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中文摘要：
为解决高维多目标优化问题中Pareto最优解集不能有效可视化这一难题，提出一种基于交互式决策的旋转基多目标可视化技术．首先利用基向量的旋转角度反映Pareto最优解中各目标的优劣程度；然后以绘制基点为初始位置，依次叠加旋转后的基向量；最终将Pareto最优解以一条独立路径映射为二维空间平面上的一条折线，得到旋转基可视化图形．基于此思想设计了高维多目标可视化模型并进行实验，结果表明，该技术有效地反映了Pareto最优解中各目标的性能、波动性以及综合性能优劣等属性情况，达到了方便决策者对Pareto最优解集进行分析和决策的目的．
英文摘要：
In order to solve the objective optimization problem problem that the Pareto optimal solutions of the high dimension multi- cannot be displayed effectively, this paper proposes a new visualization technique for high dimension multi-objective of rotation basis based on interactive decision making. Firstly, the quality of each objective in Pareto optimal solutions is reflected on the rotation angle of the basis vector. Secondly, the basis vector after rotation is stacked successively based on the basic point of the drawing as the initial position. Finally, the Pareto optimal solutions by an independent path are mapped to a polygonal line on the plane of two-dimensional space. Based on this idea mentioned above, the visualization model is designed. Experimental results show that this technique can effectively reflect many conditions, such as the performance of the Pareto optimal solutions, the fluctuation among the objectives and the quality of solutions. Meanwhile, the purpose that the decision-maker can conveniently analyze the Pareto optimal solutions and make decisions can be achieved.
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