Boolean query optimization and the 0-1 hyperbolic sum problem

  • Pierre Hansen
  • Marcus V. Poggi de Aragão
  • Celso C. Ribeiro


An “intelligent front-end” or “logic assistant” is an interactive program devised to assist the users of an information retrieval system in the formulation of their queries. In order to provide knowledge usable in such a program, we study a problem of query optimization with an average efficiency criterion. We formulate it as a new combinatorial optimization problem, which we call 0-1 hyperbolic sum, and provide an exact branch-and-bound algorithm and two heuristics (of simulated annealing and tabu search type) to solve it. Computational experience illustrating the effectiveness of the tabu search technique is reported.


Hyperbolic programming fractional programming 0-1 variables combinatorial optimization databases query optimization heuristics simulated annealing SAMD algorithm tabu search 


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  1. [1]
    E. Aarts and J. Korst,Simulated Annealing and Boltzmann Machines (Wiley, 1989).Google Scholar
  2. [2]
    R.E. Burkard and F. Rendl, A thermodynamically motivated simulation procedure for combinatorial optimization problems, Europ. J. Oper. Res. 17 (1984) 169–174.CrossRefzbMATHGoogle Scholar
  3. [3]
    V. Cerny, A thermodynamical approach to the Traveling Salesman problem: An efficient simulation algorithm, J. Optimization Theory Appl. 45 (1985) 41–51.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    A. El Baamrani, Analyse the deux méthodes heuristiques: méthode de “recuit” et méthode de “plus grande descente-plus petite remontée”, B. Sc. Essay, Faculté Universitaire Catholique de Mons (supervised by P. Hansen) (1985).Google Scholar
  5. [5]
    F. Glover, Future paths for integer programming and links with artificial intelligence, Comput. Oper. Res. 13 (1986) 533–549.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    F. Glover, Tabu search methods in artificial intelligence and operations research, ORSA Artificial Intell. Newsletter 1 (1987) 2–6.Google Scholar
  7. [7]
    F. Glover, Tabu search — Part I, ORSA J. Comput. 1 (1989) 190–206.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    F. Glover, Tabu search — Part II, ORSA J. Comput. 2 (1990) 4–32.CrossRefzbMATHGoogle Scholar
  9. [9]
    F. Glover and H.J. Greenberg, New approaches for heuristic search: A bilateral linkage with artificial intelligence, Europ. J. Oper. Res. 39 (1989) 119–130.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    P. Hansen, The steepest-ascent-mildest-descent heuristic for combinatorial programming, presentation at theConf. on Numerical Methods in Combinatorial Optimization, Capri, Italy (1986).Google Scholar
  11. [11]
    P. Hansen and B. Jaumard, Algorithms for the maximum satisfiability problem, Computing 44 (1990), in press.Google Scholar
  12. [12]
    P. Hansen, M.V. Poggi de Aragão and C.C. Ribeiro, Hyperbolic 0-1 programming and query optimization in information retrieval, to appear in Math. Programming Series B (1991).Google Scholar
  13. [13]
    M.H. Heine, A simple intelligent front-end for information retrieval systems using Boolean logic, Inform. Technol. 2 (1982) 247–260.Google Scholar
  14. [14]
    M.H. Heine, Information retrieval from classical databases from a signal detection stand point: A review, Inform. Technol. 3 (1984) 95–112.Google Scholar
  15. [15]
    M.H. Heine, Automatic optimization of search logic, contribution to theRound Table Workshop on Techniques for Access to Information and its Re-Use, Luxemburg (1986).Google Scholar
  16. [16]
    M.H. Heine, A logic assistant for the database researcher, Inform. Proc. Management 24 (1988) 323–329.CrossRefGoogle Scholar
  17. [17]
    A. Hertz and D. de Werra, The tabu search metaheuristic — How we used it, Ann. Math. AI 1 (1990) 111–121.zbMATHGoogle Scholar
  18. [18]
    S. Kirkpatrick, C.D. Gelatt and M.P. Vecchi, Optimization by simulated annealing, Science 220 (1983) 671–674.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    M.V. Poggi de Aragão,Programação hiperbólica em variáveis 0-1 e otimização de consultas a bancos de dados bibliográficos, M. Sc. Dissertation, Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil (1988).Google Scholar
  20. [20]
    M. Queyranne, private communication (1987).Google Scholar
  21. [21]
    G. Salton, A simple blueprint for automatic Boolean query processing, Inform. Proc. Management 24 (1988) 269–280.CrossRefGoogle Scholar
  22. [22]
    D. Stephany, Localisation de postes en fonction du trafic interpostes, B. Sc. Essay, Faculté Universitaire Catholique de Mons (supervised by P. Hansen) (1986).Google Scholar
  23. [23]
    C.J. Van Rijsbergen, Foundation of evaluation, J. Documentation 30 (1974) 365–373.CrossRefGoogle Scholar

Copyright information

© J.C. Baltzer A.G. Scientific Publishing Company 1990

Authors and Affiliations

  • Pierre Hansen
    • 1
  • Marcus V. Poggi de Aragão
    • 2
    • 4
  • Celso C. Ribeiro
    • 3
  1. 1.RUTCORRutgers UniversityNew BrunswickUSA
  2. 2.Ecole PolytechniqueMontréalCanada
  3. 3.Catholic University of Rio de JaneiroRio de JaneiroBrazil
  4. 4.CASNAV-Centro de Análise de Sistemas NavaisRio de JaneiroBrazil

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