Abstract
When mathematical optimization is applied to a multi-objective design problem, it is the common practice of decision support to generate Pareto optimal solutions as alternatives and clarify their trade-offs. The decision-maker selects any design solution according to his or her preferences. Although any comparison of alternatives is beneficial for its selection, in the case of combinatorial design problems, a simple comparison study cannot find the significant relationships between alternatives because of their discrete nature. This paper proposes a decision-making support method based on the dendrogram of hierarchical clustering. It is assumed that an optimal solution can be represented as a piling-up of smaller pieces, which correspond to building blocks, in the combinatorial solution space. The distance of alternatives is surveyed using schema representation defined at various levels. The structure of the solution space is reconstructed into a dendrogram through hierarchical clustering. When essential parts of schemas are identified as building blocks, they are organized into a tree-shaped graph. It is expected to help the designer's exploration of the solution space. The effectiveness of the proposed method is verified through two case studies: the global product family design problem and the permutation flowshop scheduling problem. Schemas are defined that consider the characteristics of the problems. The set of alternatives is systematized using a decision bifurcation diagram and the relationships between the building blocks identified are discussed.
