minimizing total weighted completion time in a two machine flow shop scheduling under simple linear deterioration abstract in this paper we address a two machine flow shop scheduling problem under simple linear deterioration by a simple linear deterioration function we mean that the processing time of a job is a simple linear function of its execution start time the objective is to find a sequence that minimizes total weighted completion time optimal schedules are obtained for some special cases for the general case several dominance properties and two lower bounds are derived to speed up the elimination process of a branch and bound algorithm a heuristic algorithm is also proposed to overcome the inefficiency of the branch and bound algorithm computational analysis on randomly generated problems is conducted to evaluate the branch and bound algorithm and heuristic algorithm

critical exponents of self avoiding walks on a family of truncated n simplex lattices the authors have studied self avoiding walks saws on a family of truncated n simplex lattices which provide a family of fractals in which the fractal dimension d can be varied to a wide range while the spectral dimension d is held almost fixed by means of exact renormalisation group transformations they have calculated the critical exponents nu alpha and gamma and the connectivity constant mu of the saws for n 5 and 6 they propose an approximate theory for calculating the critical exponents of the saws on fractals which is expected to be accurate at large values of n they show that the theory gives results which are in good agreement with exact values even for small values of n and leads to simple closed relations for the exponents

on optimal fourth order iterative methods free from second derivative and their dynamics in this paper new fourth order optimal root finding methods for solving nonlinear equations are proposed the classical jarratt s family of fourth order methods are obtained as special cases we then present results which describe the conjugacy classes and dynamics of the presented optimal method for complex polynomials of degree two and three the basins of attraction of existing optimal methods and our method are presented and compared to illustrate their performance

the collapse transition of linear polymers on fractal lattices the authors show that for linear polymers a collapse transition exists on several fractal lattices and obtain exact results for the critical exponents at this transition a rod like phase is found in some cases at intermediate temperatures between the swollen phase and the collapsed phase they introduce infinitesimal recursion relations with correlation function rescaling as the formal limit of a class of fractals which give a better approximation to euclidean 2d lattices the gyration radius exponent at the transition temperature lies in the range nu 1 0 546 or 0 010 in good agreement with a recent transfer matrix calculation the possible relevance of anisotropy at the collapse transition is discussed

construction of optimal order nonlinear solvers using inverse interpolation abstract there is a vast literature on finding simple roots of nonlinear equations by iterative methods these methods can be classified by order by the information used or by efficiency there are very few optimal methods that is methods of order 2 m requiring m 1 function evaluations per iteration here we give a general way to construct such methods by using inverse interpolation and any optimal two point method the presented optimal multipoint methods are tested on numerical examples and compared to existing methods of the same order of convergence

the two machine flowshop total completion time problem improved lower bounds and a branch and bound algorithm abstract this paper presents a branch and bound algorithm for the two machine flowshop scheduling problem with the objective of minimizing the sum of completion times the main feature of the branch and bound algorithm is a new lower bounding scheme that is based on a network formulation of the problem with extensive computational tests we demonstrate that the branch and bound algorithm can solve problems with up to 60 45 jobs where processing times are uniformly distributed in the 1 10 1 100 range

surface adsorption of a self avoiding polymer chain on a family of finitely ramified fractals we study the surface adsorption of a flexible self avoiding polymer chain on a family of sierpinski gasket type fractals using the real space renormalization group technique the members of this family are characterized by an integer scale factor b which runs from 2 to infinity the hausdorff dimension of these fractals tends to 2 from below as b to infinity we calculate the crossover exponent phi for the desorption transition exactly for b 2 to 6 for b to infinity we use finite size scaling arguments to show that phi to 1 4

the two machine flowshop scheduling problem with sequence independent setup times new lower bounding strategies abstract the two machine flowshop environment with sequence independent setup times has been intensely investigated both from theoretical and practical perspectives in the scheduling literature nevertheless very scant attention has been devoted to deriving effective lower bounding strategies in this paper we propose new lower bounds for the total completion time minimization criterion these bounds are based on three relaxation schemes namely the waiting time based relaxation scheme the single machine based relaxation scheme and the lagrangian relaxation scheme extensive computational study carried on instances with up to 500 jobs reveals that embedding the waiting time based bounding strategy within the lagrangian relaxation framework yields the best performance while requiring negligible cpu time

a non iterative method for solving non linear equations abstract in this paper using a hyperbolic tangent function tanh x 0 we develop a non iterative method to estimate a root of an equation f x 0 the problem of finding root is transformed to evaluating an integral and thus we need not take account of choosing initial guess the larger the value of the better the approximation to the root alternatively we employ the signum function sgn x instead of the hyperbolic tangent function which results in an exact formula for the root availability of the present method is shown by some numerical examples for which the traditional newton s method is not appropriate

stronger lagrangian bounds by use of slack variables applications to machine scheduling problems lagrangian relaxation is a powerful bounding technique that has been applied successfully to manynp hard combinatorial optimization problems the basic idea is to see annp hard problem as an easy to solve problem complicated by a number of nasty side constraints we show that reformulating nasty inequality constraints as equalities by using slack variables leads to stronger lower bounds the trick is widely applicable but we focus on a broad class of machine scheduling problems for which it is particularly useful we provide promising computational results for three problems belonging to this class for which lagrangian bounds have appeared in the literature the single machine problem of minimizing total weighted completion time subject to precedence constraints the two machine flow shop problem of minimizing total completion time and the single machine problem of minimizing total weighted tardiness

zipping transition in a model of two crosslinked polymers we study a model of two self avoiding walks that are allowed to cross an attractive energy is associated with each crossing we present a number of exact results on the free energy of this model and show the existence of a zipping temperature below which the number of crossings becomes macroscopic we give heuristic arguments which show that in d 2 and d 3 this zipping transition occurs at infinite temperature exact enumeration and monte carlo simulations on the square lattice strongly support this conjecture and lead to a precise value for the crossover exponent

generalized pairwise interchanges and machine scheduling abstract in this paper a generalization of pairwise interchanges is considered and applied to machine scheduling problems it is shown how these swap operators can be used to compute bounds for branch and bound procedures to prove dominance properties and to define a high performance neighborhood for local search methods

renormalisation on sierpinski type fractals presents a family of deterministic fractals which generalise the d dimensional sierpinski gaskets and establishes their order of ramification and their fractal and spectral dimensions random walks on these fractals are renormalisable and lead to rational not necessarily polynomial mapping

the two machine flowshop total completion time problem branch and bound algorithms based on network flow formulation abstract we consider the flowshop problem on two machines with sequence independent setup times to minimize total completion time large scale network flow formulations of the problem are suggested together with strong lagrangian bounds based on these formulations to cope with their size filtering procedures are developed to solve the problem to optimality we embed the lagrangian bounds into two branch and bound algorithms the best algorithm is able to solve all 100 job instances of our testbed with setup times and all 140 job instances without setup times thus significantly outperforming the best algorithms in the literature

some fourth order iterative methods for solving nonlinear equations abstract in this paper we present some fourth order iterative methods for solving nonlinear equations which contains the well known king s fourth order family as a particular case per iteration the methods require two function and one first derivative evaluations numerical comparisons are made with several other existing methods to show the performance of the presented methods

certain improvements of newton s method with fourth order convergence in this paper we present two new schemes one is third order and the other is fourth order these are improvements of second order methods for solving nonlinear equations and are based on the method of undetermined coefficients we show that the fourth order method is more efficient than the fifth order method due to kou et al j kou y li x wang some modifications of newton s method with fifth order covergence j comput appl math 209 2007 146 152 numerical examples are given to support that the methods thus obtained can compete with other iterative methods

critical exponents of the self avoiding walks on a family of finitely ramified fractals the authors have studied the self avoiding walks saw on a family of finitely ramified fractals the first member b 2 of the family is the two dimensional sierpinski gasket while the last member b infinity appears to be a wedge of the homogeneous triangular lattice by means of the exact renormalisation group transformations they have calculated the critical exponents alpha nu and gamma and the connectivity constant mu of saw on each member of a sequence 2 or b or 8 of the studied fractal family the obtained exact results are compared with the recent phenomenological proposals and with the results believed to be exact in the case of a homogeneous two dimensional lattice

asymptotic form of the spectral dimension of the sierpinski gasket type of fractals the authors have studied the spectral dimension d48t of an infinite class of fractals the first member b 2 of the class is the two dimensional sierpinski gasket while the last member b infinity appears to be a wedge of the ordinary triangular lattice by studying the electric resistance of the fractals they have been able to calculate exact values of d for the first 200 members of the class an analysis of the obtained data reveals that for large b the spectral dimension should approach the upper limit of 2 according to the formula d approximately 2 constant ln b beta where beta is not larger than one this result implies among other things that the scaling exponents of the resistivity and diffusion constant should logarithmically vanish at the fractal lattice crossover

on a general class of multipoint root finding methods of high computational efficiency a general class of n point iterative methods for solving nonlinear equations is constructed by combining methods of newton s type and an arbitrary two point method of the fourth order of convergence it is proved that these methods have the convergence order 2 n requiring only n 1 function evaluations per iteration in this way it is demonstrated that the proposed class of methods supports the kung traub hypothesis 1974 on the upper bound 2 n of the order of multipoint methods based on n 1 function evaluations consequently this class possess as high as possible computational efficiency in the sense of the kung traub hypothesis numerical examples are included to demonstrate exceptional convergence speed with only few function evaluations

interpenetration of two chains different in sizes some exact results abstract a model of two interacting polymer chains has been proposed to study the effect of penetration of one chain into the other we show that small chain penetrates more in comparison to the long chain we also find a condition in which both chains cannot grow on their own or polymerize but can grow polymerize in zipped form

the two machine total completion time flow shop problem in this paper we study the np hard scheduling problem of minimizing total completion time in a two machine flow shop five known lower bounds are discussed and two new ones are presented a new dominance criterion is also proposed several versions of a branch and bound method are derived by applying both individually and combined these lower bounds a heuristic procedure is also presented that uses a constructive o n2 time method which computes a good starting solution together with a neighborhood search based on pairwise interchanges computational results show that the exact method can handle problems of up to 30 jobs in size within a reasonable amount of time and that the heuristic procedure has an average error of less than 0 5 from the optimal value and less than 2 7 from the lower bound

on generalized multipoint root solvers with memory the improved versions of the kung traub family and the zheng li huang family of n point derivative free methods for solving nonlinear equations are proposed the convergence speed of the modified families is considerably accelerated by employing a self correcting parameter this parameter is calculated in each iteration using information from the current and previous iteration so that the proposed families can be regarded as the families with memory the increase of convergence order is attained without any additional function evaluations meaning that these families with memory possess high computational efficiency numerical examples are included to confirm theoretical results and demonstrate convergence behaviour of the proposed methods

critical behaviour of two interacting linear polymer chains exact results for a state of interpenetration of chains on a fractal lattice a model of two interacting chemically different linear polymer chains on a fractal lattice is proposed to study segregation and interpenetration of chains using the real space renormalization group transformation the value of the contact exponent at the point of the interpenetration transition is calculated exactly for the 2d sierpinski gasket

derivative free two point methods with and without memory for solving nonlinear equations abstract two families of derivative free two point iterative methods for solving nonlinear equations are constructed these methods use a suitable parametric function and an arbitrary real parameter it is proved that the first family has the convergence order four requiring only three function evaluations per iteration in this way it is demonstrated that the proposed family without memory supports the kung traub hypothesis 1974 on the upper bound 2n of the order of multipoint methods based on n 1 function evaluations further acceleration of the convergence rate is attained by varying a free parameter from step to step using information available from the previous step this approach leads to a family of two step self accelerating methods with memory whose order of convergence is at least 2 5 4 236 and even 2 6 4 449 in special cases the increase of convergence order is attained without any additional calculations so that the family of methods with memory possesses a very high computational efficiency numerical examples are included to demonstrate exceptional convergence speed of the proposed methods using only few function evaluations

