AbstractProblems having the mathematical structure of a quadratic assignment problem are found in a diversity of contexts: by the economist in assigning a number of plants or indivisible operations to a number of different geographical locations; by the architect or indusatrial engineer in laying out activities, offices, or departments in a building; by the human engineer in arranging the indicators and controls in an operators control room; by the electronics engineer in laying out components on a backboard; by the computer systems engineer in arranging information in drum and disc storage; by the production scheduler in sequencing work through a production facility; and so on.In this paper we discuss several types of algorithms for solving such problems, presenting a unifying framework for some of the existing algorithms, and dcscribing some new algorithms. All of the algorithms discussed proceed first to a feasible solution and then to better and better feasible solutions, until ultimately one is discovered which is shown to be optimal.