functional data clustering via piecewise constant nonparametric density estimation in this paper we present a novel way of analyzing and summarizing a collection of curves based on piecewise constant density estimation the curves are partitioned into clusters and the dimensions of the curves points are discretized into intervals the cross product of these univariate partitions forms a data grid of cells which represents a nonparametric estimator of the joint density of the curves and point dimensions the best model is selected using a bayesian model selection approach and retrieved using combinatorial optimization algorithms the proposed method requires no parameter setting and makes no assumption regarding the curves beyond functional data it can be applied to distributional data the practical interest of the approach for functional data and distributional data exploratory analysis is presented on two real world datasets

improvement and comparison of heuristics for solving the uncapacitated multisource weber problem the multisource weber problem is to locate simultaneouslym facilities in the euclidean plane to minimize the total transportation cost for satisfying the demand ofn fixed users each supplied from its closest facility many heuristics have been proposed for this problem as well as a few exact algorithms heuristics are needed to solve quickly large problems and to provide good initial solutions for exact algorithms we compare various heuristics i e alternative location allocation cooper 1964 projection bongartz et al 1994 tabu search brimberg and mladenovic 1996a p median plus weber hansen et al 1996 genetic search and several versions of variable neighbourhood search based on empirical tests that are reported it is found that most traditional and some recent heuristics give poor results when the number of facilities to locate is large and that variable neighbourhood search gives consistently best results on average in moderate computing time

ll filters a new class of order statistic filters the ll filters are introduced to generate the order statistic filters l filters and the nonrecursive linear or finite duration impulse response fir filters such estimators are particularly effective filtering signals that do not necessarily follow gaussian distributions they can be designed to restore one dimensional or multidimensional signals corrupted by noise of impulsive type such filters are appealing since they are suitable for being made robust against the presence of spurious outliers in the data

variable neighborhood search for the vertex weighted k cardinality tree problem this paper presents some new heuristics based on variable neighborhood search to solve the vertex weighted k cardinality tree problem an efficient local search procedure is also developed for use within these heuristics our computational results demonstrate that the new heuristics substantially outperform the state of the art methodologies including a tabu search and genetic algorithm recently proposed in the literature we also show that a decomposition approach is best for larger problem sizes than previously investigated thus our findings advance in a significant way the capacity to solve this important class of problems

search with evolutionary ruin and stochastic rebuild a theoretic framework and a case study on exam timetabling this paper presents a state transition based formal framework for a new search method called evolutionary ruin and stochastic recreate which tries to learn and adapt to the changing environments during the search process it improves the performance of the original ruin and recreate principle by embedding an additional phase of evolutionary ruin to mimic the survival of the fittest mechanism within single solutions this method executes a cycle of solution decomposition evolutionary ruin stochastic recreate and solution acceptance until a certain stopping condition is met the solution decomposition phase first uses some problem specific knowledge to decompose a complete solution into its components and assigns a score to each component the evolutionary ruin phase then employs two evolutionary operators namely selection and mutation to destroy a certain fraction of the solution and the next stochastic recreate phase repairs the broken solution last the solution acceptance phase selects a specific strategy to determine the probability of accepting the newly generated solution hence optimisation is achieved by an iterative process of component evaluation solution disruption and stochastic constructive repair from the state transitions point of view this paper presents a probabilistic model and implements a markov chain analysis on some theoretical properties of the approach unlike the theoretical work on genetic algorithm and simulated annealing which are based on state transitions within the space of complete assignments our model is based on state transitions within the space of partial assignments the exam timetabling problems are used to test the performance in solving real world hard problems

a reduced variable neighborhood search algorithm for uncapacitated multilevel lot sizing problems multilevel lot sizing mlls problems which involve complicated product structures with interdependence among the items play an important role in the material requirement planning mrp system of modern manufacturing assembling lines in this paper we present a reduced variable neighborhood search rvns algorithm and several implemental techniques for solving uncapacitated mlls problems computational experiments are carried out on three classes of benchmark instances under different scales small medium and large compared with the existing literature rvns shows good performance and robustness on a total of 176 tested instances for the 96 small sized instances the rvns algorithm can find 100 of the optimal solutions in less computational time for the 40 medium sized and the 40 large sized instances the rvns algorithm is competitive against other methods enjoying good effectiveness as well as high computational efficiency in the calculations rvns updated 7 17 5 best known solutions for the medium sized instances and 16 40 best known solutions for the large sized instances

