Multiobjectivization with NSGA-II on the noiseless BBOB testbed

The idea of multiobjectivization is to reformulate a singleobjective problem as a multiobjective one. In one of the scarce studies proposing this idea for problems in continuous domains, the distance to the closest neighbor (dcn) in the population of a multiobjective algorithm has been used as the additional (dynamic) second objective. As no comparison with other state-of-the-art single-objective optimizers has been presented for this idea, we have benchmarked two variants (with and without the second dcn objective) of the original NSGA-II algorithm using two different mutation operators on the noiseless BBOB'2013 testbed. It turns out that multiobjectivization helps for several of the 24 benchmark functions, but that, compared to the best algorithms from BBOB'2009, a significant performance loss is visible. Moreover, on some functions, the choice of the mutation operator has a stronger impact on the performance than whether multiobjectivization is employed or not.