Co-Evolutionary Algorithm and Extended Schema Theorem

Evolutionary Algorithms (EAs) are population-based optimization methods based on the principle of Darwinian natural selection. The representative methodology in EAs is genetic algorithm (GA) proposed by J. H. Holland, and the theoretical foundations of GA are the Schema Theorem and the Building Block Hypothesis. In the meaning of these foundational concepts, simple genetic algorithm (SGA) allocate more trials to the schemata whose average fitness remains above average. Although SGA does well in many applications as an optimization method, still it does not guarantee the convergence of a global optimum in GA-hard problems and deceptive problems. Therefore as an alternative scheme, there is a growing interest in a co-evolutionary system, where two populations constantly interact and co-evolve in contrast with traditional single population evolutionary algorithm. In this paper we show why the co-evolutionary algorithm works better than SGA in terms of an extended schema theorem. And predator-prey co-evolution and symbiotic co-evolution, typical approaching methods to co-evolution, are reviewed, and dynamic fitness landscape associated with co-evolution is explained. And the experimental results show a co-evolutionary algorithm works well in optimization problems even though in deceptive functions.