color level sets a multi phase method for structural topology optimization with multiple materials in this paper we address the problem of structural shape and topology optimization in a multi material domain a level set method is employed as an alternative approach to the popular homogenization based methods of rule of mixtures for multi material modeling a multi phase level set model is adapted for material and topology representation this model eliminates the need for a material interpolation or phase mixing scheme it only requires m level set functions to represent a structure of n 2m different material phases in a principle similar to combining colors from the three primary colors therefore this multi phase model may be referred to as a color level set representation which has its unique benefits it is flexible to handle complex topologies it substantially reduces the number of model functions when n 3 it automatically avoids the problem of overlap between material phases of a conventional partitioning approach we describe numerical techniques for efficient and robust implementation of the method by embedding a rectilinear grid in a fixed finite element mesh defined on a reference design domain this would separate the issues of accuracy in numerical calculations of the physical equation and in the level set model propagation a gradient projection method is described for incorporating multiple constraints in the problem finally the benefits and the advantages of the developed method are illustrated with several 2d examples of mean compliance minimization of multi material structures

implementation of an adaptive finite element approximation of the mumford shah functional we present and detail a method for the numerical solving of the mumford shah problem based on a finite element method and on adaptive meshes we start with the formulation introduced in 13 detail its numerical implementation and then propose a variant which is proved to converge to the mumford shah problem a few experiments are illustrated

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

boundary behaviour of the unique solution to a singular dirichlet problem with a convection term by karamata regular variation theory and constructing comparison functions we derive that the boundary behaviour of the unique solution to a singular dirichlet problem u b x g u u q u 0 x u 0 which is independent of u q w here is a bounded domain with smooth boundary in r n r q 0 2 lims 0 g s a ndb is nonnegative on which may be vanishing on the boundary

cooperative metaheuristics for the permutation flowshop scheduling problem in this work we propose cooperative metaheuristic methods for the permutation flowshop scheduling problem considering two objectives separately total tardiness and makespan we use the island model where each island runs an instance of the algorithm and communications start when the islands have reached certain level of evolution that is communication is not allowed from the beginning of the execution subsequent ones occur when new better solutions are found we carry out an exhaustive comparison of the cooperative methods against the sequential counterparts running in completely comparable scenarios results have been carefully analysed by means of statistical procedures and we can conclude that the cooperative methods yield much better results than the sequential algorithms and state of the art methods running in the same number of processors but without communications the proposed cooperative schemes are easy to apply to other algorithms and problems

a discrete artificial bee colony algorithm for the total flowtime minimization in permutation flow shops obtaining an optimal solution for a permutation flowshop scheduling problem with the total flowtime criterion in a reasonable computational timeframe using traditional approaches and optimization tools has been a challenge this paper presents a discrete artificial bee colony algorithm hybridized with a variant of iterated greedy algorithms to find the permutation that gives the smallest total flowtime iterated greedy algorithms are comprised of local search procedures based on insertion and swap neighborhood structures in the same context we also consider a discrete differential evolution algorithm from our previous work the performance of the proposed algorithms is tested on the well known benchmark suite of taillard the highly effective performance of the discrete artificial bee colony and hybrid differential evolution algorithms is compared against the best performing algorithms from the existing literature in terms of both solution quality and cpu times ultimately 44 out of the 90 best known solutions provided very recently by the best performing estimation of distribution and genetic local search algorithms are further improved by the proposed algorithms with short term searches the solutions known to be the best to date are reported for the benchmark suite of taillard with long term searches as well

a multiphase level set framework for image segmentation using the mumford and shah model we propose a new multiphase level set framework for image segmentation using the mumford and shah model for piecewise constant and piecewise smooth optimal approximations the proposed method is also a generalization of an active contour model without edges based 2 phase segmentation developed by the authors earlier in t chan and l vese 1999 in scale space 99 m nilsen et al eds lncs vol 1682 pp 141 151 and t chan and l vese 2001 ieee ip 10 2 266 277 the multiphase level set formulation is new and of interest on its own by construction it automatically avoids the problems of vacuum and overlaps it needs only log n level set functions for n phases in the piecewise constant cases it can represent boundaries with complex topologies including triple junctionss in the piecewise smooth case only two level set functions formally suffice to represent any partition based on the four color theorem finally we validate the proposed models by numerical results for signal and image denoising and segmentation implemented using the osher and sethian level set method

a comprehensive review and evaluation of permutation flowshop heuristics in this work we present a review and comparative evaluation of heuristics and metaheuristics for the well known permutation flowshop problem with the makespan criterion a number of reviews and evaluations have already been proposed however the evaluations do not include the latest heuristics available and there is still no comparison of metaheuristics furthermore since no common benchmarks and computing platforms are used the results cannot be generalised we propose a comparison of 25 methods ranging from the classical johnson s algorithm or dispatching rules to the most recent metaheuristics including tabu search simulated annealing genetic algorithms iterated local search and hybrid techniques for the evaluation we use the standard test of taillard eur j operation res 64 1993 278 composed of 120 instances of different sizes in the evaluations we use the experimental design approach to obtain valid conclusions on the effectiveness and efficiency of the different methods tested

heuristics for a flowshop scheduling problem with stepwise job objective function abstract in this work we introduce the flowshop scheduling problem with delivery dates and cumulative payoffs this problem is a variation of the flowshop scheduling problem with job release dates that maximizes the total payoff with a stepwise job objective function this paper contributes towards proposing a mathematical formulation for this new problem and an original constructive heuristic additionally we develop a new benchmark of 300 hard instances which are available in a public repository besides we provide primal and dual bounds for them extensive computational experiments were carried out taking into account classical constructive heuristics and hybrid local searches results show the merit of the ff heuristic when compared to other classical heuristics for flowshop scheduling problems additionally we compare an iterated local search ils an iterated greedy search igs and a biased random key genetic algorithm brkga both customized for the studied problem and a commercial mixed integer programming solver the comparison between these methods showed that the brkga starting with a solution from ff heuristic is able to find the best solutions in a very short period of time iterated local search and the commercial solver presented significantly worse results than the aforementioned methods

piecewise linear approximation of vector valued images and curves via second order variational model variational models are known to work well for addressing image restoration regularization problems however most of the methods proposed in the literature are defined for scalar inputs and are used on multiband images such as rgb or multispectral imagery by the composition of a simple band wise processing this involves suboptimal results and may introduce artifacts only in a few cases variational models are extended to the case of vector valued inputs however the known implementations are restricted to the first order models while the second order models are never considered thus typical problems of the first order models such as the staircasing effect cannot be overtaken this paper considers a second order functional model to function approximation with free discontinuities given by blake zisserman bz and proposes an efficient minimization algorithm in the case of vector valued inputs in the bz model the hessian of the solution is penalized outside a set of finite length therefore the solution is forced to be piecewise linear moreover the model allows the formation of free discontinuities and free gradient discontinuities the proposed algorithm is applied to difficult color image restoration regularization problems and to piecewise linear approximation of curves in space

approximation by γ convergence of a curvature depending functional in visual reconstruction where r2 is a bounded open set the image domain h1 denotes the one dimensional hausdorff measure and g l is the input image the functional has to be minimized over all closed sets c and all u c1 c the function u represents a denoised approximation of the input image g and c represents the set of boundaries of the segmentation the mumford and shah variational model can be extended to several visual reconstruction problems see march 29 computation of depth from stereo images shah 39 computation of optical flow nesi 34 shape from shading shah 40 the existence of minimizers of gms has been proved independently by dal maso morel and solimini 21 and de giorgi carriero and leaci 23 using the compactness and lower semicontinuity theorems of ambrosio 3 mumford and shah 33 studied the properties of minimizers u c of gms assuming that c is a finite union of simple c1 1 curves meeting and meeting each other only at their endpoints they proved that the vertices of c may only be i triple points where three curves meet with equal angles ii points on the boundary of where one curve meets perpendicularly iii crack tips where a curve ends and meets nothing in computer vision the constraints imposed on the segmentations highlighted by such results constitute a drawback of the variational model in particular corners and t junctions which are relevant features for pattern recognition are distorted since the length measure is not sensitive to corners and junctions to allow for such singularities in the segmentations it is necessary to consider curvature depending energies functionals

an adaptive finite element approximation of a variational model of brittle fracture the energy of the francfort marigo model of brittle fracture can be approximated in the sense of gamma convergence by the ambrosio tortorelli functional in this work we formulate and analyze two adaptive finite element algorithms for the computation of its local minimizers for each algorithm we combine a newton type method with residual driven adaptive mesh refinement we present two theoretical results which demonstrate convergence of our algorithms to local minimizers of the ambrosio tortorelli functional

