optimal annealing schedules for a modified tsallis statistics in this paper for a number of example systems optimal schedules for simulated annealing with a modified tsallis statistics for various parameters q are analyzed it turns out that in general depending on the objective function minimizing the mean energy or maximizing the ground state probability different schedules have to be chosen furthermore the optimal objective function value reached with the optimal schedule shows a monotonic dependency on q where better values are reached for smaller q thus in stochastic optimization the limit case q corresponding to threshold accepting should be chosen in order to get the best possible optimization results with as little effort as possible

the noising methods a generalization of some metaheuristics abstract in this paper an exhaustive review of the principles and of the applications of the noising methods recent combinatorial optimization metaheuristics is attempted the features and the variants of the noising methods are detailed and the tunings of their parameters when applied to different combinatorial optimization problems are summarized the links between the noising methods and two other metaheuristics namely the simulated annealing method and the threshold accepting algorithm are also studied and that the noising methods can be considered as generalizations of these metaheuristics when their components are properly chosen is shown

an efficient tabu search approach for the 0 1 multidimensional knapsack problem abstract in this paper we describe a new approach to tabu search ts based on strategic oscillation and surrogate constraint information that provides a balance between intensification and diversification strategies new rules needed to control the oscillation process are given for the 0 1 multidimensional knapsack 0 1 mkp based on a portfolio of test problems from the literature our method obtains solutions whose quality is at least as good as the best solutions obtained by previous methods especially with large scale instances these encouraging results confirm the efficiency of the tunneling concept coupled with surrogate information when resource constraints are present

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

pure adaptive search for finite global optimization pure adaptive search is a stochastic algorithm which has been analyzed for continuous global optimization when a uniform distribution is used in pas it has been shown to have complexity which is linear in dimension we define strong and weak variations of pas in the setting of finite global optimization and prove analogous results in particular for then dimensional lattice 1 k n the expected number of iterations to find the global optimum is linear inn many discrete combinatorial optimization problems although having intractably large domains have quite small ranges the strong version of pas for all problems and the weak version of pas for a limited class of problems has complexity the order of the size of the range

probabilistic local search algorithms for concave cost transportation network problems in practice concave cost transportation problems are characterized as np hard therefore cost functions are usually simplified as linear in order to facilitate problem solving however linear cost functions may not reflect actual operations which generally results in decreased operational performance this research employs the techniques of simulated annealing and threshold accepting to develop several heuristics that would efficiently solve these concave cost transportation network problems a network generator has also been designed to generate many instances on an hp workstation to test the heuristics the preliminary results show that these heuristics are potentially useful

a generalized steepest descent approximation for the zeros of m accretive operators a necessary and sufficient condition is proved for a generalized steepest descent approximation to converge to the zeros of m accretive operators related results deal with the convergence of the scheme to fixed points of pseudocontractive maps

simultaneous lotsizing and scheduling by combining local search with dual reoptimization abstract the contribution of this paper is twofold on the one hand the particular problem of integrating lotsizing and scheduling of several products on a single capacitated production line is modelled and solved taking into account sequence dependent setup times thereby continuous lotsizes meeting deterministic dynamic demands are to be determined and scheduled with the objective of minimizing inventory holding costs and sequence dependent setup costs on the other hand a new general algorithmic approach is presented a dual reoptimization algorithm is combined with a local search heuristic for solving a mixed integer programming problem this idea is applied to the above lotsizing and scheduling problem by embedding a dual network flow algorithm into threshold accepting and simulated annealing respectively computational tests show the effectiveness of the new solution method

on the neighborhood structure of the traveling salesman problem generated by local search moves when trying to find approximate solutions for the traveling salesman problem with heuristic optimization algorithms small moves called lin k opts are often used in our paper we provide exact formulas for the numbers of possible tours into which a randomly chosen tour can be changed with a lin k opt furthermore we compare the quality of the results to which the various moves lead

