Functional Dependency and Degeneracy: Detailed Analysis of the GAuGE System

This paper explores the mapping process of the GAuGE system, a recently introduced position-independent genetic algorithm, that encodes both the positions and the values of individuals at the genotypic level. A mathematical formalisation of its mapping process is presented, and is used to characterise the functional dependency feature of the system. An analysis of the effect of degeneracy in this functional dependency is then performed, and a mathematical theorem is given, showing that the introduction of degeneracy reduces the position specification bias of individuals. Experimental results are given, that backup these findings.