What Makes a Problem Hard for a Genetic Algorithm? Some Anomalous Results and Their Explanation
Machine Learning - Special issue on genetic algorithms
The Simple Genetic Algorithm: Foundations and Theory
The Simple Genetic Algorithm: Foundations and Theory
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
A Fixed Point Analysis Of A Gene Pool GA With Mutation
GECCO '02 Proceedings of the Genetic and Evolutionary Computation Conference
Real royal road functions: where crossover provably is essential
Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
State Aggregation and Population Dynamics in Linear Systems
Artificial Life
The equation for response to selection and its use for prediction
Evolutionary Computation
Schemata evolution and building blocks
Evolutionary Computation
Coarse graining selection and mutation
FOGA'05 Proceedings of the 8th international conference on Foundations of Genetic Algorithms
Fitness-proportional negative slope coefficient as a hardness measure for genetic algorithms
Proceedings of the 9th annual conference on Genetic and evolutionary computation
On the movement of vertex fixed points in the simple GA
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
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We show that there are unimodal fitness functions and genetic algorithm (GA) parameter settings where the GA, when initialized with a random population, will not move close to the fitness peak in a practically useful time period. When the GA is initialized with a population close to the fitness peak, the GA will be able to stay close to the fitness peak. Roughly speaking, the parameter settings involve strong recombination, weak selection, and require mutation. This "bistability" phenomenon has been previously investigated with needle-in-the-haystack fitness functions, but this fitness, when used with a GA with random initialization, requires a population size exponential in the string length for the GA to have nontrivial behavior. We introduce sloping-plateau fitness functions which show the bistability phenomenon and should scale to arbitrary string lengths. We introduce and use an unitation infinite population model to investigate the bistability phenomenon. For the fitnesses and GAs considered in the paper, we show that the use of crossover moves the GA to its fixed point faster in comparison to the same GA without crossover.