cross validation in survival analysis the predictive value of a statistical model is conceptually different from the explained variation in this paper we construct a measure of the predictive value of the cox proportional hazards model computed from the leave one out regression coefficients these coefficients can also be used to calculate a shrinkage factor which can be applied to improve the predictions and that can be used in r2 type measures of the proportion of explained variation our methods are illustrated by a study of chemotherapy for advanced ovarian cancer

an efficient hybrid multi objective particle swarm optimization with a multi objective dichotomy line search recently more research works are focused on multi objective particle swarm optimization algorithm mopso due to its ability of global and local search for solving multi objective optimization problems moops however most of existing mopsos cannot achieve satisfactory results in solution quality this paper proposes an efficient hybrid multi objective particle swarm optimization with a multi objective dichotomy line search mols named mols mopso to deal with such problem mols mopso combines an effective particle updating strategy with the local search of mols the effective particle updating strategy is used for global search to deal with premature convergence and diversity maintenance within the swarm the mols is periodically activated for fast local search to converge toward the pareto front the exploratory capabilities are enhanced more efficiently by keeping a desirable balance between global search and local search so as to ensure sufficient diversity and well distribution amongst the solutions of the non dominated fronts while retaining at the same time the convergence to the pareto optimal front comparing mols mopso with various state of the art multi objective optimization algorithms developed recently the comparative study shows the effectiveness of mols mopso which not only assures a better convergence to the pareto frontier but also illustrates a good diversity and distribution of solutions

the fuzzy set theory approach to the vehicle routing problem when demand at nodes is uncertain abstract the problem of vehicle routing when demand at the nodes is uncertain is considered the quantities to be picked up at the nodes are assumed to be only approximately known a network with one depot from which vehicles depart and to which they return after completing their service is considered the paper develops a model to design vehicle routing when demand at the nodes is uncertain the model is based on the heuristic sweeping algorithm the rules of fuzzy arithmetic and fuzzy logic

a block approach for single machine scheduling with release dates and due dates abstract the problem of scheduling jobs on a single machine subject to given release dates and due dates is considered a new algorithm of the branch and bound type for solving this problem is proposed the approach used in the paper is fully based on the eliminative properties of a block of jobs and in contradiction to the existing algorithms it does not require any heuristic method to generate a current solution in a search tree however a heuristic may be used in order to obtain a good initial solution extensive computational experiments show a high efficiency of the algorithm

methods for multi objective optimization an analysis decomposition based methods are often cited as the solution to multi objective nonconvex optimization problems with an increased number of objectives these methods employ a scalarizing function to reduce the multi objective problem into a set of single objective problems which upon solution yield a good approximation of the set of optimal solutions this set is commonly referred to as pareto front in this work we explore the implications of using decomposition based methods over pareto based methods on algorithm convergence from a probabilistic point of view namely we investigate whether there is an advantage of using a decomposition based method for example using the chebyshev scalarizing function over pareto based methods we find that under mild conditions on the objective function the chebyshev scalarizing function has an almost identical effect to pareto dominance relations when we consider the probability of finding superior solutions for algorithms that follow a balanced trajectory we propose the hypothesis that this seemingly contradicting result compared with currently available empirical evidence signals that the disparity in performance between pareto based and decomposition based methods is due to the inability of the former class of algorithms to follow a balanced trajectory we also link generalized decomposition to the results in this work and show how to obtain optimal scalarizing functions for a given problem subject to prior assumptions on the pareto front geometry

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

an improved bl algorithm for genetic algorithm of the orthogonal packing of rectangles this paper proposes an improved bl algorithm for genetic algorithm of the orthogonal packing of rectangles some improvements on the fitness function of genetic algorithm for the orthogonal packing of rectangles are also suggested solutions of two numerical examples show the effectiveness of these improvements

word maps isotopy and entropy on trouve des diffeomorphismes de basse entropie dans chaque classe d isotopie sur s 3 s 3

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

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

shrinkage based diagonal discriminant analysis and its applications in high dimensional data high dimensional data such as microarrays have brought us new statistical challenges for example using a large number of genes to classify samples based on a small number of microarrays remains a difficult problem diagonal discriminant analysis support vector machines and k nearest neighbor have been suggested as among the best methods for small sample size situations but none was found to be superior to others in this article we propose an improved diagonal discriminant approach through shrinkage and regularization of the variances the performance of our new approach along with the existing methods is studied through simulations and applications to real data these studies show that the proposed shrinkage based and regularization diagonal discriminant methods have lower misclassification rates than existing methods in many cases

the permutation flow shop with buffers a tabu search approach the paper deals with the criteria of makespan minimisation for the permutation flow shop problem with buffers of limited capacity located between successive machines as the problem is np hard an approximation algorithm is proposed which has been designed using a non trivial generalisation of the block elimination properties known for the classic flow shop problem this algorithm is able to achieve excellent results for problems up to 200 jobs and 20 machines as it exploits the structural properties defined in the problem and combines these with a local search technique controlled by a tabu search strategy

heuristic algorithms for the three dimensional bin packing problem abstract the three dimensional bin packing problem 3bp consists of allocating without overlapping a given set of three dimensional rectangular items to the minimum number of three dimensional identical finite bins the problem is np hard in the strong sense and finds many industrial applications we introduce a tabu search framework exploiting a new constructive heuristic for the evaluation of the neighborhood extensive computational results on standard benchmark instances show the effectiveness of the approach with respect to exact and heuristic algorithms from the literature

some results of the worst case analysis for flow shop scheduling abstract known approximation algorithms recommended for the permutation flow shop problem with the weighted sum of completion times have a worst case performance ratio which is unknown or known but unlimited we propose new algorithms with this ratio equal to m k k where k is the worst case performance ratio of an algorithm which solves an auxiliary k machine problem worst case analyses of other approximation algorithms for the mean completion time and the makespan criteria are also presented

efficient heuristics for flowshop sequencing with the objectives of makespan and flowtime minimisation in this paper we analyse the performance of flowshop sequencing heuristics with respect to the objectives of makespan and flowtime minimisation for flowtime minimisation we propose the strategy employed by the neh heuristic to construct partial solutions results show that this approach outperforms the common fast heuristics for flowtime minimisation while performing similarly or slightly worse than others which on reward prove to be much more cpu time consuming additionally the suggested approach is well balanced with respect to makespan and flowtime minimisation based on the previous results two algorithms are proposed for the sequencing problem with multiple objectives makespan and flowtime minimisation these algorithms provide the decision maker with a set of heuristically efficient solutions such that he she may choose the most suitable sequence for a given ratio between costs associated with makespan and those assigned to flowtime computational experience shows both algorithms to perform better than the current heuristics designed for the two criteria problem

a combinatorial particle swarm optimization for solving multi mode resource constrained project scheduling problems the particle swarm optimization pso has been widely used to solve continuous problems the discrete problems have just begun to be also solved by the discrete pso however the combinatorial problems remain a prohibitive area to the pso mainly in case of integer values in this paper we propose a combinatorial pso cpso algorithm that we take up challenge to use in order to solve a multi mode resource constrained project scheduling problem mrcpsp the results that have been obtained using a standard set of instances after extensive experiments prove to be very competitive in terms of number of problems solved to optimality by comparing average deviations and percentages of optima found our cpso algorithm outperforms the simulated annealing algorithm and it is close to the pso algorithm

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

algebraic entropy and the action of mapping class groups on character varieties abstract we extend the definition of algebraic entropy to endomorphisms of affine varieties we then calculate the algebraic entropy of the action of elements of mapping class groups on various character varieties and show that it is equal to a quantity we call the spectral radius a generalization of the dilatation of a pseudo anosov mapping class our calculations are compatible with all known calculations of the topological entropy of this action

a tabu search based algorithm for the fuzzy clustering problem the fuzzy clustering problem fcp is a mathematical program which is difficult to solve since it is nonconvex which implies possession of many local minima the fuzzy c means heuristic is the widely known approach to this problem but it is guaranteed only to yield local minima in this paper we propose a new approach to this problem which is based on tabu search technique and aims at finding a global solution of fcp we compare the performance of the algorithm with the fuzzy c means algorithm

an empirical investigation of meta heuristic and heuristic algorithms for a 2d packing problem abstract in this paper we consider the two dimensional 2d rectangular packing problem where a fixed set of items have to be allocated on a single object two heuristics which belong to the class of packing procedures that preserve bottom left bl stability are hybridised with three meta heuristic algorithms genetic algorithms ga simulated annealing sa naive evolution ne and local search heuristic hill climbing this study compares the hybrid algorithms in terms of solution quality and computation time on a number of packing problems of different size in order to show the effectiveness of the design of the different algorithms their performance is compared to random search rs and heuristic packing routines

an efficient heuristic for scheduling in a flowshop to minimize total weighted flowtime of jobs the problem of scheduling in a flowshop is considered with the objective of minimizing the total weighted flowtime of jobs a heuristic algorithm is developed by the introduction of lower bounds on the completion times of jobs and the development of heuristic preference relations for the scheduling problem under study an improvement scheme is incorporated in the heuristic to enhance the quality of its solution the proposed heuristic with and without the improvement scheme and the existing heuristics are evaluated by a large number of randomly generated problems the results of an extensive computational investigation for various problem sizes are presented it has been observed that both versions of the proposed heuristic perform better than the existing heuristics in giving a superior solution quality and that the proposed heuristic without the improvement scheme yields a good solution by requiring a negligible cpu time in addition an experimental investigation is carried out to evaluate the effectiveness of the improvement scheme when implemented in the proposed heuristic and the existing heuristics as well as the effectiveness of a variant of the scheme the results are also discussed

