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Báo cáo hóa học: " Research Article Hybrid Method for a Class of Stochastic Bi-Criteria Optimization Problems"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Hybrid Method for a Class of Stochastic Bi-Criteria Optimization Problems | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 745162 12 pages doi 10.1155 2010 745162 Research Article Hybrid Method for a Class of Stochastic Bi-Criteria Optimization Problems Zhong Wan AiYun Hao FuZheng Meng and Chaoming Hu School of Mathematical Sciences and Computing Technology Central South University Changsha Hunan China Correspondence should be addressed to Zhong Wan wanmath@163.com 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 decisionmaker. 1. Introduction In many fields of industrial engineering and management sciences there often exist some uncertainties such as the return rate of security and the amounts of demand and supply. Recently many attentions have been paid to construct optimization models with uncertain .