Interactive Coordination of Objective Decompositions in Multiobjective Programming
针对多目标规划中目标过多的问题，将向量目标函数分解为子问题，并证明分解解与传统标量化解的关系；提出两种交互协调方法，通过求解小规模子问题并结合决策者偏好与灵敏度分析来找到原问题的任意解，适用于投资组合优化等场景。
To remedy challenges resulting from a high number of objectives in multiobjective programming and multicriteria decision making, this paper chooses to decompose the vector objective function and characterizes the relationships between solutions for the original problem and the collection of decomposed subproblems. In particular, it is shown how solutions that are found using this decomposition approach relate to solutions found by traditional scalarization techniques. For the selection of a final solution, two interactive coordination methods are proposed that allow to find any solution for the original problem by merely solving the smaller-sized subproblems, while integrating both preferences of the decision maker and trade-off information obtained from a sensitivity analysis. A theoretical foundation for the procedures is established, and their application is illustrated for portfolio optimization and a design selection problem.