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

Zutong Wang; Jiansheng Guo; Mingfa Zheng; Youshe Yang

doi:10.3934/jimo.2015.11.13

Article Contents

2015, Volume 11, Issue 1: 13-26. Doi: 10.3934/jimo.2015.11.13

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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
2.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049
3.
Department of Mathematics, Xijing College, Xi'an, 710236

Received: April 30, 2013

Revised: October 31, 2013

Published: December 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 90C29; Secondary: 90B50.

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References

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