bergeʼs maximum theorem for noncompact image sets abstract this note generalizes berge s maximum theorem to noncompact image sets it also clarifies the results from feinberg kasyanov and zadoianchuk 2013 7 on the extension to noncompact image sets of another berge s theorem that states semi continuity of value functions here we explain that the notion of a k inf compact function introduced there is applicable to metrizable topological spaces and to more general compactly generated topological spaces for hausdorff topological spaces we introduce the notion of a k n inf compact function n stands for nets in k inf compactness which coincides with k inf compactness for compactly generated and in particular for metrizable topological spaces

the lack of a priori distinctions between learning algorithms this is the first of two papers that use off training set ots error to investigate the assumption free relationship between learning algorithms this first paper discusses the senses in which there are no a priori distinctions between learning algorithms the second paper discusses the senses in which there are such distinctions in this first paper it is shown loosely speaking that for any two algorithms a and b there are as many targets or priors over targets for which a has lower expected ots error than b as vice versa for loss functions like zero one loss in particular this is true if a is cross validation and b is anti cross validation choose the learning algorithm with largest cross validation error this paper ends with a discussion of the implications of these results for computational learning theory it is shown that one cannot say if empirical misclassification rate is low the vapnik chervonenkis dimension of your generalizer is small and the training set is large then with high probability your ots error is small other implications for membership queries algorithms and punting algorithms are also discussed

rigorous results for random 2 p sat in recent years there has been significant interest in the study of random k sat formulae for a given set of n boolean variables let bk denote the set of all possible disjunctions of k distinct non complementary literals from its variables k clauses a random k sat formula fk n m is formed by selectinguniformly and independently m clauses from bk and takingtheir conjunction motivated by insights from statistical mechanics that suggest a possible relationship between the order of phase transitions and computational complexity monasson and zecchina phys rev e 56 2 1997 1357 proposed the random 2 p sat model for a given p 0 1 a random 2 p sat formula f2 p n m has m randomly chosen clauses over n variables where pm clauses are chosen from b3 and 1 p m from b2 usingthe heuristic replica method of statistical mechanics monasson and zecchina gave a number of non rigorous predictions on the behavior of random 2 p sat formulae in this paper we give the 1rst rigorous results for random 2 p sat including the following surprising fact for p 2 5 with probability 1 o 1 a random 2 p sat formula is satisfiable if its 2 sat subformula is satisfiable that is for p 6 2 5 random 2 p sat behaves like random 2 sat

a non dominance based online stopping criterion for multi objective evolutionary algorithms a non dominance criterion based metric that tracks the growth of an archive of non dominated solutions over a few generations is proposed to generate a convergence curve for multi objective evolutionary algorithms moeas it was observed that similar to single objective optimization problems there were significant advances toward the pareto optimal front in the early phase of evolution while relatively smaller improvements were obtained as the population matured this convergence curve was used to terminate the moea search to obtain a good trade off between the computational cost and the quality of the solutions two analytical and two crashworthiness optimization problems were used to demonstrate the practical utility of the proposed metric

some optimal inapproximability results we prove optimal up to an arbitrary e 0 inapproximability results for max e k sat for k 3 maximizing the number of satisfied linear equations in an over determined system of linear equations modulo a prime p and set splitting as a consequence of these results we get improved lower bounds for the efficient approximability of many optimization problems studied previously in particular for max e2 sat max cut max di cut and vertex cover

berge s theorem for noncompact image sets abstract for an upper semi continuous set valued mapping from one topological space to another and for a lower semi continuous function defined on the product of these spaces berge s theorem states lower semi continuity of the minimum of this function taken over the image sets it assumes that the image sets are compact for hausdorff topological spaces this paper extends berge s theorem to set valued mappings with possible noncompact image sets and studies relevant properties of minima

optimality inequalities for average cost markov decision processes and the stochastic cash balance problem for general state and action space markov decision processes we present sufficient conditions for the existence of solutions of the average cost optimality inequalities these conditions also imply the convergence of both the optimal discounted cost value function and policies to the corresponding objects for the average costs per unit time case inventory models are natural applications of our results we describe structural properties of average cost optimal policies for the cash balance problem an inventory control problem where the demand may be negative and the decision maker can produce or scrap inventory we also show the convergence of optimal thresholds in the finite horizon case to those under the expected discounted cost criterion and those under the expected discounted costs to those under the average costs per unit time criterion

modifications of real code genetic algorithm for global optimization a series of modifications to the real coded genetic algorithm for the task of locating the global minimum of multidimensional functions are presented here these modifications include a new stopping rule a novel mutation mechanism and a periodically application of a local search procedure the proposed modifications are tested on a series of optimization problems and the results are reported

a markov chain analysis of genetic algorithms with power of 2 cardinality alphabets abstract in this paper we model the run time behavior of gas using higher cardinality representations as markov chains define the states of the markov chain and derive the transition probabilities of the corresponding transition matrix we analyze the behavior of this chain and obtain bounds on its convergence rate and bounds on the runtime complexity of the ga we further investigate the effects of using binary versus higher cardinality representation of a search space

