Simple genetic algorithm (SGA) is a population-based optimization method based on the Darwinian natural selection. The theoretical foundations of SGA are the Schema Theorem and the Building Block Hypothesis. Although SGA does well in many applications as an optimization method, it still does not guarantee the convergence of a global optimum in GA-hard problems and deceptive problems. As an alternative schema, therefore, there is a growing interest in a co-evolutionary system where two populations constantly interact and cooperate each other. In this paper we propose a schema co-evolutionary algorithm (SCEA) and show why the SCEA works better than SGA in terms of an extended schema theorem. The experimental analyses using the Walsh-Schema Transform show that the SCEA works well in GA-hard problems including deceptive problems.

In this paper, we propose a self-nonself recognition algorithm based on positive and negative selection used in the developing process of T cells. The anomaly detection algorithm based on negative selection is a representative model among self-recognition method and it has been applied to computer immune systems in recent years. In biological immune systems, T cells are produced through both positive and negative selection. Positive selection is the process used to determine a MHC receptor that recognizes self-molecules. Negative selection is the process used to determine an antigen receptor that recognizes antigens, or nonself cells. In this paper, we propose a self-recognition algorithm based on the positive selection and also propose a fusion algorithm based on both positive and negative selection. To verify the effectiveness of the proposed system, we show simulation results for detecting some infected data obtained from cell changes and string changes in the self-file.

When we try to solve Multiobjective Optimization Problems (MOPs) using an evolutionary algorithm, the Pareto Genetic Algorithm (Pareto GA) introduced by Goldberg in 1989 has now become a sort of standard. After the first introduction, this approach was further developed and lead to many applications. All of these approaches are based on Pareto ranking and use the fitness sharing function to maintain diversity. On the other hand in the early 50's another scheme was presented by Nash. This approach introduced the notion of Nash Equilibrium and aimed at solving optimization problems having multiobjective functions that are originated from Game Theory and Economics. Since the concept of Nash Equilibrium as a solution of these problems was introduced, game theorists have attempted to formalize aspects of the equilibrium solution. The Nash Genetic Algorithm (Nash GA), which is introduced by Sefrioui, is the idea to bring together genetic algorithms and Nash strategy. The aim of this algorithm is to find the Nash Equilibrium of MOPs through the genetic process. Another central achievement of evolutionary game theory is the introduction of a method by which agents can play optimal strategies in the absence of rationality. Not the rationality but through the process of Darwinian selection, a population of agents can evolve to an Evolutionary Stable Strategy (ESS) introduced by Maynard Smith in 1982. In this paper, we propose Game theory based Co-Evolutionary Algorithm (GCEA) and try to find the ESS as a solution of MOPs. By applying newly designed co-evolutionary algorithm to several MOPs, the first we will confirm that evolutionary game can be embodied by co-evolutionary algorithm and this co-evolutionary algorithm can find ESSs as a solutions of MOPs. The second, we show optimization performance of GCEA by applying this model to several test MOPs and comparing with the solutions of previously introduced evolutionary optimization algorithms.