A CMA stochastic differential equation approach for many-objective optimization

In multiobjective optimization problems, Pareto dominance-based search techniques are known to lose their efficiency in problems with a large number of objective functions - the many-objective problems. This paper proposes an algorithm based on a stochastic differential equation approach combined with an evolutionary strategy for dealing with such problems. The proposed algorithm is intended to both allow the determination of tight Pareto-optimal solutions in many-objective problems (which is a difficult task for usual evolutionary algorithms) and to find a solution set that performs a relatively uniform sampling of the Pareto-optimal set (which is a deficiency of the known stochastic differential equation approach). The proposed algorithm is shown to attain such goals at a relatively low computational cost.