a multi start threshold accepting algorithm for multiple objective continuous optimization problems a multi start threshold accepting algorithm with an adaptive memory ms ta is proposed to solve multiple objective continuous optimization problems the aim of this paper is to find efficiently multiple pareto optimal solutions comparisons are carried out with multiple objective taboo search algorithm and genetic algorithm experiments on literature problems show that the proposed algorithm is more effective the presented multi start adaptive algorithm improves the best known results by a significant margin copyright 2010 john wiley sons ltd

packing a multidisperse system of hard disks in a circular environment we consider the problem of finding the densest closed packing of hard disks with proposed different radii in a circular environment such that the radius of the circumcircle is minimal with our approach we are able to find denser packings for various problem instances than known from the literature both for the dynamics of the simulation and for the optimum values of the radii of the circumcircles we find various scaling laws

fuzzy rule base generation for classification and its minimization via modified threshold accepting this paper addresses the application of a modified threshold accepting algorithm mta for minimizing the number of rules in a fuzzy rule based classification system while guaranteeing high classification power in terms of computational time required the mta outperforms the ga approaches which are applied to this multi objective combinatorial optimization problem in the literature the number of rules used and the classification power are taken as the objectives the original model of ishibuchi et al ieee trans fuzzy systems 3 1995 260 270 is further modified by employing various aggregators such as the operator compensatory and fuzzy and and a convex combinations of min and max operators in place of product and min operators the performance of the present model is demonstrated in the case of fisher s well known iris data and other data appearing in literature less computational time needed in all cases and better classification rate in testing phase in leave one out technique are important contributions of the present model

low complexity ml detectors for generalized spatial modulation systems spatial modulation sm combined with spatial multiplexing is a newly developed transmission scheme in multiple input multiple output mimo systems the resultant system referred to as generalized sm gsm can use the maximum likelihood ml detector jointly detecting the antenna subset as index and symbol vector as known the ml detector can achieve optimum performance however its computational complexity can be prohibitively high when the dimension of the gsm system is large in this paper we propose new methods to solve the problem the main idea is to split the detection into two stages one for the as index and the other for the symbol vector for the detection of the as index we develop two methods referred to as gaussian approximation and qr projection once the as index is detected conventional low complexity ml detectors can be applied for the detection of the symbol vector the diversity order for the proposed methods are further analyzed and an enhanced method is also proposed to achieve near optimum performance finally the proposed methods are extended to conduct soft detection of gsm systems simulations show that our methods significantly outperform existing ones while the detection complexity remains similar

threshold selecting strategy for best possible ground state detection with genetic algorithms genetic algorithms are a standard heuristic to find states of low energy in complex state spaces as given by physical systems such as spin glasses but also in combinatorial optimization the paper considers the problem of selecting individuals in the current population in genetic algorithms for crossover many schemes have been considered in literature as possible crossover selection strategies we show for a large class of quality measures that the best possible probability distribution for selecting individuals in each generation of the algorithm execution is a rectangular distribution over the individuals sorted by their energy values this means uniform probabilities have to be assigned to a group of the individuals with lowest energy in the population but probabilities equal to zero to individuals which are corresponding to energy values higher than a fixed cutoff which is equal to a certain rank in the vector sorted by the energy of the states in the current population the considered strategy is dubbed threshold selecting the proof applies basic arguments of markov chains and linear optimization and makes only a few assumptions on the underlying principles and hence applies to a large class of algorithms

further improvements in the calculation of censored quantile regressions censored quantile regressions of powell 1984 1986 are very powerful inferencing tools in economics and engineering as the calculation of censored quantile regressions involves minimizing a nonconvex and nondifferentiable function global optimization techniques can be the only breakthroughs the first implementation of a global optimization technique namely threshold accepting of fitzenberger and winker 1998 2007 is challenged by the genetic algorithm ga in this paper the results show that the ga provides substantial improvements over threshold accepting for cases with randomly distributed censoring points

