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Analyzing probabilistic models in hierarchical boa on traps and spin glasses.pdf

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Analyzing probabilistic models in hierarchical boa on traps and spin glasses

Analyzing Probabilistic Models in Hierarchical BOA on Traps and Spin Glasses Mark Hauschild, Martin Pelikan, Claudio F. Lima, and Kumara Sastry IlliGAL Report No. 2007008 January 2007 Illinois Genetic Algorithms Laboratory University of Illinois at Urbana-Champaign 117 Transportation Building 104 S. Mathews Avenue Urbana, IL 61801 Office: (217) 333-2346 Fax: (217) 244-5705 Analyzing Probabilistic Models in Hierarchical BOA on Traps and Spin Glasses Mark Hauschild Missouri Estimation of Distribution Algorithms Laboratory (MEDAL) Dept. of Math and Computer Science, 320 CCB University of Missouri at St. Louis One University Blvd., St. Louis, MO 63121 mwh308@ Martin Pelikan Missouri Estimation of Distribution Algorithms Laboratory (MEDAL) Dept. of Math and Computer Science, 320 CCB University of Missouri at St. Louis One University Blvd., St. Louis, MO 63121 pelikan@ Claudio F. Lima Informatics Laboratory (UALG-ILAB) Department of Electronics and Computer Science Engineering University of Algarve Campus de Gambelas, 8000-117 Faro, Portugal clima@ualg.pt Kumara Sastry Illinois Genetic Algorithms Laboratory (IlliGAL) Department of Industrial and Enterprise Systems Engineering University of Illinois at Urbana-Champaign, Urbana IL 61801 ksastry@ January 2007 Abstract The hierarchical Bayesian optimization algorithm (hBOA) can solve nearly decomposable and hierarchical problems of bounded difficulty in a robust and scalable manner by building and sampling probabilistic models of promising solutions. This paper analyzes probabilistic models in hBOA on two common test problems: concatenated traps and 2D Ising spin glasses with periodic boundary conditions. We argue that although Bayesian networks with local structures can encode complex probability distributions, analyzing these models in hBOA is relatively straightforward and the results of such analyses may provide practitioners with useful infor- mation about their problems. The results show that the probabilistic models in