Abstract
The Number Partitioning Problem (MNP) remains as one of the simplest-to-describe yet hardest-to-solve combinatorial optimization problems. In this paper we use the MNP as a surrogate for several related real-world problems, to test new heuristics ideas. To be precise, we study the use of weight-matching techniques to devise smart memetic operators. Several options are considered and evaluated for that purpose. The positive computational results indicate that — despite the MNP may be not the best scenario for exploiting these ideas — the proposed operators can be really promising tools for dealing with more complex problems of the same family.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliography
C.C. Aggarwal, J.B. Orlin, and R.P. Tai. Optimized crossover for the independent set problem. Operations Research, 45 (2): 226–234, 1997.
M.F. Arguello, T.A. Feo, and O. Goldschmidt. Randomized methods for the number partitioning problem. Computers & Operations Research,23(2):103111,1996.
E. Balas and W. Niehaus. Finding large cliques in arbitrary graphs by bipartite matching. In D.S. Johnson and M.A. Trick, editors, Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, volume DIMACS 26, pages 29–51. American Mathematical Society, 1996.
R. Berretta and P. Moscato. The number partitioning problem: An open challenge for evolutionary computation? In D. Come, M. Dorigo, and F. Glover, editors, New Ideas in Optimization, pages 261–278. McGraw-Hill, 1999.
A. Caprara and M. Fischetti. Branch-and-cut algorithms. In M. Dell’Amico, F. Maffioli, and S. Martello, editors, Annotated bibliographies in combinatorial optimization, pages 45 — 63. John Wiley and Sons, Chichester, 1997.
P. Cheeseman, B. Kanefsky, and W.M. Taylor. Where the Really Hard Problems Are. In Proceedings of the Twelfth International Joint Conference on Artificial Intelligence, IJCAI-91, Sydney, Australia, pages 331–337, 1991.
L. Davis. Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York NY, 1991.
F.F. Ferreira and J.F. Fontanari. Probabilistic analysis of the number partitioning problem. Journal of Physics A: Math. Gen, pages 3417–3428, 1998.
F. Glover and M. Laguna. Tabu Search. Kluwer Academic Publishers, Norwell, Massachusetts, USA, 1997.
M. Gorges-Schleuter. ASPARAGOS: An asynchronous parallel genetic optimization strategy. In J. David Schaffer, editor, Proceedings of the Third International Conference on Genetic Algorithms, pages 422–427, San Mateo, CA, 1989. Morgan Kaufmann Publishers.
M. Gorges-Schleuter. Explicit Parallelism of Genetic Algorithms through Population Structures. In H.-P. Schwefel and R. Männer, editors, Parallel Problem Solving from Nature I, volume 496 of Lecture Notes in Computer Science, pages 150–159. Springer-Verlag, Berlin, Germany, 1991.
D.S. Johnson, C. R. Aragon, L. A. McGeoch, and C. Schevon. Optimization by simulated annealing: An experimental evaluation; Part II: Graph coloring and number partitioning. Operations Research, 39 (3): 378–406, 1991.
D.R. Jones and M.A. Beltramo. Solving partitioning problems with genetic algorithms. In R.K Belew and L.B. Booker, editors, Proceedings of the Fourth International Conference on Genetic Algorithms, pages 442–449, San Mateo, CA, 1991. Morgan Kaufmann.
N. Karmarkar and R.M. Karp. The differencing method of set partitioning. Report UCB/CSD 82/113, University of California, Berkeley, CA, 1982.
S. Kirkpatrick, C.D. Gelatt Jr., and M.P. Vecchi. Optimization by simmulated annealing. Science, 220 (4598): 671–680, 1983.
D. Kirovski, M. Ercegovac, and M. Potkonjak. Low-power behavioral synthesis optimization using multiple-precision arithmetic. In ACM-IEEE Design Automation Conference, pages 568–573. ACM Press, 1999.
R. Korf. A complete anytime algorithm for number partitioning. Artificial Intelligence, 106: 181–203, 1998.
M. Laguna and P. Laguna. Applying Tabu Search to the 2-dimensional Ising spin glass. International Journal of Modern Physics C–Physics and Computers, 6 (1): 11–23, 1995.
E.L. Lawler and D.E. Wood. Branch and bounds methods: A survey. Operations Research, 4 (4): 669–719, 1966.
D.L. Mammen and T. Hogg. A new look at the easy-hard-easy pattern of combinatorial search difficulty. Journal of Artificial Intelligence Research, 7: 47–66, 1997.
S. Mertens. Phase transition in the number partitioning problem. Physical Review Letters, 81 (20): 4281–4284, 1998.
S. Mertens. Random costs in combinatorial optimization. Physical Review Letters, 84 (6): 1347–1350, 2000.
D.G. Mitchell, B. Selman, and H.J. Levesque. Hard and easy distributions for SAT problems. In P. Rosenbloom and P. Szolovits, editors, Proceedings of the Tenth National Conference on Artificial Intelligence, pages 459–465, Menlo Park, California, 1992. AAAI Press.