extended bayesian information criteria for model selection with large model spaces summary the ordinary bayesian information criterion is too liberal for model selection when the model space is large in this paper we re examine the bayesian paradigm for model selection and propose an extended family of bayesian information criteria which take into account both the number of unknown parameters and the complexity of the model space their consistency is established in particular allowing the number of covariates to increase to infinity with the sample size their performance in various situations is evaluated by simulation studies it is demonstrated that the extended bayesian information criteria incur a small loss in the positive selection rate but tightly control the false discovery rate a desirable property in many applications the extended bayesian information criteria are extremely useful for variable selection in problems with a moderate sample size but with a huge number of covariates especially in genome wide association studies which are now an active area in genetics research

solving the unconstrained optimization problem by a variable neighborhood search this paper presents variable neighborhood search vns for the problem of finding the global minimum of a nonconvex function the variable neighborhood search which changes systematically neighborhood structures in the search for finding a better solution is used to guide a set of standard improvement heuristics this algorithm was tested on some standard test functions and successful results were obtained its performance was compared with the other algorithms and observed to be better

operating characteristics and extensions of the false discovery rate procedure summary we investigate the operating characteristics of the benjamini hochberg false discovery rate procedure for multiple testing this is a distribution free method that controls the expected fraction of falsely rejected null hypotheses among those rejected the paper provides a framework for understanding more about this procedure we first study the asymptotic properties of the deciding point d that determines the critical p value from this we obtain explicit asymptotic expressions for a particular risk function we introduce the dual notion of false non rejections and we consider a risk function that combines the false discovery rate and false non rejections we also consider the optimal procedure with respect to a measure of conditional risk

a competitive and cooperative co evolutionary approach to multi objective particle swarm optimization algorithm design multi objective particle swarm optimization mopso is an optimization technique inspired by bird flocking which has been steadily gaining attention from the research community because of its high convergence speed on the other hand in the face of increasing complexity and dimensionality of today s application coupled with its tendency of premature convergence due to the high convergence speeds there is a need to improve the efficiency and effectiveness of mopso in this paper a competitive and cooperative co evolutionary approach is adapted for multi objective particle swarm optimization algorithm design which appears to have considerable potential for solving complex optimization problems by explicitly modeling the co evolution of competing and cooperating species the competitive and cooperative co evolution model helps to produce the reasonable problem decompositions by exploiting any correlation interdependency between components of the problem the proposed competitive and cooperative co evolutionary multi objective particle swarm optimization algorithm ccpso is validated through comparisons with existing state of the art multi objective algorithms using established benchmarks and metrics simulation results demonstrated that ccpso shows competitive if not better performance as compared to the other algorithms

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

the lasso method for variable selection in the cox model summary i propose a new method for variable selection and shrinkage in cox s proportional hazards model my proposal minimizes the log partial likelihood subject to the sum of the absolute values of the parameters being bounded by a constant because of the nature of this constraint it shrinks coe cients and produces some coe cients that are exactly zero as a result it reduces the estimation variance while providing an interpretable final model the method is a variation of the lasso proposal of tibshirani designed for the linear regression context simulations indicate that the lasso can be more accurate than stepwise selection in this setting

exact solution of the two dimensional finite bon packing problem given a set of rectangular pieces to be cut from an unlimited number of standardized stock pieces bins the two dimensional finite bin packing problem is to determine the minimum number of stock pieces that provide all the pieces the problem is np hard in the strong sense and finds many practical applications in the cutting and packing area we analyze a well known lower bound and determine its worst case performance we propose not lower bounds which are used within a branch and bound algorithm for the exact solution of the problem extensive computational testing on problem instances from the literature involving up to 120 pieces shows the effectiveness of the proposed approach

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

improvement heuristic for the flow shop scheduling problem an adaptive learning approach abstract we propose an improvement heuristic approach for the general flow shop problem n m cmax based on the idea of adaptive learning the approach employs a one pass heuristic to give a good starting solution in the search space and uses a weight parameter to perturb the data of the original problem to obtain improved solutions the weights are then adjusted employing a learning strategy which involves reinforcement and backtracking the learning is similar to that in neural networks the random perturbation allows a non deterministic local search we apply the improvement heuristic approach in conjunction with three well known heuristics in the literature namely palmer s slope index cds and neh we test our approach on several benchmark problem sets including taillard s carlier s heller s and reeves we compare our results to the best known upper bound solutions and find that for many problems we match the best known upper bound for one problem we discover a new upper bound

a priori optimization consider a complete graph g v e in which each node is present with probability p we are interested in solving combinatorial optimization problems on subsets of nodes which are present with a certain probability we introduce the idea of a priori optimization as a strategy competitive to the strategy of reoptimization under which the combinatorial optimization problem is solved optimally for every instance we consider four problems the traveling salesman problem tsp the minimum spanning tree vehicle routing and traveling salesman facility location we discuss the applicability of a priori optimization strategies in several areas and show that if the nodes are randomly distributed in the plane the a priori and reoptimization strategies are very close in terms of performance we characterize the complexity of a priori optimization and address the question of approximating the optimal a priori solutions with polynomial time heuristics with provable worst case guarantees finally we use the tsp as an example to find practical solutions based on ideas of local optimality

