Hypervolume based multiobjective evolutionary algorithms (MOEA) nowadays seem to be the first choice when handling multiobjective optimization problems with many, i.e., at least three objectives. Experimental studies have shown that hypervolume-based search algorithms as SMS-EMOA can outperform established algorithms like NSGA-II and SPEA2. One problem remains with most of the hypervolume based algorithms: the best known algorithm for computing the hypervolume needs time exponentially in the number of objectives. To save computation time during hypervolume computation which can be better spent in the generation of more solutions, we propose a general approach how objective reduction techniques can be incorporated into hypervolume based algorithms. Different objective reduction strategies are developed and then compared in an experimental study on two test problems with up to nine objectives. The study indicates that the (temporary) omission of objectives can improve hypervolume based MOEAs drastically in terms of the achieved hypervolume indicator values.
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