What is Support Vector Machine (SVM)

Evolutionary algorithms (EA) (Rechenberg, 1965) belong to a family of stochastic search algorithms inspired by natural evolution. In the last years, EA were used successfully to produce efficient solutions for a great number of hard optimization problems (Beasley, 1997). These algorithms operate on a population of potential solutions and apply a survival principle according to a fitness measure associated to each solution to produce better approximations of the optimal solution. At each iteration, a new set of solutions is created by selecting individuals according to their level of fitness and by applying to them several operators. These operators model natural processes, such as selection, recombination, mutation, migration, locality and neighborhood. Although the basic idea of EA is straightforward, solutions coding, size of population, fitness function and operators must be defined in compliance with the kind of problem to optimize. Multi-class problems with binary SVM (Support Vector Machine) classifiers are commonly treated as a decomposition in several binary sub-problems. An open question is how to properly choose all models for these sub-problems in order to have the lowest error rate for a specific SVM multi-class scheme. In this paper, we propose a new approach to optimize the generalization capacity of such SVM multi-class schemes. This approach consists in a global selection of models for sub-problems altogether and is denoted as multi-model selection. A multi-model selection can outperform the classical individual model selection used until now in the literature, but this type of selection defines a hard optimisation problem, because it corresponds to a search a efficient solution into a huge space. Therefore, we propose an adapted EA to achieve that multi-model selection by defining specific fitness function and recombination operator.