Evolutionary computation has started to receive significant attention during the last decade, although the origins can be traced back to the late 1950s. This article surveys the history as well as the current state of this rapidly growing field. We describe the purpose, the general structure and the working principles of different approaches, including genetic algorithms (GA) (with links to genetic programming (GP) and classifier systems (CS)), evolution strategies (ES), and evolutionary programming (EP), by analysis and comparison of their most important constituents (i.e., representations, variation operators, reproduction and selection mechanism). Finally, we give a brief overview on the manifold of application domains, although this necessarily must remain incomplete.

. The theory of evolutionary computation has been enhanced rapidly during the last decade. This survey is the attempt to summarize the results regarding the limit and finite time behavior of evolutionary algorithms with finite search spaces and discrete time scale. Results on evolutionary algorithms beyond finite space and discrete time are also presented but with reduced elaboration. Keywords: evolutionary algorithms, limit behavior, finite time behavior 1. Introduction The field of evolutionary computation is mainly engaged in the development of optimization algorithms which design is inspired by principles of natural evolution. In most cases, the optimization task is of the following type: Find an element x 2 X such that f(x ) f(x) for all x 2 X , where f : X ! IR is the objective function to be maximized and X the search set. In the terminology of evolutionary computation, an individual is represented by an element of the Cartesian product X \Theta A, where A is a possibly...

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.

The task of finding minimal elements of a partially ordered set is a generalization of the task of finding the global minimum of a real-valued function or of finding pareto--optimal points of a multicriteria optimization problem. It is shown that evolutionary algorithms are able to converge to the set of minimal elements in finite time with probability one, provided that the search space is finite, the time-invariant variation operator is associated with a positive transition probability function and that the selection operator obeys the so--called `elite preservation strategy.'

This paper provides conditions under which evolutionary algorithms with an elitist selection rule will converge to the global optimum of some function whose domain may be an arbitrary space. These results generalize the previously developed convergence theory for binary and Euclidean search spaces to general search spaces. I. Introduction The term evolutionary algorithm (EA) is a collective name for those probabilistic optimization algorithms whose design is inspired by principles of biological evolution. Although particular EAs may differ considerably at a first glance, there are more similarities than differences. In fact, a general convergence theory is possible. We shall suppose that some EA is used to minimize a real--valued objective function f : M! IR that is bounded from below, that is, f(x) ? \Gamma1 for all x 2 M. No further assumptions are imposed on the search space M. It will be shown that a specific class of evolutionary algorithms will converge to the global optimum of...

This paper shows a theoretical property on the Markov chain of genetic algorithms: the stationary distribution focuses on the uniform population with the optimal solution as mutation and crossover probabilities go to zero and some selective pressure defined in this paper goes to infinity. Moreover, as a result, a sufficient condition for ergodicity is derived when a simulated annealing-like strategy is considered. Additionally, the uniform crossover counterpart of the Vose-Liepins formula is derived using the Markov chain model. Keywords--- genetic algorithms, simulated annealing, Markov chain. I. INTRODUCTION Genetic algorithms (GAs) are stochastic search techniques widely applied to combinatorial optimization problems [11], [14], [29], [30], [31], [32], [33]. GAs move from population to population. Each population consists of chromosomes (individuals) which represent candidate solutions to the optimization problem. A new population is formed by transforming individuals of the curre...

Bounds on the convergent rate is an important problem in the foundations of genetic algorithm. This paper obtained some bounds on the convergent rate of genetic algorithms by Markov chain theory. The main result is that the algorithms convergence in geometric rate under the meaning of probability measure. I.

In the past decades, many theoretical results related to the time complexity of evolutionary algorithms (EAs) on different problems are obtained. However, there is not any general and easy-to-apply approach designed particularly for populationbased EAs on unimodal problems. In this paper, we first generalize the concept of the takeover time to EAs with mutation, then we utilize the generalized takeover time to obtain the mean first hitting time of EAs and, thus, propose a general approach for analyzing EAs on unimodal problems. As examples, we consider the so-called (N + N) EAs and we show that, on two well-known unimodal problems, LEADINGONES and ONEMAX, the EAs with the bitwise mutation and two commonly used selection schemes both need O(n ln n + n2 /N) and O(n ln ln n + n ln n/N) generations to find the global optimum, respectively. Except for the new results above, our approach can also be applied directly for obtaining results for some population-based EAs on some other unimodal problems. Moreover, we also discuss when the general approach is valid to provide us tight bounds of the mean first hitting times and when our approach should be combined with problem-specific knowledge to get the tight bounds. It is the first time a general idea for analyzing population-based EAs on unimodal problems is discussed theoretically.

Abstract. We analyze the fitness dynamics of a (1+1) mutation-only genetic algorithm (GA) operating on a family of simple time-dependent fitness functions. Resulting models of behavior are used in the prediction of GA performance on this fitness function. The accuracy of performance predictions are compared to actual GA runs, and results are discussed in relation to analyses of the stationary version of the dynamic fitness landscape and to prior work performed in the field of evolutionary optimization of dynamic fitness functions. 1.

Introduction Performance analysis of genetic computing using unbounded or exponential population sizes or population updates across generations [27,21,25,28,29,22,8] may not be directly applicable to real practical problems where we always have to deal with a bounded (small) population size [9,23,26]. 1 Preliminary version published in: Proc. 7th Int'nl Workshop on Algorithmic Learning Theory, Lecture Notes in Artificial Intelligence, Vol. 1160, Springer-Verlag, Heidelberg, 1996, 67-82. 2 Partially supported by the European Union through NeuroCOLT ESPRIT Working Group Nr. 8556, and by NWO through NFI Project ALADDIN under Contract number NF 62-376. Author's affilliations are CWI and the University of Amsterdam. Preprint submitted to Elsevier Preprint Considering small population sizes it is at once obvious that the size and constitution of the population or population updates may have a major impact on the evolu