on the effectiveness of immune inspired mutation operators in some discrete optimization problems abstract artificial immune systems have been widely applied to a variety of complex real world problems however theoretical studies on artificial immune system are still limited and there is a strong need for building a rigorous theoretical foundation to better understand these heuristics this paper contributes to a theoretical runtime analysis of immune inspired hypermutations on some discrete optimization problems in particular we are interested in the performance comparison among somatic contiguous hypermutations chm standard bit mutations sbm and local mutation we reveal that the immune inspired hypermutations can significantly outperform the standard bit mutation most often used in evolutionary algorithms on some well known pseudo boolean functions including trap and hierarchical if and only if functions and instances of two combinatorial optimization problems namely the max cut problem and the minimum s t cut problem the proofs give some insights into the relationships between the problem characteristics and algorithmic features the results of the analysis help strengthen the usefulness of artificial immune systems

on the convergence rates of genetic algorithms this paper discusses the convergence rates of genetic algorithms by using the minorization condition in the markov chain theory we classify genetic algorithms into two kinds one with time invariant genetic operators another with time variant genetic operators for the former case we have obtained the bound on its convergence rate on the general state space for the later case we have bounded its convergence rate on the finite state space

a theoretical and empirical study on unbiased boundary extended crossover for real valued representation we present a new crossover operator for real coded genetic algorithms employing a novel methodology to remove the inherent bias of pre existing crossover operators this is done by transforming the topology of the hyper rectangular real space by gluing opposite boundaries and designing a boundary extension method for making the fitness function smooth at the glued boundary we show the advantages of the proposed crossover by comparing its performance with those of existing ones on test functions that are commonly used in the literature and a nonlinear regression on a real world dataset

hesitant adaptive search the distribution of the number of iterations to convergence hesitant adaptive search is a stochastic optimisation procedure which accommodates hesitation or pausing at objective function values it lies between pure adaptive search which strictly improves at each iteration and simulated annealing with constant temperature which allows backtracking or the acceptance of worse function values in this paper we build on an earlier work and make two contributions first we link hesitant adaptive search to standard counting process theory and second we use this to derive the exact distribution of the number of iterations of hesitant adaptive search to termination

hit and run algorithms for the identification of nonredundant linear inequalities two probabilistic hit and run algorithms are presented to detect nonredundant constraints in a full dimensional system of linear inequalities the algorithms proceed by generating a random sequence of interior points whose limiting distribution is uniform and by searching for a nonredundant constraint in the direction of a random vector from each point in the sequence in the hypersphere directions algorithm the direction vector is drawn from a uniform distribution on a hypersphere in the computationally superior coordinate directions algorithm a search is carried out along one of the coordinate vectors the algorithms are terminated through the use of a bayesian stopping rule computational experience with the algorithms and the stopping rule will be reported

pure adaptive search in global optimization pure adaptive seach iteratively constructs a sequence of interior points uniformly distributed within the corresponding sequence of nested improving regions of the feasible space that is at any iteration the next point in the sequence is uniformly distributed over the region of feasible space containing all points that are strictly superior in value to the previous points in the sequence the complexity of this algorithm is measured by the expected number of iterations required to achieve a given accuracy of solution we show that for global mathematical programs satisfying the lipschitz condition its complexity increases at mostlinearly in the dimension of the problem

truth revelation in approximately efficient combinatorial auctions some important classical mechanisms considered in microeconomics and game theory require the solution of a difficult optimization problem this is true of mechanisms for combinatorial auctions which have in recent years assumed practical importance and in particular of the gold standard for combinatorial auctions the generalized vickrey auction gva traditional analysis of these mechanisms in particular their truth revelation properties assumes that the optimization problems are solved precisely in reality these optimization problems can usually be solved only in an approximate fashion we investigate the impact on such mechanisms of replacing exact solutions by approximate ones specifically we look at a particular greedy optimization method we show that the gva payment scheme does not provide for a truth revealing mechanism we introduce another scheme that does guarantee truthfulness for a restricted class of players we demonstrate the latter property by identifying natural properties for combinatorial auctions and showing that for our restricted class of players they imply that truthful strategies are dominant those properties have applicability beyond the specific auction studied

on the convergence of algorithms with implications for stochastic and nondifferentiable optimization studies of the convergence of algorithms often revolve around the existence of a function with respect to which monotonic descent is required in this paper we show that under relatively lenient conditions stage dependent descent not necessarily monotonic is sufficient to guarantee convergence this development also provides the impetus to examine optimization algorithms we show that one of the important avenues in the study of convergence namely the theory of epi convergence imposes stronger conditions than are necessary to establish the convergence of an optimization algorithm working from a relaxation of epi convergence we introduce the notion of compatibility and prove several results that permit relaxations of conditions imposed by previous approaches to algorithmic convergence finally to illustrate the usefulness of the concepts we combine stage dependent descent with results derivable from compatibility to provide a basis for the convergence of a general algorithmic statement that might be used for stochastic and nondifferentiable optimization

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

grover s quantum algorithm applied to global optimization grover s quantum computational search procedure can provide the basis for implementing adaptive global optimization algorithms a brief overview of the procedure is given and a framework called grover adaptive search is set up a method of durr and hoyer and one introduced by the authors fit into this framework and are compared

a direct stochastic algorithm for global search this paper presents a new algorithm called probabilistic global search lausanne pgsl pgsl is founded on the assumption that optimal solutions can be identified through focusing search around sets of good solutions tests on benchmark problems having multi parameter non linear objective functions revealed that pgsl performs better than genetic algorithms and advanced algorithms for simulated annealing in 19 out of 23 cases studied furthermore as problem sizes increase pgsl performs increasingly better than these other approaches empirical evidence of the convergence of pgsl is provided through its application to lennard jones cluster optimisation problem finally pgsl has already proved to be valuable for engineering tasks in areas of design diagnosis and control

on the analysis of the 1 1 evolutionary algorithm many experimental results are reported on all types of evolutionary algorithms but only few results have been proved a step towards a theory on evolutionary algorithms in particular the so called 1 1 evolutionary algorithm is performed linear functions are proved to be optimized in expected time o nlnn but only mutation rates of size 1 n can ensure this behavior for some polynomial of degree 2 the optimization needs exponential time the same is proved for a unimodal function both results were not expected by several other authors finally a hierarchy result is proved moreover methods are presented to analyze the behavior of the 1 1 evolutionary algorithm

recent developments and trends in global optimization many optimization problems in engineering and science require solutions that are globally optimal these optimization problems are characterized by the nonconvexity of the feasible domain or the objective function and may involve continuous and or discrete variables in this paper we highlight some recent results and discuss current research trends on deterministic and stochastic global optimization and global continuous approaches to discrete optimization

