Application of dendrogram-directed design space exploration to bi-objective permutation flow-shop scheduling problem

Abstract

In this study, we propose a method for structurally understanding the differences and similarities among the alternatives of a bi-objective permutation scheduling problem. Although metaheuristics-based optimization technique can exploit Pareto-optimal solutions, it is still difficult for decision-makers to identify the preferred solution among them. In scheduling problems, a distinctive category of combinatorial optimization problems, situations frequently arise in which objective function values are similar despite having different combinatorial structures. Effective decision-making requires a method that focuses on the internal information of the alternatives rather than a simple comparison study of the objective functions. This study applies the dendrogram-directed design space exploration technique to a permutation flow-shop scheduling problem by arranging its modeling scheme. The technique systematically organizes the structure of alternatives and systematizes their features into a tree-shaped graph to provide decision-makers with valuable insights. Clarifying the leverage points of the combinatorial problem with a graph reduces the cognitive burden on decision-makers. As the dendrogram systematically bifurcates the alternatives, the exclusive OR of a pair of clusters indicates their characteristics and differences. A model using the design structure matrix is proposed to abstract the characteristics of alternatives for scheduling problems, and a method for classifying and structuring the analysis of alternatives using it is proposed. Decision-makers can explore the characteristics of leverage points by referring to their position in the objective function space. The proposed technique is demonstrated by applying it to a simple benchmark problem.