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On the taxonomy of optimization problems under estimation of distribution algorithms
Carlos Echegoyen1, Alexander Mendiburu, Roberto Santana
1Intelligent Systems Group, Department of Computer Science and Artificial Intelligence, The University of the Basque Country (UPV/EHU). Paseo Manuel de Lardizábal 1. 20018 San Sebastian, Spain. carlos.echegoyen@ehu.es
Evolutionary Computation
|November 10, 2012
Summary
This study introduces a problem taxonomy for estimation of distribution algorithms (EDAs) by defining an equivalence relation. It reveals how the probabilistic model dictates algorithm behavior and problem partitioning in optimization.
Area of Science:
- Optimization
- Computer Science
- Artificial Intelligence
Background:
- Understanding search algorithm behavior is crucial in optimization.
- Estimation of Distribution Algorithms (EDAs) are a key area of study.
- Problem taxonomies are needed to classify optimization challenges.
Purpose of the Study:
- To establish foundations for problem taxonomies under EDAs.
- To group optimization problems based on EDA behavior.
- To define an equivalence relation for partitioning the problem space.
Main Methods:
- Utilizing an infinite population model with rank-based selection.
- Defining an equivalence relation between objective functions.
- Analyzing the probabilistic model's role in problem partitioning.
Main Results:
- The probabilistic model determines the number of distinct algorithm behaviors.
- Functions are grouped into equivalence classes based on EDA behavior.
- Univariate EDAs show a direct relationship with Hamming distance neighborhood systems.
Conclusions:
- The proposed taxonomy classifies problems for EDAs.
- The probabilistic model is central to understanding EDA performance.
- All functions belong to the same equivalence class without probabilistic model restrictions.
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