Understanding cooperative co-evolutionary dynamics via simple fitness landscapes

Abstract

Cooperative co-evolution is often used to solve difficult optimization problems by means of problem decomposition. Its performance for such tasks can vary widely from good to disappointing. One of the reasons for this is that attempts to improve co-evolutionary performance using traditional EC analysis techniques often fail to provide the necessary insights into the dynamics of co-evolutionary systems, a key factor affecting performance. In this paper we use two simple fitness landscapes to illustrate the importance of taking a dynamical systems approach to analyzing co-evolutionary algorithms in order to understand them better and to improve their problem solving performance.

The dynamics of the best individuals in co-evolution

“…Additionally, although this paper has focused on cooperative setups, our previous work (Popovici and De Jong, 2004;Popovici and De Jong, 2005b) showed that the methods described here can be used to gain insights into competitive co-evolution as well.…”

“…This technique was first introduced in (Popovici and De Jong, 2004) and has been improved since then. We have already successfully used it to gain insight into the way co-evolutionary algorithms work, both in competitive (Popovici and De Jong, 2005b) and cooperative setups (Popovici and De Jong, 2005a;Popovici and De Jong, 2005c). In this paper we describe this technique and use it to extend our previous results.…”

“…Others have used dynamical systems theory (Alligood et al, 1996) as their analysis tool (e.g., (Bucci and Pollack, 2002;Cliff and Miller, 1995;Ficici and Pollack, 1998)). Still others have focused more on understanding the differences between EC and CoEC dynamics (such as (Luke and Wiegand, 2003;Popovici and De Jong, 2005c;Pagie and Mitchell, 2002)). …”

Assessing Hierarchical Cooperative CoEvolution

“…This approach is in contrast to other works employing mathematical functions as a test-bed for the study of evolutionary approaches. Particularly for the case of coevolutionary algorithms, mathematical functions based on few independent variables are usually employed [17,13], decomposing the overall problem in few and very simple entities. However, this approach can not reveal the power of each algorithm and its capability to address difficult problems.…”

“…This is particularly the approach followed by coevolutionary algorithms which utilize separate populations to evolve partial entities of the problem [14,17]. In order to formulate a composite problem solution, individuals within different populations have to be selected, put together and operate in parallel [1,13]. Each population can use its own evolutionary parameters (e.g.…”