Interactive coordination of objective decompositions in multiobjective programming

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 smallersized 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.