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Evolutionary learning and hierarchical Markov systems
H M Hastings1, S Waner, Y R Wu
1Department of Mathematics, Hofstra University, Hempstead, NY 11550.
Bio Systems
|January 1, 1989
Summary
Evolutionary learning systems and classical evolutionary processes are formally described as hierarchical Markov processes. This framework simplifies analyzing convergence and limiting behaviors in these complex systems.
Area of Science:
- Computational Science
- Theoretical Computer Science
- Evolutionary Computation
Background:
- Evolutionary learning systems and classical evolutionary processes are complex computational models.
- Understanding their convergence and limiting behaviors is crucial but challenging.
- Existing formalisms may not fully capture the hierarchical nature of these systems.
Purpose of the Study:
- To formally describe evolutionary learning systems and classical evolutionary processes.
- To introduce a novel framework for analyzing their properties.
- To simplify the study of convergence criteria and limiting behaviors.
Main Methods:
- Formal modeling of evolutionary systems as hierarchical Markov processes.
- Utilizing graph theory concepts, specifically rules and meta-rules for movement.
- Applying mathematical analysis to hierarchical Markovian structures.
Main Results:
- Demonstrated that evolutionary systems can be represented as hierarchical Markov processes.
- Showcased how this representation simplifies convergence analysis.
- Provided a unified framework for understanding limiting behaviors.
Conclusions:
- The hierarchical Markov process model offers a powerful simplification for evolutionary systems.
- This approach facilitates deeper theoretical insights into evolutionary computation and learning.
- The framework derived from graph-based rules and meta-rules is effective.