Genetic-Algorithm-Based Approaches to Classification Problems

In this chapter, we explain how multi-objective genetic algorithms can be applied to the design of fuzzy rule-based systems for pattern classification problems. For a multi-class pattern classification problem with many continuous attributes (e.g., wine classification with 13 continuous attributes [1]), a fuzzy rule-based classification system is designed by a multi-objective genetic algorithm [2, 3] with two objectives: to minimize the size of the fuzzy rule-based classification system and to maximize its performance [4, 5]. The size of the fuzzy rule-based classification system is expressed by the number of fuzzy if-then rules, and its performance is measured by the number of correctly classified training patterns. In our approach to the design of the fuzzy rule-based classification system, first a large number of fuzzy if-then rules are generated from training patterns as candidate rules for the rule selection. Then a small number of fuzzy if-then rules are selected from the candidate rules by the two-objective genetic algorithm. The two-objective genetic algorithm tries to find all the non-dominated solutions (i.e., non-dominated rule sets) of the rule selection problem with the above-mentioned objectives. One difficulty of the rule selection method for high-dimensional pattern classification problems with many continuous attributes is that the number of candidate fuzzy if-then rules becomes intractably large. For example, the number of candidate rules is 613 ≅ 1.3 × 1010 for the wine classification problem with 13 continuous attributes if we have six fuzzy sets (terms) on each axis of the 13-dimensional pattern space.