This proposal is concerned with the restoration of service in a power system that has lost some or all of its load. In a blackout or brownout situation, the system may separate into separate islands and it is necessary to first restore the load within the islands and then restore the interconnections among the islands. The restoration is proposed to be done with a hierarchical multi-layer approach consisting of a direct control layer, an optimizing layer, and an adaptive layer. The focus here is on the last two layers with the problem formulated as a multi-stage multi-objective sequential decision problem. The problem of power system restoration after a blackout is an important one but has been very difficult to formulate in a rigorous mathematical way. A new formulation is to be developed in this approach. Any success at better restoration techniques will lead to shorter periods of power outages.