Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 745162, 12 pages
Research Article

Hybrid Method for a Class of Stochastic Bi-Criteria Optimization Problems

School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan, China

Received 24 June 2010; Accepted 20 October 2010

Academic Editor: Kok Teo

Copyright © 2010 Zhong Wan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study a class of stochastic bi-criteria optimization problems with one quadratic and one linear objective functions and some linear inequality constraints. A hybrid method of chance-constrained programming (CCP) combined with variance expectation (VE) is proposed to find the optimal solution of the original problem. By introducing the expectation level, the bi-criteria problem is converted into a single-objective problem. By introducing the confidence level and the preference level of decision maker, we obtain a relaxed robust deterministic formulation of the stochastic problem. Then, an interactive algorithm is developed to solve the obtained deterministic model with three parameters, reflecting the preferences of decision maker. Numerical experiments show that the proposed method is superior to the existing methods. The optimal solution obtained by our method has less violation of the constraints and reflects the satisfaction degree of decision-maker.