One of the most important and widely faced optimization problems in real applications is the interval multiobjective optimization problems (IMOPs). The state-of-the-art evolutionary algorithms (EAs) for IMOPs (IMOEAs) need a great deal of objective function evaluations to find a final Pareto front with good convergence and even distribution. Further, the final Pareto front is of great uncertainty. In this paper, we incorporate several local searches into an existing IMOEA, and propose a memetic algorithm (MA) to tackle IMOPs. At the start, the existing IMOEA is utilized to explore the entire decision space; then, the increment of the hyper-volume is employed to develop an activation strategy for every local search procedure; finally, the local search procedure is conducted by constituting its initial population, whose center is an individual with a small uncertainty and a big contribution to the hyper-volume, taking the contribution of an individual to the hyper-volume as its fitness function, and performing the conventional genetic operators. The proposed MA is empirically evaluated on 10 benchmark IMOPs as well as an uncertain solar desalination optimization problem and compared with three state-of-the-art algorithms with no local search procedure. The experimental results demonstrate the applicability and effectiveness of the proposed MA.