Hyper-spherical inversion transformations in multi-objective evolutionary optimization

Evolutionary multi-objective algorithms are widely considered to have two goals: convergence towards the true pareto front and maintaining a diverse set of solutions. Here we are primarily concerned with the first goal of convergence, in particular when one or more variables must converge to a common value. Using a well-known test suite, we discuss the difficulties that are currently impeding convergence and then propose that by transforming the decision space using the geometric properties of hyper-spherical inversions we can converge to the true pareto front. Future extensions of this work and its application to multi-objective linear programming are discussed.