Evolutionary algorithms (EAs) have been applied with success to many numerical and combinatorial optimization problems in recent years. However, they often lose their effectiveness and advantages when applied to large and complex problems, e.g., those with high dimensions. Although cooperative coevolution has been proposed as a promising framework for tackling high-dimensional optimization problems, only limited studies were reported by decomposing a high-dimensional problem into single variables (dimensions). Such methods of decomposition often failed to solve nonseparable problems, for which tight interactions exist among different decision variables. In this paper, we propose a new cooperative coevolution framework that is capable of optimizing large scale nonseparable problems. A random grouping scheme and adaptive weighting are introduced in problem decomposition and coevolution. Instead of conventional evolutionary algorithms, a novel differential evolution algorithm is adopted. Theoretical analysis is presented in this paper to show why and how the new framework can be effective for optimizing large nonseparable problems. Extensive computational studies are also carried out to evaluate the performance of newly proposed algorithm on a large number of benchmark functions with up to 1000 dimensions. The results show clearly that our framework and algorithm are effective as well as efficient for large scale evolutionary optimisation problems. We are unaware of any other evolutionary algorithms that can optimize 1000-dimension nonseparable problems as effectively and efficiently as we have done.