This study investigates bilevel optimization problems with multiple objectives at both upper and lower levels. For such problems, for every feasible solution at the upper level, there is a corresponding set of Pareto-optimal solutions at the lower level. In typical bilevel evolutionary algorithms, the upper level solution is evaluated for each of these lower level Pareto solutions during the search. This incurs significant computational expense while searching for the overall (upper level) Pareto optimal front. In this study, we aim to reduce this expense by selectively evaluating the upper level solutions with only some of the lower-level solutions during the search. Towards this end, a direction-based selective evaluation scheme is introduced. Numerical experiments demonstrate that the proposed approach improves search accuracy and convergence rate, particularly for problems where the initial search starts far from the Pareto front.