多目标规划问题的棱锥有效解

Polyhedral-Cone Efficient Solution in Multi-objective Programming

对于多目标规划问题,本文通过引进一类新的凸锥——棱锥,建立了棱锥有效解的概念.在决策者根据隐含的效用函数给出区间偏爱信息的基础上,本文构建了相应的棱锥对应于偏爱信息的2个参数——偏爱信息强度和偏爱信息方向.其次,进一步讨论了多目标规划问题中的决策者区间偏爱信息和棱锥有效解集之间的关系.最后,给出数值例子说明这种区间偏爱信息、棱锥和棱锥有效解集之间的关系.

This paper introduces a class of convex cones,named polyhedral cone,and corresponding concept of polyhedral-cone efficient solution to multi-objective programming problems.Based on the interval preference information to an underlying utility function presented by decision maker,a coordinated convex cone with two parameters,preference information intensity and preference information direction is constructed.Further discussion about the relationship between the set of polyhedral-cone efficient solutions and the interval preference information with respect to multi-objective programming problems is also elaborated.Finally,numerical examples to illustrate the relationship among interval preference information,polyhedral cones and the set of polyhedral-cone efficient solutions are provided.