基于几何投影的多目标优化降维方法  

Dimensionality reduction based on geometric projection for manyobjective optimization

作　　者：苏远平[1] 徐立鸿[1] 

机构地区：[1]同济大学电子与信息工程学院,上海201804

出　　处：《控制与决策》2013年第8期1173-1177,1189,共6页Control and Decision

基　　金：国家863计划项目(2012AA10A507);国家自然科学基金项目(61174090)

摘　　要：实际优化问题中可能包含很多目标,这些目标并不都是相互冲突的,有些目标是相互冗余的,因此实际的Pareto前沿面的维数比目标空间的维数要少.为了提高进化算法的效率,减少计算量,提出一种基于几何投影的方法米实现多目标优化问题的降维.首先通过辨别Pareto前沿在二维坐标面上的投影形状,寻找投影区的边界曲线;然后根据投影区的面积和边界曲线的单调性来计算目标之问的冲突度.数值仿真表明了该方法的有效性.There can be a large number of objectives in a certain optimization problem, but not all objectives are necessarily in conflict with each other, while some objectives are redundant. The true dimensionality of the Pareto front is less than the original number of objectives. Such redundant objectives can be removed from the set of objectives without loss of the structure of the Pareto front to improve computation and convergence. An approach based on geometric projection is proposed for dimensionality reduction. In this approach, the Pareto front can be mapped to a 2-dimensional coordinate plane which consists of the two arbitrary objectives in the original set of objectives, and the borderline can be identified. The conflict degree between the two objectives can be calculated by calculating the area of the projection and analyzing the monotonicity of the borderline curve. Simulation results show the effectiveness of the approach.

关 键 词：降维 几何投影 冗余目标 冲突度 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]