Self-adaptation is an efficient way to control the strategy parameters of an EA automatically during optimization. It is based on implicit evolutionary search in the space of strategy parameters, and has been proven well as on-line parameter control method for a variety of strategy parameters, from local to global ones. Our proposed SAMOEA is a two level algorithm. The outer level is the algorithm that is responsible for the self adaptive techniques and is based on a MOGA implementation. The inner level consists of eMEGA instances. Both the outer and inner algorithm are variations of our previously proposed MEGA framework. The outer MOGA operates on a chromosome of elements, while the inner eMEGA instances operate on molecular graph chromosomes.