摘要
传统单目标二层规划模型得到的最优解往往无法使上下级双方都满意.为此,通过在上层规划中同时考虑下级的目标函数,建立了原问题的上层为双目标规划的一个新模型.上下级可通过协商在该模型的Pareto-最优解集中找到双方满意解.对此模型设计了求解的多目标进化算法,用传统优化算法求解下层规划的单目标问题,而对上层的双目标规划问题则采用基于NSGA-Ⅱ的多目标进化算法求解.数值试验表明我们所提出的算法是有效的.
In the classical single-objective bi-level programming problems, the final optimal solutions are always non-satisfactory to the decision makers in both upper and lower levels. To improve such situations, a new model with two objectives in the upper level is presented through taking into account the objective in the lower level in the same time. A multi-objective evolutionary algorithm for the bi-objective bi-level programming problems is presented. The single objective programming in the lower level is solved with traditional optimization algorithms, while a multi-objective evolutionary algorithm based on NSGAⅡ is used to solve the bi-objective programming problem in the upper level. The performance of the proposed algorithm is illustrated using a numerical example in the published literature.
出处
《系统工程理论与实践》
EI
CSCD
北大核心
2006年第5期106-110,共5页
Systems Engineering-Theory & Practice
基金
国家自然科学基金(70301005)
教育部南开-天津大学刘徽应用数学中心资助项目