tabu enhanced iterated greedy algorithm a case study in the quadratic multiple knapsack problem abstract iterated greedy search is a simple and effective metaheuristic for combinatorial problems its flexibility enables the incorporation of components from other metaheuristics with the aim of obtaining effective and powerful hybrid approaches we propose a tabu enhanced destruction mechanism for iterated greedy search that records the last removed objects and avoids removing them again in subsequent iterations the aim is to provide a more diversified and successful search process with regards to the standard destruction mechanism which selects the solution components for removal completely at random we have considered the quadratic multiple knapsack problem as the application domain for which we also propose a novel local search procedure and have developed experiments in order to assess the benefits of the proposal the results show that the tabu enhanced iterated greedy approach in conjunction with the new local search operator effectively exploits the problem knowledge associated with the requirements of the problem considered attaining competitive results with regard to the corresponding state of the art algorithms

an existence and uniqueness result for the singular lane emden fowler equation abstract using a fixed point theorem of general concave operators we present in this paper criteria which guarantee the existence and uniqueness of positive solutions for the singular lane emden fowler equation

existence and convergence for quasi static evolution in brittle fracture this paper investigates the mathematical well posedness of the variational model of quasi static growth for a brittle crack proposed by francfort and marigo in 15 the starting point is a time discretized version of that evolution which results in a sequence of minimization problems of mumford and shah type functionals the natural weak setting is that of special functions of bounded variation and the main difficulty in showing existence of the time continuous quasi static growth is to pass to the limit as the time discretization step tends to 0 this is performed with the help of a jump transfer theorem which permits under weak convergence assumptions for a sequence un of sbv functions to its bv limit u to transfer the part of the jump set of any test field that lies in the jump set of u onto that of the converging sequence un in particular it is shown that the notion of minimizer of a mumford and shah type functional for its own jump set is stable under weak convergence assumptions furthermore our analysis justifies numerical methods used for computing the time continuous quasi static evolution 2003 wiley periodicals inc

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

a mumford shah level set approach for geometric image registration a new method for nonrigid registration of multimodal images is presented due to the large interdependence of segmentation and registration the approach is based on simultaneous segmentation and edge alignment the two processes are directly coupled and thus benefit from using complementary information of the entire underlying data set the approach is formulated as a bivariate variational free discontinuity problem in the mumford shah framework a geometric variable describing the contour set and a functional variable which represents the underlying deformation are simultaneously identified the contour set is represented by a level set function we derive a regularized gradient flow and describe an efficient numerical implementation using finite element discretization and multigrid techniques finally we illustrate the method in several applications such as multimodal intrapatient registration and reconstruction by registration to a reference object

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

approaching the rank aggregation problem by local search based metaheuristics abstract encouraged by the success of applying metaheuristics algorithms to other ranking based problems kemeny ranking problem and parameter estimation for mallows distributions in this paper we deal with the rank aggregation problem rap which can be viewed as a generalization of the kemeny problem to arbitrary rankings while in the kemeny problem the input is a set of permutations the rap consists in obtaining the consensus permutation for a sample of arbitrary rankings this is an np hard problem which can be approached by using greedy heuristic algorithms e g borda such algorithms are fast but the solutions so obtained are far to be optimal in this paper we propose the use of more complex search processes to deal with the rap in particular we perform a comparative study among some local based search metaheuristics hill climbing hc iterated local search ils variable neighborhood search vns and greedy randomized adaptive search procedure grasp we provide a complete analysis of the experimental study regarding accuracy and number of iterations required to reach the best solution from the results we can conclude that the selection of a suitable neighborhood plays a key role and that depending on the available resources cpu time a different algorithm vns ils or grasp could be the proper choice

the weighted independent domination problem integer linear programming models and metaheuristic approaches abstract this work deals with the so called weighted independent domination problem which is an np hard combinatorial optimization problem in graphs in contrast to previous work this paper considers the problem from a non theoretical perspective the first contribution consists in the development of three integer linear programming models second two greedy heuristics are proposed finally the last contribution is a population based iterated greedy metaheuristic which is applied in two different ways 1 the metaheuristic is applied directly to each problem instance and 2 the metaheuristic is applied at each iteration of a higher level framework known as construct merge solve and adapt to sub instances of the tackled problem instances the results of the considered algorithmic approaches show that integer linear programming approaches can only compete with the developed metaheuristics in the context of graphs with up to 100 nodes when larger graphs are concerned the application of the populated based iterated greedy algorithm within the higher level framework works generally best the experimental evaluation considers graphs of different types sizes densities and ways of generating the node and edge weights

an ensemble of discrete differential evolution algorithms for solving the generalized traveling salesman problem in this paper an ensemble of discrete differential evolution algorithms with parallel populations is presented in a single populated discrete differential evolution dde algorithm the destruction and construction dc procedure is employed to generate the mutant population whereas the trial population is obtained through a crossover operator the performance of the dde algorithm is substantially affected by the parameters of dc procedure as well as the choice of crossover operator in order to enable the dde algorithm to make use of different parameter values and crossover operators simultaneously we propose an ensemble of dde edde algorithms where each parameter set and crossover operator is assigned to one of the parallel populations each parallel parent population does not only compete with offspring population generated by its own population but also the offspring populations generated by all other parallel populations which use different parameter settings and crossover operators as an application area the well known generalized traveling salesman problem gtsp is chosen where the set of nodes is divided into clusters so that the objective is to find a tour with minimum cost passing through exactly one node from each cluster the experimental results show that none of the single populated variants was effective in solving all the gtsp instances whereas the edde performed substantially better than the single populated variants on a set of problem instances furthermore through the experimental analysis of results the performance of the edde algorithm is also compared against the best performing algorithms from the literature ultimately all of the best known averaged solutions for larger instances are further improved by the edde algorithm

positive solution for singular boundary value problems abstract a sufficient condition for the existence of positive solutions of the nonlinear boundary value problem u t f t u t 0 0 u 0 u 1 0 is constructed where f 0 1 0 0 is continuous f t u is locally lipschitz continuous and f t u u is strictly decreasing in u 0 for each t 0 1

a variable iterated greedy algorithm for the traveling salesman problem with time windows this paper presents a variable iterated greedy algorithm for solving the traveling salesman problem with time windows tsptw to identify a tour minimizing the total travel cost or the makespan separately the tsptw has several practical applications in both production scheduling and logistic operations the proposed algorithm basically relies on a greedy algorithm generating an increasing number of neighboring solutions through the use of the idea of neighborhood change in variable neighborhood search vns algorithms in other words neighboring solutions are generated by destructing a solution component and re constructing the solution again with variable destruction sizes in addition the proposed algorithm is hybridized with a vns algorithm employing backward and forward 1 opt local searches to further enhance the solution quality the performance of the proposed algorithm was tested on several benchmark suites from the literature experimental results confirm that the proposed algorithm is either competitive to or even better than the best performing algorithms from the literature ultimately new best known solutions are obtained for 38 out of 125 problem instances of the recently proposed benchmark suite whereas 15 out of 31 problem instances are also further improved for the makespan criterion

approximation of a brittle fracture energy with a constraint of non interpenetration linear fracture mechanics or at least the initiation part of that theory can be framed in a variational context as a minimization problem over a sbd type space the corresponding functional can in turn be approximated in the sense of convergence by a sequence of functionals involving a phase field as well as the displacement field we show that a similar approximation persists if additionally imposing a non interpenetration constraint in the minimization namely that only nonnegative normal jumps should be permissible 2010 mathematics subject classification 26a45

existence and global asymptotic behavior of positive solutions for nonlinear problems on the half line abstract in this paper we aim at studying the existence uniqueness and the exact asymptotic behavior of positive solutions to the following boundary value problem 1 a a u a t u 0 t 0 lim t 0 u t 0 lim t u t t 0 where 1 a is a continuous function on 0 positive and differentiable on 0 such that 1 a is integrable on 0 1 and 0 1 a t d t here t 0 t 1 a s d s for t 0 and a is a nonnegative continuous function that is required to satisfy some assumptions related to the karamata classes of regularly varying functions our arguments are based on monotonicity methods

a simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem over the last decade many metaheuristics have been applied to the flowshop scheduling problem ranging from simulated annealing or tabu search to complex hybrid techniques some of these methods provide excellent effectiveness and efficiency at the expense of being utterly complicated in fact several published methods require substantial implementation efforts exploit problem specific speed up techniques that cannot be applied to slight variations of the original problem and often re implementations of these methods by other researchers produce results that are quite different from the original ones in this work we present a new iterated greedy algorithm that applies two phases iteratively named destruction were some jobs are eliminated from the incumbent solution and construction where the eliminated jobs are reinserted into the sequence using the well known neh construction heuristic optionally a local search can be applied after the construction phase our iterated greedy algorithm is both very simple to implement and as shown by experimental results highly effective when compared to state of the art methods

existence of positive solutions of singular elliptic boundary value problems in a ball this paper deals with existence theorems of positive solutions for singular elliptic boundary value problems in a ball the results of this paper are generalizations of those proved by authors cited in the references

existence theorem for a minimum problem with free discontinuity set we study the variational problem where is an open set in n n 2g l q l 1 q o andh n 1 is the n 1 dimensional hausdorff measure

