Data mining based on clustering and association rule analysis for knowledge discovery in multiobjective topology optimization

Abstract Optimum design problems, including structural optimization problems, often include multiple objectives. A multiobjective optimization problem usually provides a number of optimal solutions, called non-dominated solutions or Pareto-optimal solutions. In multiobjective topology optimization scenarios, decision makers face the challenging task of choosing the most effective solution that meets their needs; serial comparisons among a set of Pareto-optimal solution are cumbersome, as are trial-and-error attempts to find an appropriate solution among a host of alternatives. On the other hand, the recent integration of data mining techniques in multiobjective optimization methods can provide decision makers with important, highly pertinent, and useful knowledge. In this paper, we propose a data mining technique for knowledge discovery in multiobjective topology optimization. The proposed method sequentially applies clustering and association rule analysis to a Pareto-optimal solution set. First, clustering is applied in the design space and the result is then visualized in the objective space. After clustering, detailed features in each cluster are analyzed based on the concept of association rule analysis, so that characteristic substructures can be extracted from each cluster of solutions. In four numerical examples, we demonstrate that the proposed method provides pertinent knowledge that aids comprehension of the key substructures responsible for one or more desired performances, thereby giving decision makers a useful tool for discovery of particularly effective design solutions.