large neighborhood search for multi trip vehicle routing abstract we consider the multi trip vehicle routing problem in which each vehicle can perform several routes during the same working shift to serve a set of customers the problem arises when customers are close to each other or when their demands are large a common approach consists of solving this problem by combining vehicle routing heuristics with bin packing routines in order to assign routes to vehicles we compare this approach with a heuristic that makes use of specific operators designed to tackle the routing and the assignment aspects of the problem simultaneously two large neighborhood search heuristics are proposed to perform the comparison we provide insights into the configuration of the proposed algorithms by analyzing the behavior of several of their components in particular we question the impact of the roulette wheel mechanism we also observe that guiding the search with an objective function designed for the multi trip case is crucial even when exploring the solution space of the vehicle routing problem we provide several best known solutions for benchmark instances

variable neighborhood search principles and applications abstract systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization called variable neighborhood search vns we present a basic scheme for this purpose which can easily be implemented using any local search algorithm as a subroutine its effectiveness is illustrated by solving several classical combinatorial or global optimization problems moreover several extensions are proposed for solving large problem instances using vns within the successive approximation method yields a two level vns called variable neighborhood decomposition search vnds modifying the basic scheme to explore easily valleys far from the incumbent solution yields an efficient skewed vns svns heuristic finally we show how to stabilize column generation algorithms with help of vns and discuss various ways to use vns in graph theory i e to suggest disprove or give hints on how to prove conjectures an area where metaheuristics do not appear to have been applied before

a multi threaded local search algorithm and computer implementation for the multi mode resource constrained multi project scheduling problem abstract the article describes a solution approach for the multi mode resource constrained multi project scheduling problem our key ideas are based on the concepts of variable neighborhood search together with iterated local search a particular focus of this work is devoted towards the parallel implementation of such local search solution techniques with the increasing availability of parallel multi core computer hardware we believe that such techniques are about to gain attractiveness in the future experiments have been conducted on benchmark instances of the mista 2013 challenge as well as on the well known mmlib datasets the approach described in this article ranked second in the challenge and found new best results to 1371 of the 4320 mmlib instances note that the source code of our implementation has been made available under http dx doi org 10 17632 cw95t56hjv 1 the software may be freely used for non profit research education purposes

permutation filters a class of nonlinear filters based on set permutations introduces and analyzes a new class of nonlinear filters that have their roots in permutation theory the authors show that a large body of nonlinear filters proposed to date constitute a proper subset of permutation filters spl pscr filters in particular rank order filters weighted rank order filters and stack filters embody limited permutation transformations of a set indeed by using the full potential of a permutation group transformation one can design very efficient estimation algorithms permutation groups inherently utilize both rank order and temporal order information thus the estimation of nonstationary processes in gaussian nongaussian environments with frequency selection can be effectively addressed an adaptive design algorithm that minimizes the mean absolute error criterion is described as well as a more flexible adaptive algorithm that attains the optimal permutation filter under a deterministic least normed error criterion simulation results are presented to illustrate the performance of permutation filters in comparison with other widely used filters

revisiting dynamic programming for finding optimal subtrees in trees in this paper we revisit an existing dynamic programming algorithm for finding optimal subtrees in edge weighted trees this algorithm was sketched by maffioli in a technical report in 1991 first we adapt this algorithm for the application to trees that can have both node and edge weights second we extend the algorithm such that it does not only deliver the values of optimal trees but also the trees themselves finally we use our extended algorithm for developing heuristics for the k cardinality tree problem in undirected graphs g with node and edge weights this np hard problem consists of finding in the given graph a tree with exactly k edges such that the sum of the node and the edge weights is minimal in order to show the usefulness of our heuristics we conduct an extensive computational analysis that concerns most of the existing problem instances our results show that with growing problem size the proposed heuristics reach the performance of state of the art metaheuristics therefore this study can be seen as a cautious note on the scaling of metaheuristics

design and performance of combination filters for signal restoration a class of nonlinear moving window filters is investigated for restoration and detection of signals embedded in additive white gaussian and non gaussian noise the filters of this class called combination filters c filters use both rank order and temporal order information from the input observation sequence within finite processing windows to produce the outputs a c filter combines the characteristics of linear fir finite impulse response filters and nonlinear filters of the order statistics type the output of a c filter in each processing window is defined to be the rank order dependent weighting of temporal order data both analytical and training procedures for designing the c filters are considered to get further improvement in overall performance the authors extend the concept of c filters and introduce a class of generalized c filters gc filters which are shown to have desirable properties performance characteristics of c and gc filters in signal restoration are considered through computer simulation

a hybrid particle swarm optimization variable neighborhood search algorithm for constrained shortest path problems abstract in this paper a well known np hard problem the constrained shortest path problem is studied as efficient metaheuristic approaches are required for its solution a new hybridized version of particle swarm optimization algorithm with variable neighborhood search is proposed for solving this significant combinatorial optimization problem particle swarm optimization pso is a population based swarm intelligence algorithm that simulates the social behavior of social organisms by using the physical movements of the particles in the swarm a variable neighborhood search vns algorithm is applied in order to optimize the particles position in the proposed algorithm the particle swarm optimization with combined local and global expanding neighborhood topology psolgent a different equation for the velocities of particles is given and a novel expanding neighborhood topology is used another issue in the application of the vns algorithm in the constrained shortest path problem is which local search algorithms are suitable from this problem in this paper a number of continuous local search algorithms are used the algorithm is tested in a number of modified instances from the tsplib and comparisons with classic versions of pso and with other versions of the proposed method are performed also the results of the algorithm are compared with the results of a number of metaheuristic and evolutionary algorithms the results obtained are very satisfactory and strengthen the efficiency of the algorithm

on the use of multi neighbourhood structures within a tabu based memetic approach to university timetabling problems finding a good university timetabling system is not a simple task for a higher educational organisation as a result many approaches to generating sufficiently good solutions have been introduced this is mainly due to the high complexity within the search landscape moreover each educational organisation has its own rules and specifications in this paper a tabu based memetic algorithm that hybridises a genetic algorithm with a tabu search algorithm is proposed as an improved algorithm for university timetabling problems this algorithm is employed on a set of neighbourhood structures during the search process with the aim of gaining significant improvements in solution quality the sequence of neighbourhood structures has been considered to understand its effect on the search space random best and general sequences of neighbourhood structures have been evaluated in this work the concept of a tabu list is embedded to control the selection of neighbourhood structures that are not dependent on the problem domains during the optimisation process after the crossover and mutation operators are applied to the selected solutions from the population pool the algorithm will penalise neighbourhood structures that are unable to generate better solutions the proposed algorithm has been applied and evaluated against the latest methodologies in the literature with respect to standard benchmark problems we demonstrate that the proposed algorithm produces some of the best known results when tested on itc2007 competition datasets

an adaptive multiphase approach for large unconditional and conditional p median problems abstract a multiphase approach that incorporates demand points aggregation variable neighbourhood search vns and an exact method is proposed for the solution of large scale unconditional and conditional p median problems the method consists of four phases in the first phase several aggregated problems are solved with a local search with shaking procedure to generate promising facility sites which are then used to solve a reduced problem in phase 2 using vns or an exact method the new solution is then fed into an iterative learning process which tackles the aggregated problem phase 3 phase 4 is a post optimisation phase applied to the original disaggregated problem for the p median problem the method is tested on three types of datasets which consist of up to 89 600 demand points the first two datasets are the birch and the tsp datasets whereas the third is our newly geometrically constructed dataset that has guaranteed optimal solutions the computational experiments show that the proposed approach produces very competitive results the proposed approach is also adapted to cater for the conditional p median problem with interesting results

variable neighbourhood search for bandwidth reduction the problem of reducing the bandwidth of a matrix consists of finding a permutation of rows and columns of a given matrix which keeps the non zero elements in a band as close as possible to the main diagonal this np complete problem can also be formulated as a vertex labelling problem on a graph where each edge represents a non zero element of the matrix we propose a variable neighbourhood search based heuristic for reducing the bandwidth of a matrix which successfully combines several recent ideas from the literature empirical results for an often used collection of 113 benchmark instances indicate that the proposed heuristic compares favourably to all previous methods moreover with our approach we improve best solutions in 50 of instances of large benchmark tests

column generation algorithms for exact modularity maximization in networks finding modules or clusters in networks currently attracts much attention in several domains the most studied criterion for doing so due to newman and girvan phys rev e 69 026113 2004 is modularity maximization many heuristics have been proposed for maximizing modularity and yield rapidly near optimal solution or sometimes optimal ones but without a guarantee of optimality there are few exact algorithms prominent among which is a paper by xu et al eur phys j b 60 231 2007 modularity maximization can also be expressed as a clique partitioning problem and the row generation algorithm of grotschel and wakabayashi math program 45 59 1989 applied we propose to extend both of these algorithms using the powerful column generation methods for linear and non linear integer programming performance of the four resulting algorithms is compared on problems from the literature instances with up to 512 entities are solved exactly moreover the computing time of previously solved problems are reduced substantially

upper and lower bounding procedures for minimum rooted k subtree problem abstract given an undirected graph and a fixed root node on it the minimum rooted k subtree problem is the problem of finding a minimum cost connected subtree with exactly k edges that includes the root node applications of this problem appear in several fields the problem is proved to be np hard due to the existence of a root node we are able to derive a greedy procedure that gives a stronger lower bound to this problem than those in earlier studies heuristics are also discussed to obtain an upper bound computational results indicate that the proposed lower bounding procedure is effective when k is small especially for grid type graphs we observe that the upper and lower bounds frequently coincide with each other

transform domain lms algorithm the concept of transform domain adaptive filtering is introduced in certain applications filtering in the transform domain results in great improvements in convergence rate over the conventional time domain adaptive filtering the relationship between several existing frequency domain adaptive filtering algorithms is established applications of the discrete fourier transform dft and the discrete cosine transform dct domain adaptive filtering algorithms in the areas of speech processing and adaptive line enhancers are discussed

skewed vns enclosing second order algorithm for the degree constrained minimum spanning tree problem we develop ideas to enhance the performance of the variable neighborhood search vns by guiding the search in the shaking phase and by employing the skewed strategy for this purpose second order algorithms and skewed functions expressing structural differences are embedded in an efficient vns proposed in the literature for the degree constrained minimum spanning tree problem given an undirected graph with weights associated with its edges the degree constrained minimum spanning tree problem consists in finding a minimum spanning tree of the given graph subject to constraints on node degrees computational experiments are conducted on the largest and hardest benchmark instances found in the literature to date we report results showing that the vns with the proposed strategies improved the best known solutions for all the hardest benchmark instances moreover these new best solutions significantly reduced the gaps with respect to tight lower bounds reported in the literature

nested general variable neighborhood search for the periodic maintenance problem abstract in this paper we study the periodic maintenance problem given a set of m machines and a horizon of t periods find indefinitely repeating itself maintenance schedule such that at most one machine can be serviced at each period in addition all the machines must be serviced at least once for any cycle in each period the machine i generates a servicing cost b i or an operating cost which depends on the last period in which i was serviced the operating cost of each machine i in a period equals a i times the number of periods since the last servicing of that machine the main objective is to find a cyclic maintenance schedule of a periodicity t that minimizes total cost to solve this problem we propose a new mixed integer programming formulation and a new heuristic method based on general variable neighborhood search called nested general variable neighborhood search the performance of this heuristic is shown through an extensive experimentation on a diverse set of problem instances

a note on solving large p median problems abstract in a previous paper we presented a tree search algorithm for the p median problem the problem of locating p facilities medians on a network which was based upon la grangean relaxation and subgradient optimisation that algorithm solved optimally problems with an arbitrary number of medians and having up to 200 vertices in this note we show that it is possible to enhance that algorithm to solve optimally problems having up to 900 vertices using the cray 1s computer

or software orsep operations research software exchange program edited by professor h w hamacher k_tree k_subgraph a program package for minimal weighted k cardinality trees and subgraphs

heuristic concentration two stage solution construction abstract by utilizing information from multiple runs of an interchange heuristic we construct a new solution that is generally better than the best local optimum previously found this new two stage approach to combinatorial optimization is demonstrated in the context of the p median problem two layers of optimization are superimposed the first layer is a conventional heuristic the second is a heuristic or exact procedure which draws on the concentrated solution set generated by the initial heuristic the intention is to provide an alternative heuristic procedure which when dealing with large problems has a higher probability of producing optimal solutions than existing methods the procedure is fairly general and appears to be applicable to combinatorial problems in a number of contexts

a variable neighborhood search heuristic for periodic routing problems the aim of this paper is to propose a new heuristic for the periodic vehicle routing problem pvrp without time windows the pvrp extends the classical vehicle routing problem vrp to a planning horizon of several days each customer requires a certain number of visits within this time horizon while there is some flexibility on the exact days of the visits hence one has to choose the visit days for each customer and to solve a vrp for each day our method is based on variable neighborhood search vns computational results are presented that show that our approach is competitive and even outperforms existing solution procedures proposed in the literature also considered is the special case of a single vehicle i e the periodic traveling salesman problem ptsp it is shown that slight changes of the proposed vns procedure is also competitive for the ptsp

a higher order method for stationary shock problems an equidistant finite difference method is proposed for quasilinear singularly perturbed boundary value problems the method uses a combination of one sided schemes and a third order three point scheme it is easy to implement and produces third order accuracy away from shocks

an efficient tabu search procedure for the p median problem abstract in this paper we present a new solution heuristic for the p median problem the algorithm is based on tabu search principles and uses short term and long term memory as well as strategic oscillation and random tabu list sizes our proposed procedure is compared with two other move heuristics a well known interchange heuristic and a recent hybrid heuristic in computational tests on networks ranging in size up to 500 nodes the new heuristic is found to be superior with respect to the quality of solutions produced

an improved column generation algorithm for minimum sum of squares clustering given a set of entities associated with points in euclidean space minimum sum of squares clustering mssc consists in partitioning this set into clusters such that the sum of squared distances from each point to the centroid of its cluster is minimized a column generation algorithm for mssc was given by du merle et al in siam journal scientific computing 21 1485 1505 the bottleneck of that algorithm is the resolution of the auxiliary problem of finding a column with negative reduced cost we propose a new way to solve this auxiliary problem based on geometric arguments this greatly improves the efficiency of the whole algorithm and leads to exact solution of instances with over 2 300 entities i e more than 10 times as much as previously done

