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Finite Markov Chain Results in Evolutionary Computation: A Tour d'Horizon
, 1998
"... . 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 ..."
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Cited by 69 (2 self)
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. 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...
From an individual to a population: An analysis of the first hitting time of populationbased evolutionary algorithms
 IEEE Transactions on Evolutionary Computation
, 2002
"... Almost all analyses of time complexity of evolutionary algorithms (EAs) have been conducted for (1+1) EAs only. Theoretical results on the average computation time of populationbased EAs are few. However, the vast majority of applications of EAs use a population size that is greater than one. The u ..."
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Cited by 56 (17 self)
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Almost all analyses of time complexity of evolutionary algorithms (EAs) have been conducted for (1+1) EAs only. Theoretical results on the average computation time of populationbased EAs are few. However, the vast majority of applications of EAs use a population size that is greater than one. The use of population has been regarded as one of the key features of EAs. It is important to understand in depth what the real utility of population is in terms of the time complexity of EAs, when EAs are applied to combinatorial optimization problems. This paper compares (1 + 1) EAs and (N + N) EAs theoretically by deriving their first hitting time on the same problems. It is shown that a population can have a drastic impact on an EA’s average computation time, changing an exponential time to a polynomial time (in the input size) in some cases. It is also shown that the first hitting probability can be improved by introducing a population. However, the results presented in this paper do not imply that populationbased EAs will always be better than (1 + 1) EAs for all possible problems. I.
Towards an analytic framework for analysing the computation time of evolutionary algorithms
 Artificial Intelligence
, 2003
"... 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 optim ..."
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Cited by 54 (18 self)
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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.
A new approach to estimating the expected first hitting time of . . .
, 2008
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Analysis of Computational Time of Simple Estimation of Distribution Algorithms
, 2010
"... Estimation of distribution algorithms (EDAs) are widely used in stochastic optimization. Impressive experimental results have been reported in the literature. However, little work has been done on analyzing the computation time of EDAs in relation to the problem size. It is still unclear how well ED ..."
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Cited by 11 (5 self)
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Estimation of distribution algorithms (EDAs) are widely used in stochastic optimization. Impressive experimental results have been reported in the literature. However, little work has been done on analyzing the computation time of EDAs in relation to the problem size. It is still unclear how well EDAs (with a finite population size larger than two) will scale up when the dimension of the optimization problem (problem size) goes up. This paper studies the computational time complexity of a simple EDA, i.e., the univariate marginal distribution algorithm (UMDA), in order to gain more insight into EDAs complexity. First, we discuss how to measure the computational time complexity of EDAs. A classification of problem hardness based on our discussions is then given. Second, we prove a theorem related to problem hardness and the probability conditions of
Conditions for the convergence of evolutionary algorithms
 Journal of Systems Architecture
, 2001
"... This paper presents a theoretical analysis of the convergence conditions for evolutionary algorithms. The necessary and sufficient conditions, necessary conditions, and sufficient conditions for the convergence of evolutionary algorithms to the global optima are derived, which describe their limitin ..."
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Cited by 11 (2 self)
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This paper presents a theoretical analysis of the convergence conditions for evolutionary algorithms. The necessary and sufficient conditions, necessary conditions, and sufficient conditions for the convergence of evolutionary algorithms to the global optima are derived, which describe their limiting behaviors. Their relationships are explored. Upper and lower bounds of the convergence rates of the evolutionary algorithms are given. I.
Pure strategy or mixed strategy
 Evolutionary Computation in Combinatorial Optimization (LNCS 7245
, 2012
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A Robust Algorithm for Solving Nonlinear Programming Problems
"... In this paper, we introduce a new algorithm for solving nonlinear programming (NLP) problems. It is an extension of Guo’s algorithm[1] which possesses enhanced capabilities for solving NLP problems. These capabilities include: a) advancing the variable subspace, b) adding a search process over subsp ..."
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Cited by 1 (1 self)
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In this paper, we introduce a new algorithm for solving nonlinear programming (NLP) problems. It is an extension of Guo’s algorithm[1] which possesses enhanced capabilities for solving NLP problems. These capabilities include: a) advancing the variable subspace, b) adding a search process over subspaces and normalized constraints, c) using an adaptive penalty function, and d) adding the ability to deal with integer NLP problems, 01 NLP problems, and mixedinteger NLP problems which have equality constraints. These four enhancements increase the capabilities of the algorithm to solve nonlinear programming problems in a more robust and universal way. This paper will present results of numerical experiments which show that the new algorithm is not only more robust and universal than its competitors, but also its performance level is higher than any others in the literature. 1 INTRODUCTION TO GUO’S ALGORITHM
Research Article On the Convergence of BiogeographyBased Optimization for Binary Problems
"... which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Biogeographybased optimization (BBO) is an evolutionary algorithm inspired by biogeography, which is the study of themigration of species between habitats. A finite Markov cha ..."
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which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Biogeographybased optimization (BBO) is an evolutionary algorithm inspired by biogeography, which is the study of themigration of species between habitats. A finite Markov chain model of BBO for binary problems was derived in earlier work, and some significant theoretical results were obtained. This paper analyzes the convergence properties of BBO on binary problems based on the previously derived BBOMarkov chain model. Analysis reveals that BBO with only migration and mutation never converges to the global optimum. However, BBO with elitism, which maintains the best candidate in the population from one generation to the next, converges to the global optimum. In spite of previously published differences between genetic algorithms (GAs) and BBO, this paper shows that the convergence properties of BBO are similar to those of the canonical GA. In addition, the convergence rate estimate of BBO with elitism is obtained in this paper and is confirmed by simulations for some simple representative problems. 1.
unknown title
"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: