Genetically breeding populations of computer programs to solve problems in artificial intelligence

This paper describes the recently developed "genetic programming" paradigm which genetically breeds populations of computer programs to solve problems. In genetic programming, the individuals in the population are hierarchical computer programs of various sizes and shapes. Three applications to problems in artificial intelligence are presented. Introduction and Overview This paper describes the recently developed "genetic programming" paradigm which genetically breeds populations of computer programs to solve problems. In genetic programming, the individuals in the population are hierarchical compositions of functions and arguments of various sizes and shapes. Each of these individual computer programs is evaluated for its fitness in handling the problem environment and a simulated evolutionary process is driven by this measure of fitness. In this paper, the genetic programming paradigm is illustrated with three problems. The first problem involves genetically breeding a population of computer programs to allow an "artificial ant" to traverse an irregular trail. The second problem involves genetically breeding a minimax control strategy in a differential game with an independently-acting pursuer and evader. The third problem involves genetically breeding a minimax strategy for a player of a simple discrete two-person game represented by a game tree in extensive form. Background on Genetic Algorithms Genetic algorithms are highly parallel mathematical algorithms that transform populations of individual mathematical objects (typically fixed-length binary character strings) into new populations using operations patterned after (1) natural genetic operations such as sexual recombination (crossover) and (2) fitness proportionate reproduction (Darwinian survival of the fittest). Genetic algorithms begin with an initial population of individuals (typically randomly generated) and then iteratively (1) evaluate the individuals in the population for fitness with respect to the problem environment and (2) perform genetic operations on various individuals in the population to produce a new population. John Holland of the University of Michigan presented the pioneering formulation of genetic algorithms for fixed-length character strings in Adaptation in Natural and Artificial Systems (Holland 1975). Holland established, among other things, that the genetic algorithm is a mathematically near optimal approach to adaptation in that it maximizes expected overall average payoff when the adaptive process is viewed as a multi-armed slot machine problem requiring an optimal allocation of future trials given currently available information. Recent work in genetic algorithms and genetic classifier systems can be surveyed in Goldberg (1989), Davis (1987), and Schaffer (1989). Background on Genetic Programming Paradigm Representation is a key issue in genetic algorithm work because genetic algorithms directly manipulate the coded representation of the problem and because the representation scheme can severely limit the window by which the system observes its world. Fixed length character strings present difficulties for some problems — particularly problems in artificial intelligence where the desired solution is hierarchical and where the size and shape of the solution is unknown in advance. The need for more powerful representations has been recognized for some time (De Jong 1985, De Jong 1987, De Jong 1988). The structure of the individual mathematical objects that are manipulated by the genetic algorithm can be more complex than the fixed length character strings. Smith (1980) departed from the early fixed-length character strings by introducing variable length strings, including strings whose elements were if-then rules (rather than single characters). Holland's introduction of the classifier system (1986) continued the trend towards increasing the complexity of the structures undergoing adaptation. The classifier system is a cognitive architecture into which the genetic algorithm is embedded so as to allow adaptive modification of a population of string-based if-then rules (whose condition and action parts are fixed length binary strings). In addition, we have recently shown that entire com-