a multi parameter family of three step eighth order iterative methods locating a simple root a multi parameter family of three step eighth order iterative methods free from second derivatives are proposed in this paper to find a simple root of nonlinear algebraic equations convergence analysis as well as numerical experiments confirms the eighth order convergence and asymptotic error constants

minimizing total completion time in a two machine we consider the problem of minimizing total completion time in a two machine owshop we present a heuristic with worst case bound 2 where and denote the minimum and maximum processing time of all operations furthermore we analyze four special cases equal processing times on the first machine equal processing times on the second machine processing a job on the first machine takes time no less than its processing on the second machine and processing a job on the first machine takes time no more than its processing on the second machine we prove that the rst special case is np hard in the strong sense and present an o n log n approximation algorithm for it with worst case bound 4 3 we repeat the easy polynomial algorithms for the cases two and three and show that problem four is solvable in polynomial time as well

interpolatory multipoint methods with memory for solving nonlinear equations abstract a general way to construct multipoint methods for solving nonlinear equations by using inverse interpolation is presented the proposed methods belong to the class of multipoint methods with memory in particular a new two point method with memory with the order 5 17 2 4 562 is derived computational efficiency of the presented methods is analyzed and their comparison with existing methods with and without memory is performed on numerical examples it is shown that a special choice of initial approximations provides a considerably great accuracy of root approximations obtained by the proposed interpolatory iterative methods

a new family of eighth order iterative methods for solving nonlinear equations a family of eighth order iterative methods with four evaluations for the solution of nonlinear equations is presented kung and traub conjectured that an iteration method without memory based on n evaluations could achieve optimal convergence order 2 n 1 the new family of eighth order methods agrees with the conjecture of kung traub for the case n 4 therefore this family of methods has efficiency index equal to 1 682 numerical comparisons are made with several other existing methods to show the performance of the presented methods

a class of two step steffensen type methods with fourth order convergence abstract based on steffensen s method we derive a one parameter class of fourth order methods for solving nonlinear equations in the proposed methods an interpolating polynomial is used to get a better approximation to the derivative of the given function each member of the class requires three evaluations of the given function per iteration therefore this class of methods has efficiency index which equals 1 587 kung and traub conjectured an iteration using n evaluations of f or its derivatives without memory is of convergence order at most 2 n 1 the new class of fourth order methods agrees with the conjecture of kung traub for the case n 3 numerical comparisons are made to show the performance of the presented methods

a branch and bound algorithm for three machine flowshop scheduling problem to minimize total completion time with separate setup times in this paper we address the three machine flowshop scheduling problem setup times are considered separate from processing times and the objective is to minimize total completion time we show that the three site distributed database scheduling problem can be modeled as a three machine flowshop scheduling problem a lower bound is developed and a dominance relation is established moreover an upper bound is developed by using a three phase hybrid heuristic algorithm furthermore a branch and bound algorithm incorporating the developed lower bound dominance relation and the upper bound is presented computational analysis on randomly generated problems is conducted to evaluate the lower and upper bounds the dominance relation and the branch and bound algorithm the analysis shows the efficiency of the upper bound and hence it can be used for larger size problems as a heuristic algorithm

an effective differential evolution algorithm for permutation flow shop scheduling problem the permutation flow shop problem pfssp is an np hard problem of wide engineering and theoretical background in this paper a hybrid differential evolution de called l hde is proposed to solve the flow shop scheduling problem which combines the de with the individual improving scheme iis and greedy based local search first to make de suitable for pfssp a new largest rank rule lrv based on a random key is introduced to convert the continuous position in de to the discrete job permutation so that the de can be used for solving pfssp second the neh heuristic was combined with the random initialization to initialize the population with certain quality and diversity third the iis based local search is used for improving the diversity of population and enhancing the quality of the solution with a certain probability fourth the greedy based local search is designed to help the algorithm to escape from local minimum additionally simulations and comparisons based on pfssp benchmarks are carried out which show that our algorithm is both effective and efficient

