  The decomposition-based multi-objective evolutionary algorithm (MOEA/D) does
not directly optimize a given multi-objective function $f$, but instead
optimizes $N + 1$ single-objective subproblems of $f$ in a co-evolutionary
manner. It maintains an archive of all non-dominated solutions found and
outputs it as approximation to the Pareto front. Once the MOEA/D found all
optima of the subproblems (the $g$-optima), it may still miss Pareto optima of
$f$. The algorithm is then tasked to find the remaining Pareto optima directly
by mutating the $g$-optima.
  In this work, we analyze for the first time how the MOEA/D with only standard
mutation operators computes the whole Pareto front of the OneMinMax benchmark
when the $g$-optima are a strict subset of the Pareto front. For standard bit
mutation, we prove an expected runtime of $O(n N \log n + n^{n/(2N)} N \log n)$
function evaluations. Especially for the second, more interesting phase when
the algorithm start with all $g$-optima, we prove an $\Omega(n^{(1/2)(n/N + 1)}
\sqrt{N} 2^{-n/N})$ expected runtime. This runtime is super-polynomial if $N =
o(n)$, since this leaves large gaps between the $g$-optima, which require
costly mutations to cover.
  For power-law mutation with exponent $\beta \in (1, 2)$, we prove an expected
runtime of $O\left(n N \log n + n^{\beta} \log n\right)$ function evaluations.
The $O\left(n^{\beta} \log n\right)$ term stems from the second phase of
starting with all $g$-optima, and it is independent of the number of
subproblems $N$. This leads to a huge speedup compared to the lower bound for
standard bit mutation. In general, our overall bound for power-law suggests
that the MOEA/D performs best for $N = O(n^{\beta - 1})$, resulting in an
$O(n^\beta \log n)$ bound. In contrast to standard bit mutation, smaller values
of $N$ are better for power-law mutation, as it is capable of easily creating
missing solutions.
