Finite Markov chain analysis of genetic algorithms
Proceedings of the Second International Conference on Genetic Algorithms on Genetic algorithms and their application
Simulating quadratic dynamical systems is PSPACE-complete (preliminary version)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A computational view of population genetics
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Linear analysis of genetic algorithms
Theoretical Computer Science
Theory of evolutionary algorithms: a bird's eye view
Theoretical Computer Science - Special issue on evolutionary computation
Statistical dynamics of the Royal Road genetic algorithm
Theoretical Computer Science - Special issue on evolutionary computation
Theoretical Computer Science - Special issue on evolutionary computation
Theoretical Computer Science
The Simple Genetic Algorithm: Foundations and Theory
The Simple Genetic Algorithm: Foundations and Theory
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
How to analyse evolutionary algorithms
Theoretical Computer Science - Natural computing
Global Convergence of Genetic Algorithms: A Markov Chain Analysis
PPSN I Proceedings of the 1st Workshop on Parallel Problem Solving from Nature
Theoretical Aspects of Evolutionary Algorithms
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
On the Expected Runtime and the Success Probability of Evolutionary Algorithms
WG '00 Proceedings of the 26th International Workshop on Graph-Theoretic Concepts in Computer Science
Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory
Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory
Introduction to Evolutionary Computing
Introduction to Evolutionary Computing
Genetic Programming and Evolvable Machines
An Extension of Geiringer's Theorem for a Wide Class of Evolutionary Search Algorithms.
Evolutionary Computation
Evolutionary Computation
Some results about the Markov chains associated to GPs and general EAs
Theoretical Computer Science - Foundations of genetic algorithms
A markov chain framework for the simple genetic algorithm
Evolutionary Computation
Simple genetic algorithms with linear fitness
Evolutionary Computation
Modeling simple genetic algorithms
Evolutionary Computation
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As practitioners we are interested in the likelihood of the population containing a copy of the optimum. The dynamic systems approach, however, does not help us to calculate that quantity. Markov chain analysis can be used in principle to calculate the quantity. However, since the associated transition matrices are enormous even for modest problems, it follows that in practice these calculations are usually computationally infeasible. Therefore, some improvements on this situation are desirable. In this paper, we present a method for modeling the behavior of finite population evolutionary algorithms (EAs), and show that if the population size is greater than 1 and much less than the cardinality of the search space, the resulting exact model requires considerably less memory space for theoretically running the stochastic search process of the original EA than the Nix and Vose-style Markov chain model. We also present some approximate models that use still less memory space than the exact model. Furthermore, based on our models, we examine the selection pressure by fitness-proportionate selection, and observe that on average over all population trajectories, there is no such strong bias toward selecting the higher fitness individuals as the fitness landscape suggests.