two hybrid meta heuristics for the finite horizon elsp in flexible flow lines with unrelated parallel machines this article addresses the economic lot sizing and scheduling problem in flexible flow lines with unrelated parallel machines over a finite planning horizon the objective is determination of a cyclic schedule that minimizes the sum of setup and inventory holding costs per unit time without any stock out a new mixed zero one nonlinear mathematical programming has been developed for the problem due to difficulty of obtaining the optimal solution especially for medium and large sized problems we have also proposed two algorithms a hybrid genetic algorithm hga and a simulated annealing sa two efficient constructive heuristic algorithms have been also proposed that provide some initial solutions for the algorithms moreover a new local search approach has been proposed to improve solution quality of algorithms the two proposed solution methods are compared on 180 randomly generated problems computational results indicate the superiority of the proposed hga in compare to the sa with respect to the solution quality but the proposed sa outperforms the proposed hga with respect to the required computations time

some aspects of scatter search in the flow shop problem abstract the flow shop scheduling problem with the makespan criterion is a certain strongly np hard case from the domain of or this problem having simple formulation contrasting with its troublesome complex and time consuming solution methods is ideal for testing the quality of advanced combinatorial optimization algorithms although many excellent approximate algorithms for the flow shop problem have been provided up till now in the literature some theoretical and experimental problems associated with an algorithm s activity still remain unexamined in this paper we provide a new view on the solution space and the search process relying upon it we are proposing the new approximate algorithm which applies some properties of neighborhoods refers to the big valley phenomenon uses some elements of the scatter search as well as the path relinking technique this algorithm shows up to now unprecedented accuracy obtainable within a short time on a pc which has been confirmed in a wide variety of computer tests good properties of the algorithm remain scalable if the size of instances increases

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

case study on statistically estimating minimum makespan for flow line scheduling problems abstract lower bounds are typically used to evaluate the performance of heuristics for solving combinatorial minimization problems in the absence of tight analytical lower bounds optimal objective function values may be estimated statistically in this paper extreme value theory is used to construct confidence interval estimates of the minimum makespan achievable when scheduling nonsimilar groups of jobs on a two stage flow line experimental results based on randomly sampled solutions to each of 180 randomly generated test problems revealed that i least squares parameter estimators outperformed standard analytical estimators for the weibull approximation to the distribution of the sample minimum makespan ii to evaluate each weibull fit reliably both the anderson darling and kolmogorov smirnov goodness of fit tests should be used and iii applying a local improvement procedure to a large sample of randomly generated initial solutions improved the probability that the resulting weibull fit yielded a confidence interval covering the minimum makespan

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

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

the risk inflation criterion for multiple regression a new criterion is proposed for the evaluation of variable selection procedures in multiple regression this criterion which we call the risk inflation is based on an adjustment to the risk essentially the risk inflation is the maximum increase in risk due to selecting rather than knowing the correct predictors a new variable selection procedure is obtained which in the case of orthogonal predictors substantially improves on aic c p and bic and is close to optimal in contrast to aic c p and bic which use dimensionality penalties of 2 2 and log n respectively this new procedure uses a penalty 2 log p where p is the number of available predictors for the case of nonorthogonal predictors bounds for the optimal penalty are obtained

a comparison of estimators to evaluate the discriminatory power of time to event models discrimination measures for continuous time to event outcomes have become an important tool in medical decision making the idea behind discrimination measures is to evaluate the performance of a prediction model by measuring its ability to distinguish between observations having an event and those having no event researchers proposed a variety of approaches to estimate discrimination measures from a set of right censored data these approaches rely on different regularity assumptions that are needed to ensure consistency of the respective estimators typical examples of regularity assumptions include the proportional hazards assumption in cox regression and the random censoring assumption because regularity assumptions are often violated in practice conducting a sensitivity analysis of the estimators is of considerable interest the aim of the paper is to analyze and to compare the most popular estimators of discrimination measures for event time outcomes on the basis of the results of an extensive simulation study and the analysis of molecular data we investigate the behavior of the estimators in situations where the underlying regularity assumptions do not hold we show that violations of the regularity assumptions may induce a nonignorable bias and may therefore result in biased medical decision making

