Tree-Search Algorithms for Quadratic Assignment Problems

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 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.

[1]  A. H. Land,et al.  A Problem of Assignment with Inter-Related Costs , 1963 .

[2]  A. S. Manne,et al.  On the Solution of Discrete Programming Problems , 1956 .

[3]  M. Breuer.  The formulation of some allocation and connection problems as integer programs , 1966 .

[4]  R. A. Rutman.  An algorithm for placement of interconnected elements based on minimum wire length , 1964, AFIPS '64 (Spring).

[5]  P. Gilmore.  Optimal and Suboptimal Algorithms for the Quadratic Assignment Problem , 1962 .

[6]  W. L. Maxwell,et al.  THE SCHEDULING OF SINGLE MACHINE SYSTEMS: A REVIEW∗ , 1964 .

[7]  A. M. Geoffrion.  Integer Programming by Implicit Enumeration and Balas’ Method , 1967 .

[8]  Elwood S. Buffa,et al.  The Facilities Layout Problem in Perspective , 1966 .

[9]  C. Carl Pegels.  PLANT LAYOUT AND DISCRETE OPTIMIZING , 1966 .

[10]  F. Hillier,et al.  Quadratic Assignment Problem Algorithms and the Location of Indivisible Facilities , 1966 .

[11]  D. R. Fulkerson,et al.  Flows in Networks. , 1964 .

[12]  M. M. Flood.  The Traveling-Salesman Problem , 1956 .

[13]  Thomas E. Vollmann,et al.  An Experimental Comparison of Techniques for the Assignment of Facilities to Locations , 1968, Oper. Res..

[14]  T. Koopmans,et al.  Assignment Problems and the Location of Economic Activities , 1957 .

[15]  Solomon W. Golomb,et al.  Backtrack Programming , 1965, JACM.

[16]  Elwood S. Buffa,et al.  A Heuristic Algorithm and Simulation Approach to Relative Location of Facilities , 1963 .

[17]  J. W. Gavett,et al.  The Optimal Assignment of Facilities to Locations by Branch and Bound , 1966, Oper. Res..

[18]  E. Lawler.  The Quadratic Assignment Problem , 1963 .

[19]  J. H. Ahrens,et al.  Suboptimal algorithms for the quadratic assignment problem , 1968 .

[20]  A. Land,et al.  An Automatic Method for Solving Discrete Programming Problems , 1960, 50 Years of Integer Programming.