optimal l p l q estimates for parabolic boundary value problems with inhomogeneous data in this paper we investigate vector valued parabolic initial boundary value problems mathcal a t x d mathcal b j t x d subject to general boundary conditions in domains g in mathbb r n with compact c 2m boundary the top order coefficients of mathcal a are assumed to be continuous we characterize optimal l p l q regularity for the solution of such problems in terms of the data we also prove that the normal ellipticity condition on mathcal a and the lopatinskii shapiro condition on mathcal a mathcal b 1 dots mathcal b m are necessary for these l p l q estimates as a byproduct of the techniques being introduced we obtain new trace and extension results for sobolev spaces of mixed order and a characterization of triebel lizorkin spaces by boundary data

a note on worst case analysis of approximation algorithms for a scheduling problem abstract worst case analyses of two approximation algorithms for the m machine permutation flow shop problem are presented worst case performane ratios m 2 o 1 m for the former and m 1 for the latter algorithm are found

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

parabolic equations with vmo coefficients in sobolev spaces with mixed norms an lq lp theory of divergence and non divergence form parabolic equations is presented the main coefficients are supposed to belong to the class vmox which in particular contains all measurable functions depending only on t the method of proving simplifies the methods previously used in the case p q

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

a note on heuristics of flow shop scheduling we present an omn two group tg heuristic for the m machine n job permutation flow shop scheduling problem we show that heuristic tg has a worst case performance ratio of m 1 2 we also establish worst case bounds for several heuristics proposed in the past

a fast tabu search algorithm for the permutation flow shop problem abstract a fast and easily implementable approximation algorithm for the problem of finding a minimum makespan in the permutation flow shop is presented the algorithm is based on a tabu search technique with a specific neighborhood definition which employs a block of jobs notion computational experiments up to 500 jobs and 20 machines show its excellent numerical properties

flow shop scheduling problems with deteriorating jobs on no idle dominant machines abstract in this paper we study the permutation flow shop scheduling problems with deteriorating jobs on no idle dominant machines the objective is to minimize one of the two regular performance criteria namely makespan and total completion time for each objective the following dominant machines constraint idm ddm idm ddm and ddm idm are considered we present a polynomial time solution algorithm for each of the four cases

a fast algorithm for determining the propagation path of multiple diffracted rays we present a fast algorithm for path computation of multiple diffracted rays relevant to ray tracing techniques the focus is on double diffracted rays but generalizations are also mentioned the novelty of our approach is in the use of an analytical geometry procedure which permits to re write the problem as a simple nonlinear equation this procedure permits a convergence analysis of the algorithms involved in the numerical resolution of such nonlinear equation moreover we also indicate how to choose the iteration starting point to obtain convergence of the locally convergent newton method as in previous works explicit solutions are obtained in the relevant cases of parallel or incident diffraction edges

an efficient ray tracing algorithm for multiple straight wedge diffraction we present an efficient algorithm for the tracing of multiply edge diffracted rays the algorithm assumes a given sequence of infinite edges and complete visibility among them the ray tracing problem is formulated as the minimization of the ray total path length since such a cost function is strictly convex except for coplanar edges in the plane wave far field regime then the problem admits a unique global minimum and allows the use of a modified newton search algorithm which exhibits a very high converging rate we also propose a convenient starting point to effectively initialize the minimization algorithm the proposed algorithm is tested by some numerical examples that show its efficiency and effectiveness

higher order elliptic and parabolic equations with vmo assumptions and general boundary conditions abstract we prove mixed l p l q estimates with p q 1 for higher order elliptic and parabolic equations on the half space r d 1 with general boundary conditions which satisfy the lopatinskii shapiro condition we assume that the elliptic operators a have leading coefficients which are in the class of vanishing mean oscillations both in the time variable and the space variable in the proof we apply and extend the techniques developed by krylov 24 as well as dong and kim in 13 to produce mean oscillation estimates for equations on the half space with general boundary conditions