empirical extensions of the lasso penalty to reduce the false discovery rate in high dimensional cox regression models correct selection of prognostic biomarkers among multiple candidates is becoming increasingly challenging as the dimensionality of biological data becomes higher therefore minimizing the false discovery rate fdr is of primary importance while a low false negative rate fnr is a complementary measure the lasso is a popular selection method in cox regression but its results depend heavily on the penalty parameter usually is chosen using maximum cross validated log likelihood max cvl however this method has often a very high fdr we review methods for a more conservative choice of we propose an empirical extension of the cvl by adding a penalization term which trades off between the goodness of fit and the parsimony of the model leading to the selection of fewer biomarkers and as we show to the reduction of the fdr without large increase in fnr we conducted a simulation study considering null and moderately sparse alternative scenarios and compared our approach with the standard lasso and 10 other competitors akaike information criterion aic corrected aic bayesian information criterion bic extended bic hannan and quinn information criterion hqic risk information criterion ric one standard error rule adaptive lasso stability selection and percentile lasso our extension achieved the best compromise across all the scenarios between a reduction of the fdr and a limited raise of the fnr followed by the aic the ric and the adaptive lasso which performed well in some settings we illustrate the methods using gene expression data of 523 breast cancer patients in conclusion we propose to apply our extension to the lasso whenever a stringent fdr with a limited fnr is targeted copyright 2016 john wiley sons ltd

solving multiobjective vehicle routing problem with stochastic demand via evolutionary computation abstract this paper considers the routing of vehicles with limited capacity from a central depot to a set of geographically dispersed customers where actual demand is revealed only when the vehicle arrives at the customer the solution to this vehicle routing problem with stochastic demand vrpsd involves the optimization of complete routing schedules with minimum travel distance driver remuneration and number of vehicles subject to a number of constraints such as time windows and vehicle capacity to solve such a multiobjective and multi modal combinatorial optimization problem this paper presents a multiobjective evolutionary algorithm that incorporates two vrpsd specific heuristics for local exploitation and a route simulation method to evaluate the fitness of solutions a new way of assessing the quality of solutions to the vrpsd on top of comparing their expected costs is also proposed it is shown that the algorithm is capable of finding useful tradeoff solutions for the vrpsd and the solutions are robust to the stochastic nature of the problem the developed algorithm is further validated on a few vrpsd instances adapted from solomon s vehicle routing problem with time windows vrptw benchmark problems

the algebraic entropy of the special linear character automorphisms of a free group on two generators in this note we establish a connection between the dynamical de gree or algebraic entropy of a certain class of polynomial automorphisms of r 3 and the maximum topological entropy of the action when restricted to compact invariant subvarieties indeed when there is no cancellation of lead ing terms in the successive iterates of the polynomial automorphism the two quantities are equal in general however the algebraic entropy overestimates the topological entropy these polynomial automorphisms arise as extensions of mapping class actions of a punctured torus s on the relative su 2 character varieties of s embedded inr 3 it is known that the topological entropy of these mapping class actions is maximized on the relative character variety comprised of reducible characters those whose boundary holonomy is 2 here we cal culate the algebraic entropy of the induced polynomial automorphisms on the character varieties and show that it too solely depends on the topology of s

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

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

genetic local search for multi objective flowshop scheduling problems this paper addresses flowshop scheduling problems with multiple performance criteria in such a way as to provide the decision maker with approximate pareto optimal solutions genetic algorithms have attracted the attention of researchers in the nineties as a promising technique for solving multi objective combinatorial optimization problems we propose a genetic local search algorithm with features such as preservation of dispersion in the population elitism and use of a parallel multi objective local search so as intensify the search in distinct regions the concept of pareto dominance is used to assign fitness to the solutions and in the local search procedure the algorithm is applied to the flowshop scheduling problem for the following two pairs of objectives i makespan and maximum tardiness ii makespan and total tardiness for instances involving two machines the algorithm is compared with branch and bound algorithms proposed in the literature for such instances and larger ones involving up to 80 jobs and 20 machines the performance of the algorithm is compared with two multi objective genetic local search algorithms proposed in the literature computational results show that the proposed algorithm yields a reasonable approximation of the pareto optimal set

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

modeling vehicle routing with uncertain demands as a stochastic program properties of the corresponding solution abstract in this paper we address the issue of different mathematical models for the stochastic vehicle routing problem svrp this problem is inherently much more difficult than the generic deterministic vehicle routing problem vrp for which optimal procedures can solve only small problems presently we cannot even begin optimal solution procedures for the svrp for any problem size exceeding 3 nodes thus we need to examine modeling approaches to this problem in order to exploit the structure and solution properties we present a multistate stochastic model for the svrp we prove that this model has an interesting minimal graph representation in which a svrp solution corresponds to a hamiltonian cycle we also present a markov decision model for the problem concluding with a discussion of solution prospects and directions

