Ashanti Alert Act of 2018 This bill directs the Department of Justice (DOJ) to establish a national communications network—the Ashanti Alert communications network—to support regional and local search efforts for missing adults. The Ashanti Alert communications network must be integrated with the Blue Alert communications network (i.e., the communications network that supports efforts to search for and apprehend violent offenders who injure, kill, or pose an imminent danger to law enforcement). The bill authorizes appropriations for FY2019-FY2022 to carry out the Ashanti Alert communications network. It amends the Justice Assistance Act of 1984 to eliminate existing authority for DOJ to award grants under the Emergency Federal Law Enforcement Assistance Program through FY2022.