The Cooperative Coevolutionary (1+1) EA

Abstract

Coevolutionary algorithms are a variant of evolutionary algorithms which are aimed for the solution of more complex tasks than traditional evolutionary algorithms.One example is a general cooperative coevolutionary framework for function optimization.A thorough and rigorous introductory research in which the optimization potential of cooperative coevolution is studied is presented. Using the cooperative coevolutionary framework as a startin point, the CC (1+1)EA is defined and investigated.The main interest is in the analysis of the expected optimization time.The research concentrates on separability since this is a key property of objective functions.It is shown that separability alone is not sufficient to yield any advantage of the CC (1+1)EA over its traditional,non-coevolutionary counterpart.Such an advantage is demonstrated to have one basis in the increased explorative possibilities of the cooperative coevolutionary algorithm.For inseparable functions,the cooperative coevolutionary set-up can be harmful.We prove that for some objective functions the CC (1+1)EA fails to locate a lobal optimum with probability converging to 1 exponentially fast,even in in finite time;however,inseparability alone is not sufficient for an objective function to cause difficulties.It is demonstrated that the CC (1+1)EA may perform equal to its traditional counterpart and even may outperform it on certain inseparable functions. When implementing the CC (1+1)the use of a parallel computer makes a big difference.For sequential and arallel implementationsdi ?erent variants of the algorithm are more natural.It is proved that both variants are equivalent for separable objective functions but can show very different performance on inseparable functions.The two variants are compared when applied to the approximation of a carefully designed example problem.