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

adaptive lasso for cox s proportional hazards model summary we investigate the variable selection problem for cox s proportional hazards model and propose a unified model selection and estimation procedure with desired theoretical properties and computational convenience the new method is based on a penalized log partial likelihood with the adaptively weighted l1 penalty on regression coefficients providing what we call the adaptive lasso estimator the method incorporates different penalties for different coefficients unimportant variables receive larger penalties than important ones so that important variables tend to be retained in the selection process whereas unimportant variables are more likely to be dropped theoretical properties such as consistency and rate of convergence of the estimator are studied we also show that with proper choice of regularization parameters the proposed estimator has the oracle properties the convex optimization nature of the method leads to an efficient algorithm both simulated and real examples show that the method performs competitively

scheduling to minimize the sum of weighted flowtime and weighted tardiness of jobs in a flowshop with sequence dependent setup times abstract efficient heuristics for scheduling jobs in a static flowshop with sequence dependent setup times of jobs are presented in this paper the objective is to minimize the sum of weighted flowtime and weighted tardiness of jobs two heuristic preference relations are used to construct a good heuristic permutation sequence of jobs thereafter an improvement scheme is implemented once and twice on the heuristic sequence to enhance the quality of the solution an existing heuristic a random search procedure and a greedy local search are used as benchmark methods for relatively evaluating the proposed heuristics an extensive performance analysis has shown that the proposed heuristics are computationally faster and more effective in yielding solutions of better quality than the benchmark procedures

hybrid genetic algorithm for permutation flowshop scheduling problems with total flowtime minimization in this paper a hga hybrid genetic algorithm is proposed for permutation flowshop scheduling problems pfsp with total flowtime minimization which are known to be np hard one of the chromosomes in the initial population is constructed by a suitable heuristic and the others are yielded randomly an artificial chromosome is generated by a weighted simple mining gene structure with which a new crossover operator is presented additionally two effective heuristics are adopted as local search to improve all generated chromosomes in each generation the hga is compared with one of the most effective heuristics and a recent meta heuristic on 120 benchmark instances experimental results show that the hga outperforms the other two algorithms for all cases furthermore hga obtains 115 best solutions for the benchmark instances 92 of which are newly discovered

on solving multiobjective bin packing problems using evolutionary particle swarm optimization abstract the bin packing problem is widely found in applications such as loading of tractor trailer trucks cargo airplanes and ships where a balanced load provides better fuel efficiency and safer ride in these applications there are often conflicting criteria to be satisfied i e to minimize the bins used and to balance the load of each bin subject to a number of practical constraints unlike existing studies that only consider the issue of minimum bins a multiobjective two dimensional mathematical model for bin packing problems with multiple constraints mobpp 2d is formulated in this paper to solve mobpp 2d problems a multiobjective evolutionary particle swarm optimization algorithm moepso is proposed without the need of combining both objectives into a composite scalar weighting function moepso incorporates the concept of pareto s optimality to evolve a family of solutions along the trade off surface extensive numerical investigations are performed on various test instances and their performances are compared both quantitatively and statistically with other optimization methods to illustrate the effectiveness and efficiency of moepso in solving multiobjective bin packing problems

a hybrid genetic local search algorithm for the permutation flowshop scheduling problem traditionally the permutation flowshop scheduling problem pfsp was with the criterion of minimizing makespan the permutation flowshop scheduling problem to minimize the total flowtime has attracted more attention from researchers in recent years in this paper a hybrid genetic local search algorithm is proposed to solve this problem with each of both criteria the proposed algorithm hybridizes the genetic algorithm and a novel local search scheme that combines two local search methods the insertion search is and the insertion search with cut and repair iscr it employs the genetic algorithm to do the global search and two local search methods to do the local search two local search methods play different roles in the search process the insertion search is responsible for searching a small neighborhood while the insertion search with cut and repair is responsible for searching a large neighborhood furthermore the orthogonal array based crossover operator is designed to enhance the ga s capability of intensification the experimental results show the advantage of combining the two local search methods the performance of the proposed hybrid genetic algorithm is very competitive for the pfsp with the total flowtime criterion it improved 66 out of the 90 current best solutions reported in the literature in short term search and it also improved all the 20 current best solutions reported in the literature in long term search for the pfsp with the makespan criterion the proposed algorithm also outperforms the other three methods recently reported in the literature

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

worst case analysis of heuristics for the bin packing problem with general cost structures we consider the famous bin packing problem where a set of items must be stored in bins of equal capacity in the classical version the objective is to minimize the number of bins used motivated by several optimization problems that occur in the context of the storage of items we study a more general cost structure where the cost of a bin is a concave function of the number of items in the bin the objective is to store the items in such a way that total cost is minimized such cost functions can greatly alter the way the items should be assigned to the bins we show that some of the best heuristics developed for the classical bin packing problem can perform poorly under the general cost structure on the other hand the so called next fit increasing heuristic has an absolute worst case bound of no more than 1 75 and an asymptotic worst case bound of 1 691 for any concave and monotone cost function our analysis also provides a new worst case bound for the well studied next tit decreasing heuristic when

the two and m machine flowshop scheduling problems with bicriteria of makespan and mean flowtime abstract this paper considers the flowshop scheduling problem with the objective of minimizing the weighted sum of makespan and mean flowtime even though the two machine problem has been addressed and several heuristics have been established in the literature these heuristics have not been compared in this paper a comparison of these available heuristics in the literature is conducted moreover three new heuristic algorithms are proposed which can be utilized for both the two machine and m machine problems computational experiments indicate that the proposed heuristics are superior to all the existing heuristics in the literature including a genetic algorithm two dominance relations are also developed one for the two machine and the other for the three machine problem experimental results show that both relations are efficient