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

a posteriori error control for the binary mumford shah model the binary mumford shah model is a widespread tool for image segmentation and can be considered as a basic model in shape optimization with a broad range of applications in computer vision ranging from basic segmentation and labeling to object reconstruction this paper presents robust a posteriori error estimates for a natural error quantity namely the area of the non properly segmented region to this end a suitable strictly convex and non constrained relaxation of the originally non convex functional is investigated and repin s functional approach for a posteriori error estimation is used to control the numerical error for the relaxed problem in the l norm in combination with a suitable cut out argument a fully practical estimate for the area mismatch is derived this estimate is incorporated in an adaptive meshing strategy two different adaptive primal dual finite element schemes and the most frequently used finite difference discretization are investigated and compared numerical experiments show qualitative and quantitative properties of the estimates and demonstrate their usefulness in practical applications

a phase field method for joint denoising edge detection and motion estimation in image sequence processing the estimation of optical flow fields from image sequences is incorporated in a mumford shah approach for image denoising and edge detection possibly noisy image sequences are considered as input and a piecewise smooth image intensity a piecewise smooth motion field and a joint discontinuity set are obtained as minimizers of the functional the method simultaneously detects image edges and motion field discontinuities in a rigorous and robust way it is able to handle information on motion that is concentrated on edges inherent to it is a natural multiscale approximation that is closely related to the phase field approximation for edge detection by ambrosio and tortorelli we present an implementation for two dimensional image sequences with finite elements in space and time this leads to three linear systems of equations which have to be solved in a suitable iterative minimization procedure numerical results and different applications underline the robustness of the approach presented

γ convergence for high order phase field fracture continuum and isogeometric formulations abstract we consider high order phase field functionals introduced in borden et al 2014 and provide a rigorous proof that these functionals converge to a sharp crack brittle fracture energy we take into account three dimensional problems in linear elastic fracture mechanics and functionals defined both in sobolev spaces and in spaces of tensor product b splines in the latter convergence holds when the mesh size vanishes faster than the internal length of the phase field model on the theoretical level this condition is natural since the size of the phase field layer around the crack itself scales like the internal length on the numerical level it should be satisfied by local h refinement technically convergence holds in the sense of convergence with respect to the strong topology of l 1 while the sharp crack energy is defined in g s b d 2 the constraint on the phase field to take values in 0 1 is taken into account both in the sobolev setting and in the iso geometric setting in the latter it requires a special treatment since the projection operator on the space of tensor product b splines is not lagrangian i e interpolatory

an iterated greedy heuristic for the sequence dependent setup times flowshop problem with makespan and weighted tardiness objectives iterated greedy ig algorithms are based on a very simple principle are easy to implement and can show excellent performance in this paper we propose two new ig algorithms for a complex flowshop problem that results from the consideration of sequence dependent setup times on machines a characteristic that is often found in industrial settings the first ig algorithm is a straightforward adaption of the ig principle while the second incorporates a simple descent local search furthermore we consider two different optimization objectives the minimization of the maximum completion time or makespan and the minimization of the total weighted tardiness extensive experiments and statistical analyses demonstrate that despite their simplicity the ig algorithms are new state of the art methods for both objectives

piecewise affine approximations for functions of bounded variation bv functions cannot be approximated well by piecewise constant functions but this work will show that a good approximation is still possible with countably piecewise affine functions in particular this approximation is area strictly close to the original function and the mathrm l 1 l1 difference between the traces of the original and approximating functions on a substantial part of the mesh can be made arbitrarily small necessarily the mesh needs to be adapted to the singularities of the bv function to be approximated and consequently the proof is based on a blow up argument together with explicit constructions of the mesh in the case of mathrm w 1 1 w1 1 sobolev functions we establish an optimal mathrm w 1 1 w1 1 error estimate for approximation by piecewise affine functions on uniform regular triangulations the piecewise affine functions are standard quasi interpolants obtained by mollification and lagrange interpolation on the nodes of triangulations and the main new contribution here compared to for instance clement rairo anal numer 9 r 2 77 84 1975 and verfurth m2an math model numer anal 33 4 1766 1782 1999 is that our error estimates are in the mathrm w 1 1 w1 1 norm rather than merely the mathrm l 1 l1 norm

