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This paper proposes the Necessary-preference-enhanced Evolutionary Multiobjective Optimizer (NEMO), a combination of an evolutionary multiobjective optimization method, NSGA-II, and an interactive multiobjective optimization method, GRIP. In the course of NEMO, the decision maker is able to introduce preference information in a holistic way, by simply comparing some pairs of solutions and specifying which solution is preferred, or comparing intensities of preferences between pairs of solutions. From this information, the set of all compatible value functions is derived using GRIP, and a properly modified version of NSGA-II is then used to search for a representative set of all Pareto-optimal solutions compatible with this set of derived value functions. As we show, this allows to focus the search on the region most preferred by the decision maker, and thereby speeds up convergence.