Finding a kernel mapping function for support vector machines (SVMs) is a key step towards construction of a high-performanced SVM-based classifier. While some recent methods exploited an evolutional approach to construct a suitable multifunction kernel, most of them searched randomly and diversely. In this paper, the concept of a family of identical-structured kernel trees is proposed to enable exploration of structure space using genetic programming whereas to pursue investigation of parameter space on a certain tree using evolution strategy. To control balance between structure and parameter search towards an optimal kernel, simulated annealing is introduced. By experiments on a number of benchmark datasets in the UCI and text classification collection, the proposed method is shown to be able to find a better optimal solution than other search methods, including grid search and gradient search. Copyright © 2010 The Institute of Electronics, Information and Communication Engineers.