an optimal steffensen type family for solving nonlinear equations abstract in this paper a general family of steffensen type methods with optimal order of convergence for solving nonlinear equations is constructed by using newton s iteration for the direct newtonian interpolation it satisfies the conjecture proposed by kung and traub h t kung j f traub optimal order of one point and multipoint iteration j assoc comput math 21 1974 634 651 that an iterative method based on m evaluations per iteration without memory would arrive at the optimal convergence of order 2 m 1 its error equations and asymptotic convergence constants are obtained finally it is compared with the related methods for solving nonlinear equations in the numerical examples

dynamics of iterative families with memory based on weight functions procedure abstract in this paper we analyze the stability of a parametric family of iterative methods with memory for solving nonlinear equations this family is obtained from an optimal class of fourth order schemes without memory designed by means of weight functions procedure by studying the real fixed and critical points of the rational function resulting from the application of the family with memory on quadratic polynomials the best elements of the family in terms of absence of chaotic behavior are selected finally a numerical study is performed verifying the dynamical theoretical results

a super fast tri parametric iterative method with memory for the first time a tri parametric method with memory for solving nonlinear equations is constructed at which a super fast convergence rate is achieved by using only three functional evaluations subsequently a very high computational efficiency index nearly 2 is attained finally to support the theory some numerical experiments are reported

three point methods with and without memory for solving nonlinear equations abstract a new family of three point derivative free methods for solving nonlinear equations is presented it is proved that the order of convergence of the basic family without memory is eight requiring four function evaluations which means that this family is optimal in the sense of the kung traub conjecture further accelerations of convergence speed are attained by suitable variation of a free parameter in each iterative step this self accelerating parameter is calculated using information from the current and previous iteration so that the presented methods may be regarded as the methods with memory the self correcting parameter is calculated applying the secant type method in three different ways and newton s interpolatory polynomial of the second degree the corresponding r order of convergence is increased from 8 to 4 1 5 2 8 472 9 10 and 11 the increase of convergence order is attained without any additional function calculations providing a very high computational efficiency of the proposed methods with memory another advantage is a convenient fact that these methods do not use derivatives numerical examples and the comparison with existing three point methods are included to confirm theoretical results and high computational efficiency

improved lower bounds for minimizing the sum of completion times of n jobs over m machines in a flow shop abstract the paper considers the classic n job m machine scheduling problem where the objective is to minimize the sum of completion times a procedure is presented for obtaining m 1 new machine based lower bounds the result is an improved overall lower bound

an improved branch and bound algorithm for the two machine total completion time flow shop problem we consider the two machine total completion time flow shop scheduling problem this problem is known to be np hard in the strong sense an improved lagrangean relaxation approach is proposed two new dominance criteria are introduced to curtail the enumeration tree a branch and bound algorithm capable of solving to optimality medium size problem instances is presented

critical behavior of two interacting linear polymer chains in a good solvent a model of two interacting chemically different linear polymer chains is solved exactly using the real space renormalization group transformation on a family of sierpinski gasket type fractals and on a truncated 4 simplex lattice the members of the family of the sierpinski gasket type fractals are characterized by an integer scale factorb which runs from 2 to the hausdorff dimensiond f of these fractals tends to 2 from below asb we calculate the contact exponenty for the transition from the state of segregation to a state in which the two chains are entangled forb 2 5 using arguments based on the finite size scaling theory we show that forb y 2 v b d f wherev is the end toend distance exponent of a chain for a truncated 4 simplex lattice it is shown that the system of two chains either remains in a state in which these chains are intermingled in such a way that they cannot be told apart in the sense that the chemical difference between the polymer chains completely drop out of the thermodynamics of the system or in a state in which they are either zipped or entangled we show the region of existence of these different phases separated by tricritical lines the value of the contact exponenty is calculated at the tricritical points

on generalized biparametric multipoint root finding methods with memory a general family of biparametric n point methods with memory for solving nonlinear equations is proposed using an original accelerating procedure with two parameters this family is based on derivative free classes of n point methods without memory of interpolatory type and steffensen like method with two free parameters the convergence rate of the presented family is considerably increased by self accelerating parameters which are calculated in each iteration using information from the current and previous iteration and newton s interpolating polynomials with divided differences the improvement of convergence order is achieved without any additional function evaluations so that the proposed family has a high computational efficiency numerical examples are included to confirm theoretical results and demonstrate convergence behavior of the proposed methods

