a repairing technique for the local search of the job shop problem abstract the local search technique has become a widely used tool for solving many combinatorial optimization problems in the case of the job shop the implementation of such a technique is not straightforward at all due to the existence of the technological constraints among the operations that belong to the same job their presence renders a certain set of schedules infeasible consequently special attention is required when defining optimization algorithms to prevent the possibility of reaching an infeasible schedule during execution traditionally the problem is tackled on the neighborhood level by using only a limited set of moves for which feasibility inherently holds this paper proposes an alternative way to avoid infeasibility by incorporating a repairing technique into the mechanism for applying moves to a schedule whenever an infeasible move is being applied a repairing mechanism rearranges the underlying schedule in such a way that the feasibility of the move is restored the possibility of reaching infeasible solutions is therefore eliminated on the lowest possible conceptual level consequently neighborhood functions need not to be constrained to a limited set of feasible moves any more

solving the flexible job shop scheduling problem with sequence dependent setup times abstract this paper addresses the flexible job shop scheduling problem with sequence dependent setup times and where the objective is to minimize the makespan we first present a mathematical model which can solve small instances to optimality and also serves as a problem representation after studying structural properties of the problem using a disjunctive graph model we develop a tabu search algorithm with specific neighborhood functions and a diversification structure extensive experiments are conducted on benchmark instances test results first show that our algorithm outperforms most existing approaches for the classical flexible job shop scheduling problem additional experiments also confirm the significant improvement achieved by integrating the propositions introduced in this study

maximization of a matrix function related to the dittert conjecture abstract let k n denote the set of all nonnegative n n matrices whose entries have sum n and let j n 1 n n n for k 1 n and for a k n with row sum s r 1 r n and column sums c 1 c n let k be defined by k a q k i r i j c j per a we propose a problem of maximizing k of which the dittert conjecture is a special case and obtain some results related to this problem many of known theorems for n are shown to hold for k k 1 n

a general approach for optimizing regular criteria in the job shop scheduling problem even though a very large number of solution methods has been developed for the job shop scheduling problem a majority has been designed for the makespan criterion in this paper we propose a general approach for optimizing any regular criterion in the job shop scheduling problem the approach is a local search method that uses a disjunctive graph model and neighborhoods generated by swapping critical arcs the connectivity property of the neighborhood structure is proved and a novel efficient method for evaluating moves is presented besides its generality another prominent advantage of the proposed approach is its simple implementation that only requires to tune the range of one parameter extensive computational experiments carried out on various criteria makespan total weighted flow time total weighted tardiness weighted sum of tardy jobs maximum tardiness show the efficiency of the proposed approach best results were obtained for some problem instances taken from the literature

the monotonicity of and the đokovic conjectures on permanents of doubly stochastic matrices abstract let n denote the set of all n n doubly stochastic matrices and let j n 1 n n n for a n and any integer k 1 k n let pk a denote the sum of all subpermanents of order k of a and let d k a p k a n k 1 2 nk p k 1 a for k 2 n a n is called a dk minimizing matrix on n if d k a d k x x n the okovic conjecture asserts that if a is a dk minimizing matrix on n then dk a 0 k 2 n in this paper we prove that if a is a positive dk minimizing matrix on n then dk a 0 and a jn k 2 n and we settle the conjecture for an n 2 dimensional face of n we also prove the monotonicity of the permanent for a x y u v n where each of the blocks of a is a matrix of equal entries and for any a n with n 1 identical rows

monotonicity of permanents of certain doubly stochastic circulant matrices abstract let pk a k 2 n denote the sum of the permanents of all k k submatrices of the n n matrix a a conjecture of okovic which is stronger than the famed van der waerden permanent conjecture asserts that the functions pk 1 jn a k 2 n are strictly increasing in the interval 0 1 for every doubly stochastic matrix a here jn is the n n matrix all whose entries are equal 1 n in the present paper it is proved that the conjecture holds true for the circulant matrices a in pn 0 1 and a nj n i n p n n 2 where in and pn are respectively the n n identify matrix and the n n permutation matrix with 1 s in positions 1 2 2 3 n 1 n n 1

