2 Interactive Genetic Algorithms with Individual ’ s Uncertain Fitness

Interactive genetic algorithms (IGAs), proposed in mid 1980s, are effective methods to solve an optimization problem with implicit or fuzzy indices (Dawkins, 1986). These algorithms combine traditional evolution mechanism with a user’s intelligent evaluation, and the user assigns an individual’s fitness rather than a function that is difficult or even impossible to explicitly express. Up to now, they have been successfully applied in many fields, e.g. face identification (Caldwell & Johnston, 1991), fashion design (Kim & Cho, 2000), music composition (Tokui & Iba, 2000), hearing aid fitting (Takagi & Ohsaki, 2007). The obvious character of IGAs, compared with traditional genetic algorithms (TGAs), is that the user assigns an individual’s fitness. The user compares different individuals in the same generation and assigns fitness based on their phenotypes through a human-computer interface. The frequent interaction results in user fatigue. Therefore, IGAs often have small population size and a small number of evolutionary generations (Takagi, 2001), which influences these algorithms’ performance to some degree and restricts their applications in complicated optimization problems. Accordingly, how to evaluate an individual and express its fitness becomes one of the key problems in IGAs. Since user fatigue results from the user’s evaluation on an individual and expression of its fitness, in order to alleviate user fatigue, a possible alternative is to change the approach to express an individual’s fitness. The goal of this chapter is to alleviate user fatigue by adopting some appropriate approaches to express an individual’s fitness. An accurate number is a commonly used approach to express an individual’s fitness. As is well known, the user’s cognitive is uncertain and gradual, therefore the evaluation of an individual by the user and the expression of its fitness should also be uncertain and gradual. It is difficult to reflect the above character if we adopt an accurate number to express an individual’s fitness. We will present two kinds of uncertain numbers to express an individual’s fitness in this chapter, one is an interval described with the lower limit and the upper limit, the other is a fuzzy number described with a Gaussian membership function. These expressions of an individual’s uncertain fitness well accord with the user’s fuzzy cognitive on the evaluated object. In addition, we will propose some effective strategies to compare different individuals in the same generation on condition of an individual’s uncertain fitness. We will obtain the probability of an individual dominance by use of the probability of interval dominance, and O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg