Convergence Rates of (1+1) Evolutionary Multiobjective Optimization Algorithms

Convergence analyses of evolutionary multiobjective optimization algorithms typically deal with the convergence in limit (stochastic convergence) or the run time. Here, for the first time concrete results for convergence rates of several popular algorithms on certain classes of continuous functions are presented. We consider the algorithms in the version of using a (1+1) selection scheme. Then, SMS-EMOA and IBEA + achieve linear convergence rate, proved by showing algorithmic equivalence to the single-objective (1+1)-EA with self-adaptation, whereas NSGA-II and SPEA2 have a sub-linear convergence rate, proved by reducing them to a multiobjective algorithm with known properties.