doubly stochastic matrices with equal subpermanents abstract it has been conjectured that if a is a doubly stochastic n n matrix such that per a i j pera for all i j then either a j n then n n matrix with each entry equal to 1 n or up to permutations of rows and columns a 1 2 i n p n where p n is a full cycle permutation matrix this conjecture is proved

new search spaces for sequencing problems with application to job shop scheduling in this paper search heuristics are developed for generic sequencing problems with emphasis on job shop scheduling the proposed methods integrate problem specific heuristics common to operations research and local search approaches from artificial intelligence in order to obtain desirable properties from both the applicability of local search to a wide range of problems and the incorporation of problem specific information are both properties of the proposed algorithms two methods are proposed both of which are based on novel definitions of solution spaces and of neighborhoods in these spaces applications of the proposed methodology are developed for job shop scheduling problems and can be easily applied with any scheduling objective to demonstrate effectiveness the method is tested on the job shop scheduling problem with the minimum makespan objective encouraging results are obtained

on a conjecture of e dittert abstract let kn denote the set of all n x n nonnegative matrices whose entries have sum n and let be a real valued function defined on kn by x in 1 n j 1cj n per x for x e kn with row sum vector r1 rn and column sum vector cl hellip cn for the same x let ij x k irk 1 jc1 per x i j a kn is called a maximizing matrix if a x for all x kn dittert s conjecture asserts that jn 1 n n n is the unique maximizing matrix on kn in this paper the following are proved i if a aij is a maximizing matrix on kn then ij a a if aij 0 and ij a a if aij 0 ii the conjecture is true for n 3

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

two simulated annealing based heuristics for the job shop scheduling problem abstract in this paper we present two simulated annealing based algorithms for the classical general job shop scheduling problem where the objective is to minimize the makespan we consider sets of jobs consisting of tasks and sets of machines which can handle at most one task at a time to represent the problem we employ the model of disjunctive graphs simulated annealing has been applied to this problem earlier e g by van laarhoven et al where the neighborhood function is based on reversing a single arc of a longest path of the underlying graph in our approach we analyze a neighborhood function which involves a non uniform generation probability to obtain the neighbors of a schedule we reverse more than a single arc of longest paths and perform a control on the increase of the makespan the selection of the arcs depends on the number of longest paths to which a particular arc belongs furthermore we have designed two cooling schedules which employ a detailed analysis of the objective function depending on the specified neighborhood relation the expected run times can be either o n2 e or o n3 e m for the first cooling schedule and o n5 2 e m1 2 or o n7 2 e m1 2 for the second cooling schedule where n is the number of tasks m the number of machines and e represents o ln ln n ln n our computational experiments on small to large benchmark problems have shown that within short series of consecutive trials relatively stable results equal or close to optimal solutions are repeatedly obtained including the well known benchmark problems ft10 and la38 we could improve five upper bounds for the yn1 yn4 swv12 swv13 and swv15 benchmark problems e g for swv13 the gap between the lower and the former upper bound has been shortened by about 57 in our approach we rely only on basic information about the given problem instance

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

forensic identification with imperfect evidence mortera uniroma3 it summary we study the problem of forensic identification when the trace evidence from the scene of the crime is imperfect for example it might be measured with error or be partially missing a general framework for imperfect data is developed and applied in particular to the following cases singly and in combination measurement error in the recorded information at the scene of the crime binning i e discretisation of an originally continuous crime measurement paternity testing in which the dna profiles of the child and of the mother provide partial information on the true father s dna two types of laboratory error one in which the error is equally distributed among all possible results and a second in which there is a bias in the error mechanism producing a false match and partial data as when there is information on the offender s dna profile but not on his racial group

a note on the convexity of the sum of subpermanents let denote the set of all n x n doubly stochastic matrices and let ok a be the sum of all subpermanents of order ic of matrix a we prove that az a and os a are convex on 0 for n 2 2 and n 2 4 respectively and also conjecture the following for every k 2 3 there exists nk 2 k 1 such that the inequality gk yj 1 cx a 5 cwk jn 1 cr gk a holds for all o e 0 l and all a e c12 with n 2 nk where j l n c 1 e r it is shown that this conjecture is true for k 5 4 with n3 4 and n4 6

a graph theoretic decomposition of the job shop scheduling problem to achieve scheduling robustness in this paper we study the weighted tardiness job shop scheduling problem taking into consideration the presence of random shop disturbances a basic thesis of the paper is that global scheduling performance is determined primarily by a subset of the scheduling decisions to be made by making these decisions in an a priori static fashion which maintains a global perspective overall performance efficiency can be achieved further by allowing the remaining decisions to be made dynamically flexibility can be retained in the schedule to compensate for unforeseen system disturbances we develop a decomposition method that partitions job operations into an ordered sequence of subsets this decomposition identifies and resolves a crucial subset of scheduling decisions through the use of a branch and bound algorithm we conduct computational experiments that demonstrate the performance of the approach under deterministic cases and the robustness of the approach under a wide range of processing time perturbations we show that the performance of the method is superior particularly for low to medium levels of disturbances

a fast taboo search algorithm for the job shop problem a fast and easily implementable approximation algorithm for the problem of finding a minimum makespan in a job shop is presented the algorithm is based on a taboo search technique with a specific neighborhood definition which employs a critical path and blocks of operations notions computational experiments up to 2 000 operations show that the algorithm not only finds shorter makespans than the best approximation approaches but also runs in shorter time it solves the well known 10 10 hard benchmark problem within 30 seconds on a personal computer

scatter search with path relinking for the flexible job shop scheduling problem abstract the flexible job shop scheduling is a challenging problem due to its high complexity and the huge number of applications it has in real production environments in this paper we propose effective neighborhood structures for this problem including feasibility and non improving conditions as well as procedures for fast estimation of the neighbors quality these neighborhoods are embedded into a scatter search algorithm which uses tabu search and path relinking in its core to develop these metaheuristics we define a novel dissimilarity measure which deals with flexibility we conducted an experimental study to analyze the proposed algorithm and to compare it with the state of the art on standard benchmarks in this study our algorithm compared favorably to other methods and established new upper bounds for a number of instances

general local search methods abstract this paper is a tutorial introduction to three recent yet widely used general heuristics simulated annealing tabu search and genetic algorithms a relatively precise description and an example of application are provided for each of the methods as well as a tentative evaluation and comparison from a pragmatic point of view

an alternative framework to lagrangian relaxation approach for job shop scheduling abstract a new lagrangian relaxation lr approach is developed for job shop scheduling problems in the approach operation precedence constraints rather than machine capacity constraints are relaxed the relaxed problem is decomposed into single or parallel machine scheduling subproblems these subproblems which are np complete in general are approximately solved by using fast heuristic algorithms the dual problem is solved by using a recently developed surrogate subgradient method that allows approximate optimization of the subproblems since the algorithms for subproblems do not depend on the time horizon of the scheduling problems and are very fast our new lr approach is efficient particularly for large problems with long time horizons for these problems the machine decomposition based lr approach requires much less memory and computation time as compared to a part decomposition based approach as demonstrated by numerical testing

problem difficulty for tabu search in job shop scheduling tabu search algorithms are among the most effective approaches for solving the job shop scheduling problem jsp yet we have little understanding of why these algorithms work so well and under what conditions we develop a model of problem difficulty for tabu search in the jsp borrowing from similar models developed for sat and other np complete problems we show that the mean distance between random local optima and the nearest optimal solution is highly correlated with the cost of locating optimal solutions to typical random jsps additionally this model accounts for the cost of locating sub optimal solutions and provides an explanation for differences in the relative difficulty of square versus rectangular jsps we also identify two important limitations of our model first model accuracy is inversely correlated with problem difficulty and is exceptionally poor for rare very high cost problem instances second the model is significantly less accurate for structured non random jsps our results are also likely to be useful in future research on difficulty models of local search in sat as local search cost in both sat and the jsp is largely dictated by the same search space features similarly our research represents the first attempt to quantitatively model the cost of tabu search for any np complete problem and may possibly be leveraged in an effort to understand tabu search in problems other than job shop scheduling