fuzzy rule based classification with featureselector and modified threshold accepting abstract this paper highlights the need to reduce the dimension of the feature space in classification problems of high dimensions without sacrificing the classification power considerably we propose a methodology for classification tasks which comprises three phases i feature selection ii automatic generation of fuzzy if then rules and iii reduction of the rule base while retaining its high classification power the first phase is executed by using featureselector a software developed solely for feature extraction in pattern recognition and classification problems this is for the first time that the featureselector is used as a preprocessor for rule based classification systems in the second phase a standard fuzzy rule based classification system is modified and invoked with the most important features extracted by the featureselector as the new set of features in the third phase a modified threshold accepting algorithm mta proposed elsewhere by the authors ravi et al fuzzy sets and systems forthcoming is used for minimizing the number of rules in the classification system while guaranteeing high classification power the number of rules used and the classification power are taken as the objectives for this multi objective combinatorial global optimization problem the methodology proposed here has been successfully demonstrated for two well known problems i the wine classification problem which includes 13 feature variables in its original form and ii the wisconsin breast cancer determination problem which has 9 feature variables in conclusion the results are encouraging as there is no remarkable reduction in the classification power in both the problems despite the fact that some features have been deleted from the study by resorting to feature selection also the mta outperformed the original threshold accepting algorithm for the test problems considered here the authors suggest that classification problems having higher feature dimensions can be solved successfully within the framework of the methodology presented here the high classification powers obtained for both the problems when working with less feature variables than the original number is the significant achievement of this study

a new randomized algorithm to approximate the star discrepancy based on threshold accepting we present a new algorithm for estimating the star discrepancy of arbitrary point sets similar to the algorithm for discrepancy approximation of winker and fang siam j numer anal 34 1997 pp 2028 2042 it is based on the optimization algorithm threshold accepting our improvements include amongst others a nonuniform sampling strategy which is more suited for higher dimensional inputs and additionally takes into account the topological characteristics of given point sets and rounding steps which transform axis parallel boxes on which the discrepancy is to be tested into critical test boxes these critical test boxes provably yield higher discrepancy values and contain the box that exhibits the maximum value of the local discrepancy we provide comprehensive experiments to test the new algorithm our randomized algorithm computes the exact discrepancy frequently in all cases where this can be checked i e where the exact discrepancy of the point set can be computed in feasible time most importantly in higher dimensions the new method behaves clearly better than all previously known methods

a threshold accepting heuristic with intense local search for the solution of special instances of the traveling salesman problem in real life scheduling variations of the standard traveling salesman problem are very often encountered the aim of this work is to present a new heuristic method for solving three such special instances with a common approach the proposed algorithm uses a variant of the threshold accepting method enhanced with intense local search while the candidate solutions are produced through an insertion heuristic scheme the main characteristic of the algorithm is that it does not require modifications and parameter tuning in order to cope with the three different problems computational results on a variety of real life and artificial problems are presented at the end of this work and prove the efficiency and the ascendancy of the proposed method over other algorithms found in the literature

two phased hybrid local search for the periodic capacitated arc routing problem the periodic capacitated arc routing problem pcarp is a challenging general model with important applications the pcarp has two hierarchical optimization objectives a primary objective of minimizing the number of vehicles fv and a secondary objective of minimizing the total cost fc in this paper we propose an effective two phased hybrid local search hls algorithm for the pcarp the first phase makes a particular effort to optimize the primary objective while the second phase seeks to further optimize both objectives by using the resulting number of vehicles of the first phase as an upper bound to prune the search space for both phases combined local search heuristics are devised to ensure an effective exploration of the search space experimental results on 63 benchmark instances demonstrate that hls performs remarkably well both in terms of computational efficiency and solution quality in particular hls discovers 44 improved best known values new upper bounds for the total cost objective fc while attaining all the known optimal values regarding the objective of the number of vehicles fv to our knowledge this is the first pcarp algorithm reaching such a performance key components of hls are analyzed to better understand their contributions to the overall performance

a characteristic condition for convergence of steepest descent approximation to accretive operator equations in the present paper a sufficient and necessary condition for convergence of steepest descent approximation to accretive operator equations is established and for the sufficiency part a specific error estimation is also given

