Cooperative coevolutionary algorithm (CCEA) has proven to be a very powerful means of solving optimization problems through problem decomposition. CCEA implies the use of several populations, each population having the aim of finding a partial solution for a component of the considered problem. Populations evolve separately and they interact only when individuals are evaluated. Interactions are made to obtain complete solutions by combining partial solutions, or collaborators, from each of the populations. In this respect, we can think of various interaction modes. The goal of this research is to develop a CCEA for a supply chain network design (SCND) problem and identify which interaction mode gives the best performance for this problem. We present general design principle of CCEA for the SCND problem, which require several co-evolving populations. We classify these populations into two groups and classify the collaborator selection scheme into two types, the random-based one and the best fitness-based one. By combining both two groups of population and two types of collaborator selection schemes, we consider four possible interaction modes. We also consider two modes of updating populations, the sequential mode and the parallel mode. Therefore, by combining both four possible interaction modes and two modes of updating populations, we investigate seven possible solution algorithms. Experiments for each of these solution algorithms are conducted on a few test problems. The results show that the mode of the best fitness-based collaborator applied to both groups of populations combined with the sequential update mode outperforms the other modes for all the test problems.