Strategic Withdrawal of Agencies for Meaningful Placement Act of 2018 or the SWAMP Act This bill: (1) repeals the requirement that all offices attached to the seat of government be exercised in the District of Columbia, and not elsewhere; and (2) prohibits new construction or major renovation of certain executive agency headquarters in the Washington Metropolitan area. The General Services Administration (GSA) must: (1) establish a process to allow an executive agency to request GSA to issue a solicitation for the relocation of its headquarters; (2) allow any state to bid for the relocation of the agency's headquarters; and (3) in consultation with the executive agency, select a state for the relocation of the agency's headquarters using a competitive bidding procedure based on certain considerations.