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A new approach for uncertain multiobjective programming problem based on $\mathcal{P}_{E}$ principle
1. | Materiel Management and Safety Engineering College, Air Force Engineering University, Xi'an, 710051, China, China |
2. | School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, China |
3. | Department of Mathematics, Xijing College, Xi'an, 710236, China |
References:
[1] |
A. Arturo, A. Graham and G. Stuart, Multi-objective planning of distributed energy resources: A review of the state-of-the-art, Renewable and Sustainable Energy Reviews, 14 (2010), 1353-1366. |
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C. Anthony, K. Juyoung, L. Seungjae and K. Youngchan, Stochastic multi-objective models for network design problem, Expert Systems with Applications, 37 (2010), 1608-1619. |
[3] |
Y. Bai and C. Guo, Doubly nonnegative relaxation method for solving multiple objective quadratic programming problems, Journal of Industrial and Management Optimization, 10 (2014), 543-556.
doi: 10.3934/jimo.2014.10.543. |
[4] |
C. Chen, T. C. Edwin Cheng, S. Li and X. Yang, Nonlinear augmented Lagrangian for nonconvex multiobjective optimization, Journal of Industrial and Management Optimization, 7 (2011), 157-174.
doi: 10.3934/jimo.2011.7.157. |
[5] |
C. M. Fonseca and P. J. Fleming, Genetic algorithms for multiobjective optimization: Formulation,discussion,and generalization, The Fifth International Conference on Genetic Algorithms, (1993), 416-423. |
[6] |
M. Kaisa, Nonlinear Multi-objective Optimization, Kluwer Academic Publishers, 1999. |
[7] |
B. Liu, Uncertainty Theory, $2^{nd}$ edition, Springer-Verlag, 2007. |
[8] |
B. Liu, Some research problems in uncertainty theory, Journal of Uncertain System, 3 (2009), 3-10. |
[9] |
B. Liu, Theory and Practice of Uncertain Programming, Springer-Verlag, 2009.
doi: 10.1007/978-3-540-89484-1. |
[10] |
B. Liu, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, An introduction to its axiomatic foundations. Studies in Fuzziness and Soft Computing, 154. Springer-Verlag, Berlin, 2004.
doi: 10.1007/978-3-540-39987-2. |
[11] |
B. Liu, Uncertainty Theory, $4^{th}$ edition, http://orsc.edu.cn/liu/ut.pdf, 2012. |
[12] |
B. Liu, Why is there a need for uncertainty theory?, Journal of Uncertain System, 5 (2012), 3-20. |
[13] |
B. Liu and X. W. Chen, Uncertain Multiobjective Programming and Uncertain Goal Programming, Technical report, Uncertainty Theory Laboratory, 2012. |
[14] |
C. Rafael, C. Emilio, M. M. Maria del and R. Lourdes, Stochastic approach versus multi-objective approach for obtaining efficient solutions in stochastic multi-objective programming problems, European Journal of Operational Research, 158 (2004), 633-648.
doi: 10.1016/S0377-2217(03)00371-0. |
[15] |
Jr. J. Teghem and P. L. Kunsch, Application of multi-objective stochastic linear programming to power systems planning, Engineering Costs and Production Economics, 9 (1985), 83-89.
doi: 10.1016/0167-188X(85)90013-8. |
show all references
References:
[1] |
A. Arturo, A. Graham and G. Stuart, Multi-objective planning of distributed energy resources: A review of the state-of-the-art, Renewable and Sustainable Energy Reviews, 14 (2010), 1353-1366. |
[2] |
C. Anthony, K. Juyoung, L. Seungjae and K. Youngchan, Stochastic multi-objective models for network design problem, Expert Systems with Applications, 37 (2010), 1608-1619. |
[3] |
Y. Bai and C. Guo, Doubly nonnegative relaxation method for solving multiple objective quadratic programming problems, Journal of Industrial and Management Optimization, 10 (2014), 543-556.
doi: 10.3934/jimo.2014.10.543. |
[4] |
C. Chen, T. C. Edwin Cheng, S. Li and X. Yang, Nonlinear augmented Lagrangian for nonconvex multiobjective optimization, Journal of Industrial and Management Optimization, 7 (2011), 157-174.
doi: 10.3934/jimo.2011.7.157. |
[5] |
C. M. Fonseca and P. J. Fleming, Genetic algorithms for multiobjective optimization: Formulation,discussion,and generalization, The Fifth International Conference on Genetic Algorithms, (1993), 416-423. |
[6] |
M. Kaisa, Nonlinear Multi-objective Optimization, Kluwer Academic Publishers, 1999. |
[7] |
B. Liu, Uncertainty Theory, $2^{nd}$ edition, Springer-Verlag, 2007. |
[8] |
B. Liu, Some research problems in uncertainty theory, Journal of Uncertain System, 3 (2009), 3-10. |
[9] |
B. Liu, Theory and Practice of Uncertain Programming, Springer-Verlag, 2009.
doi: 10.1007/978-3-540-89484-1. |
[10] |
B. Liu, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, An introduction to its axiomatic foundations. Studies in Fuzziness and Soft Computing, 154. Springer-Verlag, Berlin, 2004.
doi: 10.1007/978-3-540-39987-2. |
[11] |
B. Liu, Uncertainty Theory, $4^{th}$ edition, http://orsc.edu.cn/liu/ut.pdf, 2012. |
[12] |
B. Liu, Why is there a need for uncertainty theory?, Journal of Uncertain System, 5 (2012), 3-20. |
[13] |
B. Liu and X. W. Chen, Uncertain Multiobjective Programming and Uncertain Goal Programming, Technical report, Uncertainty Theory Laboratory, 2012. |
[14] |
C. Rafael, C. Emilio, M. M. Maria del and R. Lourdes, Stochastic approach versus multi-objective approach for obtaining efficient solutions in stochastic multi-objective programming problems, European Journal of Operational Research, 158 (2004), 633-648.
doi: 10.1016/S0377-2217(03)00371-0. |
[15] |
Jr. J. Teghem and P. L. Kunsch, Application of multi-objective stochastic linear programming to power systems planning, Engineering Costs and Production Economics, 9 (1985), 83-89.
doi: 10.1016/0167-188X(85)90013-8. |
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