Evolutionary programming can solve black-box function optimisation problems by evolving a population of numerical vectors. The variation component in the evolutionary process is supplied by a mutation operator, which is typically a Gaussian, Cauchy, or Lévy probability distribution. In this paper, we use genetic programming to automatically generate mutation operators for an evolutionary programming system, testing the proposed approach over a set of function classes, which represent a source of functions. The empirical results over a set of benchmark function classes illustrate that genetic programming can evolve mutation operators which generalise well from the training set to the test set on each function class. The proposed method is able to outperform existing human designed mutation operators with statistical significance in most cases, with competitive results observed for the rest.

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In this study we use Genetic Programming (GP) as an offline hyper-heuristic to evolve a mutation operator for Evolutionary Programming. This is done using the Gaussian and uniform distributions as the terminal set, and arithmetic operators as the function set. The mutation operators are automatically designed for a specific function class. The contribution of this paper is to show that a GP can not only automatically design a mutation operator for Evolutionary Programming (EP) on functions generated from a specific function class, but also can design more general mutation operators on functions generated from groups of function classes. In addition, the automatically designed mutation operators also show good performance on new functions generated from a specific function class or a group of function classes.

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