  Semantics in the context of Genetic Program (GP) can be understood as the
behaviour of a program given a set of inputs and has been well documented in
improving performance of GP for a range of diverse problems. There have been a
wide variety of different methods which have incorporated semantics into
single-objective GP. The study of semantics in Multi-objective (MO) GP,
however, has been limited and this paper aims at tackling this issue. More
specifically, we conduct a comparison of three different forms of semantics in
MOGP. One semantic-based method, (i) Semantic Similarity-based Crossover (SSC),
is borrowed from single-objective GP, where the method has consistently being
reported beneficial in evolutionary search. We also study two other methods,
dubbed (ii) Semantic-based Distance as an additional criteriOn (SDO) and (iii)
Pivot Similarity SDO. We empirically and consistently show how by naturally
handling semantic distance as an additional criterion to be optimised in MOGP
leads to better performance when compared to canonical methods and SSC. Both
semantic distance based approaches made use of a pivot, which is a reference
point from the sparsest region of the search space and it was found that
individuals which were both semantically similar and dissimilar to this pivot
were beneficial in promoting diversity. Moreover, we also show how the
semantics successfully promoted in single-objective optimisation does not
necessary lead to a better performance when adopted in MOGP.