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

reflections from multiple surfaces without edges an algorithm is presented for calculating the positions of the specular points that appear when a collection of reflecting surfaces is illuminated by an external source the set of specular points is represented as the fixed point of a certain mapping and this fixed point is calculated by the method of successive approximations msa the msa is an iterative technique which is essentially different from a search or shooting and bouncing ray technique the latter require much larger numbers of functional evaluations especially when the number n of reflecting surfaces is greater than unity a search technique requires a number of function evaluations that varies exponentially with n whereas the number of function evaluations required by the msa varies linearly with n

an efficient heuristic approach to the scheduling of jobs in a flowshop abstract three heuristic algorithms for flowshop scheduling with the objective of minimizing total flowtime are presented in this paper since the flowshop scheduling problem has been found to be an np complete problem the development of heuristic algorithms that guarantee fairly accurate solutions becomes necessary the proposed algorithms are found to give consistently near optimal solutions and fare better than the existing methods

restricted neighborhood in the tabu search for the flowshop problem this paper deals with the minimizing weighted tardiness of jobs in a scheduling problem where the structure is that of the proportionate flowshop a modified version of the widmer hertz algorithm for the makespan problem is presented improving the computational performance by reducing the size of the neighborhoods the heuristic tests were applied to 720 flowshop problems from 10 to 50 jobs

tight bounds for permutation flow shop scheduling in flow shop scheduling there are m machines and n jobs such that every job has to be processed on the machines in the fixed order 1 m in the permutation flow shop problem it is also required that each machine process the set of all jobs in the same order formally given n jobs along with their processing times on each machine the goal is to compute a single permutation of the jobs n n that minimizes the maximum job completion time makespan of the schedule resulting from the previously best known approximation guarantee for this problem was o m log m 1 2 sviridenko m 2004 a note on permutation flow shop problem ann oper res 129 247 252 in this paper we obtain an improved o min m1 2 n1 2 approximation algorithm for the permutation flow shop scheduling problem by finding a connection between the scheduling problem and the longest increasing subsequence problem our approximation ratio is relative to the lower bounds of maximum job length and maximum machine load and is the best possible such result this also resolves an open question from potts et al potts c d shmoys d williamson 1991 permutation vs nonpermutation flow shop schedules oper res lett 10 281 284 by algorithmically matching the gap between permutation and nonpermutation schedules we also consider the weighted completion time objective for the permutation flow shop scheduling problem using a natural linear programming relaxation and our algorithm for the makespan objective we obtain an o min m1 2 n1 2 approximation algorithm for minimizing the total weighted completion time improving on the previously best known guarantee of em for any constant e 0 smutnicki c 1998 some results of the worst case analysis for flow shop scheduling eur j oper res 109 66 87 we give a matching lower bound on the integrality gap of our linear programming relaxation

some efficient heuristic methods for the flow shop sequencing problem abstract in this paper the best heuristic methods known up to now are compared to solve the flow shop sequencing problem and we improve the complexity of the best one next this problem is applied to taboo search a new technique to solve combinatorial optimization problems and computational experiments are reported finally a parallel taboo search algorithm is presented and experimental results show that this heuristic allows very good speed up

minimizing maximum completion time in a proportionate flow shop with one machine of different speed a flow shop with identical machines is called a proportionate flow shop in this paper we consider the variant of the n job m machine proportionate flow shop scheduling problem in which only one machine is different and job processing times are inversely proportional to machine speeds the objective is to minimize maximum completion time we describe some optimality conditions and show that the problem is np complete we provide two heuristic procedures whose worst case performance ratio is less than two extensive experiments with various sizes are conducted to show the performance of the proposed heuristics

a note on flow shop scheduling problems with a learning effect on no idle dominant machines abstract this paper considers some permutation flow shop scheduling problems with a learning effect on no idle dominant machines the objective is to minimize maximum completion time this objective is considered under following dominant machines constraint idm ddm idm ddm and ddm idm we present a polynomial time solution algorithm for each of the above cases

solvability and maximal regularity of parabolic evolution equations with coefficients continuous in time abstract we establish maximal regularity of type lp for a parabolic evolution equation u t a t u t f t with a c 0 t l d a 0 x and construct the corresponding evolution family on the underlying banach space x our proofs are based on the operator sum method and the use of evolution semigroups the results are applied to parabolic partial differential equations with continuous coefficients

higher order elliptic and parabolic systems with variably partially bmo coefficients in regular and irregular domains abstract the solvability in sobolev spaces is proved for divergence form complex valued higher order parabolic systems in the whole space on a half space and on a reifenberg flat domain the leading coefficients are assumed to be merely measurable in one spacial direction and have small mean oscillations in the orthogonal directions on each small cylinder the directions in which the coefficients are only measurable vary depending on each cylinder the corresponding elliptic problem is also considered