Hyper-spherical inversion transformations in multi-objective evolutionary optimization

Multi-objective evolutionary algorithms are widely considered to have two goals: convergence towards the true Pareto front and maintaining a diverse set of solutions. The primary concern here is with the first goal of convergence, in particular when one or more variables must converge to a constant value. Using a number of well known test problems, the difficulties that are currently impeding convergence are discussed and then a new method is proposed that transforms the decision space using the geometric properties of hyper-spherical inversions to converge towards/onto the true Pareto front. Future extensions of this work and its application to multi-objective optimisation is discussed.