runtime analysis of a multi objective evolutionary algorithm for obtaining finite approximations of pareto fronts previous theoretical analyses of evolutionary multi objective optimization emo mostly focus on obtaining approximations of pareto fronts however in practical applications an appropriate value of is critical but sometimes for a multi objective optimization problem mop with unknown attributes difficult to determine in this paper we propose a new definition for the finite representation of the pareto front the adaptive pareto front which can automatically accommodate the pareto front accordingly it is more practical to take the adaptive pareto front or its approximation termed the adaptive pareto front as the goal of an emo algorithm we then perform a runtime analysis of a m 1 multi objective evolutionary algorithm m 1 moea for three mops including a discrete mop with a polynomial pareto front denoted as a polynomial dmop a discrete mop with an exponential pareto front denoted as an exponential dmop and a simple continuous two objective optimization problem sctop by employing an estimator based update strategy in the m 1 moea we show that 1 for the polynomial dmop the whole pareto front can be obtained in the expected polynomial runtime by setting the population size m equal to the number of pareto vectors 2 for the exponential dmop the expected polynomial runtime can be obtained by keeping m increasing in the same order as that of the problem size n and 3 the diversity mechanism guarantees that in the expected polynomial runtime the moea can obtain an adaptive pareto front of sctop for any given precision theoretical studies and numerical comparisons with nsga ii demonstrate the efficiency of the proposed moea and should be viewed as an important step toward understanding the mechanisms of moeas

nested partitions method for global optimization we propose a new randomized method for solving global optimization problems this method the nested partitions np method systematically partitions the feasible region and concentrates the search in regions that are the most promising the most promising region is selected in each iteration based on information obtained from random sampling of the entire feasible region and local search the method hence combines global and local search we first develop the method for discrete problems and then show that the method can be extended to continuous global optimization the method is shown to converge with probability one to a global optimum in finite time in addition we provide bounds on the expected number of iterations required for convergence and we suggest two stopping criteria numerical examples are also presented to demonstrate the effectiveness of the method

modeling simulating and parameter fitting of biochemical kinetic experiments in many chemical and biological applications systems of differential equations containing unknown parameters are used to explain empirical observations and experimental data the differential equations are typically nonlinear and difficult to analyze requiring numerical methods to approximate the solutions compounding this difficulty are the unknown parameters in the differential equation system which must be given specific numerical values in order for simulations to be run estrogen receptor protein dimerization is used as an example to demonstrate model construction reduction simulation and parameter estimation mathematical computational and statistical methods are applied to empirical data to deduce kinetic parameter estimates and guide decisions regarding future experiments and modeling the process demonstrated serves as a pedagogical example of quantitative methods being used to extract parameter values from biochemical data models

when ignorance helps graphical multicast cost sharing games in non cooperative games played on highly decentralized networks the assumption that each player knows the strategy adopted by any other player may be too optimistic or even infeasible in such situations the set of players of which each player knows the chosen strategy can be modeled by means of a social knowledge graph in which nodes represent players and there is an edge from i to j if i knows j following the framework introduced in 7 we study the impact of social knowledge graphs on the fundamental multicast cost sharing game in which all the players want to receive the same communication from a given source in an undirected network in the classical complete information case such a game is known to be highly inefficient since its price of anarchy can be as high as the total number of players r we first show that under our incomplete information setting pure nash equilibria always exist only if the social knowledge graph is directed acyclic dag we then prove that the price of stability of any dag is at least 12log r and provide a dag lowering the classical price of anarchy to a value between 12log r and log 2 r if specific instances of the game are concerned that is if the social knowledge graph can be selected as a function of the instance we show that the price of stability is at least 4 r r 3 and that the same bound holds also for the price of anarchy of any social knowledge graph not only dags moreover we provide a nearly matching upper bound by proving that for any fixed instance there always exists a dag yielding a price of anarchy less than 4 our results open a new window on how the performances of non cooperative systems may benefit from the lack of total knowledge among players

convergence analysis and improvements of quantum behaved particle swarm optimization motivated by concepts in quantum mechanics and particle swarm optimization pso quantum behaved particle swarm optimization qpso was proposed as a variant of pso with better global search ability although it has been shown to perform well in finding optimal solutions for many optimization problems there has so far been little theoretical analysis on its convergence and performance this paper presents a convergence analysis and performance evaluation of the qpso algorithm and it also proposes two variants of the qpso algorithm first we investigate in detail the convergence of the qpso algorithm on a probabilistic metric space and prove that the qpso algorithm is a form of contraction mapping and can converge to the global optimum this is the first time that the theory of probabilistic metric spaces has been employed to analyze a stochastic optimization algorithm we provided a new definition for the convergence rate of a stochastic algorithm as well as definitions for three types of convergence according to the correlations between the convergence rate and the objective function values with these definitions the effectiveness of the qpso is evaluated by computing and analyzing the time complexity and the convergence rate of the algorithm then the qpso with random mean best position qpso rm and the qpso with ranking operator qpso ro are proposed as two improvements of the qpso algorithm finally some empirical studies on popular benchmark functions are performed in order to make a full performance evaluation and comparison between qpso qpso rm qpso ro and other variants of pso

markov chain analysis of evolutionary algorithms on onemax function from coupon collector s problem to 1 1 ea abstract the theoretical investigation of evolutionary algorithms eas has increased our understanding of the computational mechanism of algorithms onemax is a test function most frequently and deeply studied in the field of eas in this work a method is presented for describing the runtime properties of 1 1 ea on onemax this method is motivated by the work of erdos and renyi treating the coupon collector s problem they showed that the success probability of the coupon collector s problem is given by a function of double exponential form and that the number of uncollected coupons follows the poisson distribution today the double exponential function is called gumbel function which is one of three fundamental functions in extreme value statistics we introduce an algorithm that is a variant of the 1 1 ea first order evolutionary algorithm fo ea fo ea takes into account only the effect of single bit mutations in the 1 1 ea which in general includes multiple bit mutations we modified the method of erdos and renyi to apply fo ea we apply the gumbel distribution for calculating the success probability of the 1 1 ea on onemax this method turns out to give a sufficiently reliable estimation for success probabilities even in the tail region