record breaking optimization results using the ruin and recreate principle a new optimization principle is presented solutions of problems are partly but significantly ruined and rebuilt or recreated afterwards performing this type of change frequently one can obtain astounding results for classical optimization problems the new method is particularly suited for more complex optimization problems discontinuous ones problems with hard to find admissible solutions problems with complex objectives or many constraints the method is an all purpose heuristic numerical results are given for the traveling salesman problem for the vehicle routing problem with time windows and for network optimization numerical evidence for the quality of the proposed principle is given for most of the instances of a research library of problems the ruin and recreate r r implementation achieved the best published results for many instances better or much better solutions could be found

fuzzy global optimization of complex system reliability the problem of optimizing the reliability of complex systems has been modeled as a fuzzy multi objective optimization problem three different kinds of optimization problems reliability optimization of a complex system with constraints on cost and weight optimal redundancy allocation in a multistage mixed system with constraints on cost and weight and optimal reliability allocation in a multistage mixed system with constraints on cost weight and volume have been solved four numerical examples have been solved to demonstrate the effectiveness of the present methodology the influence of various kinds of aggregators is also studied the inefficiency of the noncompensatory min operator has been demonstrated one of the well known global optimization meta heuristics the threshold accepting has been invoked to take care of the optimization part of the model a software has been developed to implement the above model the results obtained are encouraging

threshold accepting a general purpose optimization algorithm appearing superior to simulated annealing abstract a new general purpose algorithm for the solution of combinatorial optimization problems is presented the new threshold accepting method is even simpler structured than the wellknown simulated annealing approach the power of the new algorithm is demonstrated by computational results concerning the traveling salesman problem and the problem of the construction of error correcting codes moreover deterministic versions of the new heuristic turn out to perform nearly equally well consuming only a fraction of the computing time of the stochastic versions as an example the deterministic threshold accepting method yields very near to optimum tours for the famous 442 cities traveling salesman problem of grotschel within 1 to 2 s of cpu time

search space smoothing for combinatorial optimization problems commonly there are two types of local search approaches known to treat combinatorial optimization problems with very complex search space structure one is to introduce very complicated types of local move classes allowing a bypass of high energetic barriers separating different minima the second is introducing a control parameter i e temperature in physics terminology dependent state space walker which is depending on this control parameter more or less easily able to climb over barriers a third less well known but very obvious approach is to smooth the search space i e to eliminate barriers between low energy configurations and therefore to allow a fast and easy approach to the global optimum this procedure will be discussed in depth in the following work

a decomposition approach for the general lotsizing and scheduling problem for parallel production lines abstract this paper presents a novel solution heuristic to the general lotsizing and scheduling problem for parallel production lines glsppl the glsppl addresses the problem of simultaneously deciding about the sizes and schedules of production lots on parallel heterogeneous production lines with respect to scarce capacity sequence dependent setup times and deterministic dynamic demand of multiple products its objective is to minimize inventory holding sequence dependent setup and production costs the new heuristic iteratively decomposes the multi line problem into a series of single line problems which are easier to solve different approaches for decomposition and for the iteration between a modified multi line master problem and the single line subproblems are proposed they are compared with an existing solution method for the glsppl by means of medium sized and large practical problem instances from different types of industries the new methods prove to be superior with respect to both solution quality and computation time

computing the optimal protocol for finite time processes in stochastic thermodynamics asking for the optimal protocol of an external control parameter that minimizes the mean work required to drive a nanoscale system from one equilibrium state to another in finite time schmiedl and seifert t schmiedl and u seifert phys rev lett 98 108301 2007 found the euler lagrange equation to be a nonlocal integrodifferential equation of correlation functions for two linear examples we show how this integrodifferential equation can be solved analytically for nonlinear physical systems we show how the optimal protocol can be found numerically and demonstrate that there may exist several distinct optimal protocols simultaneously and we present optimal protocols that have one two and three jumps respectively

new spatial measure for dispersed dot halftoning assuring good point distribution in any density as a core component of dispersed dot halftoning this paper focuses on the definition of new measures for giving or measuring good point distributions in a plane by defining good point distributions from a purely geometric viewpoint of circle packing it is shown that the energy defined by a certain strong convex function satisfies the necessary conditions for obtaining good point distributions in any point density by minimizing the energy the energy with such the conditions are mathematically plain and there are no obscure parameters the theory is also significantly motivated by a requirement of the adjustability to discrete spaces and it is shown that the conditions actually work well also in the spaces as an application by using technically simple methods dispersed dot halftone masks are designed and goodness of point distributions of masks are estimated

