分级指标排序与折衷指标排序研究

多指标排序是排序领域的重要研究方向，其中的分级指标排序与折衷指标排序是富有理论意义和应用价值的研究选题。分级指标排序问题要求找到一个排序首先使得主指标达到最优再使得次指标达到最优，并依次类推；而折衷指标排序问题则需要找到一些合理的排序使得代表多方利益的多个指标达到数值上的均衡。在经典的双指标排序模型中，有十多个问题的计算复杂性尚未解决；现代排序模型中又涌现出大量的具有很强的应用背景的多指标排序问题。本项目针对分级指标排序与折衷指标排序在经典机器环境下对单代理排序模型和多代理排序模型进行研究。本项目的目标是在分级指标排序与折衷指标排序的计算复杂性分类、算法设计和算法分析方面建立系统有效的研究方法，解决三至五个多指标排序中的历史遗留问题，并在其它多指标问题的研究中得到一系列富有创新性的研究成果。

Multi-criteria scheduling is an important research direction in the scheduling field, in which hierarchical criteria scheduling and tradeoff criteria scheduling are two research topics with theoretical significance and application value. A hierarchical criteria scheduling problem requires to find a schedule that first optimizes the primary criterion and then optimizes the secondary criterion, and so on; but a tradeoff criteria scheduling problem wants to obtain some reasonable schedules so that multi-criteria, which represent multiple interests, achieve numerical equilibrium. In the classical bi-criteria scheduling model, the computational complexity of more than ten problems has been open; and in the modern scheduling models, a large number of multi-criteria scheduling problems with strong application background emerge. For hierarchical criteria scheduling and tradeoff criteria scheduling, this project will take research under the classical machine environment for the single-agent scheduling model and the multi-agent scheduling model. The goal of this project is to establish systematic and effective research methods in the aspects of computational complexity classification, algorithm design, and algorithm analysis of hierarchical criteria scheduling and tradeoff criteria scheduling, solve three to five open problems in the field of multi-criteria scheduling, and obtain a series of innovative research results in the research for other multi-criteria scheduling problems.