An Incremental and Non-generational Coevolutionary Algorithm

Abstract

The central idea of coevolution lies in the fact that the fitness of an individual depends on its performance against the current individuals of the opponent population. However, coevolution has been shown to have problems [2,5]. Methods and techniques have been proposed to compensate the flaws in the general concept of coevolution [2]. In this article we propose a different approach to implementing coevolution, called incremental coevolutionary algorithm (ICA) in which some of these problems are solved by design. In ICA, the importance of the coexistance of individuals in the same population is as important as the individuals in the opponent population. This is similar to the problem faced by learning classifier systems (LCSs) [1,4]. We take ideas from these algorithms and put them into ICA. In a coevolutionary algorithm, the fitness landscape depends on the opponent population, therefore it changes every generation. The individuals selected for reproduction are those more promising to perform better against the fitness landscape represented by the opponent population. However, if the complete population of parasites and hosts are recreated in every generation, the offspring of each new generation face a fitness landscape unlike the one they where bred to defeat. Clearly, a generational approach to coevolution can be too disruptive. Since the fitness landscape changes every generation, it also makes sense to incrementally adjust the fitness of individuals in each one. These two ideas define the main approach of the ICA: the use of a non-generational genetic algorithm and the incremental adjustment of the fitness estimation of an individual. The formal definition of ICA can be seen in figure 1. ICA has some interesting properties. First of all, it is not generational. Each new individual faces a similar fitness landscape than its parents. The fitness landscape changes gradually, allowing an arms race to occur. Since opponents are chosen proportional to their fitness, an individual has a greater chance of facing good opponents. If a particular strength is found in a population, individuals that have it will propagate and will have a greater probability of coming into competition (both because more individuals carry the strength, and because a