P. Moscato. On Evolution, Search, Optimization, Genetic Algorithms and Martial Arts: Towards Memetic Algorithms. Technical Report Caltech Concurrent Computation Program, Report. 826, California Institute of Technology, Pasadena, California, USA, 1989.
P. Moscato. An Introduction to Population Approaches for Optimization and Hierarchical Objective Functions: The Role of Tabu Search. Annals of Operations Research, 41 (1–4): 85–121, 1993.
P. Moscato. Memetic algorithms: A short introduction. In D. Corne, M. Dorigo, and F. Glover, editors, New Ideas in Optimization, pages 219–234. McGraw-Hill, 1999.
P. Moscato and C. Cotta. A gentle introduction to memetic algorithms. In F. Glover and G. Kochenberger, editors, Handbook of Metaheuristics, pages 105–144. Kluwer Academic Publishers, Boston MA, 2003.
P. Moscato and M. G. Norman. A Memetic Approach for the Traveling Salesman Problem Implementation of a Computational Ecology for Combinatorial Optimization on Message-Passing Systems. In M. Valero, E. Onate, M. Jane, J. L. Larriba, and B. Suarez, editors, Parallel Computing and Transputer Applications, pages 177–186, Amsterdam, 1992. IOS Press.
H. Mühlenbein. Evolution in Time and Space — The Parallel Genetic Algorithm. In Gregory J.E. Rawlins, editor, Foundations of Genetic Algorithms, pages 316–337, San Mateo, CA, 1991. Morgan Kaufmann Publishers.
M.G. Norman and P. Moscato. A competitive and cooperative approach to complex combinatorial search. In Proceedings of the 20th Informatics and Operations Research Meeting, pages 3.15–3.29, Buenos Aires, 1991.
C.H. Papadimitriou. Computational Complexity. Addison-Wesley, 1994.
N.J. Radcliffe. The algebra of genetic algorithms. Annals of Mathematics and Artificial Intelligence, 10: 339–384, 1994.
N.J. Radcliffe and P.D. Surry. Fitness Variance of Formae and Performance Prediction. In L.D. Whitley and M.D. Vose, editors, Proceedings of the Third Workshop on Foundations of Genetic Algorithms, pages 51–72, San Francisco, 1994a. Morgan Kaufmann.
N.J. Radcliffe and P.D. Surry. Formal Memetic Algorithms. In T. Fogarty, editor, Evolutionary Computing: AISB Workshopvolume 865 of Lecture Notes in Computer Sciencepages 1–16. Springer-Verlag, Berlin, 1994b.
W. Ruml. Stochastic approximation algorithms for number partitioning. Technical Report TR-17–93, Harvard University, Cambridge, MA, USA, 1993. available via ftp://das-ftp.harvard.edu/techreports/tr-17–93.ps.gz.
W. Ruml, J.T. Ngo, J. Marks, and S.M. Shieber. Easily searched encodings for number partitioning. Journal of Optimization Theory and Applications, 89 (2): 251–291, 1996.
R. Slootmaekers, H. Van Wulpen, and W. Joosen. Modelling genetic search agents with a concurrent object-oriented language. In P. Sloot, M. Bubak, and B. Hertzberger, editors, High-Performance Computing and Networking, volume 1401 of Lecture Notes in Computer Science, pages 843–853. Springer, Berlin, 1998.
B.M. Smith and M.E. Dyer. Locating the phase transition in binary constraint satisfaction. Artificial Intelligence, 81 (1–2): 155–181, 1996.
G. Sorkin. Theory and Practice of Simulated Annealing on Special Energy Landscapes. Ph.d. thesis, University of California at Berkeley, Berkeley, CA, 1992.
R.H. Storer. Number partitioning and rotor balancing. In Talk at the INFORMS Conference, Optimization Techniques Track, TD15.2, 2001.
R.H. Storer, S.W. Flanders, and S.D. Wu. Problem space local search for number partitioning. Annals of Operations Research, 63: 465–487, 1996.
R. Tanese. Distributed genetic algorithms. In J.D. Schaffer, editor, Proceedings of the Third International Conference on Genetic Algorithms, pages 434–439, San Mateo, CA, 1989. Morgan Kaufmann.
D.H. Wolpert and W.G. Macready. No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation, 1 (1): 67–82, 1997.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media New York
About this chapter
Cite this chapter
Berretta, R., Cotta, C., Moscato, P. (2003). Enhancing the Performance of Memetic Algorithms by Using a Matching-Based Recombination Algorithm. In: Metaheuristics: Computer Decision-Making. Applied Optimization, vol 86. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-4137-7_4
Download citation
DOI: https://doi.org/10.1007/978-1-4757-4137-7_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5403-9
Online ISBN: 978-1-4757-4137-7
eBook Packages: Springer Book Archive