American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Stochastic maximum principle for non-zero sum differential games of FBSDEs with impulse controls and its application to finance
  • JIMO Home
  • This Issue
  • Next Article
    The optimal price discount, order quantity and minimum quantity in newsvendor model with group purchase
January  2015, 11(1): 13-26. doi: 10.3934/jimo.2015.11.13

A new approach for uncertain multiobjective programming problem based on $\mathcal{P}_{E}$ principle

Zutong Wang 1, , Jiansheng Guo 1, , Mingfa Zheng 2, and  Youshe Yang 3,

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

Received  May 2013 Revised  November 2013 Published  May 2014

On the basis of the uncertainty theory, this paper is devoted to the uncertain multiobjective programming problem. Firstly, several principles are provided to define the relationship between uncertain variables. Then a new approach is proposed for obtaining Pareto efficient solutions in uncertain multiobjective programming problem based on $\mathcal{P}_{E}$ principle, which involves transforming the uncertain multiobjective problem into a problem with only one uncertain objective function, and its validity has been proved. Due to the complexity of this problem, it is very suitable for the use of genetic algorithm. Finally, a numerical example is presented to illustrate the novel approach proposed, and the genetic algorithm is adopted to solve it.
Keywords: Uncertain programming, genetic algorithms., multiobjective programming, uncertainty theory.
Mathematics Subject Classification: Primary: 90C29; Secondary: 90B5.
Citation: Zutong Wang, Jiansheng Guo, Mingfa Zheng, Youshe Yang. A new approach for uncertain multiobjective programming problem based on $\mathcal{P}_{E}$ principle. Journal of Industrial & Management Optimization, 2015, 11 (1) : 13-26. doi: 10.3934/jimo.2015.11.13
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.   Google Scholar

[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.   Google Scholar

[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.  doi: 10.3934/jimo.2014.10.543.  Google Scholar

[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.  doi: 10.3934/jimo.2011.7.157.  Google Scholar

[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.   Google Scholar

[6]

M. Kaisa, Nonlinear Multi-objective Optimization,, Kluwer Academic Publishers, (1999).   Google Scholar

[7]

B. Liu, Uncertainty Theory,, $2^{nd}$ edition, (2007).   Google Scholar

[8]

B. Liu, Some research problems in uncertainty theory,, Journal of Uncertain System, 3 (2009), 3.   Google Scholar

[9]

B. Liu, Theory and Practice of Uncertain Programming,, Springer-Verlag, (2009).  doi: 10.1007/978-3-540-89484-1.  Google Scholar

[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, (2004).  doi: 10.1007/978-3-540-39987-2.  Google Scholar

[11]

B. Liu, Uncertainty Theory,, $4^{th}$ edition, (2012).   Google Scholar

[12]

B. Liu, Why is there a need for uncertainty theory?,, Journal of Uncertain System, 5 (2012), 3.   Google Scholar

[13]

B. Liu and X. W. Chen, Uncertain Multiobjective Programming and Uncertain Goal Programming,, Technical report, (2012).   Google Scholar

[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.  doi: 10.1016/S0377-2217(03)00371-0.  Google Scholar

[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.  doi: 10.1016/0167-188X(85)90013-8.  Google Scholar

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.   Google Scholar

[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.   Google Scholar

[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.  doi: 10.3934/jimo.2014.10.543.  Google Scholar

[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.  doi: 10.3934/jimo.2011.7.157.  Google Scholar

[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.   Google Scholar

[6]

M. Kaisa, Nonlinear Multi-objective Optimization,, Kluwer Academic Publishers, (1999).   Google Scholar

[7]

B. Liu, Uncertainty Theory,, $2^{nd}$ edition, (2007).   Google Scholar

[8]

B. Liu, Some research problems in uncertainty theory,, Journal of Uncertain System, 3 (2009), 3.   Google Scholar

[9]

B. Liu, Theory and Practice of Uncertain Programming,, Springer-Verlag, (2009).  doi: 10.1007/978-3-540-89484-1.  Google Scholar

[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, (2004).  doi: 10.1007/978-3-540-39987-2.  Google Scholar

[11]

B. Liu, Uncertainty Theory,, $4^{th}$ edition, (2012).   Google Scholar

[12]

B. Liu, Why is there a need for uncertainty theory?,, Journal of Uncertain System, 5 (2012), 3.   Google Scholar

[13]

B. Liu and X. W. Chen, Uncertain Multiobjective Programming and Uncertain Goal Programming,, Technical report, (2012).   Google Scholar

[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.  doi: 10.1016/S0377-2217(03)00371-0.  Google Scholar

[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.  doi: 10.1016/0167-188X(85)90013-8.  Google Scholar

[1]

Ardeshir Ahmadi, Hamed Davari-Ardakani. A multistage stochastic programming framework for cardinality constrained portfolio optimization. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 359-377. doi: 10.3934/naco.2017023
[2]

Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399
[3]

Cicely K. Macnamara, Mark A. J. Chaplain. Spatio-temporal models of synthetic genetic oscillators. Mathematical Biosciences & Engineering, 2017, 14 (1) : 249-262. doi: 10.3934/mbe.2017016
[4]

Tao Wu, Yu Lei, Jiao Shi, Maoguo Gong. An evolutionary multiobjective method for low-rank and sparse matrix decomposition. Big Data & Information Analytics, 2017, 2 (1) : 23-37. doi: 10.3934/bdia.2017006
[5]

Xu Zhang, Xiang Li. Modeling and identification of dynamical system with Genetic Regulation in batch fermentation of glycerol. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 393-403. doi: 10.3934/naco.2015.5.393
[6]

Habib Ammari, Josselin Garnier, Vincent Jugnon. Detection, reconstruction, and characterization algorithms from noisy data in multistatic wave imaging. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 389-417. doi: 10.3934/dcdss.2015.8.389
[7]

Rabiaa Ouahabi, Nasr-Eddine Hamri. Design of new scheme adaptive generalized hybrid projective synchronization for two different chaotic systems with uncertain parameters. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2361-2370. doi: 10.3934/dcdsb.2020182
[8]

Guillaume Bal, Wenjia Jing. Homogenization and corrector theory for linear transport in random media. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1311-1343. doi: 10.3934/dcds.2010.28.1311
[9]

Felix Finster, Jürg Fröhlich, Marco Oppio, Claudio F. Paganini. Causal fermion systems and the ETH approach to quantum theory. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1717-1746. doi: 10.3934/dcdss.2020451
[10]

Vieri Benci, Sunra Mosconi, Marco Squassina. Preface: Recent progresses in the theory of nonlinear nonlocal problems. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : i-i. doi: 10.3934/dcdss.2020446
[11]

Namsu Ahn, Soochan Kim. Optimal and heuristic algorithms for the multi-objective vehicle routing problem with drones for military surveillance operations. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021037
[12]

W. Cary Huffman. On the theory of $\mathbb{F}_q$-linear $\mathbb{F}_{q^t}$-codes. Advances in Mathematics of Communications, 2013, 7 (3) : 349-378. doi: 10.3934/amc.2013.7.349
[13]

John Leventides, Costas Poulios, Georgios Alkis Tsiatsios, Maria Livada, Stavros Tsipras, Konstantinos Lefcaditis, Panagiota Sargenti, Aleka Sargenti. Systems theory and analysis of the implementation of non pharmaceutical policies for the mitigation of the COVID-19 pandemic. Journal of Dynamics & Games, 2021  doi: 10.3934/jdg.2021004

2019 Impact Factor: 1.366

Tools

Metrics

  • PDF downloads (88)
  • HTML views (0)
  • Cited by (8)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences