Cooperative Coevolution (CC) is a widely used framework for solving large-scale continuous constrained optimization problems. This approach decomposes this kind of problem into smaller, more manageable subproblems by grouping the objective function and constraint variables. The efficiency of the CC framework depends mainly on the group size and the grouping strategy. In this paper, we propose a CC-based algorithm, which in its first part uses a recently published grouping method called CEDG, which groups variables into subcomponents of appropriate size with high accuracy and low computational cost. In the second part, we use a variant of differential evolution called CSaNSDE to solve the generated subproblems. The CEDG and CSaNSDE methods are used under the CC framework. The resulting algorithm, called CC-CEDG, is evaluated on a scalable benchmark function set with constraints, up to 1000 dimensions. Results show that CC-CEDG outperforms other advanced algorithms for solving large constrained optimization problems.