MOEA/D-CMA Made Better with (l+l)-CMA-ES

Integrating non-elitist evolution strategies into MOEA/D is challenging because the former usually requires many samples for updates, which is costly for MOEAID. In contrast, we suggest using (1+ 1)-ES for three reasons: fewer samples needed for updates, lower computational overhead, and better flexibility for subproblem collaboration. To verify this, we introduce (1+1)-MOEA/D-CMA, where each subproblem is solved by a different (1+1)-ES solver, and the solvers collaborate through a novel solution injection scheme. Comprehensive experiments show that the proposed algorithm performs better than several widely used algorithms. More importantly, owing to the lightweight nature of (1+1)-CMA-ES, the algorithm is shown to run faster and scale better to large population sizes, than other MOEA/D variants based on (µ/µw, λ)-CMA-ES.