a new discrete particle swarm optimization approach for the single machine total weighted tardiness scheduling problem with sequence dependent setup times in this paper we present a new discrete particle swarm optimization dpso approach to face the np hard single machine total weighted tardiness scheduling problem in presence of sequence dependent setup times differently from previous approaches the proposed dpso uses a discrete model both for particle position and velocity and a coherent sequence metric we tested the proposed dpso mainly over a benchmark originally proposed by cicirello in 2003 and available online the results obtained show the competitiveness of our dpso which is able to outperform the best known results for the benchmark in addition we also tested the dpso on a set of benchmark instances from orlib for the single machine total weighted tardiness problem and we analysed the role of the dpso swarm intelligence mechanisms as well as the local search intensification phase included in the algorithm

a binary particle swarm optimization algorithm inspired by multi level organizational learning behavior abstract recently nature inspired algorithms have increasingly attracted the attention of researchers due to the fact that in bpso the position vectors consisting of 0 and 1 can be seen as a decision behavior support or oppose in this paper we propose a bpso with hierarchical structure bpso hs for short on the basis of multi level organizational learning behavior at each iteration of bpso hs particles are divided into two classes named leaders and followers and different evolutionary strategies are used in each class in addition the mutation strategy is adopted to overcome the premature convergence and slow convergent speed during the later stages of optimization the algorithm was tested on two discrete optimization problems traveling salesman and bin packing as well as seven real parameter functions the experimental results showed that the performance of bpso hs was significantly better than several existing algorithms

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

enhanced speciation in particle swarm optimization for multi modal problems abstract in this paper we present a novel multi modal optimization algorithm for finding multiple local optima in objective function surfaces we build from species based particle swarm optimization spso by using deterministic sampling to generate new particles during the optimization process by implementing proximity based speciation coupled with speciation of isolated particles and by including turbulence regions around already found solutions to prevent unnecessary function evaluations instead of using error threshold values the new algorithm uses the particle s experience geometric mean and exclusion factor to detect local optima and stop the algorithm the performance of each extension is assessed with leave it out tests and the results are discussed we use the new algorithm called isolated speciation based particle swarm optimization ispso and a benchmark algorithm called niche particle swarm optimization nichepso to solve a six dimensional rainfall characterization problem for 192 rain gages across the united states we show why it is important to find multiple local optima for solving this real world complex problem by discussing its high multi modality solutions found by both algorithms are compared and we conclude that ispso is more reliable than nichepso at finding optima with a significantly lower objective function value

the three dimensional bin packing problem the problem addressed in this paper is that of orthogonally packing a given set of rectangular shaped items into the minimum number of three dimensional rectangular bins the problem is strongly np hard and extremely difficult to solve in practice lower bounds are discussed and it is proved that the asymptotic worst case performance ratio of the continuous lower bound is an exact algorithm for filling a single bin is developed leading to the definition of an exact branch and bound algorithm for the three dimensional bin packing problem which also incorporates original approximation algorithms extensive computational results involving instances with up to 90 items are presented it is shown that many instances can be solved to optimality within a reasonable time limit

algorithms for the vehicle routing and scheduling problems with time window constraints this paper considers the design and analysis of algorithms for vehicle routing and scheduling problems with time window constraints given the intrinsic difficulty of this problem class approximation methods seem to offer the most promise for practical size problems after describing a variety of heuristics we conduct an extensive computational study of their performance the problem set includes routing and scheduling environments that differ in terms of the type of data used to generate the problems the percentage of customers with time windows their tightness and positioning and the scheduling horizon we found that several heuristics performed well in different problem environments in particular an insertion type heuristic consistently gave very good results

a multi objective memetic algorithm based on locality sensitive hashing for one to many to one dynamic pickup and delivery problem this paper presents an early attempt to solve one to many to one dynamic pickup and delivery problem dpdp by proposing a multi objective memetic algorithm called lsh moma which is a synergy of multi objective evolutionary algorithm and locality sensitive hashing lsh based local search three objectives namely route length response time and workload are optimized simultaneously in an evolutionary framework in each generation of lsh moma lsh based rectification and local search are imposed to repair and improve the individual solutions lsh moma is evaluated on four benchmark dpdps and the experimental results show that lsh moma is efficient in obtaining optimal tradeoff solutions of the three objectives