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

an iterated greedy heuristic for a market segmentation problem with multiple attributes this research has been supported by the mexican national council for science and technology conacyt through grants cb2005 01 48499y and cb2011 01 166397 and a scholarship for graduate studies and by the universidad autonoma de nuevo leon through its scientific and technological research support program paicyt grants ca1478 07 ce012 09 it511 10 and ce331 15 ruben ruiz is partially supported by the spanish ministry of economy and competitiveness under the project scheyard optimization of scheduling problems in container yards no dpi2015 65895 r financed by feder funds we would like to thank rafael frinhani richard fuchshuber and their corresponding research teams for providing us the source code of their algorithms to carry out the corresponding tests furthermore we are grateful to the editor and the four anonymous reviewers for their careful reading of our manuscript and their constructive comments and suggestions which helped us improve its quality

new fixed point theorems for mixed monotone operators and local existence uniqueness of positive solutions for nonlinear boundary value problems abstract in this article we present a new fixed point theorem for a class of general mixed monotone operators which extends the existing corresponding results moreover we establish some pleasant properties of nonlinear eigenvalue problems for mixed monotone operators based on them the local existence uniqueness of positive solutions for nonlinear boundary value problems which include neumann boundary value problems three point boundary value problems and elliptic boundary value problems for lane emden fowler equations is proved the theorems for nonlinear boundary value problems obtained here are very general

existence and optimal estimates of solutions for singular nonlinear dirichlet problems abstract by applying the properties of the unique classical solution to the singular boundary value problem on half line p s g p s p s 0 s 0 p 0 0 lims p s b 0 and constructing the new comparison functions they show the existence and the optimal global estimates of solutions to singular nonlinear dirichlet problems u k x g u u 0 x u 0 where is a bounded domain with smooth boundary in rn g s is nonincreasing and positive in 0 1 g t dt and lim s 0 g s k c is positive in and may be singular or zero on the boundary

superlinear elliptic equations with singular coefficients on the boundary abstract in this paper a superlinear elliptic equation whose coefficient diverges on the boundary is studied in any bounded domain under the zero dirichlet boundary condition although the equation has a singularity on the boundary a solution is smooth on the closure of the domain indeed it is proved that the problem has a positive solution and infinitely many solutions without positivity which belong to c 1 or c 2 moreover it is proved that a positive solution has a higher order regularity up to c

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

local search methods for the flowshop scheduling problem with flowtime minimization abstract flowshop scheduling is a very active research area this problem still attracts a considerable amount of interest despite the sheer amount of available results total flowtime minimization of a flowshop has been actively studied and many effective algorithms have been proposed in the last few years new best solutions have been found for common benchmarks at a rapid pace however these improvements many times come at the cost of sophisticated algorithms complex methods hinder potential applications and are difficult to extend to small problem variations replicability of results is also a challenge in this paper we examine simple and easy to implement methods that at the same time result in state of the art performance the first two proposed methods are based on the well known iterated local search ils and iterated greedy ig frameworks which have been applied with great success to other flowshop problems additionally we present extensions of these methods that work over populations something that we refer to as population based ils pils and population based ig piga respectively we calibrate the presented algorithms by means of the design of experiments doe approach extensive comparative evaluations are carried out against the most recent techniques for the considered problem in the literature the results of a comprehensive computational and statistical analysis show that the presented algorithms are very effective furthermore we show that despite their simplicity the presented methods are able to improve 12 out of 120 best known solutions of taillard s flowshop benchmark with total flowtime criterion

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

multiphase image segmentation via modica mortola phase transition we propose a novel multiphase segmentation model built upon the celebrated phase transition model of modica and mortola in material sciences and a properly synchronized fitting term that complements it the proposed sine sinc model outputs a single multiphase distribution from which each individual segment or phase can be easily extracted theoretical analysis is developed for the gamma convergence behavior of the proposed model and the existence of its minimizers since the model is not quadratic nor convex for computation we adopted the convex concave procedure cccp that has been developed in the literatures of both computational nonlinear pdes and neural computation numerical details and experiments on both synthetic and natural images are presented

shifting representation search for hybrid flexible flowline problems this paper considers the hybrid flexible flowline scheduling problem with a set of additional restrictions and generalizations that are common in practice these include precedence constraints sequence dependent setup times time lags machine eligibility and release times there are many potential solution representations for this problem ranging from simple and compact to more complex and complete typically when choosing the degree of detail of the solution representation a tradeoff can be found between efficiency of the algorithm and the size of the search space several adaptations of existing methods are introduced memetic algorithm iterated local search iterated greedy as well as a novel algorithm called shifting representation search srs this new method starts with an iterated greedy algorithm applied to a permutation version of the problem and at a given time switches to an iterated local search on the full search space as far as we know this shift of the solution representation is new in the scheduling literature experimental results and statistical tests clearly prove the superiority of srs compared with classical and existing methods

an eigenerosion approach to brittle fracture the present work is concerned with the verification and validation of a variant of the eigenfracture scheme of schmidt et al 2009 based on element erosion which we refer to as eigenerosion eigenerosion is derived from the general eigenfracture scheme by restricting the eigendeformations in a binary sense they can be either zero in which case the local behavior is elastic or they can be equal to the local displacement gradient in which case the corresponding material neighborhood is failed or eroded when combined with a finite element approximation this scheme gives rise to element erosion i e the elements can be either intact in which case their behavior is elastic or be completly failed or eroded and have no load bearing capacity we verify the eigenerosion scheme through comparisons with analytical solutions and through convergence studies for mode i fracture propagation both in two and three dimensions and for structured and random meshes finally by way of validation we apply the eigenerosion scheme to the simulation of mixed modes i iii experiments in poly methyl methacrylate plates

iterated greedy for the maximum diversity problem abstract the problem of choosing a subset of elements with maximum diversity from a given set is known as the maximum diversity problem many algorithms and methods have been proposed for this hard combinatorial problem including several highly sophisticated procedures by contrast in this paper we present a simple iterated greedy metaheuristic that generates a sequence of solutions by iterating over a greedy construction heuristic using destruction and construction phases extensive computational experiments reveal that the proposed algorithm is highly effective as compared to the best so far metaheuristics for the problem under consideration

a variational shape optimization approach for image segmentation with a mumford shah functional we introduce a novel computational method for a mumford shah functional which decomposes a given image into smooth regions separated by closed curves casting this as a shape optimization problem we develop a gradient descent approach at the continuous level that yields nonlinear pde flows we propose time discretizations that linearize the problem and space discretization by continuous piecewise linear finite elements the method incorporates topological changes such as splitting and merging for detection of multiple objects space time adaptivity and a coarse to fine approach to process large images efficiently we present several simulations that illustrate the performance of the method and investigate the model sensitivity to various parameters

solving the flowshop scheduling problem with sequence dependent setup times using advanced metaheuristics abstract this paper deals with the permutation flowshop scheduling problem in which there are sequence dependent setup times on each machine commonly known as the sdst flowshop the optimisation criteria considered is the minimisation of the makespan or cmax genetic algorithms have been successfully applied to regular flowshops before and the objective of this paper is to assess their effectiveness in a more realistic and complex environment we present two advanced genetic algorithms as well as several adaptations of existing advanced metaheuristics that have shown superior performance when applied to regular flowshops we show a calibration of the genetic algorithm s parameters and operators by means of a design of experiments doe approach for evaluating the proposed algorithms we have coded several if not all known sdst flowshop specific algorithms all methods are tested against an augmented benchmark based on the instances of taillard the results show a clear superiority of the algorithms proposed especially for the genetic algorithms regardless of instance type and size

a scatter search algorithm for the distributed permutation flowshop scheduling problem abstract the distributed permutation flowshop problem has been recently proposed as a generalization of the regular flowshop setting where more than one factory is available to process jobs distributed manufacturing is a common situation for large enterprises that compete in a globalized market the problem has two dimensions assigning jobs to factories and scheduling the jobs assigned to each factory despite being recently introduced this interesting scheduling problem has attracted attention and several heuristic and metaheuristic methods have been proposed in the literature in this paper we present a scatter search ss method for this problem to optimize makespan ss has seldom been explored for flowshop settings in the proposed algorithm we employ some advanced techniques like a reference set made up of complete and partial solutions along with other features like restarts and local search a comprehensive computational campaign including 10 existing algorithms together with statistical analyses shows that the proposed scatter search algorithm produces better results than existing algorithms by a significant margin moreover all 720 known best solutions for this problem are improved

an effective hybrid discrete differential evolution algorithm for the flow shop scheduling with intermediate buffers in this paper an effective hybrid discrete differential evolution hdde algorithm is proposed to minimize the maximum completion time makespan for a flow shop scheduling problem with intermediate buffers located between two consecutive machines different from traditional differential evolution algorithms the proposed hdde algorithm adopted job permutation to represent individuals and applies job permutation based mutation and crossover operations to generate new candidate solutions moreover a one to one selection scheme with probabilistic jumping is used to determine whether the candidates will become members of the target population in next generation in addition an efficient local search algorithm based on both insert and swap neighborhood structures is presented and embedded in the hdde algorithm to enhance the algorithm s local searching ability computational simulations and comparisons based on the well known benchmark instances are provided it shows that the proposed hdde algorithm is not only capable to generate better results than the existing hybrid genetic algorithm and hybrid particle swarm optimization algorithm but outperforms two recently proposed discrete differential evolution dde algorithms as well especially the hdde algorithm is able to achieve excellent results for large scale problems with up to 500 jobs and 20 machines