extended grasp for the job shop scheduling problem with total weighted tardiness objective abstract the paper proposes a heuristic for the job shop scheduling problem with minimizing the total weighted tardiness of jobs as objective it is built upon the well known metaheuristic grasp and strengthened with an inclusion of specific local search components the design is based on an advanced disjunctive graph model which enables capturing solution schedules through a tree graph called critical tree the tree graph allows for effectively steering a first descent search algorithm which further incorporates powerful neighborhood operators and a fast move evaluation procedure based on heads updating additionally amplifying and path relinking is adaptively applied to the best schedules discovered we present computational results of the new heuristic on two famous sets of benchmark instances we identify ten new best solutions and we demonstrate the high potential of the approach through a comparison with state of the art methods

measuring heterogeneity in forensic databases using hierarchical bayes models summary as currently defined dna fingerprint profiles do not uniquely identify individuals for criminal cases involving dna evidence forensic scientists evaluate the conditional probability that an unknown but distinct individual matches the crime sample given that the defendant matches estimates of the conditional probability of observing matching profiles are based on reference populations maintained by forensic testing laboratories each of these databases is heterogeneous being composed of subpopulations of different heritages this heterogeneity has an impact on the weight of the evidence a hierarchical bayes model is formulated that incorporates the key physical characteristics inherent in these data with the help of markov chain monte carlo sampling levels of heterogeneity are estimated for three major ethnic groups in the database of lifecodes corporation

handling flexibility in a generalised job shop with a fuzzy approach abstract in this paper we deal with a particular scheduling problem inspired by a practical case coming from a belgian pharmaceutical company this problem has some particularities with respect to the classical job shop problem the principal one is the existence of a delay between the end of an operation and the start of the next operation of the same job this delay is not fixed but belongs generally to an interval range of possible values a resolution method the horizon method has been proposed in the deterministic case fixed data and strict constraints in this method the horizon time of each machine is discretised by unit times and at each unit time a binary value is associated all the operations applied on the machines horizons are logic operations or and right or left shifting and so on unfortunately this method does not take into account several aspects of the problem the existence of a preference relation on the possible values of the delay between successive operations and of flexible due dates in this work we modelise such flexible parameters using the fuzzy logic we propose a new method generalizing the horizon method this new method try to find for the realisation of the jobs a compromise between the choice of good values for the delay between couples of successive operations of the same job and good values for the completion time of the jobs

coherent analysis of forensic identification evidence a murder has been committed and there is a known population of possible suspects the identification evidence available based on information at the scene of the crime is that the criminal may have a certain characteristic information may also be available on a set of suspects about which of them have the characteristic we discuss the problem of assessing who is the guilty party taking particular account of the following complicating features the evidence at the scene of the crime may be unreliable the suspects examined may have been chosen by means of a search process which might itself be informative we also examine the effect of the assumed population dependence structure for the relevant identification characteristics

a filter and fan approach to the job shop scheduling problem the job shop scheduling problem jssp is a notoriously difficult problem in combinatorial optimization extensive investigation has been devoted to developing efficient algorithms to find optimal or near optimal solutions this paper proposes a new heuristic algorithm for the jssp that effectively combines the classical shifting bottleneck procedure sbp with a dynamic and adaptive neighborhood search procedure our new search method based on a filter and fan f f procedure uses the sbp as a subroutine to generate a starting solution and to enhance the best schedules produced the f f approach is a local search procedure that generates compound moves by a strategically abbreviated form of tree search computational results carried out on a standard set of 43 benchmark problems show that our f f algorithm performs more robustly and effectively than a number of leading metaheuristic algorithms and rivals the best of these algorithms

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12