stochastic runtime analysis of a cross entropy algorithm for traveling salesman problems abstract this article analyzes the stochastic runtime of a cross entropy algorithm mimicking an max min ant system with iteration best reinforcement it investigates the impact of magnitude of the sample size on the runtime to find optimal solutions for tsp instances for simple tsp instances that have a 1 n valued distance function and a unique optimal solution we show that sample size n ln n results in a stochastically polynomial runtime and n o ln n results in a stochastically exponential runtime where stochastically means with a probability of 1 n 1 and n represents number of cities in particular for n ln n we prove a stochastic runtime of o n n 6 with the vertex based random solution generation and a stochastic runtime of o n n 3 ln n with the edge based random solution generation these runtimes are very close to the best known expected runtime for variants of max min ant system with best so far reinforcement by choosing a small n ln n they are obtained for the stronger notion of stochastic runtime and analyze the runtime in most cases we also inspect more complex instances with n vertices positioned on an m m grid when the n vertices span a convex polygon we obtain a stochastic runtime of o n 4 m 5 with the vertex based random solution generation and a stochastic runtime of o n 3 m 5 for the edge based random solution generation when there are k o 1 many vertices inside a convex polygon spanned by the other n k vertices we obtain a stochastic runtime of o n 4 m 5 n 6 k 1 m with the vertex based random solution generation and a stochastic runtime of o n 3 m 5 n 3 k m with the edge based random solution generation these runtimes are better than the expected runtime for the so called ea reported in a recent article and again obtained for the stronger notion of stochastic runtime

multidimensional color image storage retrieval and compression based on quantum amplitudes and phases abstract in this study we propose a new representation method for multidimensional color images called an n qubit normal arbitrary superposition state nass where n qubits represent the colors and coordinates of 2 n pixels e g a three dimensional color image of 1024 1024 1024 using only 30 qubits based on nass we present an n 1 qubit normal arbitrary superposition state with relative phases nassrp and an n 2 qubit normal arbitrary superposition state with three components nasstc for lossless and lossy quantum compression respectively we also design three general quantum circuits to generate nass nassrp and nasstc states where we retrieve an image from a quantum system using different projection measurement operators finally we define the quantum compression ratio and analyze lossless and lossy quantum compression algorithms of multidimensional quantum images for the first time we implemented the compression of multidimensional color images on a quantum computer thus we address the theoretical and practical aspects of image processing on a quantum computer

theoretical analysis of evolutionary algorithms with an infinite population size in continuous space part ii analysis of the diversification role of crossover for pt i see ibid p 102 19 in this part of the paper the authors concentrate on the unique diversification role of the crossover operator in genetic algorithms the explorative behavior of a generic crossover operator is revealed through a detailed large sample analysis recursive equations for the population distributions are derived for a uniform crossover operator in multi dimensional continuous space showing how the crossover operator probes new regions of the solution space while keeping the population within the feasible region the results of this analysis can be extended to the setting of a discrete space in a straightforward manner shedding much light on the understanding of the essential role of crossover in genetic algorithms

approximating the revenue maximization problem with sharp demands we consider the revenue maximization problem with sharp multi demand in which m indivisible items have to be sold to n potential buyers each buyer i is interested in getting exactly d i items and each item j gives a benefit v ij to buyer i we distinguish between unrelated and related valuations in the former case the benefit v ij is completely arbitrary while in the latter each item j has a quality q j each buyer i has a value v i and the benefit v ij is defined as the product v i q j the problem asks to determine a price for each item and an allocation of bundles of items to buyers with the aim of maximizing the total revenue that is the sum of the prices of all the sold items the allocation must be envy free that is each buyer must be happy with her assigned bundle and cannot improve her utility we first prove that for related valuations the problem cannot be approximated to a factor o m 1 e for any e 0 unless p np and that such result is asymptotically tight in fact we provide a simple m approximation algorithm even for unrelated valuations we then focus on an interesting subclass of proper instances that do not contain buyers a priori known not being able to receive any item for such instances we design an interesting 2 approximation algorithm and show that no 2 e approximation is possible for any 0 e 1 unless p np we observe that it is possible to efficiently check if an instance is proper and if discarding useless buyers is allowed an instance can be made proper in polynomial time without worsening the value of its optimal solution

statistical dynamics of the royal road genetic algorithm abstract metastability is a common phenomenon many evolutionary processes both natural and artificial alternate between periods of stasis and brief periods of rapid change in their behavior in this paper an analytical model for the dynamics of a mutation only genetic algorithm ga is introduced that identifies a new and general mechanism causing metastability in evolutionary dynamics the ga s population dynamics is described in terms of flows in the space of fitness distributions the trajectories through fitness distribution space are derived in closed form in the limit of infinite populations we then show how finite populations induce metastability even in regions where fitness does not exhibit a local optimum in particular the model predicts the occurrence of fitness epochs periods of stasis in population fitness distributions at finite population size and identifies the locations of these fitness epochs with the flow s hyperbolic fixed points this enables exact predictions of the metastable fitness distributions during the fitness epochs as well as giving insight into the nature of the periods of stasis and the innovations between them all these results are obtained as closed form expressions in terms of the ga s parameters an analysis of the jacobian matrices in the neighborhood of an epoch s metastable fitness distribution allows for the calculation of its stable and unstable manifold dimensions and so reveals the state space s topological structure more general quantitative features of the dynamics fitness fluctuation amplitudes epoch stability and speed of the innovations are also determined from the jacobian eigenvalues the analysis shows how quantitative predictions for a range of dynamical behaviors that are specific to the finite population dynamics can be derived from the solution of the infinite population dynamics the theoretical predictions are shown to agree very well with statistics from ga simulations we also discuss the connections of our results with those from population genetics and molecular evolution theory

diffusion and reaction in random media and models of evolution processes a diffusion equation including source terms representing randomly distributed sources and sinks is considered for quasilinear growth rates the eigenvalue problem is equivalent to that of the quantum mechanical motion of electrons in random fields correspondingly there exist localized and extended density distributions dependent on the statistics of the random field and on the dimension of the space besides applications in physics nonequilibrium processes in pumped disordered solid materials a new evolution model is discussed which considers evolution as hill climbing in a random landscape

convergence guarantees for generalized adaptive stochastic search methods for continuous global optimization this paper presents some simple technical conditions that guarantee the convergence of a general class of adaptive stochastic global optimization algorithms by imposing some conditions on the probability distributions that generate the iterates these stochastic algorithms can be shown to converge to the global optimum in a probabilistic sense these results also apply to global optimization algorithms that combine local and global stochastic search strategies and also those algorithms that combine deterministic and stochastic search strategies this makes the results applicable to a wide range of global optimization algorithms that are useful in practice moreover this paper provides convergence conditions involving the conditional densities of the random vector iterates that are easy to verify in practice it also provides some convergence conditions in the special case when the iterates are generated by elliptical distributions such as the multivariate normal and cauchy distributions these results are then used to prove the convergence of some practical stochastic global optimization algorithms including an evolutionary programming algorithm in addition this paper introduces the notion of a stochastic algorithm being probabilistically dense in the domain of the function and shows that under simple assumptions this is equivalent to seeing any point in the domain with probability 1 this in turn is equivalent to almost sure convergence to the global minimum finally some simple results on convergence rates are also proved

