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Classic kernel-based classifiers use only a single kernel, but the real-world applications have emphasized the need to consider a combination of kernels - also known as a multiple kernel (MK) - in order to boost the classification accuracy by adapting better to the characteristics of the data. Our purpose is to automatically design a complex multiple kernel by evolutionary means. In order to achieve this purpose we propose a hybrid model that combines a Genetic Programming (GP) algorithm and a kernel-based Support Vector Machine (SVM) classifier. In our model, each GP chromosome is a tree that encodes the mathematical expression of a multiple kernel. The evolutionary search process of the optimal MK is guided by the fitness function (or efficiency) of each possible MK. The complex multiple kernels which are evolved in this manner (eCMKs) are compared to several classic simple kernels (SKs), to a convex linear multiple kernel (cLMK) and to an evolutionary linear multiple kernel (eLMK) on several real-world data sets from UCI repository. The numerical experiments show that the SVM involving the evolutionary complex multiple kernels perform better than the classic simple kernels. Moreover, on the considered data sets, the new multiple kernels outperform both the cLMK and eLMK - linear multiple kernels. These results emphasize the fact that the SVM algorithm requires a combination of kernels more complex than a linear one in order to boost its performance. [ABSTRACT FROM AUTHOR]