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

sequencing of jobs in some production system abstract we consider a real life problem of scheduling clients orders in the production of concrete blocks in a factory of building industry this problem can be modelled as a hybrid flow shop scheduling problem with mixed no wait no store constraints and mixed bottleneck non bottleneck machines the objective function is to minimize maximum completion time to solve the problem we propose an approximation algorithm based on the tabu search approach

the emergence of scaling laws search dynamics in a particle swarm optimization abstract this paper investigates the search dynamics of a fundamental particle swarm optimization pso algorithm via gathering and analyzing the data of the search area during the optimization process the pso algorithm exhibits a distinct performance when optimizing different functions which induces the emergence of different search dynamics during the optimization process the simulation results show that the performance is tightly related to the search dynamics which results from the interaction between the pso algorithm and the landscape of the solved problems the levy type scaling laws search dynamics emerges from the process in which the pso algorithm shows good performance while the brownian dynamics appears after the algorithm has stagnated due to the premature convergence the levy dynamics characterized by a large number of intensive local searches punctuated by long range transfers is an indicator of good performance which allows the algorithm to achieve an efficient balance between exploration and exploitation so as to improve the search efficiency

a tabu search heuristic for the vehicle routing problem with stochastic demands and customers this paper considers a version of the stochastic vehicle routing problem where customers are present at locations with some probabilities and have random demands a tabu search heuristic is developed for this problem comparisons with known optimal solutions on problems whose sizes vary from 6 to 46 customers indicate that the heuristic produces an optimal solution in 89 45 of cases with an average deviation of 0 38 from optimality

single facility resource allocation under capacity based economies and diseconomics of scope we consider the optimal allocation of a resource in a single facility production environment in the presence of capacity based economies and diseconomies of scope this setting generalizes the usual approach to single facility resource allocation by allowing for the effective capacity of a facility to be a nonlinear function of the number of different items produced or the services delivered by the facility economies or diseconomies of scope are attributable to factors such as production changeover time overall process management requirements and complementary production requirements that vary with the product or service mix we consider the problem setting in which the effective capacity depends on the number of tasks assigned to the facility the resulting model scope generalizes the well known 0 1 knapsack problem we also consider the more general problem gencap in which capacity consumption depends on the specific set of tasks assigned to the facility we define tabu search heuristics as well as exact branch and bound algorithms for scope and gencap on the basis of extensive computational experience the solution procedures are seen to be extremely effective in particular the heuristics consistently obtain high quality solutions to the test problems furthermore the tractability of solving problems to optimality is demonstrated through the solution of scope problems having as many as 500 tasks and gencap problems involving as many as 50 tasks and more than 16 500 nonlinear capacity interactions

a particle swarm optimization algorithm for makespan and total flowtime minimization in the permutation flowshop sequencing problem abstract in this paper a particle swarm optimization algorithm pso is presented to solve the permutation flowshop sequencing problem pfsp with the objectives of minimizing makespan and the total flowtime of jobs for this purpose a heuristic rule called the smallest position value spv borrowed from the random key representation of bean j c bean genetic algorithm and random keys for sequencing and optimization orsa journal of computing 6 2 1994 154 160 was developed to enable the continuous particle swarm optimization algorithm to be applied to all classes of sequencing problems in addition a very efficient local search called variable neighborhood search vns was embedded in the pso algorithm to solve the well known benchmark suites in the literature the pso algorithm was applied to both the 90 benchmark instances provided by taillard e taillard benchmarks for basic scheduling problems european journal of operational research 64 1993 278 285 and the 14 000 random narrow random and structured benchmark instances provided by watson et al j p watson l barbulescu l d whitley a e howe contrasting structured and random permutation flowshop scheduling problems search space topology and algorithm performance orsa journal of computing 14 2 2002 98 123 for makespan criterion the solution quality was evaluated according to the best known solutions provided either by taillard or watson et al the total flowtime criterion was evaluated with the best known solutions provided by liu and reeves j liu c r reeves constructive and composite heuristic solutions to the p ci scheduling problem european journal of operational research 132 2001 439 452 and rajendran and ziegler c rajendran h ziegler ant colony algorithms for permutation flowshop scheduling to minimize makespan total flowtime of jobs european journal of operational research 155 2 2004 426 438 for the total flowtime criterion 57 out of the 90 best known solutions reported by liu and reeves and rajendran and ziegler were improved whereas for the makespan criterion 195 out of the 800 best known solutions for the random and narrow random problems reported by watson et al were improved by the vns version of the pso algorithm

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

linear model selection by cross validation abstract we consider the problem of selecting a model having the best predictive ability among a class of linear models the popular leave one out cross validation method which is asymptotically equivalent to many other model selection methods such as the akaike information criterion aic the c p and the bootstrap is asymptotically inconsistent in the sense that the probability of selecting the model with the best predictive ability does not converge to 1 as the total number of observations n we show that the inconsistency of the leave one out cross validation can be rectified by using a leave n v out cross validation with n v the number of observations reserved for validation satisfying n v n 1 as n this is a somewhat shocking discovery because nv n 1 is totally opposite to the popular leave one out recipe in cross validation motivations justifications and discussions of some practical aspects of the use of the leave n v out cross validation method are provided and results