Linearization of multi-objective multi-quadratic 0-1 programming problems

  • Abstract
  • Keywords
  • References
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  • Abstract

    A linearization technique is developed for multi-objective multi-quadratic 0-1 programming problems with linear and quadratic constraints to reduce it to multi-objective linear mixed 0-1 programming problems. The method proposed in this paper needs only O (kn) additional continuous variables where k is the number of quadratic constraints and n is the number of initial 0-1 variables.

    Keywords: Knapsack Constraint, Linearization, Multi-Objective, Multi-Quadratic, Optimal Solution.

  • References

    1. C.A. Floudas and V. Visweswaran, Quadratic optimization, in: R. Horst, P.M. Paradalos (Eds.), Handbook of Global Optimization, Kluwer Academic Publishers, Dordrecht, 1995, 217-269.
    2. C.T. Chang and C.C. Chang, A linearization method for mixed 0-1 polynomial programs, Computers and Operations Research 27 (2000) 1005-1016.
    3. F. Glover and E. Woolsey, Further reduction of 0-1 polynomial programs to 0-1 linear programming, Operations Research, 21 (1) (1973) 156-161.
    4. F. Glover and E. Woolsey, Converting the 0-1 polynomial programming program, Operations Research, 22(1) (1974) 180-182.
    5. L. J. Watters, Reduction of integer polynomial programming to 0-1 linear programming problems, Operations Research 15 (1967) 1171-1174.
    6. P.M. Pardalos, L.D. Iasemidis, D.S. Shiau et al, Quadratic binary programming and dynamic system approach to determine the predictability of epileptic seizures, Journal of Combinatorial Optimization 5 (1) (2001) 9-26.
    7. P.M. Pardalos, L.D. Iasemidis, D.S. Shiau et al, Prediction of human epileptic seizures based on optimization and phase changes of brain electrical activity, Optimization Methods and Software 18 (1) (2003) 81-104.
    8. P.M. Pardalos, W. Chaovalitwongse, O.A. Prokopyev, A new linearization technique for multi-quadratic 0-1 programming problems, Operations Research Letters 32 (2004) 517-522.
    9. P.M. Pardalos, W. Chaovalitwongse, L.D. Iasemidis et al, Seizure warning algorithm based on optimization and nonlinear dynamics, Mathematical Programming Ser. B 101 (2004) 365-385.
    10. R. Kapoor and S.R. Arora, Linearization of 0-1 multi-quadratic fractional programming problem, Asia Pacific Journal of Operational Research 26(1) (2009) 59-84.
    11. S. Acharya and M.P. Biswal, Linearization technique for multi-choice quadratic Programming Problem, International Journal of Optimization, Theory, Methods and Applications, 3(1) (2011) 45-62.
    12. W.P. Adams and H.D. Sherali, Linearization strategies for a class of 0-1 mixed integer programming problems, Operations Research 38 (2) (1990) 217-226.
    13. X. He, A. Chen and W. Chaovalitwongse et al, An improved linearization technique for a class of quadratic 0-1 programming problems, Optimization Letters 6(1) (2012) 31-41.




Article ID: 1924
DOI: 10.14419/ijams.v2i2.1924

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