Representation Development from Pareto-Coevolution

Abstract

Abstract. Genetic algorithms generally use a fixed problem representation that maps variables of the search space to variables of the problem, and operators of variation that are fixed over time. This limits their scalability on non-separable problems. To address this issue, methods have been proposed that coevolve explicitly represented modules. An open question is how modules in such coevolutionary setups should be evaluated. Recently, Pareto-coevolution has provided a theoretical basis for evaluation in coevolution. We define a notion of functional modularity, and objectives for module evaluation based on Pareto-Coevolution. It is shown that optimization of these objectives maximizes functional modularity. The resulting evaluation method is developed into an algorithm for variable length, open ended development of representations called DevRep. DevRep successfully identifies large partial solutions and greatly outperforms fixed length and variable length genetic algorithms on several test problems, including the 1024-bit Hierarchical-XOR problem.

Assessing Hierarchical Cooperative CoEvolution

“…[1,8,14]). This is also the case with Pareto coevolutionary approaches [2,5,6,9] which mainly aim at balancing between different criteria in multi-objective optimization problems. The issue of collaborator selection is very important, especially when investigating large systems consisting of many components.…”

“…This higher level search can be implemented by means of one more evolutionary process [2,15]. The process of simultaneous evolution of partial components and assemblies of components, can be organized hierarchically, formulating a multiple level scheme consisting of gradually more complex assemblies.…”

“…In contrast to [4], our approach is capable of coevolving larger assemblies of cooperating species, while at the same time, emphasizes the independence of substructures utilizing multiple and potentially separate criteria to guide partial evolutionary processes. Other approaches on hierarchical problem solving investigate the design of system components sharing the same set of objectives, and thus, they can not address effectively distributed systems consisting of heterogeneous substructures [16,3,2]. Additionally, they don't utilize specialized subpopulations that have been proved to facilitate significantly the evolutionary process [8].…”

Coevolving Antibodies with a Rich Representation of Grammatical Evolution

“…The standard genetic algorithm makes it unlikely that mutually exclusive partial solutions will persist as no mechanism for protecting mutually exclusive partial solutions is present [8]. Algorithms focusing on modularity report scalability for certain classes of problems with regularities [7,8,17,18] and describe under what circumstances modularity may or may not be beneficial [19].…”

“…Instead, a co-evolving interpreter may exploit information or features in the genome in a number of ways. Indeed, a central issue in evolutionary computing is the adaptive identification and recombination of meaningful features and a number of relevant past studies have used coevolution [7,8,18] or artificial immune systems [36,38] to address modularity and feature detection in evolutionary algorithms.…”