On the Scalability of Real-Coded Bayesian Optimization Algorithm

@article{citeulike:2998497, abstract = {Estimation of distribution algorithms (EDAs) are major tools in evolutionary optimization. They have the ability to uncover the hidden regularities of problems and then exploit them for effective search. Real-coded Bayesian optimization algorithm (rBOA) which brings the power of discrete BOA to bear upon the continuous domain has been regarded as a milestone in the field of numerical optimization. It has been empirically observed that the rBOA solves, with subquadratic scaleup behavior, numerical optimization problems of bounded difficulty. This underlines the scalability of rBOA (at least) in practice. However, there is no firm theoretical basis for this scalability. The aim of this paper is to carry out a theoretical analysis of the scalability of rBOA in the context of additively decomposable problems with real-valued variables. The scalability is measured by the growth of the number of fitness function evaluations (in order to reach the optimum) with the size of the problem. The total number of evaluations is computed by multiplying the population size for learning a correct probabilistic model (i.e., population complexity) and the number of generations before convergence, (i.e., convergence time complexity). Experimental results support the scalability model of rBOA. The rBOA shows a subquadratic (in problem size) scalability for uniformly scaled decomposable problems.}, author = {Ahn, Chang W. and Ramakrishna, R. S. }, booktitle = {Evolutionary Computation, IEEE Transactions on}, citeulike-article-id = {2998497}, doi = {http://dx.doi.org/10.1109/TEVC.2007.902856}, journal = {Evolutionary Computation, IEEE Transactions on}, keywords = {eda, ga, theory}, number = {3}, pages = {307--322}, posted-at = {2008-07-14 10:35:27}, priority = {2}, title = {On the Scalability of Real-Coded Bayesian Optimization Algorithm}, url = {http://dx.doi.org/10.1109/TEVC.2007.902856}, volume = {12}, year = {2008} }

TY - JOUR ID - citeulike:2998497 L3 - citeulike-article-id:2998497 N2 - Estimation of distribution algorithms (EDAs) are major tools in evolutionary optimization. They have the ability to uncover the hidden regularities of problems and then exploit them for effective search. Real-coded Bayesian optimization algorithm (rBOA) which brings the power of discrete BOA to bear upon the continuous domain has been regarded as a milestone in the field of numerical optimization. It has been empirically observed that the rBOA solves, with subquadratic scaleup behavior, numerical optimization problems of bounded difficulty. This underlines the scalability of rBOA (at least) in practice. However, there is no firm theoretical basis for this scalability. The aim of this paper is to carry out a theoretical analysis of the scalability of rBOA in the context of additively decomposable problems with real-valued variables. The scalability is measured by the growth of the number of fitness function evaluations (in order to reach the optimum) with the size of the problem. The total number of evaluations is computed by multiplying the population size for learning a correct probabilistic model (i.e., population complexity) and the number of generations before convergence, (i.e., convergence time complexity). Experimental results support the scalability model of rBOA. The rBOA shows a subquadratic (in problem size) scalability for uniformly scaled decomposable problems. IS - 3 JF - Evolutionary Computation, IEEE Transactions on EP - 322 TI - On the Scalability of Real-Coded Bayesian Optimization Algorithm VL - 12 T2 - Evolutionary Computation, IEEE Transactions on SP - 307 KW - eda KW - ga KW - theory AU - Ahn, Chang AU - Ramakrishna, RS PY - 2008/// UR - http://dx.doi.org/10.1109/TEVC.2007.902856 ER -