An analysis of reproduction and crossover in a binary-coded genetic algorithm
Proceedings of the Second International Conference on Genetic Algorithms on Genetic algorithms and their application
Reducing bias and inefficiency in the selection algorithm
Proceedings of the Second International Conference on Genetic Algorithms on Genetic algorithms and their application
Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
Toward an extrapolation of the simulated annealing convergence theory onto the simple genetic algorithm144438
Genetic algorithms + data structures = evolution programs (2nd, extended ed.)
Genetic algorithms + data structures = evolution programs (2nd, extended ed.)
Parallel recombinative simulated annealing: a genetic algorithm
Parallel Computing
An introduction to genetic algorithms
An introduction to genetic algorithms
Linear analysis of genetic algorithms
Theoretical Computer Science
Finite Markov chain results in evolutionary computation: a tour d'horizon
Fundamenta Informaticae
Genetic algorithms: bridging the convergence gap
Theoretical Computer Science - Special issue on evolutionary computation
On the convergence rates of genetic algorithms
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
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Programming and Evolvable Machines
An Evolutionary Algorithm for Integer Programming
PPSN III Proceedings of the International Conference on Evolutionary Computation. The Third Conference on Parallel Problem Solving from Nature: Parallel Problem Solving from Nature
PPSN IV Proceedings of the 4th International Conference on Parallel Problem Solving from Nature
An Asymptotic Theory of Genetic Algorithms
AE '95 Selected Papers from the European conference on Artificial Evolution
Spline Interpolation with Genetic Algorithms
SMA '97 Proceedings of the 1997 International Conference on Shape Modeling and Applications (SMA '97)
Optimization with Genetic Algorithms in Multi-Species Environments
ICCIMA '03 Proceedings of the 5th International Conference on Computational Intelligence and Multimedia Applications
An Analysis of Two-Parent Recombinations for Real-Valued Chromosomes in an Infinite Population
Evolutionary Computation
Form Invariance and Implicit Parallelism
Evolutionary Computation
Theoretical Analysis of Mutation-Adaptive Evolutionary Algorithms
Evolutionary Computation
Convergence in Evolutionary Programs with Self-Adaptation
Evolutionary Computation
General cardinality genetic algorithms
Evolutionary Computation
Schema theory for genetic programming with one-point crossover and point mutation
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
Coevolutionary convergence to global optima
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartI
Theory of coevolutionary genetic algorithms
ISPA'03 Proceedings of the 2003 international conference on Parallel and distributed processing and applications
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
An Extension of Geiringer's Theorem for a Wide Class of Evolutionary Search Algorithms.
Evolutionary Computation
Convergence to global optima for genetic programming systems with dynamically scaled operators
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Analysis of a multiobjective evolutionary algorithm on the 0-1 knapsack problem
Theoretical Computer Science
Some results about the Markov chains associated to GPs and general EAs
Theoretical Computer Science - Foundations of genetic algorithms
Evolutionary Computation
Genetic Programming and Evolvable Machines
A new method for modeling the behavior of finite population evolutionary algorithms
Evolutionary Computation
Structure of Multi-Stage Composite Genetic Algorithm (MSC-GA) and its performance
Expert Systems with Applications: An International Journal
Optimizing the performance of GNU-chess with a genetic algorithm
Proceedings of the 13th International Conference on Humans and Computers
SEAL'06 Proceedings of the 6th international conference on Simulated Evolution And Learning
Evolutionary singularity filter bank optimization for fingerprint image enhancement
EuroGP'06 Proceedings of the 2006 international conference on Applications of Evolutionary Computing
FOGA'05 Proceedings of the 8th international conference on Foundations of Genetic Algorithms
Entropy search for information-efficient global optimization
The Journal of Machine Learning Research
Proceedings of the twelfth workshop on Foundations of genetic algorithms XII
An extension of geiringer's theorem for a wide class of evolutionary search algorithms
Evolutionary Computation
Hi-index | 5.24 |
We present a theoretical framework for an asymptotically converging, scaled genetic algorithm which uses an arbitrary-size alphabet and common scaled genetic operators. The alphabet can be interpreted as a set of equidistant real numbers and multiple-spot mutation performs a scalable compromise between pure random search and neighborhood-based change on the alphabet level. We discuss several versions of the crossover operator and their interplay with mutation. In particular, we consider uniform crossover and gene-lottery crossover which does not commute with mutation. The Vose-Liepins version of mutation-crossover is also integrated in our approach. In order to achieve convergence to global optima, the mutation rate and the crossover rate have to be annealed to zero in proper fashion, and unbounded, power-law scaled proportional fitness selection is used with logarithmic growth in the exponent. Our analysis shows that using certain types of crossover operators and large population size allows for particularly slow annealing schedules for the crossover rate. In our discussion, we focus on the following three major aspects based upon contraction properties of the mutation and fitness selection operators: (i) the drive towards uniform populations in a genetic algorithm using standard operations, (ii) weak ergodicity of the inhomogeneous Markov chain describing the probabilistic model for the scaled algorithm, (iii) convergence to globally optimal solutions. In particular, we remove two restrictions imposed in Theorem 8.6 and Remark 8.7 of (Theoret. Comput. Sci. 259 (2001) 1) where a similar type of algorithm is considered as described here: mutation need not commute with crossover and the fitness function (which may come from a coevolutionary single species setting) need not have a single maximum.