  We contribute to the efficient approximation of the Pareto-set for the
classical $\mathcal{NP}$-hard multi-objective minimum spanning tree problem
(moMST) adopting evolutionary computation. More precisely, by building upon
preliminary work, we analyse the neighborhood structure of Pareto-optimal
spanning trees and design several highly biased sub-graph-based mutation
operators founded on the gained insights. In a nutshell, these operators
replace (un)connected sub-trees of candidate solutions with locally optimal
sub-trees. The latter (biased) step is realized by applying Kruskal's
single-objective MST algorithm to a weighted sum scalarization of a sub-graph.
  We prove runtime complexity results for the introduced operators and
investigate the desirable Pareto-beneficial property. This property states that
mutants cannot be dominated by their parent. Moreover, we perform an extensive
experimental benchmark study to showcase the operator's practical suitability.
Our results confirm that the sub-graph based operators beat baseline algorithms
from the literature even with severely restricted computational budget in terms
of function evaluations on four different classes of complete graphs with
different shapes of the Pareto-front.