a model for the quasi static growth of brittle fractures existence and approximation results we give a precise mathematical formulation of a variational model for the irreversible quasi static evolution of brittle fractures proposed by g a francfort and j j marigo and based on griffith s theory of crack growth in the two dimensional case we prove an existence result for the quasi static evolution and show that the total energy is an absolutely continuous function of time although we cannot exclude the possibility that the bulk energy and the surface energy may present some jump discontinuities this existence result is proved by a time discretization process where at each step a global energy minimization is performed with the constraint that the new crack contains all cracks formed at the previous time steps this procedure provides an effective way to approximate the continuous time evolution

metaheuristics for the linear ordering problem with cumulative costs the linear ordering problem with cumulative costs lopcc is a variant of the well known linear ordering problem in which a cumulative propagation makes the objective function highly non linear the lopcc has been recently introduced in the context of mobile phone telecommunications in this paper we propose two metaheuristic methods for this np hard problem the first one is based on the grasp methodology while the second one implements an iterated greedy strategic oscillation procedure we also propose a post processing based on path relinking to obtain improved outcomes we compare our methods with the state of the art procedures on a set of 218 previously reported instances the comparison favors the iterated greedy strategic oscillation with the path relinking post processing which is able to identify 87 new best objective function values

approximation of functional depending on jumps by elliptic functional via t convergence we show how it is possible to approximate the mumford shah see 29 image segmentation functional by elliptic functionals defined on sobolev spaces the heuristic idea is to consider functionals h u z with z ranging between 0 and 1 and related to the set k the minimizing zh are near to 1 in a neighborhood of the set k and far from the neighborhood they are very small the neighborhood shrinks as h for a similar approach to the problem compare kulkarni see 25 the approximation of h to takes place in a variational sense the de giorgi f convergence

γ convergence approximation of fracture and cavitation in nonlinear elasticity our starting point is a variational model in nonlinear elasticity that allows for cavitation and fracture that was introduced by henao and mora corral arch rational mech anal 197 619 655 2010 the total energy to minimize is the sum of the elastic energy plus the energy produced by crack and surface formation it is a free discontinuity problem since the crack set and the set of new surface are unknowns of the problem the expression of the functional involves a volume integral and two surface integrals and this fact makes the problem numerically intractable in this paper we propose an approximation in the sense of convergence by functionals involving only volume integrals which makes a numerical approximation by finite elements feasible this approximation has some similarities to the modica mortola approximation of the perimeter and the ambrosio tortorelli approximation of the mumford shah functional but with the added difficulties typical of nonlinear elasticity in which the deformation is assumed to be one to one and orientation preserving

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

the asymptotic behaviour of the unique solution for the singular lane emden fowler equation abstract by karamata regular variation theory and constructing comparison functions we show the exact asymptotic behaviour of the unique classical solution u c 2 c near the boundary to a singular dirichlet problem u k x g u u 0 x u 0 where is a bounded domain with smooth boundary in r n g c 1 0 0 lim t 0 g t g t for each 0 for some 0 and k c loc for some 0 1 is nonnegative on which is also singular near the boundary

the boundary value problem for quasilinear degenerate and singular elliptic systems abstract in this paper using the contraction mapping principle and the shooting method we obtain the existence and uniqueness of the local solutions and the global solutions to a class of quasilinear degenerate elliptic systems with the p laplacian like as its principal and with singularity on the boundary we also obtain the continuous dependence of the solution on the boundary data two examples are given to illustrate the applications of the theorems

iterated greedy local search methods for unrelated parallel machine scheduling abstract this work deals with the parallel machine scheduling problem which consists in the assignment of n jobs on m parallel machines the most general variant of this problem is when the processing time depends on the machine to which each job is assigned to this case is known as the unrelated parallel machine problem similarly to most of the literature this paper deals with the minimization of the maximum completion time of the jobs commonly referred to as makespan c max many algorithms and methods have been proposed for this hard combinatorial problem including several highly sophisticated procedures by contrast in this paper we propose a set of simple iterated greedy local search based metaheuristics that produce solutions of very good quality in a very short amount of time extensive computational campaigns show that these solutions are most of the time better than the current state of the art methodologies by a statistically significant margin