A genetic based algorithm for the quadratic 0-1 problem

G. Schütz *

F. M. Pires †

* Escola Superior de Tecnologia, Universidade do Algarve

gschutz@ualg.pt

† Faculdade de Ciências e Tecnologia, Universidade do Algarve

mpires@ualg.pt

Abstract

In this work we present an algorithm to the unrestricted binary quadratic program. This approach combines genetic operators with greedy and heuristic procedures. We started from a genetic based algorithm and replaced the random mutation by a greedy procedure based on each variable contribution to the objective function. We also introduced in the genetic population an individual obtained by a heuristic that finds a local star minimum point. Computational experience with a set of test-problems, known from literature, is reported and analysed. Our results are quite promising.

Keywords: Quadratic 0-1 programming, Genetic Algorithms, Hybrid Algorithms

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References

1. Alidaee, B., G. Kochenberger and A. Ahmadian (1994), "0-1 quadratic programming approach for the optimal solution of two scheduling problems", Int. J. Systems Sci., 25, pp. 401-408.         [ Links ]

2. Gallo, G.; P. L. Hammer; B. Simeone (1980), "Quadratic knapsack problems", Math. Prog., 12, pp. 132-149.         [ Links ]

3. Garey M. R.; S. Johnson (1979), "Computers and Intractability: A Guide to the Theory of NP-Completeness", Freeman, S. Francisco.         [ Links ]

4. Glover, F.: G. A. Kochenberger; B. Alidaee (1998), "Adaptative memory tabu search for binary quadratic programs", Manag. Sci., 44, pp. 336-345.         [ Links ]

5. Glover, F.: G. A. Kochenberger; B. Alidaee; M. Amini (1999), "Tabu search with critical event memory: an enhanced application for binary quadratic programs" in Meta-Heuristics Advances and Trends in Local Search Paradigms for Optimization, S. Voss, S. Martello, I. H. Osman and C. Roucairol (eds).         [ Links ]

6. Gulati, V. P., Gupta, S.K., Mittal, A.K. (1984), "Unconstrained quadratic bivalent programming problem", European Journal of Operational Research, 15, pp.121-125.         [ Links ]

7. Krarup, J.; P. A. Pruzan (1978), "Computer aided layout design", Math. Prog. Study, 9, pp. 75-94.         [ Links ]

8. Lodi, A., Allemand, K., Liebling, T.M. (1999), "An evolutionary heuristic for quadratic 0-1 programming", European Journal of Operational Research, 119, pp. 662-670.         [ Links ]

9. McBride, R. D.; J. S. Yomark (1980), "An implicit enumeration algorithm for quadratic integer programming", Manag. Sci., 26, pp. 282-296.         [ Links ]

10. Pardalos, P. , G. Rodgers (1990), "Computational aspects of a branch and bound algorithm for quadratic 0-1 programming", Computing, 45, pp. 131-144.        [ Links ]

11. Pardalos, P., G. Rodgers (1992), "A branch and bound algorithm for the maximum clique problem", Comp. and Ops. Res., 19, pp. 363-375.         [ Links ]