Relative Fitness and Absolute Fitness for Co-evolutionary Systems

The commonly adopted fitness which evaluates the performance of individuals in co-evolutionary systems is the relative fitness. The relative fitness measure is a dynamic assessment subject to co-evolving population(s). Researchers apparently pay little attention to the use of absolute fitness functions in studying co-evolutionary algorithms. The first aim of this work is to define both the relative fitness and the absolute fitness for co-evolving systems. Another aim is to demonstrate the usage of the absolute and relative fitness through two case studies. One is for the Iterated Prisoners' Dilemma. Another case is for solving the Basic Alternating-Offers Bargaining Problem, for which a co-evolutionary system has been developed by means of Genetic Programming. Experiments using the relative fitness function have discovered co-adapted strategies that converge to nearly game-theoretic solutions. This finding suggests that the relative fitness essentially drives co-evolution to perfect equilibrium. On the other hand, the absolute fitness measuring co-evolving populations monitors the development of co-adaptation. Having analyzed the micro-behavior of the players' strategies based on their absolute fitness, we can explain how co-evolving populations stabilize at the perfect equilibrium.