment we formulate the problem as a bicriteria scheduling problem and develop a branch and bound procedure that iteratively solves restricted single objective scheduling problems until the set of efficient solutions is completely enumerated we report computational results and explore certain properties of the set of efficient solutions we then discuss their implications for the decision maker

a least squares finite element method for a nonlinear stokes problem in glaciology a stationary stokes problem with nonlinear rheology and with mixed no slip and sliding basal boundary conditions is considered the model describes the flow of ice in glaciers and ice sheets a least squares finite element method is developed and analyzed the method does not require that the finite element spaces satisfy an inf sup condition moreover the usage of negative sobolev norm in the least squares functional allows for the use of standard piecewise polynomials spaces for both the velocity and pressure approximations a picard type iterative method is used to linearize the stokes problem it is shown that the linearized least squares functional is coercive and continuous in an appropriate solution space so the existence and uniqueness of a weak solution immediately follows as do optimal error estimates for finite element approximations numerical tests are provided to illustrate the theory

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

the two and m machine flowshop scheduling problems with bicriteria of makespan and mean flowtime abstract this paper considers the flowshop scheduling problem with the objective of minimizing the weighted sum of makespan and mean flowtime even though the two machine problem has been addressed and several heuristics have been established in the literature these heuristics have not been compared in this paper a comparison of these available heuristics in the literature is conducted moreover three new heuristic algorithms are proposed which can be utilized for both the two machine and m machine problems computational experiments indicate that the proposed heuristics are superior to all the existing heuristics in the literature including a genetic algorithm two dominance relations are also developed one for the two machine and the other for the three machine problem experimental results show that both relations are efficient

automatic continuity of biorthogonality preservers between compact c algebras and von neumann algebras abstract we prove that every biorthogonality preserving linear surjection between two dual or compact c algebras or between two von neumann algebras is automatically continuous

a bicriteria two machine permutation flowshop problem the problem attacked in this paper is the scheduling of n jobs on two machines which are assumed to be continuously available all jobs are available at the beginning of the scheduling period setup times are included in the processing times no preemption of jobs is allowed the objective is the minimization of a weighted combination of the average job flowtime and the schedule makespan three branch and bound bb and each one of these problems is solved for five different levels of the weighting factor an analysis into the resulting efficient points is also included an improved version of fsh1 called fsh2 is developed and both heuristics are subjected to extensive numerical experimentation

an exact parallel method for a bi objective permutation flowshop problem in this paper we propose a parallel exact method to solve bi objective combinatorial optimization problems this method has been inspired by the two phase method which is a very general scheme to optimally solve bi objective combinatorial optimization problems here we first show that applying such a method to a particular problem allows improvements secondly we propose a parallel model to speed up the search experiments have been carried out on a bi objective permutation flowshop problem for which we also propose a new lower bound