Skip to main content

Advertisement

SpringerLink
Log in

Genetic algorithms and scatter search: unsuspected potentials

  • Published:
Statistics and Computing Aims and scope Submit manuscript

Abstract

We provide a tutorial survey of connections between genetic algorithms and scatter search that have useful implications for developing new methods for optimization problems. The links between these approaches are rooted in principles underlying mathematical relaxations, which became inherited and extended by scatter search. Hybrid methods incorporating elements of genetic algorithms and scatter search are beginning to be explored in the literature, and we demonstrate that the opportunity exists to develop more advanced procedures that make fuller use of scatter search strategies and their recent extensions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Aarts, E. H. L., Eiben, A. E. and van Hee, K. M. (1989). A general theory of genetic algorithms. Computing Science Notes, 89/8, Eindhoven University of Technology.

  • Ackley, D. (1987). A Connectionist Model for Genetic Hillclimbing. Kluwer, Dordrecht. Academic Publishers.

    Google Scholar 

  • Bäck, T., Hoffmeister, F. and Schwefel, H. (1991). A survey of evolution strategies. In Proceedings of the Fourth International Conference on Genetic Algorithms, eds R. Belew and L. Booker, pp. 2–9. Morgan Kaufmann, San Mateo, CA.

    Google Scholar 

  • Battiti, R. and Tecchiolli, G. (1992). Parallel biased search for combinatorial optimization: genetic algorithms and tabu search. Technical Report No. 9207–02, Instituto Per La Ricerca Scientifica E Tecnologica, Italy.

    Google Scholar 

  • Beasley, J. E. (1983). Lagrangean relaxation, In Modern Heuristic Techniques for Combinatorial Problems, ed. C. Reeves, pp. 243–298. Blackwell Scientific Publishing, Oxford.

    Google Scholar 

  • Costa, D. (1992). An evolutionary tabu search algorithm and the NHL scheduling program. ORWP 92–11, Ecole Polytechnique Fédérale de Lausanne, Switzerland.

    Google Scholar 

  • Davis, L. (1989). Adapting operator probabilities in genetic algorithms. In Proceedings of the Third International Conference on Genetic Algorithms, pp. 61–69. Morgan Kaufmann, San Mateo, CA.

    Google Scholar 

  • Davis, L. (ed.) (1991). Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York.

    Google Scholar 

  • Dorndorf, U. and Pesch, E. (1992). Evolution Based Learning in a Job Shop Scheduling Environment. Technical Report, University of Limberg, The Netherlands.

    Google Scholar 

  • Everett, H. (1963). Generalized Lagrange multiplier method for solving problems of optimal allocation of resources. Operations Research, 11, 399–417.

    CAS  PubMed  Google Scholar 

  • Fisher, M. L. (1973). Optimal solution of scheduling problems using generalized Lagrangean multipliers: Part I. Operations Research, 21, 1114–1127.

    Google Scholar 

  • Fisher, M. L. (1985). An applications oriented guide to Lagrangean relaxation. Interfaces, 15, 10–21.

    Google Scholar 

  • Fisher, M. L., Northrup, W. D. and Shapiro, J. F. (1975). Using duality to solve discrete optimization problems: theory and computation experience. Mathematical Programming Study, 3, 59–94.

    Google Scholar 

  • Fréville, A. and Plateau, G. (1992). FPBK92: An implicit enumeration code for the solution of the 0–1 bidimensional knapsack problem based on surrogate duality. Graphs and Optimization Colloquium, Grimentz, Switzerland.

  • Fréville, A. and Plateau, G. (1993). An exact search for the solution of the surrogate dual of the 0–1 bidimensional knapsack problem. European Journal of Operational Research, 68, 413–421.

    Google Scholar 

  • Gavish, B. and Pirkul, H. (1985). Efficient algorithms for solving multiconstraint zero-one knapsack problems to optimality. Mathematical Programming, 31, 78–105.

    Google Scholar 

  • Geoffrion, A. M. (1972). Duality in nonlinear programming: a simplified applications-oriented development. In Perspectives on Optimization, ed. A. M. Geoffrion. Addison-Wesley, Reading, MA.

    Google Scholar 

  • Geoffrion, A. M. (1974). Lagrangean relaxation and its uses in integer programming. Mathematical Programming Study, 2, 82–114.

    Google Scholar 

  • Glover, F. (1964). A bound escalation method for the solution of integer linear programs. Cahiers de Recherche Opérationelle, 6, 131–168.

    Google Scholar 

  • Glover, F. (1965). A multiphase-dual algorithm for the zero-one integer programming problem. Operations Research, 13, 879–919.

    Google Scholar 

  • Glover, F. (1968). Surrogate constraints. Operations Research, 16, 741–749.

    Google Scholar 

  • Glover, F. (1974). Heuristics for Integer Programming Using Surrogate Constraints. MSRS 74-6, College of Business, University of Colorado, July (also referenced in Glover (1975)).

  • Glover, F. (1975). Surrogate constraint duality in mathematical programming. Operations Research, 23, 434–451.

    Google Scholar 

  • Glover, F. (1977). Heuristics for integer programming using surrogate constraints. Decision Sciences, 8, 156–166.

    Google Scholar 

  • Glover, F. (1989). Tabu search, Part I. ORSA Journal on Computing, 1, 190–206.

    Google Scholar 

  • Glover, F. (1991). Tabu search for nonlinear and parametric optimization (with links to genetic algorithms). To appear in Discrete Applied Mathematics.

  • Glover, F. and Laguna, M. (1993). Tabu search. In Modern Heuristic Techniques for Combinatorial Problems. ed. C. Reeves, pp. 70–141. Blackwell Scientific Publishing, Oxford.

    Google Scholar 

  • Glover, F., Kelly, J. and Laguna, M. (1993). Genetic algorithms and tabu search: hybrids for optimization. To appear in Computers and Operations Research, ed. Y. Gupta.

  • Glover, F., Laguna, M., Taillard, E. and de Werra, D. (eds) (1993). Tabu search. Special issue of the Annals of Operations Research, 41.

  • Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading, MA.

    Google Scholar 

  • Greenberg, H. J. (1973a). Bounding nonconvex programs with conjugates. Operations Research, 21, 346–347.

    Google Scholar 

  • Greenberg, H. J. (1973b). The generalized penalty function surrogate model. Operations Research, 21, 162–178.

    Google Scholar 

  • Greenberg, H. J. and Pierskalla, W. P. (1970). Surrogate mathematical programs. Operations Research, 18, 924–939.

    Google Scholar 

  • Greenberg, H. J. and Pierskalla, W. P. (1973). Quasi-conjugate functions and surrogate duality. Cahiers du Centre d'Etudes de Recherche Operationelle, 15, 437–448.

    Google Scholar 

  • Held, M. and Karp, R. M. (1970). The traveling salesman problem and minimum spanning trees. Operations Research, 18, 1138–1162.

    Google Scholar 

  • Holland, J. H. (1975). Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, MI.

    Google Scholar 

  • Karwan, M. H. and Rardin, R. L. (1976). Surrogate dual multiplier search procedures in integer programming. School of Industrial Systems Engineering, Report Series No. J-77-13, Georgia Institute of Technology.

  • Karwan, M. H. and Rardin, R. L. (1979). Some relationships between Lagrangean and surrogate duality in integer programming. Mathematical Programming, 17, 230–334.

    Google Scholar 

  • Michalewicz, Z. (1992). Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag, New York.

    Google Scholar 

  • Michalewicz, Z. (1993). Evolutionary computation techniques for nonlinear programming problems. Paper presented at the IFORS 93 Conference, Lisbon, Portugal.

  • Michalewicz, Z. and Janikow, C. (1991). Genetic algorithms for numerical optimization. Statistics and Computing, 1, 75–91.

    Google Scholar 

  • Michalewicz, Z., Vignaux, G. A. and Hobbs, M. (1991). A nonstandard genetic algorithm for the nonlinear transportation problem. ORSA Journal on Computing, 3, 307–316.

    Google Scholar 

  • Moscato, P. and Tinetti, R. (1993). Blending heuristics with a population based approach.

  • Mühlenbein, H. (1993). Parallel genetic algorithms in combinatorial optimization. To appear in Computer Science and Operations Research, ed. Osman Balci. Pergamon Press, Oxford.

    Google Scholar 

  • Mühlenbein, H., Gorges-Schleuter, M. and Krämer, O. (1988). Evolution algorithms in combinatorial optimization. Parallel Computing, 7, 65–88.

    Google Scholar 

  • Nemhauser, G. and Wolsey, L. (1988). Linear and Combinatorial Optimization. John Wiley, New York.

    Google Scholar 

  • Parker, G. and Rardin, R. (1988). Discrete Optimization. Academic Press, New York.

    Google Scholar 

  • Reeves, C. (1993a). Modern Heuristic Techniques for Combinatorial Problems. Blackwell Scientific Publishing, Oxford.

    Google Scholar 

  • Reeves, C. (1993b). Diversity and diversification in genetic algorithms: some connections with tabu search. Coventry University, United Kingdom.

    Google Scholar 

  • Schrijver, A. (1986). Linear and Integer Programming. John Wiley, New York.

    Google Scholar 

  • Spears, W. M. and DeJong, K. A. (1991). On the virtues of uniform crossover. In 4th International Conference on Genetic Algorithms, La Jolla, CA.

  • Ulder, N. L. J., Pesch, E., van Laarhoven, P. J. M., Bandelt, H. J. and Aarts, E. H. L. (1991). Genetic local search algorithm for the traveling salesman problem. In Parallel Problem Solving from Nature, eds R. Maenner and H. P. Schwefel, pp. 109–116. Springer-Verlag, Berlin.

    Google Scholar 

  • de Werra, D. and Hertz, A. (1989). Tabu search technique: a tutorial and an applications to neural networks. OR Spectrum, 11, 131–141.

    CAS  PubMed  Google Scholar 

  • Whitley, D. (1993). Foundations of Genetic Algorithms 2. Morgan Kaufmann, San Mateo, CA.

    Google Scholar 

  • Wright, A. H. (1990). Genetic algorithms for real parameter optimization. In Foundations of Genetic Algorithms, ed. G. Rawlins, pp. 205–218. Morgan Kaufmann, Los Altos, CA.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Business, CB 419, University of Colorado, 80309, Boulder, CO, USA

    Fred Glover

Authors
  1. Fred Glover
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Glover, F. Genetic algorithms and scatter search: unsuspected potentials. Stat Comput 4, 131–140 (1994). https://doi.org/10.1007/BF00175357

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00175357

Keywords

Search

Navigation