A parallel heuristic for quadratic assignment problems

Abstract The quadratic assignment problem represents an important class of problems with applications as diverse as facility layout and data analysis. The importance of these applications coupled with the fact that the quadratic assignment problem is NP-hard has encouraged the development of heuristics because optimal seeking procedures have been restricted to very small versions of the problem. This paper describes a new parallel heuristic, SAGA, for the quadratic assignment problem. SAGA is a cascaded hybrid of a genetic algorithm and simulated annealing. In addition to details regarding SAGA and its implementation, this paper also describes the performance of SAGA on two standard problems taken from the literature. The results from these problems show SAGA to be superior to the most commonly employed heuristic in solution quality, and for large problems it is also superior in solution time.

[1]  Teofilo F. Gonzalez,et al.  P-Complete Approximation Problems , 1976, J. ACM.

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

[3]  Rainer E. Burkard,et al.  Entwurf von Schreibmaschinentastaturen mittels quadratischer Zuordnungsprobleme , 1977, Math. Methods Oper. Res..

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

[5]  L. D. Hopkins,et al.  Humans vs. Computer Algorithms for the Plant Layout Problem , 1980 .

[6]  R. Burkard,et al.  Numerical investigations on quadratic assignment problems , 1978 .

[7]  Willy Herroelen,et al.  On the use of flow dominance in complexity measures for facility layout problems , 1985 .

[8]  Andrew B. Whinston,et al.  On Optimal Allocation in a Distributed Processing Environment , 1982 .

[9]  David E. Goldberg,et al.  Alleles, loci and the traveling salesman problem , 1985 .

[10]  Roger C. Vergin,et al.  Comparison of Computer Algorithms and Visual Based Methods for Plant Layout , 1975 .

[11]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[12]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[13]  Jay L. Devore,et al.  Probability and statistics for engineering and the sciences , 1982 .

[14]  R Sharpe,et al.  Facility Layout Optimization Using the Metropolis Algorithm , 1985 .

[15]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[16]  T. E. Block.  Note---A Note on “Comparison of Computer Algorithms and Visual Based Methods for Plant Layout” by M. Scriabin and R. C. Vergin , 1977 .

[17]  T. L. Ward,et al.  Solving Quadratic Assignment Problems by ‘Simulated Annealing’ , 1987 .

[18]  Larry P. Ritzman.  The Efficiency of Computer Algorithms for Plant Layout , 1972 .

[19]  Denis R. Coleman.  Note--Plant Layout: Computers Versus Humans , 1977 .

[20]  Andrew Whinston,et al.  An Algorithm for the Quadratic Assignment Problem , 1970 .

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

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

[23]  N. E. Collins,et al.  Simulated annealing - an annotated bibliography , 1988 .

[24]  John F. Brotchie,et al.  A generalized design approach to solution of the non-convex quadratic programming problem , 1987 .

[25]  Ronald G. Askin,et al.  An Algorithm for NC Turret Punch Press Tool Location and Hit Sequencing , 1984 .

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

[27]  F. S. Hillier,et al.  Quantitative Tools for Plant Layout Analysis , 1963 .

[28]  Leon Steinberg,et al.  The Backboard Wiring Problem: A Placement Algorithm , 1961 .

[29]  Jean-Luc Lutton,et al.  The asymptotic behaviour of quadratic sum assignment problems: A statistical mechanics approach , 1986 .

[30]  Tarek M. Khalil,et al.  Facilities relative allocation technique (FRAT) , 1973 .

[31]  G. G. Hitchings,et al.  An efficient heuristic procedure for solving the layout design problem , 1976 .

[32]  F. Rendl,et al.  A thermodynamically motivated simulation procedure for combinatorial optimization problems , 1984 .

[33]  A. S. Carrie,et al.  Flow complexity—a data suitability index for flowline systems , 1983 .

[34]  T. E. Block.  Note---On the Complexity of Facilities Layout Problems , 1979 .

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

[36]  L. Hubert,et al.  Quadratic assignment as a general data analysis strategy. , 1976 .

[37]  B. Golden,et al.  Using simulated annealing to solve routing and location problems , 1986 .

[38]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

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