Dealing with the ever-increasing video traffic is certainly one of the major challenges facing Internet Service Providers (ISPs). In this context, the strategic placement of caches is seen as one of the most important remedies, especially with recent advances in the field of virtualization. Unlike the existing works, which only focus on the placement issue, we also consider the problem of determining the optimal amount of cache to place at each possible location. We formalize, in this paper, the problem of caches placement as a multi-objective optimization problem, in which we minimize both the average distance from which contents are retrieved and the peering links utilization. As the proposed problem is NP-hard, we propose to solve it using the Greedy Randomized Adaptive Search Procedure (GRASP) meta-heuristic. Simulations results reveal the quality of the obtained solutions compared to an exhaustive search method. At the same time, they reveal that the solution is not to put all resources at the edge or at the core, as some studies claim, but to partition them judiciously, which mainly depends on the objectives of the ISPs.