steepest descent method for equilibrium points of nonlinear systems with accretive operators let e be a real normed linear space and let a e 2e be a bounded uniformly continuous strongly accretive multi valued map with nonempty closed values such that the inclusion 0 ax has a solution x e it is proved that both the ishikawa and the mann iteration processes are bounded and converge strongly to x related results deal with the convergence of the iteration processes to fixed points of strongly pseudocontractive maps and the iterative solution of the equation 0 x fx for an accretive map f furthermore the ishikawa and mann iteration methods with errors are discussed and proofs are sketched on how our theorems extend to these methods our method of proof is of independent interest

uniform design theory and application a uniform design ud seeks design points that are uniformly scattered on the domain it has been popular since 1980 a survey of ud is given in the first portion the fundamental idea and construction method are presented and discussed and examples are given for illustration it is shown that ud s have many desirable properties for a wide variety of applications furthermore we use the global optimization algorithm threshold accepting to generate ud s with low discrepancy the relationship between uniformity and orthogonality is investigated it turns out that most ud s obtained here are indeed orthogonal

the isometry group of lp μ x is sot contractible abstract we will show that if is an atomless positive measure space x is a banach space and 1 p then the group of isometric automorphisms on the bochner space l p x is contractible in the strong operator topology we do not require or x above to be separable

fitting of tabu search to optimize functions of continuous variables summarytabu search ts is a stochastic global optimization procedure which proved e cient to solve variouscombinatorialoptimizationproblems however veryfewworksdealwithitsapplicationtoglobalminimiz ationof functions dependingon continuous variables the aim of this paper is to proposean adaptation oftstotheoptimizationofcontinuousfunctions andtostudytheinsuenceofthemainalgorithmparameterson the convergence towards the optimum in particular the application of ts to function optimizationinvolves the de nition of the current solution neighbourhood and the management of the tabu list thee ciency of ts applied to continuous global optimization has been tested in detail by using classicalmultimodal functions for which minima are known 1997 by john wiley sons ltd key words tabu search global optimization continuous variables 1 introductionthe underlying principles of tabu search ts were rst exposed by glover 1 2 more recentlyoverviewsaboutts and itsimplementationin various eldshavebeenproposed forinstancebyhertz

on mann iteration in hilbert spaces abstract let k be a compact convex subset of a real hilbert space h t k k a hemicontractive map let n be a real sequence in 0 1 satisfying appropriate conditions then for arbitrary x 0 k the sequence x n defined iteratively by x n n x n 1 1 n t x n n 1 converges strongly to a fixed point of t

geometry of integral polynomials m ideals and unique norm preserving extensions we use the aron berner extension to prove that the set of extreme points of the unit ball of the space of integral k homogeneous polynomials over a real banach space x is k x 1 with this description we show that for real banach spaces x and y if x is a nontrivial m ideal in y then ek sk sx the k th symmetric tensor product of x endowed with the injective symmetric tensor norm is never an m ideal in ek sk sy this result marks up a difference with the behavior of nonsymmetric tensors since when x is an m ideal in y it is known that ekkx the k th tensor product of x endowed with the injective tensor norm is an m ideal in ekky nevertheless if x is also asplund we prove that every integral k homogeneous polynomial in x has a unique extension to y that preserves the integral norm other applications to the metric and isomorphic theory of symmetric tensor products and polynomial ideals are also given

global iterative schemes for accretive operators abstract let e be a real q uniformly smooth banach space and a e 2e be an m accretive operator which satisfies a linear growth condition of the form ax c 1 x for some constant c 0 and for all x e it is proved that if two real sequences n and n satisfy appropriate conditions the sequence xn generated from arbitrary x0 e by xn 1 xn n un n xn z un axn n 0 converges strongly to some x a 1 0 furthermore if e is a reflexive banach space with a uniformly g teaux differentiable norm and if every weakly compact convex subset of e has the fixed point property for nonexpansive mappings and a d a e 2e is m accretive then for arbitrary z x0 e the sequence xn defined by xn 1 n un 1 n xn 1 z xn en for un axn where en e is such that en