combination can be hard approximability of the unique coverage problem we prove semilogarithmic inapproximability for a maximization problem called unique coverage given a collection of sets find a subcollection that maximizes the number of elements covered exactly once specifically assuming that mathrm np not subseteq operatorname bptime 2 n varepsilon for an arbitrary varepsilon 0 we prove o 1 log sigma n inapproximability for some constant sigma sigma varepsilon we also prove o 1 log 1 3 varepsilon n inapproximability for any varepsilon 0 assuming that refuting random instances of 3sat is hard on average and we prove o 1 log n inapproximability under a plausible hypothesis concerning the hardness of another problem balanced bipartite independent set we establish an omega 1 log n approximation algorithm even for a more general budgeted setting and obtain an omega 1 log b approximation algorithm when every set has at most b elements we also show that our inapproximability results extend to envy free pricing an important problem in computational economics we describe how the budgeted unique coverage problem motivated by real world applications has close connections to other theoretical problems including max cut maximum coverage and radio broadcasting

a decentralized quantum inspired particle swarm optimization algorithm with cellular structured population this paper proposes a decentralized form of quantum inspired particle swarm optimization qpso with cellular structured population called cqpso for keeping the population diversity and balancing the global and local search the cqpso is further improved by re designing the local attractor in the sub population called cqpso lbest in order to accelerate the diffusion of the best solution and thus enhance the performance of cqpso the particles in cqpso and cqpso lbest are distributed in a two dimensional 2d grid and only allowed to interact with their neighbors according to the specified neighborhood which plays a role in exploiting the search space inside the neighborhood the overlapping particles work for delivering the information among the nearest neighborhoods acting as exploring the search space with diffusion of solutions during the evolutionary process theoretical studies are made to analyze the global convergence of cpso and cqpso lbest based on the theory of probabilistic metric space we systematically investigate the performance of cqpso lbest on 42 benchmark functions with different properties including unimodal multimodal separated shifted rotated noisy and mis scaled and compare with a set of pso variants with different topologies and swarm based evolutionary algorithms eas the experimental results demonstrate the better performance of cqpso lbest moreover two real world problems which are two dimensional 2d iir digital filter design and economic dispatch ed problem from power systems area are used to evaluate cqpso lbest and the experimental results verified the advantages of cqpso lbest

ordering default theories and nonmonotonic logic programs first order theories are ordered under logical entailment based on the amount of information derived from theories in default logic on the other hand a theory contains default information as well as definite information to order default theories distinguishing different sorts of information is necessary to assess the information content of a default theory for this purpose we first introduce a multi valued interpretation of default theories using a ten valued bilattice it distinguishes between definite and credulous skeptical default information derived from a theory and is used for ordering default theories based on their information contents we then apply the technique to order nonmonotonic logic programs under the answer set semantics the results of this paper provide a method for comparing default theories or nonmonotonic logic programs in a manner different from the conventional extension model based viewpoint moreover they have important application to induction from nonmonotonic theories

choosing selection pressure for wide gap problems abstract to exploit an evolutionary algorithm s performance to the full extent the selection scheme should be chosen carefully empirically it is commonly acknowledged that low selection pressure can prevent an evolutionary algorithm from premature convergence and is thereby more suitable for wide gap problems however there are few theoretical time complexity studies that actually give the conditions under which a high or a low selection pressure is better in this paper we provide a rigorous time complexity analysis showing that low selection pressure is better for the wide gap problems with two optima

fixed point theorems for multivalued mappings in some classes of fuzzy metic spaces abstract using the probabilistic function of noncompactness a fixed point theorem for multivalued mappings in probabilistic metric spaces is proved as an application a fixed point theorem for multivalued mappings in fuzzy metric spaces is obtained

stochastic global optimization methods part 1 clustering methods in this stochastic approach to global optimization clustering techniques are applied to identify local minima of a real valued objective function that are potentially global three different methods of this type are described their accuracy and efficiency are analyzed in detail

on social envy freeness in multi unit markets abstract we consider a market setting in which buyers are individuals of a population whose relationships are represented by an underlying social graph given buyers valuations for the items being sold an outcome consists of a pricing of the objects and an allocation of bundles to the buyers an outcome is social envy free if no buyer strictly prefers the bundles of her neighbors in the social graph we focus on the revenue maximization problem in multi unit markets in which there are multiple copies of the same item being sold and each buyer is assigned a subset of identical items we consider four different cases that arise when considering two different buyers valuations i e single minded or general and by adopting two different forms of pricing that is item or bundle pricing for all the above cases we show the hardness of the revenue maximization problem and give corresponding approximation results all our approximation bounds are optimal or nearly optimal moreover under the assumption of social graphs of bounded treewidth we provide an optimal allocation algorithm for general valuations with item pricing finally we determine optimal bounds on the corresponding price of envy freeness that is on the worst case ratio between the maximum revenue that can be achieved without envy freeness constraints and the one obtainable in case of social relationships some of our results close hardness open questions or improve already known ones in the literature concerning the standard setting without sociality

drift analysis and average time complexity of evolutionary algorithms the computational time complexity is an important topic in the theory of evolutionary algorithms eas this paper reports some new results on the average time complexity of eas based on drift analysis some useful drift conditions for deriving the time complexity of eas are studied including conditions under which an ea will take no more than polynomial time in problem size to solve a problem and conditions under which an ea will take at least exponential time in problem size to solve a problem the paper first presents the general results and then uses several problems as examples to illustrate how these general results can be applied to concrete problems in analyzing the average time complexity of eas while previous work only considered 1 1 eas without any crossover the eas considered in this paper are fairly general which use a finite population crossover mutation and selection 2001 elsevier science b v all rights reserved

reprint of on convergence analysis of particle swarm optimization algorithm abstract particle swarm optimization pso a population based stochastic optimization algorithm has been successfully used to solve many complicated optimization problems however analysis on algorithm convergence is still inadequate till now in this paper the martingale theory is applied to analyze the convergence of the standard pso spso firstly the swarm state sequence is defined and its markov properties are examined according to the theory of spso two closed sets the optimal particle state set and optimal swarm state set are then obtained afterwards a supermartingale is derived as the evolutionary sequence of particle swarm with the best fitness value finally the spso convergence analysis is carried out in terms of the supermartingale convergence theorem our results show that spso reaches the global optimum in probability moreover the analysis on spso proves that the quantum behaved particle swarm optimization qpso is also a global convergence algorithm the proof of the spso convergence in this work is new simple and more effective without specific implementation

population size versus runtime of a simple evolutionary algorithm evolutionary algorithms eas find numerous applications and practical knowledge on eas is immense in practice sophisticated population based eas employing selection mutation and crossover are applied in contrast theoretical analysis of eas often concentrates on very simple algorithms such as the 1 1 ea where the population size equals 1 in this paper the question is addressed whether the use of a population by itself can be advantageous a population based ea that neither makes use of crossover nor any diversity maintaining operator is investigated on an example function it is shown that an increase of the population size by a constant factor decreases the expected runtime from exponential to polynomial thereby the best gap known so far is improved from superpolynomial vs polynomial to exponential vs polynomial moreover it is proved that the exponential and polynomial runtime bounds occur with a probability exponentially close to one if the population size is a constant resp a small polynomial finally a second example function where only a small population leads to a polynomial runtime and a hierarchy result on the appropriate population size are presented the analyses show formally how the population size can lead to different attractors in the search space

stochastic global optimization methods part 11 multi level methods in part ii of our paper two stochastic methods for global optimization are described that with probability 1 find all relevant local minima of the objective function with the smallest possible number of local searches the computational performance of these methods is examined both analytically and empirically

comments on theoretical analysis of evolutionary algorithms with an infinite population size in continuous space i basic properties of selection and mutation with reply this paper aims at establishing fundamental theoretical properties for a class of genetic algorithms in continuous space gacs the algorithms employ operators such as selection crossover and mutation in the framework of a multidimensional euclidean space the paper is divided into two parts the first part concentrates on the basic properties associated with the selection and mutation operators recursive formulae for the gacs in the general infinite population case are derived and their validity is rigorously proven a convergence analysis is presented for the classical case of a quadratic cost function it is shown how the increment of the population mean is driven by its own diversity and follows a modified newton s search sufficient conditions for monotonic increase of the population mean fitness are derived for a more general class of fitness functions satisfying a lipschitz condition the diversification role of the crossover operator is analyzed in part ii the treatment adds much light to the understanding of the underlying mechanism of evolution like algorithms

hesitant adaptive search for global optimisation pure adaptive search is a stochastic algorithm which has been analysed in distinct ways for finite and continuous global optimisation in this paper motivated by the behaviour of practical algorithms such as simulated annealing we extend these ideas we present a unified theory which yields both the finite and continuous results for pure adaptive search at the same time we allow our extended algorithm to hesitate before improvement continues results are obtained for the expected number of iterations to convergence for such an algorithm 1998 the mathematical programming society inc published by elsevier science b v

on the approximation ability of evolutionary optimization with application to minimum set cover evolutionary algorithms eas are heuristic algorithms inspired by natural evolution they are often used to obtain satisficing solutions in practice in this paper we investigate a largely underexplored issue the approximation performance of eas in terms of how close the solution obtained is to an optimal solution we study an ea framework named simple ea with isolated population seip that can be implemented as a single or multi objective ea we analyze the approximation performance of seip using the partial ratio which characterizes the approximation ratio that can be guaranteed specifically we analyze seip using a set cover problem that is np hard we find that in a simple configuration seip efficiently achieves an h n approximation ratio the asymptotic lower bound for the unbounded set cover problem we also find that seip efficiently achieves an h k k 18k 9 approximation ratio the currently best achievable result for the k set cover problem moreover for an instance class of the k set cover problem we disclose how seip using either one bit or bit wise mutation can overcome the difficulty that limits the greedy algorithm

pure adaptive search in monte carlo optimization pure adaptive search constructs a sequence of points uniformly distributed within a corresponding sequence of nested regions of the feasible space at any stage the next point in the sequence is chosen uniformly distributed over the region of feasible space containing all points that are equal or superior in value to the previous points in the sequence we show that for convex programs the number of iterations required to achieve a given accuracy of solution increases at most linearly in the dimension of the problem this compares to exponential growth in iterations required for pure random search

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

towards an analytic framework for analysing the computation time of evolutionary algorithms in spite of many applications of evolutionary algorithms in optimisation theoretical results on the computation time and time complexity of evolutionary algorithms on different optimisation problems are relatively few it is still unclear when an evolutionary algorithm is expected to solve an optimisation problem efficiently or otherwise this paper gives a general analytic framework for analysing first hitting times of evolutionary algorithms the framework is built on the absorbing markov chain model of evolutionary algorithms the first step towards a systematic comparative study among different eas and their first hitting times has been made in the paper

on convergence analysis of particle swarm optimization algorithm abstract particle swarm optimization pso a population based stochastic optimization algorithm has been successfully used to solve many complicated optimization problems however analysis on algorithm convergence is still inadequate till now in this paper the martingale theory is applied to analyze the convergence of the standard pso spso firstly the swarm state sequence is defined and its markov properties are examined according to the theory of spso two closed sets the optimal particle state set and optimal swarm state set are then obtained afterwards a supermartingale is derived as the evolutionary sequence of particle swarm with the best fitness value finally the spso convergence analysis is carried out in terms of the supermartingale convergence theorem our results show that spso reaches the global optimum in probability moreover the analysis on spso proves that the quantum behaved particle swarm optimization qpso is also a global convergence algorithm the proof of the spso convergence in this work is new simple and more effective without specific implementation

a large population size can be unhelpful in evolutionary algorithms the utilization of populations is one of the most important features of evolutionary algorithms eas there have been many studies analyzing the impact of different population sizes on the performance of eas however most of such studies are based on computational experiments except for a few cases the common wisdom so far appears to be that a large population would increase the population diversity and thus help an ea indeed increasing the population size has been a commonly used strategy in tuning an ea when it did not perform as well as expected for a given problem he and yao 2002 8 showed theoretically that for some problem instance classes a population can help to reduce the runtime of an ea from exponential to polynomial time this paper analyzes the role of population further in eas and shows rigorously that large populations may not always be useful conditions under which large populations can be harmful are discussed in this paper although the theoretical analysis was carried out on one multimodal problem using a specific type of eas it has much wider implications the analysis has revealed certain problem characteristics which can be either the problem considered here or other problems that lead to the disadvantages of large population sizes the analytical approach developed in this paper can also be applied to analyzing eas on other problems

convergence of a hill climbing genetic algorithm for graph matching abstract this paper presents a convergence analysis for the problem of consistent labelling using genetic search the work builds on a recent empirical study of graph matching where we showed that a bayesian consistency measure could be efficiently optimised using a hybrid genetic search procedure which incorporated a hill climbing step in the present study we return to the algorithm and provide some theoretical justification for its observed convergence behaviour the novelty of the analysis is to demonstrate analytically that the hill climbing step significantly accelerates convergence and that the convergence rate is polynomial in the size of the node set of the graphs being matched

efficient monte carlo procedures for generating points uniformly distributed over bounded regions we consider the monte carlo problem of generating points uniformly distributed within an arbitrary bounded measurable region the class of markovian methods considered generate points asymptotically uniformly distributed within the region computational experience suggests the methods are potentially superior to conventional rejection techniques for large dimensional regions

