Alternative Fitness Functions and Their Effect on the Evolution of Hierarchically-Related Individuals

The dynamics of genetic algorithms are often used to evolve a single individual that solves a particular problem. However, these same dynamics generally defeat attempts to evolve a cooperating set of individuals that jointly address a problem. This paper describes experiments performed on alternate tness functions that demonstrate the feasibility of evolving a set of hierarchically-related individuals, each addressing a different aspect of the posed problem. Of particular importance is the ability of the genetic algorithm to evolve these individuals with no a priori information on either the number of levels in the hierarchy or the number of individuals in the hierarchy. 1. When one answer is not enough Genetic algorithms used as optimizers evolve a population of individuals towards convergence at one individual that represents an answer to the posed problem [6, 2]. The theories about genetic algorithms clearly articulate that the dynamics of the genetic algorithm are well-suited to this task [6, 4]. Unfortunately, there are numerous situations when a single answer is undesirable. A biological example of this need for diversity is the human immune system. Our immune system is an excellent example of a system that is capable of evolving a dynamic set of individuals (antibodies) that cooperate to attain the goal of protecting the body. This work explores the question of evolving a cooperating set of individuals using a simpli ed immune system as the exploratory system. We begin with a description of Forrest et al.'s work on a genetic algorithm model of immune system components [3], which motivates our work. This section also de nes the particular problem being addressed in this work. Section 3 presents our genetic algorithm, including the speci cs of the tness functions used. Section 4 describes our preliminary results. The implications of these results are explored in Section 5. We conclude with a description of the further planned experiments. 2. Genetic algorithms and the immune system The job of the human immune system is to protect the body from foreign matter, called antigens. The immune system contains antibodies that recognize and bind to antigens. There are myriad complexities involved in creating and modifying antibodies to combat a particular invasion. Forrest et al. described two different aspects of the evolution demonstrated by the immune system [3]. Specifically, they rst explored how the immune system might evolve generalist antibodies, such as those that bind to bacteria. These antibodies bind to a small portion of the invading matter, but this part is common across a broad class of foreign substances. The immune system also includes a suite of antibodies that are speci c to a particular antigen. These specialist antibodies bind speci cally to one antigen and have only random similarities to others. The experimental environment consists of a given set of xed length antigens. Forrest et al. used separate tness functions to evolve successfully both specialist and generalist antibodies. They formulated the problem as a matching problem; the match score for an individual, candidate antibody, paired with a particular antigen is simply the number of complementary bit positions in the two individuals. For the generalist problem, the tness value for an individual was computed by selecting some subset of antigens and calculating the averagematch score for the individual across the selected set. For the specialist problem, a subset of individuals was selected from the population and one antigen was randomly chosen; the antibody individual with the highest match score against the chosen antigen received that match score as its tness value. The work of Forrest et al. raises the question of whether