finite difference schemes for quasilinear singular perturbation problems finite difference schemes for singularly perturbed quasilinear boundary value problems are considered the schemes have fitting factors which guarantee their uniform stability with respect to the perturbation parameter besides the usual stability in the discrete l1 norm we consider the maximum norm stability as well various schemes are compared numerically

new insertion and postoptimization procedures for the traveling salesman problem this paper describes a new insertion procedure and a new postoptimization routine for the traveling salesman problem the combination of the two methods results in an efficient algorithm genius which outperforms known alternative heuristics in terms of solution quality and computing time

accelerated tabu search for no wait flowshop scheduling problem with maximum lateness criterion abstract for the no wait flowshop scheduling problem with maximum lateness criterion properties are developed to speed up three kinds of basic operations generating candidate solutions i e the insertion of a new job into a partial sequence and the insertion and exchange neighborhood moves the properties reduce the time to evaluate a candidate from o nm to o 1 and simplify the implementation of the heuristics based on the basic operations by evaluating candidates before their generation the properties also reduce from o n 3 m to o n 2 the time complexity of well known neh heuristic and the complete evaluation of the insertion and exchange neighborhoods tabu search ts is applied to the considered problem since ts tries to find the best neighbor of the current solution in each iteration and therefore can much benefit from the speedups three different ways to use insertion and exchange neighborhoods are compared in ts computational experiments show that the speedups are more helpful as job number increases and all proposed ts algorithms are more effective and robust than the existing algorithms although two and single neighborhood ts algorithms are not significantly different two neighborhood ts algorithms are more preferable

polyhedral results and a branch and cut algorithm for the k cardinality tree problem given an undirected graph g with vertex and edge weights the k cardinality tree problem asks for a minimum weight tree of g containing exactly k edges in this paper we consider a directed graph reformulation of the problem and carry out a polyhedral investigation of the polytope defined by the convex hull of its feasible integral solutions three new families of valid inequalities are identified and two of them are proven to be facet implying for that polytope additionally a branch and cut algorithm that separates the new inequalities is implemented and computationally tested the results obtained indicate that our algorithm outperforms its counterparts from the literature such a performance could be attributed to a large extent to the use of the new inequalities and also to some pre processing tests introduced in this study

large multiple neighborhood search for the clustered vehicle routing problem abstract the clustered vehicle routing problem is a variant of the classical capacitated vehicle routing problem in which customers are partitioned into clusters and it is assumed that each cluster must have been served completely before the next cluster is served this decomposes the problem into three subproblems i e the assignment of clusters to routes the routing inside each cluster and the sequencing of the clusters in the routes the second task requires the solution of several hamiltonian path problems one for each possibility to route through the cluster we pre compute the hamiltonian paths for every pair of customers of each cluster we present a large multiple neighborhood search which makes use of multiple cluster destroy and repair operators and a variable neighborhood descent vnd for post optimization the vnd is based on classical neighborhoods such as relocate 2 opt and swap all working on the cluster level and a generalization of the balas simonetti neighborhood modifying simultaneously the intra cluster routings and the sequence of clusters in a route computational results with our new approach compare favorably to existing approaches from the literature

a survey of numerical techniques for solving singularly perturbed ordinary differential equations this survey paper contains a surprisingly large amount of material and indeed can serve as an introduction to some of the ideas and methods of singular perturbation theory starting from prandtl s work a large amount of work has been done in the area of singular perturbations this paper limits its coverage to some standard singular perturbation models considered by various workers and the numerical methods developed by numerous researchers after 1984 2000 the work done in this area during the period 1905 1984 has already been surveyed by the first author of this paper see appl math comput 30 1989 223 for details due to the space constraints we have covered only singularly perturbed one dimensional problems

on the extremal properties of the average eccentricity the eccentricity of a vertex is the maximum distance from it to another vertex and the average eccentricity ecc g of a graph g is the mean value of eccentricities of all vertices of g the average eccentricity is deeply connected with a topological descriptor called the eccentric connectivity index defined as a sum of products of vertex degrees and eccentricities in this paper we analyze extremal properties of the average eccentricity introducing two graph transformations that increase or decrease ecc g furthermore we resolve four conjectures obtained by the system autographix about the average eccentricity and other graph parameters the clique number and the independence number refute one autographix conjecture about the average eccentricity and the minimum vertex degree and correct one autographix conjecture about the domination number

analysis of difference schemes for a stationary shock problem we consider the limit function u of the solutions u varepsilon of a singularly perturbed boundary value problem in general u will be discontinuous two difference approximations of the boundary value problem are studied and the discrete values for varepsilon 0 h to 0 are compared with u error estimates of order o h and o h 2 are proved and the sharpness of numerical layers is established

monotone difference schemes for singular perturbation problems we consider numerical solutions of the boundary value problem varepsilon y f y b x y 0 0 leqq x leqq 1 y 0 a y 1 b varepsilon 0 b y geqq delta 0 with monotone difference schemes on nonuniform grids we prove general convergence results and show that the engquist osher monotone scheme will reproduce essential properties of the true solution for any grid for the inversion of the nonlinear scheme we suggest implicit time relaxation with variable time steps

heuristic concentration and tabu search a head to head comparison earlier this year two papers applying the metaheuristics tabu search ts and heuristic concentration hc to the p median problem were published in consecutive volumes of this journal here we apply the method of hc to some of the data sets which were used for computational experience in the paper on ts for these examples which we regard as being of a particularly challenging character hc discovers the superior solution superior to ts in about 95 of the cases and where the optimal solution is known the optimal solution in about 80 of the cases no general conclusion on the relative times for the two approaches can be drawn

adaptive filters based on order statistics an adaptive filter structure which is based on linear combinations of order statistics is proposed an efficient method to update the filter coefficients is presented which is based on the minimal mean square error criterion and which is similar to the widrow algorithm for the linear adaptive filters another method for coefficient update is presented which is similar to the recursive least squares rls algorithm and which has faster convergence properties the proposed filter can adapt well to a variety of noise probability distributions including impulsive noise it also performs well in the case of nonstationary signals and therefore it is suitable for image processing applications

some improvements of the nonequidistant engquist osher scheme two nonequidistant finite difference schemes for quasilinear singular perturbation problems are given and their properties are discussed and compared one of them corresponds to the equidistant lorenz modification of the engquist osher scheme the other one switches in dependence on the cell reynolds number both schemes show quadratic l 1 accuracy but the second one gives better pointwise results

the extended concentric tabu for the quadratic assignment problem abstract in this paper we propose to extend the concentric tabu search for the quadratic assignment problem to include more permissible moves two extensions are suggested and tested the computational comparisons with existing hybrid genetic algorithms provide comparable solutions to the best available algorithms

the tree representation for the pickup and delivery traveling salesman problem with lifo loading the feasible solutions of the traveling salesman problem with pickup and delivery tsppd are commonly represented by vertex lists however when the tsppd is required to follow a policy that loading and unloading operations must be performed in a last in first out lifo manner we show that its feasible solutions can be represented by trees consequently we develop a novel variable neighborhood search vns heuristic for the tsppd with last in first out loading tsppdl involving several search operators based on the tree data structure extensive experiments suggest that our vns heuristic is superior to the current best heuristics for the tsppdl in terms of solution quality while requiring no more computing time as the size of the problem increases

a mesh adaptive direct search algorithm for multiobjective optimization abstract this work studies multiobjective optimization mop of nonsmooth functions subject to general constraints we first present definitions and optimality conditions as well as some single objective formulations of mop parameterized with respect to some reference point in the space of objective functions next we propose a new algorithm called m ulti m ads multiobjective mesh adaptive direct search for mop m ulti m ads generates an approximation of the pareto front by solving a series of single objective formulations of mop generated using the nbi natural boundary intersection framework these single objective problems are solved using the m ads mesh adaptive direct search algorithm for constrained nonsmooth optimization the pareto front approximation is shown to satisfy some first order necessary optimality conditions based on the clarke calculus m ulti m ads is then tested on problems from the literature with different pareto front landscapes and on a styrene production process simulation problem from chemical engineering

fuzzy j means a new heuristic for fuzzy clustering abstract a fuzzy clustering problem consists of assigning a set of patterns to a given number of clusters with respect to some criteria such that each of them may belong to more than one cluster with different degrees of membership in order to solve it we first propose a new local search heuristic called fuzzy j means where the neighbourhood is defined by all possible centroid to pattern relocations the integer solution is then moved to a continuous one by an alternate step i e by finding centroids and membership degrees for all patterns and clusters to alleviate the difficulty of being stuck in local minima of poor value this local search is then embedded into the variable neighbourhood search metaheuristic results on five standard test problems from the literature are reported and compared with those obtained with the well known fuzzy c means heuristic it appears that solutions of substantially better quality are obtained with the proposed methods than with this former one

extended formulations and branch and cut algorithms for the black and white traveling salesman problem in this paper we study integer linear programming models and develop branch and cut algorithms to solve the black and white traveling salesman problem bwtsp bourgeois laporte semet 2003 which is a variant of the well known traveling salesman problem tsp two strategies to model the bwtsp have been used in the literature the problem is either modeled on the original graph as tsp using a single set of binary edge variables and with additional non trivial hop and distance constraints between every pair of black nodes see ghiani laporte semat 2006 or as a sequence of constrained paths composed of white nodes connecting pairs of black nodes see muter 2015 in this paper we study and develop an intermediate approach based on the observation that it is sufficient to guarantee the required distance and hop limit of the path from a given black node to the next black node without explicitly stating which one it is thus instead of stating the two constraints after adding appropriately defined variables for each pair of black nodes they are stated for each black node only that represents the source of each path based on this idea we develop several variants of position and distance dependent reformulations together with corresponding layered graph representations branch and cut algorithms are developed for all proposed formulations and empirically compared by an extensive computational study the obtained results allow us to provide insights into individual advantages and disadvantages of the different models

