Simple changes in problem formulations make a difference in multiobjective genetic fuzzy systems

Recently evolutionary multiobjective optimization (EMO) algorithms have been frequently used for the design of fuzzy rule-based systems. Such a study is often referred to as multiobjective genetic fuzzy systems (MoGFS). Whereas a large number of interesting results on MoGFS have already been reported in the literature, the search ability of EMO algorithms in MoGFS is not necessarily high because fuzzy system design is formulated as large-scale combinatorial optimization problems with many decision variables. In this paper, we show that simple changes in problem formulations of MoGFS often lead to large differences in obtained non-dominated fuzzy rule-based systems. Our idea for improving the search ability of EMO algorithms is to use multiple weighted sums with different weight vectors instead of original objectives. This idea is applicable not only to MoGFS but also to SoGFS (single-objective genetic fuzzy systems). When our idea is used in SoGFS, a two-objective problem is formulated as a weighted sum of an additional term with a small weight and the original objective. We examine the effectiveness of our idea through computational experiments on classification problems. It is clearly shown that simple changes in multiobjective problems in MoGFS often lead to large accuracy improvement.