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An evolution strategy design is presented that allows for an evolution on general quadratic manifolds. That is, it covers elliptic, parabolic, and hyperbolic equality constraints. The peculiarity of the presented algorithm design is that it is an interior point method. It evaluates the objective function only for feasible search parameter vectors and it evolves itself on the nonlinear constraint manifold. This is achieved by a closed form transformation of an individual's parameter vector, which is in contrast to iterative repair mechanisms. Results of different experiments are presented. A test problem consisting of a spherical objective function and a single hyperbolic/parabolic equality constraint is used. It is designed to be scalable in the dimension and it is used to compare the performance of the developed algorithm with other optimization methods supporting constraints. The experiments show the effectiveness of the proposed algorithm on the considered problems.

A matrix adaptation evolution strategy for optimization on general quadratic manifolds