This work proposes space partitioning, a new approach to evolutionary many-objective optimization. The proposed approach instantaneously partitions the objective space into subspaces and concurrently searches in each subspace. A partition strategy is used to define a schedule of subspace sampling, so that different subspaces can be emphasized at different generations. Space partitioning is implemented with adaptive e-ranking, a procedure that re-ranks solutions in each subspace giving selective advantage to a subset of well distributed solutions chosen from the set of solutions initially assigned rank-1 in the high dimensional objective space. Adaptation works to keep the actual number of rank-1 solutions in each subspace close to a desired number. The effects on performance of space partitioning are verified on MNK-Landscapes. Also, a comparison with two substitute distance assignment methods recently proposed for many-objective optimization is included.