  For solving combinatorial optimisation problems with metaheuristics,
different search operators are applied for sampling new solutions in the
neighbourhood of a given solution. It is important to understand the
relationship between operators for various purposes, e.g., adaptively deciding
when to use which operator to find optimal solutions efficiently. However, it
is difficult to theoretically analyse this relationship, especially in the
complex solution space of combinatorial optimisation problems. In this paper,
we propose to empirically analyse the relationship between operators in terms
of the correlation between their local optima and develop a measure for
quantifying their relationship. The comprehensive analyses on a wide range of
capacitated vehicle routing problem benchmark instances show that there is a
consistent pattern in the correlation between commonly used operators. Based on
this newly proposed local optima correlation metric, we propose a novel
approach for adaptively selecting among the operators during the search
process. The core intention is to improve search efficiency by preventing
wasting computational resources on exploring neighbourhoods where the local
optima have already been reached. Experiments on randomly generated instances
and commonly used benchmark datasets are conducted. Results show that the
proposed approach outperforms commonly used adaptive operator selection
methods.
