Toward an extrapolation of the simulated annealing convergence theory onto the simple genetic algorithm144438
The Simple Genetic Algorithm: Foundations and Theory
The Simple Genetic Algorithm: Foundations and Theory
Evolutionary Computation
Logarithmic convergence of random heuristic search
Evolutionary Computation
A Normed Space of Genetic Operators with Applications to Scalability Issues
Evolutionary Computation
Finiteness of the fixed point set for the simple genetic algorithm
Evolutionary Computation
Modeling simple genetic algorithms
Evolutionary Computation
Logarithmic convergence of random heuristic search
Evolutionary Computation
The equation for response to selection and its use for prediction
Evolutionary Computation
General cardinality genetic algorithms
Evolutionary Computation
The simple genetic algorithm and the walsh transform: Part i, theory
Evolutionary Computation
The simple genetic algorithm and the walsh transform: Part ii, the inverse
Evolutionary Computation
Crossover accelerates evolution in gas with a babel-like fitness landscape: Mathematical analyses
Evolutionary Computation
Theory of the simple genetic algorithm with α-selection
Proceedings of the 10th annual conference on Genetic and evolutionary computation
A new method for modeling the behavior of finite population evolutionary algorithms
Evolutionary Computation
Finite Markov Chain Results in Evolutionary Computation: A Tour d'Horizon
Fundamenta Informaticae
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A general form of stochastic search is described (random heuristic search), and some of its general properties are proved. This provides a framework in which the simple genetic algorithm (SGA) is a special case. The framework is used to illuminate relationships between seemingly different probabilistic perspectives of SGA behavior. Next, the SGA is formalized as an instance of random heuristic search. The formalization then used to show expected population fitness is a Lyapunov function in the infinite population model when mutation is zero and fitness is linear. In particular, the infinite population algorithm must converge, and average population fitness increases from one generation to the next. The consequence for a finite population SGA is that the expected population fitness increases from one generation to the next. Moreover, the only stable fixed point of the expected next population operator corresponds to the population consisting entirely of the optimal string. This result is then extended by way of a perturbation argument to allow nonzero mutation.