GA optimized FRBS for travel systems

Abstract

This paper reports further on work presented at MODSIM09 (Ricketts 2009), which itself extended modeling of behavioural rules for activity scheduling in the transport domain as previously published (Olaru, Smith 2005). We again report on the use of genetic algorithms to tune a modified Mamdani fuzzy rule based system (FRBS), this time focusing on the optimization of the rule set composition. A Mamdani fuzzy knowledge base system is a fuzzy logic rule based system (FRBS) initially proposed by (Mamdani 1974) as a fuzzy logic controller. One uses a combination of fuzzification, fuzzy inference and defuzzification together with a knowledge base comprising database of fuzzy sets and a rule-base of fuzzy rules. This version substitutes fuzzy selection for defuzzification and, after training, outputs predicted travel schedule decisions given a coding of an individual's situation. The tuning of such a system is an open problem. To tune the system, two genetic algorithms were applied. One, the rule-base GA (rb-GA), taking the database as fixed, attempts to firstly maximize the classification rate and secondarily minimize the size of the rule base. The other, the fuzzy set GA (fs-GA) attempts to pre-tune the partitioning of the fuzzy sets for the rb-GA using an information entropy-like measure as a heuristic. The fs-GA was the focus of (Ricketts 2009), and hence the rb-GA is the focus of this report. The population consists of 100 chromosomes, each of which is of variable length of up to 100 genes. Each gene is a pair, representing an antecedent rule and a consequent. Crossover is an asymmetric single-point variable-length operator. Several mutation operators are defined, point mutation, delete, extend, inversion. Selection is elitist, using a ranking system. Maturation consists of the translation of a chromosome into a full FRBS, and fitness is the proportion of correct predictions, further weighted according to a minimal defining length criterion to first prefer accuracy and then compactness. The effect on the convergence, classification rates and rule-set compactness of four variations was investigated.