convergence criteria for genetic algorithms in this paper we discuss convergence properties for genetic algorithms by looking at the effect of mutation on convergence we show that by running the genetic algorithm for a sufficiently long time we can guarantee convergence to a global optimum with any specified level of confidence we obtain an upper bound for the number of iterations necessary to ensure this which improves previous results our upper bound decreases as the population size increases we produce examples to show that in some cases this upper bound is asymptotically optimal for large population sizes the final section discusses implications of these results for optimal coding of genetic algorithms

the quasispecies regime for the simple genetic algorithm with ranking selection we study the simple genetic algorithm with a ranking selection mechanism linear ranking or tournament we denote by the length of the chromosomes by m the population size by pc the crossover probability and by pm the mutation probability we introduce a parameter called the selection drift which measures the selection intensity of the fittest chromosome we show that the dynamics of the genetic algorithm depend in a critical way on the parameter 1 pc 1 pm if 1 then the genetic algorithm operates in a quasispecies regime an advantageous mutant invades a positive fraction of the population with probability larger than a constant p which does not depend on m we estimate next the probability of the occurrence of a catastrophe the whole population falls below a fitness level which was previously reached by a positive fraction of the population the asymptotic results suggest the following rules 1 pc 1 pm should be slightly larger than 1 pm should be of order 1 m should be larger than ln the running time should be of exponential order in m the first condition requires that pm pc ln these conclusions must be taken with great care they come from an asymptotic regime and it is a formidable task to understand the relevance of this regime for a real world problem at least we hope that these conclusions provide interesting guidelines for the practical implementation of the simple genetic algorithm

a parallel repetition theorem we show that a parallel repetition of any two prover one round proof system mip 2 1 decreases the probability of error at an exponential rate no constructive bound was previously known the constant in the exponent in our analysis depends only on the original probability of error and on the total number of possible answers of the two provers the dependency on the total number of possible answers is logarithmic which was recently proved to be almost the best possible u feige and o verbitsky proc 11th annual ieee conference on computational complexity ieee computer society press los alamitos ca 1996 pp 70 76

a stopping criterion for multi objective optimization evolutionary algorithms this paper puts forward a comprehensive study of the design of global stopping criteria for multi objective optimization in this study we propose a global stopping criterion which is terms as mgbm after the authors surnames mgbm combines a novel progress indicator called mutual domination rate mdr indicator with a simplified kalman filter which is used for evidence gathering purposes the mdr indicator which is also introduced is a special purpose progress indicator designed for the purpose of stopping a multi objective optimization as part of the paper we describe the criterion from a theoretical perspective and examine its performance on a number of test problems we also compare this method with similar approaches to the issue the results of these experiments suggest that mgbm is a valid and accurate approach

new stopping criterion for genetic algorithms abstract genetic algorithms have been successfully applied in a wide variety of problems although widely used there are few theoretical guidelines for determining when to terminate the search one result by aytug and koehler provides a loose bound on the number of ga generations needed to see all populations and hence an optimal solution with a specified probability in this paper we derive a tighter bound this new bound is on the number of iterations required to achieve a level of confidence to guarantee that a genetic algorithm has seen all strings and hence an optimal solution

subset selection in multiple linear regression models a hybrid of genetic and simulated annealing algorithms the question of variable selection in a multiple linear regression model is a major open research topic in statistics the subset selection problem in multiple linear regression deals with the selection of a minimal subset of input variables without loss of explanatory power in this paper we adapt the genetic and simulated annealing algorithms for variable selection in multiple linear regression the performance of this hybrid heuristic method is compared to those obtained by forward selection backward elimination and classical genetic algorithm search a comparative analysis on the literature data sets and simulation data shows that our hybrid heuristic method may suggest efficient alternative to traditional subset selection methods for the variable selection problem in multiple linear regression models

average cost markov decision processes with weakly continuous transition probabilities this paper presents sufficient conditions for the existence of stationary optimal policies for average cost markov decision processes with borel state and action sets and weakly continuous transition probabilities the one step cost functions may be unbounded and the action sets may be noncompact the main contributions of this paper are i general sufficient conditions for the existence of stationary discount optimal and average cost optimal policies and descriptions of properties of value functions and sets of optimal actions ii a sufficient condition for the average cost optimality of a stationary policy in the form of optimality inequalities and iii approximations of average cost optimal actions by discount optimal actions

frequency of frequencies distributions and size dependent exchangeable random partitions abstractmotivated by the fundamental problem of modeling the frequency of frequencies fof distribution this paper introduces the concept of a cluster structure to define a probability function that governs the joint distribution of a random count and its exchangeable random partitions a cluster structure naturally arising from a completely random measure mixed poisson process allows the probability distribution of the random partitions of a subset of a population to be dependent on the population size a distinct and motivated feature that makes it more flexible than a partition structure this allows it to model an entire fof distribution whose structural properties change as the population size varies a fof vector can be simulated by drawing an infinite number of poisson random variables or by a stick breaking construction with a finite random number of steps a generalized negative binomial process model is proposed to generate a cluster structure where in the prior the number of clusters is f

genetic algorithm for constrained global optimization in continuous variables we present a stochastic global optimization algorithm referred to as a genetic algorithm ga for solving constrained optimization problems over a compact search domain it is a real coded ga that converges in probability to the optimal solution the constraints are treated through a repair operator a specific repair operator is included for linear inequality constraints

quantiles in nonrandom samples and observational studies abstract in a nonrandom sample or a nonrandomized comparison of treated and control groups methods are developed for displaying the sensitivity of confidence intervals for population quantiles to the magnitude of the departure from random selection quantiles of a single distribution and for a shift in two distributions are both discussed these confidence intervals are based on a new inequality for the distribution of the number of successes in a nonrandom sample or nonrandomized comparison the inequality has additional applications in particular it greatly accelerates the computations in a sensitivity analysis for the mantel haenszel statistic in a 2 2 s contingency table examples include a nonrandom collection of blood samples from a town with comparatively high levels of radon gas an observational study of chromosome damage from mercury and a study of the drug allopurinol as a cause of skin rash the proof of the inequality makes use of savage s lattice for ranks and holley s inequality wh

a new genetic algorithm for solving nonconvex nonlinear programming problems abstract in nonlinear programming problems especially nonconvex problems attaining the global optimum is crucial to reach this purpose the current paper represents a new genetic algorithm for solving nonconvex nonlinear programming problems the new method is simpler and more intuitive than the existing models and finds the global optimum of the problem in a reasonable time the proposed technique to attain the global optimum of problem especially in large scale problems instead of increasing the size of population which usually conduces to the curse of dimensionality that is widespread in usual genetic algorithms decomposes the main problem into several sub problems but with lower size of population in each sub problem this decomposition has been formed in such a way that it could envelop the total solution space the proposed genetic algorithm which determines the sufficient sub problems could converge to global optimum of problem to be able to measure the proposed genetic algorithm several problems have been solved in different spectrums herein it has been shown that the proposed technique both in run time and in solution quality is preferred to the usual genetic algorithm in this domain nonlinear continuous programming problems

on the vanishing discount factor approach for markov decision processes with weakly continuous transition probabilities abstract this note deals with average cost markov decision processes with borel state and control spaces possibly unbounded costs and non compact action subsets under the assumption of weak continuity of the transition law it provides an elementary proof of the existence of average cost optimal stationary policies using the vanishing discount factor approach

2 e sat is np hard we prove the following hardness result for a natural promise variant of the classical cnf satisfiability problem given a cnf formula where each clause has width w and the guarantee that there exis

a hybrid genetic algorithm with the baldwin effect here we present a new hybrid genetic algorithm hga with the baldwin effect in the hga a local search is employed to change the fitness of individuals but the acquired improvements do not change the individual itself this local search step exploits the baldwin effect some numerical applications show that this algorithm can yield the global optimum more efficiently than commonly used hgas a theorem is presented that guarantees the convergence in probability of the new hga

a general steady state distribution based stopping criteria for finite length genetic algorithms we propose two general stopping criteria for finite length simple genetic algorithms based on steady state distributions and empirically investigate the impact of mutation rate string length crossover rate and population size on their convergence our first stopping criterion is based on the second largest eigenvalue of the genetic algorithm transition matrix and the second stopping criterion is based on minorization conditions

the effect of multiple optima on the simple ga run time complexity genetic algorithms are stochastic search algorithms that have been applied to optimization problems in this paper we analyze the run time complexity of a genetic algorithm when we are interested in one of a set of distinguished solutions one such case occurs when multiple optima exist we define the worst case scenario and derive a probabilistic worst case bound on the number of iterations required to find one of these multiple solutions of interest

set intersection theorems and existence of optimal solutions the question of nonemptiness of the intersection of a nested sequence of closed sets is fundamental in a number of important optimization topics including the existence of optimal solutions the validity of the minimax inequality in zero sum games and the absence of a duality gap in constrained optimization we consider asymptotic directions of a sequence of closed sets and introduce associated notions of retractive horizon and critical directions based on which we provide new conditions that guarantee the nonemptiness of the corresponding intersection we show how these conditions can be used to obtain simple and unified proofs of some known results on existence of optimal solutions and to derive some new results including a new extension of the frank wolfe theorem for nonconvex quadratic programming

partially observable total cost markov decision processes with weakly continuous transition probabilities this paper describes sufficient conditions for the existence of optimal policies for partially observable markov decision processes pomdps with borel state observation and action sets when the goal is to minimize the expected total costs over finite or infinite horizons for infinite horizon problems one step costs are either discounted or assumed to be nonnegative action sets may be noncompact and one step cost functions may be unbounded the introduced conditions are also sufficient for the validity of optimality equations semicontinuity of value functions and convergence of value iterations to optimal values since pomdps can be reduced to completely observable markov decision processes comdps whose states are posterior state distributions this paper focuses on the validity of the above mentioned optimality properties for comdps the central question is whether the transition probabilities for the comdp are weakly continuous we introduce sufficient conditions for this and show that the tr