characteristic inequalities of uniformly convex and uniformly smooth banach spaces abstract let x be a real banach space with dual x and moduli of convexity and smoothness x e and x respectively for 1 p denotes the duality mapping from x into 2 x with gauge function t p 1 and j p denotes an arbitrary selection for j p let a r 0 0 t is strictly increasing and there exists c 0 such that t c x t 2 and f r 0 0 t is convex nondecreasing and there exists k 0 such that k x it is proved that x is uniformly convex if and only if there is a a such that x y p x p p j p x y x y x y x and x is uniformly smooth if and only if there is a f such that x y p x p p j p x y x y x y x where for given function f f x y is defined by f x y p 0 1 x ty x p t f t y x ty x dt these inequalities which have various applications can be regarded as general banach space versions of the well known polarization identity occurring in hilbert spaces

a necessary and sufficient condition for convergence of steepest descent approximation to accretive operator equations abstract a necessary and sufficient condition is established which ensures the strong convergence of the steepest descent approximation to a solution of equations involving quasi accretive operators defined on a uniformly smooth banach space

a class of convergent generalized hill climbing algorithms generalized hill climbing ghc algorithms have been presented as a modeling framework for local search strategies applied to address intractable discrete optimization minimization problems ghc algorithms include simulated annealing sa pure local search ls and threshold accepting ta among others as special cases a particular class of ghc algorithms is designed for discrete optimization problems where the objective function value of a globally optimal solution is known in this case the task is to identify an associated optimal solution this class of ghc algorithms is shown to converge and six examples are provided that illustrate the diversity of ghc algorithms within this class of convergent algorithms implications of these results are discussed

bounding the probability of success of stochastic methods for global optimization abstract in this paper we establish some bounds for the probability that stimulated annealing produces an optimal or near optimal solution such bounds are given for both asymptotical and finite number of steps in the algorithm and they depend only on the instance of the problem to be treated then we compare its performance with a randomized local search showing that actually simulated annealing behaves worse than such a very simple global optimization technique furthermore since many parallel implementations of simulated annealing exist we also address its behavior in the parallel model of computation even in this case similar bounds hold and we can prove that the most simple parallel version of randomized local search is more likely to find optimal or near optimal solutions than any version of parallel simulated annealing

the iterative solution of the equation f x tx for a monotone operator t in lp spaces suppose t is a multivalued monotone operator not necessarily continuous with open domain d t in lp 2 p f r i t and the equation f x tx has a solution q d t then there exists a neighbourhood b d t of q and a real number r1 0 such that for any r r1 for any initial guess x1 b and any singlevalued section t0 of t the sequence xn n 1 generated from x1 by xn 1 1 cn xn cn f t0xn remains in d t and converges strongly to q with xn q 0 n 1 2 furthermore for x lp e e

steepest descent approximations for accretive operator equations a necessary and sufficient condition is established for the strong convergence of the steepest descent approximation to a solution of equations involving quasi accretive operators defined on a uniformly smooth banach space miramare trieste march 1993

applying simulated annealing using different methods for the neighborhood search in forest planning problems adjacency constraints along with even flow harvest constraints are important in long term forest planning simulated annealing sa is previously successfully applied when addressing such constraints the objective of this paper was to assess the performance of sa under three new methods of introducing biased probabilities in the management unit mu selection and compare them to the conventional method that assumes uniform probabilities the new methods were implemented as a search vector approach based on the number of treatment schedules describing sequences of silvicultural treatments over time and standard deviation of net present value within mus methods 2 and 3 respectively and by combining the two approaches method 4 we constructed three hundred hypothetical forests datasets for three different landscapes characterized by different initial age class distributions young normal and old each dataset encompassed 1600 management units the evaluation of the methods was done by means of objective function values first feasible iteration and time consumption introducing a bias in the mu selection improves solutions compared to the conventional method method 1 however an increase of computational time is in general needed for the new methods method 4 is the best alternative because for large parts of the datasets produced the best average and maximum objective function values and had lower time consumption than methods 2 and 3 although method 4 performed very well methods 2 and 3 should not be neglected because for a considerable number of datasets the maximum objective function values were obtained by these methods

