Metaheuristics: Computer Decision-Making pp 257-278 | Cite as

# A Distance-Based Selection of Parents in Genetic Algorithms

## Abstract

In this paper we propose an improvement to the widely used metaheuristic genetic algorithm. We suggest a change in the way parents are selected. The method is based on examining the similarity of parents selected for mating. Computational comparisons for solving the quadratic assignment problem using a hybrid genetic algorithm demonstrate the effectiveness of the method. This conclusion is examined statistically. We also report extensive computational results of solving the quadratic assignment problem Thol50. The best variant found the best known solution 8 times out of 20 replications. The average value of the objective function was 0.001% over the best known solution. Run time for this variant is about 18 hours per replication. When run time is increased to about two days per replication the best known solution was found 7 times out of 10 replications with the other three results each being 0.001% over the best known.

## Keywords

Genetic algorithms Parent selection Quadratic Assignment Problem.## Preview

Unable to display preview. Download preview PDF.

## Bibliography

- R.K. Ahuja, J.B. Orlin, and A. Tiwari. A descent genetic algorithm for the quadratic assignment problem.
*Computers and Operations Research*, 27: 917–934, 2000.MathSciNetzbMATHCrossRefGoogle Scholar - S. Amin. Simulated jumping.
*Annals of Operations Research*, 84: 23–38, 1999.MathSciNetCrossRefGoogle Scholar - K. Anstreicher, N. Brixius, J.-P. Gaux, and J. Linderoth. Solving large quadratic assignment problems on computational grids.
*Mathematical Programming*, 91: 563–588, 2002.MathSciNetzbMATHCrossRefGoogle Scholar - G.C. Armour and E.S. Buffa. A heuristic algorithm and simulation approach to relative location of facilities.
*Management Science*, 9: 294–309, 1963.CrossRefGoogle Scholar - R. Battiti and G. Tecchiolli. The reactive tabu search.
*ORSA Journal on Computing*, 6: 126–140, 1994.zbMATHCrossRefGoogle Scholar - N.W. Brixius and K.M. Anstreicher. The Steinberg wiring problem. Working paper, The University of Iowa, 2001.Google Scholar
- R.E. Burkard. Locations with spatial interactions: The quadratic assignment problem. In P.B. Mirchandani and R.L. Francis, editors,
*Discrete Location Theory*. Wiley, Berlin, 1990.Google Scholar - R.E. Burkard and F. Rendl. A thermodynamically motivated simulation procedure for combinatorial optimization problems.
*European Journal of Operational Research*, 17: 169–174, 1984.zbMATHCrossRefGoogle Scholar - E. Çela.
*The Quadratic Assignment Problem: Theory and Algorithms*. Kluwer Academic Publishers, Dordrecht, 1998.zbMATHCrossRefGoogle Scholar - D.T. Connoly. An improved annealing scheme for the QAP.
*European Journal of Operational Research*, 46: 93–100, 1990.MathSciNetCrossRefGoogle Scholar - V.-D. Cung, T. Mautor T., P. Michelon, and A. Tavares A. A scatter search based approach for the quadratic assignment problem. In
*Proceedings of the IEEE International Conference on Evolutionary Computation and Evolutionary Programming (ICEC’97)*, pages 165–170, Indianapolis, 1997.Google Scholar - T. Drezner and Z. Drezner. Gender-specific genetic algorithms. under review, 2003.Google Scholar
- Z. Drezner. Heuristic algorithms for the solution of the quadratic assignment problem.
*Journal of Applied Mathematics and Decision Sciences*, 6: 163–173, 2002.MathSciNetCrossRefGoogle Scholar - Z. Drezner. A new genetic algorithm for the quadratic assignment problem.
*INFORMS Journal on Computing*, 2003a.Google Scholar - Z. Drezner. Robust heuristic algorithms for the quadratic assignment problem. Under review, 2003b.Google Scholar
- Z. Drezner and G.A. Marcoulides. Mapping the convergence of genetic algorithms. under review, 2003.Google Scholar
- B. Eschermann and H.J. Wunderlich. Optimized synthesis of self-testable finite state machines. In
*20th International Symposium on Fault-Tolerant Computing (FFTCS 20)*, Newcastle upon Tyne, 1990.Google Scholar - C. Fleurent and J.A. Ferland. Genetic hybrids for the quadratic assignment problem. In P. Pardalos and H. Wolkowicz, editors,
*Quadratic Assignment and Related Problems*, volume 16 of*DIMACS Series in Discrete Mathematics and Theoretical Computer Science*, pages 173–187. American Mathematical Society, 1994.Google Scholar - L. Gambardella, E. Taillard, and M. Dorigo. Ant colonies for the quadratic assignment problem.
*Journal of the Operational Research Society*, 50: 167–176, 1999.zbMATHGoogle Scholar - D.E. Goldberg.
*Genetic Algorithms in Search*,*Optimization and Machine Learning*. Addison-Wesley, Wokingham, England, 1989.Google Scholar - R.P. Grimaldi.
*Discrete and Combinatorial Mathematics: An Applied Introduction*. Addison-Wesley, Wokingham, England, 1998.Google Scholar - P.M. Hahn and J. Krarup. A hospital facility problem finally solved.
*The Journal of Intelligent Manufacturing*, 12: 487–496, 2001.CrossRefGoogle Scholar - P. Hansen and N. Mladenovié. Variable neighborhood search: Principles and applications.
*European Journal of Operational Research*, 130:449 — 467, 2001.Google Scholar - J.H. Holland.
*Adaptation in Natural and Artificial Systems*. University of Michigan Press, Ann Arbor, 1975.Google Scholar - J. Krarup and P.M. Pruzan. Computer-aided layout design.
*Mathematical Programming Study*, 9: 75–94, 1978.MathSciNetCrossRefGoogle Scholar - Y. Li, P.M. Pardalos, and M.G.C. Resende. A greedy randomized adaptive search procedure for the quadratic assignment problem. In P. Pardalos and H. Wolkowicz, editors,
*Quadratic Assignment and Related Problems*, volume 16 of*DIMACS Series in Discrete Mathematics and Theoretical Computer Science*, pages 237–261. American Mathematical Society, 1994.Google Scholar - G.A. Marcoulides. A eugenic algorithm for condcuting specification searches in structural equation modeling, 2001. Paper presented at the annual meeting of the Society of Multivariate Experimental Psychology, Monterey, CA.Google Scholar
- G.A. Marcoulides and Z. Drezner. A procedure for transforming points in multi-dimensional space to two-dimensional.
*Educational and Psychological Measurement*,53:933–940, 1993.Google Scholar - A. Misevkius. An efficient simulated annealing algorithm for the quadratic assignment problem. Technical report, Kaunas University of Technology, 2001. working paper.Google Scholar
- N. Mladenovk and P. Hansen. Variable neighborhood search.
*Computers and Operations Research*,24:1097–1100,1997.Google Scholar - P. Moscato. Memetic algorithms. In P.M. Pardalos and M.G.C. Resende, editors,
*Handbook of Applied Optimization*, pages 157–167. Oxford University Press, Oxford, U.K., 2002.Google Scholar - C.E. Nugent, T.E. Vollman, and T. Ruml. An experimental comparison of techniques for the assignment of facilities to locations.
*Operations Research*, 16: 150–173, 1968.CrossRefGoogle Scholar - M. Nyström. Solving certain large instances of the quadratic assignment problem: Steinberg’s examples. Technical report, California Institute of Technology, 1999. Working paper.Google Scholar
- F. Rendl. The quadratic assignment problem. In Z. Drezner and H. Hamacher, editors,
*Facility Location: Applications and Theory*. Springer, Berlin, 2002.Google Scholar - S. Salhi. Heuristic search methods. In G.A. Marcoulides, editor, M
*odern Methods for Business Research*. Lawrence Erlbaum Associates, Mahwah, NJ., 1998.Google Scholar - J. Skorin-Kapov. Tabu search applied to the quadratic assignment problem.
*ORSA Journal on Computing*, 2: 33–45, 1990.zbMATHCrossRefGoogle Scholar - L. Steinberg. The backboard wiring problem: a placement algorithm.
*SIAM Review*,3:37–50, 1961.Google Scholar - E.D. Taillard. Robust tabu search for the quadratic assignment problem.
*Parallel Computing*,17:443–455, 1991.Google Scholar - E.D. Taillard. Comparison of iterative searches for the quadratic assignment problem.
*Location Science*, 3: 87–105, 1995.zbMATHCrossRefGoogle Scholar - E.D. Taillard and L.M. Gambardella. Adaptive memories for the quadratic assingnment problem. Technical report, IDSIA Lugano, Switzerland, 1997. Research report.Google Scholar
- D.M. Tate and A.E. Smith. A genetic approach to the quadratic assignment problem.
*Computers and Operations Research*, 22: 73–83, 1995.zbMATHCrossRefGoogle Scholar - U.W. Thonemann and A. Bölte. Optimizing simulated annealing schedules with genetic programming. Technical report, Lehrstuhl für Betriebswirtschaftslehre, Insbes. Produktionswirtshaft, Universität Paderborn, Germany, 1993. Working paper.Google Scholar
- U.W. Thonemann and A. B?lte. An improved simulated annealing algorithm for the quadratic assignment problem. Technical report, School of Business, Department of Production and Operations Research, University of Paderborn, Germany, 1994. Working paper.Google Scholar
- M.R. Wilhelm and T.L. Ward. Solving quadratic assignment problems by simulated annealing.
*I1E Transactions*, 19: 107–119, 1987.CrossRefGoogle Scholar