Semantic-based Distance Approaches in Multi-objective Genetic Programming

Semantics in the context of Genetic Program (GP) can be understood as the\nbehaviour of a program given a set of inputs and has been well documented in\nimproving performance of GP for a range of diverse problems. There have been a\nwide variety of different methods which have incorporated semantics into\nsingle-objective GP. The study of semantics in Multi-objective (MO) GP,\nhowever, has been limited and this paper aims at tackling this issue. More\nspecifically, we conduct a comparison of three different forms of semantics in\nMOGP. One semantic-based method, (i) Semantic Similarity-based Crossover (SSC),\nis borrowed from single-objective GP, where the method has consistently being\nreported beneficial in evolutionary search. We also study two other methods,\ndubbed (ii) Semantic-based Distance as an additional criteriOn (SDO) and (iii)\nPivot Similarity SDO. We empirically and consistently show how by naturally\nhandling semantic distance as an additional criterion to be optimised in MOGP\nleads to better performance when compared to canonical methods and SSC. Both\nsemantic distance based approaches made use of a pivot, which is a reference\npoint from the sparsest region of the search space and it was found that\nindividuals which were both semantically similar and dissimilar to this pivot\nwere beneficial in promoting diversity. Moreover, we also show how the\nsemantics successfully promoted in single-objective optimisation does not\nnecessary lead to a better performance when adopted in MOGP.\n