Analysis of Computational Time of Simple Estimation of Distribution Algorithms

Estimation of distribution algorithms (EDAs) are widely used in stochastic optimization. Impressive experimental results have been reported in the literature. However, little work has been done on analyzing the computation time of EDAs in relation to the problem size. It is still unclear how well ED...

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Veröffentlicht in:IEEE transactions on evolutionary computation Jg. 14; H. 1; S. 1 - 22
Hauptverfasser: Chen, Tianshi, Tang, Ke, Chen, Guoliang, Yao, Xin
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.02.2010
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithm design and analysis
Algorithmics. Computability. Computer arithmetics
Algorithms
Application software
Applied sciences
Artificial intelligence
Complexity
Computation
Computational time complexity
Computer applications
Computer science
Computer science; control theory; systems
Distributed computing
Dynamical systems
Dynamics
Electronic design automation and methodology
estimation of distribution algorithms
Evolutionary computation
Exact sciences and technology
first hitting time
Hardness
Heuristic
heuristic optimization
Laboratories
Learning and adaptive systems
Mathematical analysis
Optimization
Stochastic processes
Studies
Theoretical computing
Time measurement
univariate marginal distribution algorithms
Probabilistic approach
first hitting time
Evolutionary algorithm
Chernoff bound
Boolean function
Finite population
Dynamical system
Computational complexity
Optimization
Stochastic programming
Dimensioning
Computational time complexity
estimation of distribution algorithms
Classification
Marginal distribution
Heuristic method
Population size
univariate marginal distribution algorithms
Time analysis
Time complexity
heuristic optimization
Mathematical programming
ISSN:1089-778X, 1941-0026
Online-Zugang:Volltext
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Zusammenfassung:Estimation of distribution algorithms (EDAs) are widely used in stochastic optimization. Impressive experimental results have been reported in the literature. However, little work has been done on analyzing the computation time of EDAs in relation to the problem size. It is still unclear how well EDAs (with a finite population size larger than two) will scale up when the dimension of the optimization problem (problem size) goes up. This paper studies the computational time complexity of a simple EDA, i.e., the univariate marginal distribution algorithm (UMDA), in order to gain more insight into EDAs complexity. First, we discuss how to measure the computational time complexity of EDAs. A classification of problem hardness based on our discussions is then given. Second, we prove a theorem related to problem hardness and the probability conditions of EDAs. Third, we propose a novel approach to analyzing the computational time complexity of UMDA using discrete dynamic systems and Chernoff bounds. Following this approach, we are able to derive a number of results on the first hitting time of UMDA on a well-known unimodal pseudo-boolean function, i.e., the LeadingOnes problem, and another problem derived from LeadingOnes, named BVLeadingOnes. Although both problems are unimodal, our analysis shows that LeadingOnes is easy for the UMDA, while BVLeadingOnes is hard for the UMDA. Finally, in order to address the key issue of what problem characteristics make a problem hard for UMDA, we discuss in depth the idea of ¿margins¿ (or relaxation). We prove theoretically that the UMDA with margins can solve the BVLeadingOnes problem efficiently.
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ISSN:1089-778X
1941-0026
DOI:10.1109/TEVC.2009.2040019