an equivalent genetic algorithm based on extended strings and its convergence analysis abstract a novel equivalent genetic algorithm based on extended strings esga is presented in this paper the esga is equivalent to the canonical genetic algorithms cgas in optimization problems whereas the manner of the group by group implementation makes it different from the conventional genetic algorithms in this paper the conditions and the rate of convergence of the esga are analyzed theoretically it is shown that the esga can converge to the global optimal solution and the average value of the times of reaching the optimal point is finite an analytical expression for the average rate of convergence of the esga is also provided

geometricity of genetic operators for real coded representation we investigate geometricity of operators for real coded genetic algorithms geometric operator is a representation independent generalization of the class of traditional mask based operators for binary strings it is defined as a function of the distance of the search space seen as a metric space although the real coded representation allows for a very familiar notion of distance namely the euclidean distance there are also other distances suiting it such as minkowski distances additionally topological transformations of the real space give rise to further notions of distance in this paper we study geometric crossover operators associated with minkowski spaces in a formal and general setting and show that some pre existing genetic operators for the real coded representation are geometric although geometric crossover operators defined in the plane are intuitive operators in higher dimensional spaces they are not trivial to understand and implement we derive formally algorithms to implement these geometric crossover operators in the generic n dimensional case we compare the performance of the presented operators with existing ones on test functions which are commonly used in the literature

the use of tail inequalities on the probable computational time of randomized search heuristics for the purpose of analyzing the time cost of evolutionary algorithms eas or other types of randomized search heuristics rshs with certain requirements on the probability of obtaining a target solution this paper proposes a new index called the probable computational time pct which complements expected running time analysis using simple tail inequalities such as markov s inequality and chebyshev s inequality we also provide basic properties of pct explicitly exhibiting the general relationships between the expected running time and the pct to present deeper estimations of the pct for specific rshs and problems we demonstrate a new inequality that is based on the general form of the chernoff inequality and previous methods such as fitness based partitions and potential functions which have been used to analyze the expected running time of rshs the precondition of the new inequality is that the total running time can be described as the sum of a linear combination of some independent geometrically distributed variables and a constant term the new inequality always provides meaningful upper bounds for the pct under such circumstances some applications of the new inequality for simple eas ant colony optimization aco and particle swarm optimization pso algorithms on simple pseudo boolean functions are illustrated in this paper

using modifications to grover s search algorithm for quantum global optimization we study the problem of finding a global optimal solution to discrete optimization problems using a heuristic based on quantum computing methods knowledge of quantum computing ideas is not necessary to read this paper we focus on a successful quantum computing method introduced by baritompa bulger and wood that we refer to as the bbw algorithm and develop two modifications first we modify the bbw algorithm to achieve a dramatic speedup that lets us extend the known bbw static schedule from 33 to 43 points thereby increasing its applicability we further modify it by converting it from a static method to a dynamic one experimental results show the value of this latter modification

general type 2 fuzzy logic systems made simple a tutorial the purpose of this tutorial paper is to make general type 2 fuzzy logic systems gt2 flss more accessible to fuzzy logic researchers and practitioners and to expedite their research designs and use to accomplish this the paper 1 explains four different mathematical representations for general type 2 fuzzy sets gt2 fss 2 demonstrates that for the optimal design of a gt2 fls one should use the vertical slice representation of its gt2 fss because it is the only one of the four mathematical representations that is parsimonious 3 shows how to obtain set theoretic and other operations for gt2 fss using type 1 t1 fs mathematics cuts play a central role 4 reviews mamdani and tsk interval type 2 it2 flss so that their mathematical operations can be easily used in a gt2 fls 5 provides all of the formulas that describe both mamdani and tsk gt2 flss 6 explains why center of sets type reduction should be favored for a gt2 fls over centroid type reduction 7 provides three simplified gt2 flss two are for mamdani gt2 flss and one is for a tsk gt2 fls all of which bypass type reduction and are generalizations from their it2 fls counterparts to gt2 flss 8 explains why gradient based optimization should not be used to optimally design a gt2 fls 9 explains how derivative free optimization algorithms can be used to optimally design a gt2 fls and 10 provides a three step approach for optimally designing flss in a progressive manner from t1 to it2 to gt2 each of which uses a quantum particle swarm optimization algorithm by virtue of which the performance for the it2 fls cannot be worse than that of the t1 fls and the performance for the gt2 fls cannot be worse than that of the it2 fls

autoepistemic logic autoepistemic logic is one of the principal modes of nonmonotonic reasoning it unifies several other modes of nonmonotonic reasoning and has important application in logic programming in the paper a theory of autoepistemic logic is developed this paper starts with a brief survey of some of the previously known results then the nature of nonmonotonicity is studied by investigating how membership of autoepistemic statements in autoepistemic theories depends on the underlying objective theory a notion similar to set theoretic forcing is introduced expansions of autoepistemic theories are also investigated expansions serve as sets of consequences of an autoepistemic theory and they can also be used to define semantics for logic programs with negation theories that have expansions are characterized and a normal form that allows the description of all expansions of a theory is introduced our results imply algorithms to determine whether a theory has a unique expansion sufficient conditions stratification that imply existence of a unique expansion are discussed the definition of stratified theories is extended and under some additional assumptions efficient algorithms for testing whether a theory is stratified are proposed the theorem characterizing expansions is applied to two classes of theories k1 theories and ae programs in each case simple hypergraph characterization of expansions of theories from each of these classes is given finally connections with stable model semantics for logic programs with negation is discussed in particular it is proven that the problem of existence of stable models is np complete authors abstract

optimizing linear functions with the 1 λ evolutionary algorithm different asymptotic runtimes for different instances abstract we analyze how the 1 evolutionary algorithm ea optimizes linear pseudo boolean functions we prove that it finds the optimum of any linear function within an expected number of o 1 n log n n iterations we also show that this bound is sharp for some linear functions e g the binary value function since previous works shows an asymptotically smaller runtime for the special case of onemax it follows that for the 1 ea different linear functions may have run times of different asymptotic order the proof of our upper bound heavily relies on a number of classic and recent drift analysis methods in particular we show how to analyze a process displaying different types of drifts in different phases our work corrects a wrongfully claimed better asymptotic runtime in an earlier work 13 we also use our methods to analyze the runtime of the 1 ea on the onemax test function and obtain a new upper bound of o n log log log for the case that is larger than o log n log log n log log log n this is the cut off point where a linear speed up ceases to exist while our results are mostly spurred from a theory driven interest they also show that choosing the right size of the offspring population can be crucial for both the binary value and the onemax test function we observe that once a linear speed up ceases to exist in fact the speed up from a larger reduces to sub logarithmic still at the price of a linear increase of the cost of each generation

adaptive search in quasi monte carlo optimization motivated by a linear time complexity result for an adaptive monte carlo algorithm we propose and analyze an adaptive deterministic algorithm we restrict a grid search to nested subregions that promise to provide improvement of the current solution and we obtain an exponential rate of convergence in function evaluations for proving the main result we restrict ourselves to functions on hypercubes in a final section we outline how to extend the method to the general case and give some numerical examples

inexact graph matching using genetic search this paper describes a framework for performing relational graph matching using genetic search there are three novel ingredients to the work firstly we cast the optimisation process into a bayesian framework by exploiting the recently reported global consistency measure of wilson and hancock as a fitness measure the second novel idea is to realise the crossover process at the level of subgraphs rather than employing string based or random crossover finally we accelerate convergence by employing a deterministic hill climbing process prior to selection since we adopt the bayesian consistency measure as a fitness function the basic measure of relational distance underpinning the technique is hamming distance our standpoint is that genetic search provides a more attractive means of performing stochastic discrete optimisation on the global consistency measure than alternatives such as simulated annealing moreover the action of the optimisation process is easily understood in terms of its action in the hamming distance domain we demonstrate empirically not only that the method possesses polynomial convergence time but also that the convergence rate is more rapid than simulated annealing we provide some experimental evaluation of the method in the matching of aerial stereograms and evaluate its sensitivity on synthetically generated graphs

free lunches on the discrete lipschitz class the no free lunch theorem states that there does not exist a genuine general purpose optimizer because all algorithms have the identical performance on average over all functions however such a result does not imply that search heuristics or optimization algorithms are futile if we are more cautious with the applicability of these methods and the search space in this paper within the no free lunch framework we firstly introduce the discrete lipschitz class by transferring the lipschitz functions i e functions with bounded slope as a measure to fulfill the notion of continuity in discrete functions we then investigate the properties of the discrete lipschitz class generalize an algorithm called subthreshold seeker for optimization and show that the generalized subthreshold seeker outperforms random search on this class finally we propose a tractable sampling test scheme to empirically demonstrate the superiority of the generalized subthreshold seeker under practical configurations this study concludes that there exist algorithms outperforming random search on the discrete lipschitz class in both theoretical and practical aspects and indicates that the effectiveness of search heuristics may not be universal but still general in some broad sense

on accelerated random search a new variant of pure random search prs for function optimization is introduced the basic finite descent accelerated random search ars algorithm is simple the search is confined to shrinking neighborhoods of a previous record generating value with the search neighborhood reinitialized to the entire space when a new record is found local maxima are avoided by including an automatic restart feature which reinitializes the search neighborhood after some number of shrink steps have been performed one goal of this article is to provide rigorous mathematical comparisons of ars to prs it is shown that the sequence produced by the ars process converges with probability one to the maximum of a continuous objective function faster than that of the prs process by adjustably large multiples of the time step theorem regarding an infinite descent no automatic restart version of ars it is shown that if the objective function satisfies a local nonflatness condition then the right tails of the distributions of inter record times are exponentially smaller than those of prs theorem performance comparisons between ars prs and three quasi newton type optimization routines are reported in attempting to find extrema of i each of a small collection of standard test functions of two variables and ii d dimensional polynomials with random roots also reported is a three way performance comparison between ars prs and a simulated annealing algorithm in attempting to solve traveling salesman problems

generalized decomposition and cross entropy methods for many objective optimization decomposition based algorithms for multi objective optimization problems have increased in popularity in the past decade although convergence to the pareto optimal front pf for such algorithms can often be superior to that of pareto based alternatives the problem of effectively distributing pareto optimal solutions in a high dimensional space has not been solved in this work we introduce a novel concept which we call generalized decomposition generalized decomposition provides a framework with which the decision maker dm can guide the underlying search algorithm toward specific regions of interest or the entire pareto front with the desired distribution of pareto optimal solutions the method simplifies many objective problems by unifying the three performance objectives of an a posteriori multi objective optimizer convergence to the pf evenly distributed pareto optimal solutions and coverage of the entire front to only one that of convergence a framework established on generalized decomposition and an estimation of distribution algorithm eda based on low order statistics namely the cross entropy method is created to illustrate the benefits of the proposed concept for many objective problems the algorithm mace gd is shown to be highly competitive with the existing best in class decomposition based algorithm moea d and a more elaborate eda method rm meda

technical note the asymptotic extreme value distribution of the sample minimum of a concave function under linear constraints we show that the minimum value of a sample of feasible points uniformly distributed over a linear constraint set is for concave functions asymptotically weibull distributed with shape parameter equal to the dimension of the feasible region

minimization by random search techniques we give two general convergence proofs for random search algorithms we review the literature and show how our results extend those available for specific variants of the conceptual algorithm studied here we then exploit the convergence results to examine convergence rates and to actually design implementable methods finally we report on some computational experience

generating random vectors uniformly distributed inside and on the surface of different regions abstract an acceptance rejection algorithm for generating random vectors uniformly distributed over inside or on the surface of a complex region inserted in a minimal multidimensional rectangle is considered for regions having simple forms simplex hypersphere hyperellipsoid several algorithms are presented as well

polynomial time algorithms for linear programming based only on primal scaling and projected gradients of a potential function this paper presents extensions and further analytical properties of algorithms for linear programming based only on primal scaling and projected gradients of a potential function the paper contains extensions and analysis of two polynomial time algorithms for linear programming we first present an extension of gonzaga s o nl iteration algorithm that computes dual variables and does not assume a known optimal objective function value this algorithm uses only affine scaling and is based on computing the projected gradient of the potential function q ln x t s sum limits j 1 n ln x j wherex is the vector of primal variables ands is the vector of dual slack variables and q n sqrt n the algorithm takes either a primal step or recomputes dual variables at each iteration we next present an alternate form of ye s o sqrt n l iteration algorithm that is an extension of the first algorithm of the paper but uses the potential function q ln x t s sum limits j 1 n ln x j sum limits j 1 n ln s j where q n sqrt n we use this alternate form of ye s algorithm to show that ye s algorithm is optimal with respect to the choice of the parameterq in the following sense suppose thatq n n t wheret 0 then the algorithm will solve the linear program in o n r l iterations wherer max t 1 t thus the value oft that minimizes the complexity bound ist 1 2 yielding ye s o sqrt n l iteration bound

a new approach to estimating the expected first hitting time of evolutionary algorithms evolutionary algorithms ea have been shown to be very effective in solving practical problems yet many important theoretical issues of them are not clear the expected first hitting time is one of the most important theoretical issues of evolutionary algorithms since it implies the average computational time complexity in this paper we establish a bridge between the expected first hitting time and another important theoretical issue i e convergence rate through this bridge we propose a new general approach to estimating the expected first hitting time using this approach we analyze eas with different configurations including three mutation operators with without population a recombination operator and a time variant mutation operator on a hard problem the results show that the proposed approach is helpful for analyzing a broad range of evolutionary algorithms moreover we give an explanation of what makes a problem hard to eas and based on the recognition we prove the hardness of a general problem

