Problems 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 industrial 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 drxan 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 describing 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.In a subsequent paper we shall discuss our computational experience with a number of these algorithms.

Problem-solving procedures based on the methods of combinatorial programming are presented for solving a class of integer programming problems in which all elements are zero or one. All of the procedures seek first a feasible solution and then successively better and better feasible solutions until ultimately one is discovered which is shown to be optimal. By representing the problem elements in a binary computer as bits in a word and employing logical "and" and "or" operations in the problem-solving process, a number of problems involving several hundred integer variables have been solved in a matter of seconds.

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In an earlier paper [Pierce, J. F. 1968. Application of combinatorial programming to a class of all-zero-one integer programming problems. Management Sci. 15 (3, November) 191-209.] combinatorial programming procedures were presented for solving a class of integer programming problems in which all elements are zero or one. By representing the problem elements in a binary computer as bits in a word and employing logical "and" and "or" operations in the problem-solving process, a number of problems involving several hundred integer variables were solved in a matter of seconds. In the present paper a number of improvements in these earlier algorithms are presented, including a new search strategy, methods for reducing the original problem, and mechanisms for feasibility filtering in multi-word problems. With these improvements problem-solving efficiency has been increased in many instances by an order of magnitude. In addition, the present paper contains computational experience obtained in solving problems for the k-best solutions.

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