a hybrid integer programming and variable neighbourhood search algorithm to solve nurse rostering problems abstract the nurse rostering problem nrp is defined as assigning a number of nurses to different shifts during a specified planning period considering some regulations and preferences this is often very difficult to solve in practice particularly by applying a sole approach in this paper we propose a novel hybrid algorithm combining the strengths of integer programming ip and variable neighbourhood search vns algorithms to design a hybrid method for solving the nrp after generating the initial solution using a greedy heuristic the solution is further improved by employing a variable neighbourhood descent algorithm then ip deeply embedded in the vns algorithm is employed within a ruin and recreate framework to assist the search process finally ip is called again to further refine the solution during the remaining time we utilise the strength of ip not only to diversify the search process but also to intensify the search efforts to identify the quality of the current solution we use a new generic scoring scheme to mark the low penalty parts of the solution based on the computational tests with 24 instances recently introduced in the literature we obtain better results with our proposed algorithm where the hybrid algorithm outperforms two state of the art algorithms and gurobi in most of the instances furthermore we introduce 11 randomly generated instances to further evaluate the efficiency of the hybrid algorithm and we make these computationally challenging instances publicly available to other researchers for benchmarking purposes

continuous scatter search an analysis of the integration of some combination methods and improvement strategies scatter search is an evolutionary method that shares with genetic algorithms a well known evolutionary approach the employment of a combination method that combines the features of two parent vectors to form several offspring furthermore it uses improvement strategies to efficiently produce the local tuning of the solutions an important aspect concerning scatter search is the trade off between the exploration abilities of the combination method and the exploitation capacity of the improvement mechanism in this paper we deal with a continuous version of the scatter search which works directly with vectors of real components our objective is to study the balance between the reliability induced by the combination method and the accuracy levels provided by the improvement mechanism in continuous scatter search to do this we analyse two combination methods that may be applied to continuous scatter search 1 the blx a operator which is one of the most effective combination methods for real coded genetic algorithms and 2 the average combination method which is the classical combination method for continuous scatter search we investigate the interrelations that exist between

a vns heuristic for escaping local extrema entrapment in normalized cut clustering normalized cut is one of the most popular graph clustering criteria the main approaches proposed for its resolution are spectral clustering methods and a multilevel approach of dhillon et al tpami 29 1944 1957 2007 called graclus their aim is to obtain good solutions in a small amount of time for large instances metaheuristics are general frameworks for stochastic searches often employed in global optimization to improve the solutions obtained by other heuristics variable neighborhood search vns is a metaheuristic which exploits systematically the idea of neighborhood change during the search in this paper we propose a vns heuristic for normalized cut segmentation computational experiments show that in most cases this vns heuristic improves significantly and in moderate time the solutions obtained by the current state of the art algorithms i e graclus and a spectral method proposed by yu and shi iccv 2003

a hybrid heuristic algorithm for the open pit mining operational planning problem this paper deals with the open pit mining operational planning problem with dynamic truck allocation the objective is to optimize mineral extraction in the mines by minimizing the number of mining trucks used to meet production goals and quality requirements according to the literature this problem is np hard so a heuristic strategy is justified we present a hybrid algorithm that combines characteristics of two metaheuristics greedy randomized adaptive search procedures and general variable neighborhood search the proposed algorithm was tested using a set of real data problems and the results were validated by running the cplex optimizer with the same data this solver used a mixed integer programming model also developed in this work the computational experiments show that the proposed algorithm is very competitive finding near optimal solutions with a gap of less than 1 in most instances demanding short computing times

order statistic filter banks filter banks play a major role in multirate signal processing where these have been successfully used in a variety of applications in the past filter banks have been developed within the framework of linear filters it is well known however that linear filters may have less than satisfactory performance whenever the underlying processes are non gaussian we introduce the nonlinear class of order statistic os filter banks that exploit the spectral characteristics of the input signal as well as its rank ordering structure the attained subband signals provide frequency and rank information in a localized time interval os filter banks can lead to significant gains over linear filter banks particularly when the input signals contain abrupt changes and details as is common with image and video signals os filter banks are formed using traditional linear filter banks as fundamental building blocks it is shown that os filter banks subsume linear filter banks and that the latter are obtained by simple linear transformations of the former to illustrate the properties of os filter banks we develop simulations showing that the learning characteristics of the lms algorithm which are used to optimize the weight taps of os filters can be significantly improved by performing the adaptation in the os subband domain

frequency analysis and synthesis of a class of nonlinear filters nonlinear filters are analyzed from a spectral point of view the equivalent frequency behavior of a filter is described by its linear part which represents the linear nonrecursive filter that best matches in the mean square sense the behavior of the filter the class considered includes all the order statistic filters l filters such as median midrange alpha trim and some new order statistic filters ll filters defined by the authors to generalize l filters and fir filters the formulation leads to a technique for imposing on the nonlinear filters a given spectral behavior a simulation of the design for a low pass ll filter is given

a discrete particle swarm optimization for lot streaming flowshop scheduling problem we consider an n job m machine lot streaming problem in a flowshop with equal size sublots where the objective is to minimize the total weighted earliness and tardiness to solve this problem we first propose a so called net benefit of movement nbm algorithm which is much more efficient than the existing linear programming model for obtaining the optimal starting and completion times of sublots for a given job sequence a new discrete particle swarm optimization dpso algorithm incorporating the nbm algorithm is then developed to search for the best sequence the new dpso improves the existing dpso by introducing an inheritance scheme inspired by a genetic algorithm into particles construction to verify the proposed dpso algorithm comparisons with the existing dpso algorithm and a hybrid genetic algorithm hga are made computational results show that the proposed dpso algorithm with a two point inheritance scheme is very competitive for the lot streaming flowshop scheduling problem

less is more basic variable neighborhood search heuristic for balanced minimum sum of squares clustering abstract clustering addresses the problem of finding homogeneous and well separated subsets called clusters from a set of given data points in addition to the points themselves in many applications there may exist constraints regarding the size of the clusters to be found particularly in balanced clustering these constraints impose that the entities be equally spread among the different clusters in this work we present a basic variable neighborhood search heuristic for balanced minimum sum of squares clustering following the recently proposed less is more approach computational experiments and statistical tests show that the proposed algorithm outperforms the current state of the art algorithm for the problem indicating that non sophisticated and easy to implement metaheuristic methods can be sufficient to produce successful results in practice

nonlinear multiresolution signal decomposition schemes ii morphological wavelets interest in multiresolution techniques for signal processing and analysis is increasing steadily an important instance of such a technique is the so called pyramid decomposition scheme this paper presents a general theory for constructing linear as well as nonlinear pyramid decomposition schemes for signal analysis and synthesis the proposed theory is based on the following ingredients 1 the pyramid consists of a finite or infinite number of levels such that the information content decreases toward higher levels and 2 each step toward a higher level is implemented by an information reducing analysis operator whereas each step toward a lower level is implemented by an information preserving synthesis operator one basic assumption is necessary synthesis followed by analysis yields the identity operator meaning that no information is lost by these two consecutive steps several examples of pyramid decomposition schemes are shown to be instances of the proposed theory a particular class of linear pyramids morphological skeleton decompositions the morphological haar pyramid median pyramids etc furthermore the paper makes a distinction between single scale and multiscale decomposition schemes i e schemes without or with sample reduction finally the proposed theory provides the foundation of a general approach to constructing nonlinear wavelet decomposition schemes and filter banks

general variable neighborhood search for the continuous optimization we suggest a new heuristic for solving unconstrained continuous optimization problems it is based on a generalized version of the variable neighborhood search metaheuristic different neighborhoods and distributions induced from different metrics are ranked and used to get random points in the shaking step we also propose vns for solving constrained optimization problems the constraints are handled using exterior point penalty functions within an algorithm that combines sequential and exact penalty transformations the extensive computer analysis that includes the comparison with genetic algorithm and some other approaches on standard test functions are given with our approach we obtain encouraging results

an interior point algorithm for minimum sum of squares clustering an exact algorithm is proposed for minimum sum of squares nonhierarchical clustering i e for partitioning a given set of points from a euclidean m space into a given number of clusters in order to minimize the sum of squared distances from all points to the centroid of the cluster to which they belong this problem is expressed as a constrained hyperbolic program in 0 1 variables the resolution method combines an interior point algorithm i e a weighted analytic center column generation method with branch and bound the auxiliary problem of determining the entering column i e the oracle is an unconstrained hyperbolic program in 0 1 variables with a quadratic numerator and linear denominator it is solved through a sequence of unconstrained quadratic programs in 0 1 variables to accelerate resolution variable neighborhood search heuristics are used both to get a good initial solution and to solve quickly the auxiliary problem as long as global optimality is not reached estimated bounds for the dual variables are deduced from the heuristic solution and used in the resolution process as a trust region proved minimum sum of squares partitions are determined for the first time for several fairly large data sets from the literature including fisher s 150 iris