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

on a general transformation of multipoint root solvers optimal multipoint methods for solving nonlinear equations of arbitrary order of convergence are investigated a low cost transformation that converts newton preconditioned methods into a derivative free variant is presented this transforming procedure preserves both algorithm body structure and order of convergence of the original scheme another useful application of the proposed transformation is the acceleration of convergence order of non optimal methods

an ostrowski type method with memory using a novel self accelerating parameter abstract in this paper an ostrowski type method with memory is proposed for solving nonlinear equations to this end we first present an optimal fourth order ostrowski type method without memory based on this method without memory an ostrowski type method with memory is given by using a simple self accelerating parameter the new self accelerating parameter is constructed by a novel way and has the properties of simple structure and easy calculation which do not increase the computational cost of the iterative method the convergence order of the new iterative method is increased from 4 to 2 5 4 2361 5 13 2 4 30278 and 2 6 4 4495 respectively numerical experiments are made to show the performance of the new method which support the theoretical results from the comparison with some known methods it is observed that the new method occupies less computing time

three step iterative methods with eighth order convergence for solving nonlinear equations a family of eighth order iterative methods for the solution of nonlinear equations is presented the new family of eighth order methods is based on king s fourth order methods and the family of sixth order iteration methods developed by chun et al per iteration the new methods require three evaluations of the function and one evaluation of its first derivative therefore this family of methods has the efficiency index which equals 1 682 kung and traub conjectured that a multipoint iteration without memory based on n evaluations could achieve optimal convergence order 2 n 1 thus we provide a new example which agrees with the conjecture of kung traub for n 4 numerical comparisons are made to show the performance of the presented methods

surface adsorption and the collapse transition of a linear polymer chain some exact results on fractal lattices we study the surface adsorption and collapse transition of a flexible self attracting self avoiding polymer chain on truncated 4 and 5 simplex lattices using real space renormalization group techniques we find phase diagrams that exhibit many different universality domains of critical behavior in the desorbed ordinary bulk regime the polymer undergoes a collapse transition from a swollen to a compact globule phase on a 4 simplex lattice but not on a 5 simplex lattice where it always remains in the swollen state in the adsorbed region on a 4 simplex lattice the polymer remains in the swollen state with a critical behavior characterized by that of a 3 simplex lattice whereas on a 5 simplex lattice it has both swollen and compact globule regions separated by a tricritical ensuremath theta line the phase diagram of a 4 simplex lattice has a pentacritical point which separates a region where the point at which the adsorbed swollen polymer coexists with both the desorbed polymer and desorbed globule is a tetracritical point from one in which it appears as the intersection of three lines of continuous transition on a 5 simplex lattice the adsorbed phase ensuremath theta line bends in the neighborhood of the special adsorption tricritical line and does not appear to meet it even for a very large value of the monomer monomer attraction

three step iterative methods with optimal eighth order convergence in this paper based on ostrowski s method a new family of eighth order methods for solving nonlinear equations is derived in terms of computational cost each iteration of these methods requires three evaluations of the function and one evaluation of its first derivative so that their efficiency indices are 1 682 which is optimal according to kung and traub s conjecture numerical comparisons are made to show the performance of the new family

minimizing total completion time in a two machine flow shop with deteriorating jobs this paper considers a two machine flow shop scheduling problem with deteriorating jobs by a deteriorating job we mean that the processing time of a job is an increasing function of its execution start time a simple linear deterioration function is assumed the objective is to find a sequence that minimizes total completion time optimal solutions are obtained for some special cases for the general case several dominance properties and two lower bounds are derived to speed up the elimination process of a branch and bound algorithm a heuristic algorithm is also proposed to overcome the inefficiency of the branch and bound algorithm computational results show that the proposed heuristic algorithm performs effectively and efficiently