convex transitivity and function spaces abstract it is shown that if x is a convex transitive banach space and 1 p then l p 0 1 x and l s 0 1 x are convex transitive here l s 0 1 x is the closed linear span of the simple functions in the bochner space l 0 1 x if h is an infinite dimensional hilbert space and c 0 l is convex transitive then c 0 l h is convex transitive some new fairly concrete examples of convex transitive spaces are provided

a genetic algorithm approach to find the best regression econometric model among the candidates although statistical modeling is a common task in different fields of science it is still difficult to estimate the best model that can accurately describe inherent characteristics of a system for which historical or experimental data are available since we may classify estimating techniques as optimizations we can model this problem as an optimization problem and solve it by a new heuristic algorithm like neural networks genetic algorithms and tabu search or by classic ones such as regression and econometric models in this paper we propose a new type of genetic algorithm to find the best regression model among all suggested and evaluate its performances by an economical case study

incorporating scatter search and threshold accepting in finding maximum likelihood estimates for the multinomial probit model this paper presents a procedure that incorporates scatter search and threshold accepting to find the maximum likelihood estimates for the multinomial probit mnp model scatter search widely used in optimization related studies is a type of evolutionary algorithm that uses a small set of solutions as the selection pool for mating and generating new solutions to search for a globally optimal solution threshold accepting is applied to the scatter search to improve computational efficiency while maintaining the same level of solution quality a set of numerical experiments based on synthetic data sets with known model specifications and error structures were conducted to test the effectiveness and efficiency of the proposed framework the results indicated that the proposed procedure enhanced performance in terms of likelihood function value and computational efficiency for mnp model estimation as compared to the original scatter search framework

application of threshold accepting to the evaluation of the discrepancy of a set of points efficient routines for multidimensional numerical integration are provided by quasi monte carlo methods these methods are based on evaluating the integrand at a set of representative points of the integration area a set may be called representative if it shows a low discrepancy however in dimensions higher than two and for a large number of points the evaluation of discrepancy becomes infeasible the use of the efficient multiple purpose heuristic threshold accepting offers the possibility to obtain at least good approximations to the discrepancy of a given set of points this paper presents an implementation of the threshold accepting heuristic an assessment of its performance for some small examples and results for larger sets of points with unknown discrepancy

iterative solution of nonlinear equations of the φ strongly accretive type abstract letq 1 and letebe a realq uniformly smooth banach space lett e ebe a lipschitz strongly accretive operator and suppose the equationtx f f e has a solution it is proved that under suitable conditions on the real sequences n n 0 and n n 0 the iteration process formula converges strongly to the unique solution of the equationtx f a related result deals with the approximation of fixed points of hemicontractive operators a class of operators which is much more general than the important class of strongly pseudocontractive operators

comparing different metaheuristic approaches for the median path problem with bounded length abstract in this paper we consider the bounded length median path problem which can be defined as the problem of locating a path shaped facility that departures from a given origin and arrives at a given destination in a network the length of the path is assumed to be bounded by a given maximum length at each vertex of the network customer point the demand for the service is given and the cost to reach the closest service point is computed the objective is to minimize the sum of these costs over all the customer points in the network we consider two local search metaheuristics the well known tabu search and the old bachelor acceptance and we propose a comparative analysis of the performances of the two procedures we implement streamlined versions of tabu search and old bachelor acceptance our main concern is to provide knowledge about the intrinsic strategy adopted by each metaheuristic and to know whether one is more appropriate than the other for our problem

the late acceptance hill climbing heuristic abstract this paper introduces a new and very simple search methodology called late acceptance hill climbing lahc it is a local search algorithm which accepts non improving moves when a candidate cost function is better than it was a number of iterations before this number appears as a single algorithmic input parameter which determines the total processing time of the search procedure the properties of this method are experimentally studied in this paper with a range of travelling salesman and exam timetabling benchmark problems also we present a fair comparison of lahc with well known search techniques which employ a cooling schedule simulated annealing sa threshold accepting ta and the great deluge algorithm gda in addition we discuss the success of the method in winning an international competition to automatically solve the magic square problem our experiments have shown that the lahc approach is simple easy to implement and yet is an effective search procedure for most of the studied instances especially for the large sized ones its average performance is better than competitor methods moreover the lahc approach has an additional advantage in contrast to the above cooling schedule based methods in its scale independence we present an example where the rescaling of a cost function in the travelling salesman problem dramatically deteriorates the performance of three cooling schedule based techniques but has absolutely no influence upon the performance of lahc

the multidimensional 0 1 knapsack problem an overview abstract the multidimensional 0 1 knapsack problem is one of the most well known integer programming problems and has received wide attention from the operational research community during the last four decades although recent advances have made possible the solution of medium size instances solving this np hard problem remains a very interesting challenge especially when the number of constraints increases this paper surveys the main results published in the literature the focus is on the theoretical properties as well as approximate or exact solutions of this special 0 1 program

applying multiple objective tabu search to continuous optimization problems with a simple neighbourhood strategy one of the first multiple objective versions of the tabu search ts algorithm is proposed by the author the idea of applying ts to multiple objective optimization is inspired from its solution structure ts works with more than one solution neighbourhood solutions at a time and this situation gives the opportunity to evaluate multiple objectives simultaneously in one run the selection and updating stages are modified to enable the original ts algorithm to work with more than one objective in this paper the multiple objective tabu search mots algorithm is applied to multiple objective non linear optimization problems with continuous variables using a simple neighbourhood strategy the algorithm is applied to four mechanical components design problems the results are compared with several other solution techniques including multiple objective genetic algorithms it is observed that mots is able to find better and much wider spread of solutions than the reported ones copyright 2005 john wiley sons ltd

characteristic conditions for convergence of generalized steepest descent approximation to multivalued accretive operator equations abstract in the present paper sufficient and necessary conditions for convergence of generalized steepest descent approximation to multivalued accretive operator equations are established for the sufficiency part and a specific error estimation is also given

a convergence analysis of generalized hill climbing algorithms generalized hill climbing ghc algorithms provide a well defined framework for describing the performance of local search algorithms for discrete optimization problems necessary and sufficient convergence conditions for ghc algorithms are presented these convergence conditions are derived using a new iteration classification scheme for ghc algorithms the implications of the necessary and the sufficient convergence conditions fur ghc algorithms with respect to existing convergence theory for simulated annealing are also discussed

influence of rounding errors on the quality of heuristic optimization algorithms abstract search space smoothing and related heuristic optimization algorithms provide an alternative approach to simulated annealing and its variants while simulated annealing traverses barriers in the energy landscape at finite temperatures search space smoothing intends to remove these barriers so that a greedy algorithm is sufficient to find the global minimum several formulas for smoothing the energy landscape have already been applied one of them making use of the finite numerical precision on a computer in this paper we thoroughly investigate the effect of finite numerical accuracy on the quality of results achieved with heuristic optimization algorithms we present computational results for the traveling salesman problem

a genetic algorithm approach to single and multiobjective structural optimization with discrete continuous variables a search procedure with a philosophical basis in molecular biology is adapted for solving single and multiobjective structural optimization problems this procedure known as a genetic algorithm ga utilizes a blending of the principles of natural genetics and natural selection a lack of dependence on the gradient information makes gas less susceptible to pitfalls of convergence to a local optimum to model the multiple objective functions in the problem formulation a co operative game theoretic approach is proposed examples dealing with single and multiobjective geometrical design of structures with discrete continuous design variables and using artificial genetic search are presented simulation results indicate that gas converge to optimum solutions by searching only a small fraction of the solution space the optimum solutions obtained using gas compare favourably with optimum solutions obtained using gradient based search techniques the results indicate that the efficiency and power of gas can be effectively utilized to solve a broad spectrum of design optimization problems with discrete and continuous variables with similar efficiency