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

first hitting times under drift abstract for the last ten years almost every theoretical result concerning the expected run time of a randomized search heuristic used drift theory making it the arguably most important tool in this domain its success is due to its ease of use and its powerful result drift theory allows the user to derive bounds on the expected first hitting time of a random process by bounding expected local changes of the process the drift this is usually far easier than bounding the expected first hitting time directly due to the widespread use of drift theory it is of utmost importance to have the best drift theorems possible we improve the fundamental additive multiplicative and variable drift theorems by stating them in a form as general as possible and providing examples of why the restrictions we keep are still necessary our additive drift theorem for upper bounds only requires the process to be lower bounded that is we remove unnecessary restrictions like a finite discrete or bounded state space as corollaries the same is true for our upper bounds in the case of variable and multiplicative drift by bounding the step size of the process we derive new lower bounding multiplicative and variable drift theorems last we also state theorems that are applicable when the process has a drift of 0 by using a drift on the variance of the process

non existence of linear universal drift functions drift analysis is a powerful tool to prove upper and lower bounds on the runtime of randomized search heuristics its most famous application is a simple proof for the classical problem how the 1 1 evolutionary algorithm ea optimizes linear pseudo boolean functions a relatively simple potential function allows to track the progress of the ea optimizing any linear function in this work we show that such beautiful proofs cease to exist if the mutation probability is slightly larger than the standard value of 1 n

the time complexity of maximum matching by simulated annealing the random heuristic search algorithm called simulated annealing is considered for the problem of finding the maximum cardinality matching in a graph it is shown that neither a basic form of the algorithm nor any other algorithm in a fairly large related class of algorithms can find maximum cardinality matchings such that the average time required grows as a polynomial in the number of nodes of the graph in contrast it is also shown for arbitrary graphs that a degenerate form of the basic annealing algorithm obtained by letting temperature be a suitably chosen constant produces matchings with nearly maximum cardinality in polynomial average time

direction choice for accelerated convergence in hit and run sampling hit and run algorithms are monte carlo procedures for generating points that are asymptotically distributed according to general absolutely continuous target distributions g over open bounded regions s applications include nonredundant constraint identification global optimization and monte carlo integration these algorithms are reversible random walks that commonly incorporate uniformly distributed step directions we investigate nonuniform direction choice and show that under regularity conditions on the region s and target distribution g there exists a unique direction choice distribution characterized by necessary and sufficient conditions depending on s and g which optimizes the doob bound on rate of convergence we include computational results demonstrating greatly accelerated convergence for this optimizing direction choice as well as for more easily implemented adaptive heuristic rules

a quantum behaved particle swarm optimization with memetic algorithm and memory for continuous non linear large scale problems abstract quantum behaved particle swarm optimization qpso a novel variant of pso inspired by quantum mechanics is a global convergence guaranteed algorithm which outperforms the original pso in search ability and has fewer parameters to control but as many other psos it is easy to fall into local optimum in solving high dimensional complex optimization problems this paper proposes an improved qpso algorithm for continuous non linear large scale problems based on memetic algorithm and memory mechanism the memetic algorithm is used to make all particles each particle corresponding to a memetic gain some experience through a local search before being involved in the evolutionary process and the memory mechanism is used to introduce a so called bird kingdom with memory capacity both of which can improve the global search ability of the algorithm another difference compared to the previous qpsos is that we let each dimension of a particle update with the same random number thus increasing the speed of convergence and enhancing the ability of local search numerical experiments are conducted to compare the proposed algorithm with different variants of pso and other swarm intelligence algorithms the experimental results show the superiority of the proposed approach on benchmark test functions

search space boundary extension method in real coded genetic algorithms abstract in real coded genetic algorithms gas some crossover operators do not work well on functions which have their optimum at the corner of the search space to cope with this problem we have proposed a boundary extension method which allows individuals to be located within a limited space beyond the boundary of the search space in this paper we give an analysis of the boundary extension methods from the viewpoint of sampling bias and perform a comparative study on the effect of applying two boundary extension methods namely the boundary extension by mirroring bem and the boundary extension with extended selection bes we were able to confirm that to use sampling methods which have smaller sampling bias had good performance on both functions which have their optimum at or near the boundaries of the search space and functions which have their optimum at the center of the search space the bes sd a bes by shortest distance selection with aging had good performance on functions which have their optimum at or near the boundaries of the search space we also confirmed that applying the bes sd a did not cause any performance degradation on functions which have their optimum at the center of the search space

polynomial affine algorithms for linear programming the method of steepest descent with scaling affine scaling applied to the potential functionq logc x i 1n logxi solves the linear programming problem in polynomial time forq n ifq n then the algorithm terminates in no more than o n2l iterations if q n sqrt n withq o n then it takes no more than o nl iterations a modified algorithm using rank 1 updates for matrix inversions achieves respectively o n4l and o n3 5l arithmetic computions

estimation of the minimum of a function using order statistics abstract suppose a is a bounded set in d and f a real function defined on a suppose m min f x x a exists using a random sample x 1 x 2 x n from a uniform distribution over a we construct a confidence interval for m using asymptotic theory our results contain some statistical results valid in general extreme value theory estimation of the main parameter of extreme value distributions

a real coded genetic algorithm with a direction based crossover operator in this paper we develop a parallel structured real coded genetic algorithm rcga named the rga rdd for numerical optimization technically the proposed rga rdd integrates three specially designed evolutionary operators the ranking selection rs direction based crossover dbx and the dynamic random mutation drm as a whole to mimic a specific evolutionary process unlike the conventional rcgas that perform evolutionary operators in a series framework the rga rdd embeds a coordinator in the inner parallel loop to organize the operations of the dbx and drm so that a higher possibility of locating the global optimum is ensured besides based on the results of a systematic parametric analysis we provide a parameter selection guideline for the settings of the proposed rga rdd furthermore a data driven optimization scheme which incorporates the uniform design for design of experiments and a shape tunable neural network for auxiliary decision support is applied to search for an optimal set of the algorithm parameters the effectiveness and applicability of the proposed rga rdd are demonstrated through a variety of benchmarked optimization problems followed by comprehensive comparisons with some existing state of the art evolutionary algorithms extensive simulation results reveal that the performance of the proposed rga rdd is superior to comparative methods in locating the global optimum for real parameter optimization problems especially for unsolved multimodal and high dimensional hybrid functions

convergence analysis of canonical genetic algorithms this paper analyzes the convergence properties of the canonical genetic algorithm cga with mutation crossover and proportional reproduction applied to static optimization problems it is proved by means of homogeneous finite markov chain analysis that a cga will never converge to the global optimum regardless of the initialization crossover operator and objective function but variants of cga s that always maintain the best solution in the population either before or after selection are shown to converge to the global optimum due to the irreducibility property of the underlying original nonconvergent cga these results are discussed with respect to the schema theorem