An Objective Penalty Functions Algorithm for Multiobjective Optimization Problem

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DOI: 10.4236/ajor.2011.14026   PDF   HTML     4,325 Downloads   8,561 Views   Citations

Abstract

By using the penalty function method with objective parameters, the paper presents an interactive algorithm to solve the inequality constrained multi-objective programming (MP). The MP is transformed into a single objective optimal problem (SOOP) with inequality constrains; and it is proved that, under some conditions, an optimal solution to SOOP is a Pareto efficient solution to MP. Then, an interactive algorithm of MP is designed accordingly. Numerical examples show that the algorithm can find a satisfactory solution to MP with objective weight value adjusted by decision maker.

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Z. Meng, R. Shen and M. Jiang, "An Objective Penalty Functions Algorithm for Multiobjective Optimization Problem," American Journal of Operations Research, Vol. 1 No. 4, 2011, pp. 229-235. doi: 10.4236/ajor.2011.14026.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] R. Benayoun, J. de Montgoler, J. Tergny and O. Larichev, “Linear Programming with Multiple Objective Functions: Stem Method (STEM),” Mathematical Programming, Vol. 1, No. 3, 1971, pp. 355-375. doi:10.1007/BF01584098
[2] A. M. Geoffrion, J. S. Dyer and A. Feinberg, “An Interactive Approach for Multi-Criterion Optimization, with an Application to the Operation of an Academic Department,” Management Science, Vol. 19, No. 4, 1972, pp. 457-368. doi:10.1287/mnsc.19.4.357
[3] S. Zionts and J. Wallenius, “An Interactive Programming Method for Solving the Multiple Criteria Problem,” Management Science, Vol. 22, No. 6, 1976, pp. 652-663. doi:10.1287/mnsc.22.6.652
[4] E. E. Rosinger, “Interactive Algorithm for Multiobjective Optimization,” Journal of Optimization Theory and Applications, Vol. 35, No. 3, 1981, pp. 339-365. doi:10.1007/BF00934907
[5] S. Zionts and J. Wallenius, “An Interactive Multiple for a Class of Underlying Nonlinear Utility Functions,” Management Science, Vol. 29, No. 5, 1983, pp. 519-529. doi:10.1287/mnsc.29.5.519
[6] S. Sadagopan and A. Ravinderan, “An Interactive Algorithm for Multiple Citeria Nonlinear Programming Problems,” European Journal of Operational Research, Vol. 25, No. 2, 1986, pp. 247-257. doi:10.1016/0377-2217(86)90089-5
[7] S. Helbig, “An Interactive Algorithm for Nonlinear Vector Optimization,” Applied Mathematics and Optimization, Vol. 22, No. 1, 1990, pp. 147-151. doi:10.1007/BF01447324
[8] M. Abd El-Hady Kassem, “Interactive Stability of Multiobjective Nonlinear Programming Problems with Fuzzy Parameters in the Constraints,” Fuzzy Sets and Systems, Vol. 73, No. 2, 1995, pp. 235-243. doi:10.1016/0165-0114(94)00317-Z
[9] B. Aghezzaf and T. Ouaderhman, “An Interactive Interior Point Algorithm for Multiobjective Linear Programming Problems,” Operations Research Letters, Vol. 29, No. 4, 2001, pp. 163-170. doi:10.1016/S0167-6377(01)00089-X
[10] M. A. Abo-Sinna and T. H. M. Abou-El-Enien, “An Interactive Algorithm for Large Scale Multiple Objective Programming Problems with Fuzzy Parameters through TOPSIS Approach,” Applied Mathematics and Computation, Vol. 177, 2006, pp. 515-527. doi:10.1016/j.amc.2005.11.030
[11] M. Luque, F. Ruiz and R. E. Steuer, “Modified Interactive Chebyshev Algorithm (MICA) for Convex Multiobjective Programming,” European Journal of Operational Research, Vol. 204, No. 3, 2010, pp. 557-564. doi:10.1016/j.ejor.2009.11.011
[12] Z. Q. Meng, Q. Y. Hu and C. Y. Dang. “A Penalty Function Algorithm with Objective Parameters for Nonlinear Mathematical Programming,” Journal of Industrial and Management Optimization, Vol. 5, No. 3, 2009, pp. 585- 601. doi:10.3934/jimo.2009.5.585
[13] F. H. Clarke, “Optimization and Nonsmooth Analysis,” John-Wiley & Sons, New York, 1983.

  
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