  The field of multiobjective evolutionary algorithms (MOEAs) often emphasizes
its popularity for optimization problems with conflicting objectives. However,
it is still theoretically unknown how MOEAs perform for different degrees of
conflict, even for no conflicts, compared with typical approaches outside this
field.
  As the first step to tackle this question, we propose the OneMaxMin$_k$
benchmark class with the degree of the conflict $k\in[0..n]$, a generalized
variant of COCZ and OneMinMax. Two typical non-MOEA approaches, scalarization
(weighted-sum approach) and $\epsilon$-constraint approach, are considered. We
prove that for any set of weights, the set of optima found by scalarization
approach cannot cover the full Pareto front. Although the set of the optima of
constrained problems constructed via $\epsilon$-constraint approach can cover
the full Pareto front, the general used ways (via exterior or nonparameter
penalty functions) to solve such constrained problems encountered difficulties.
The nonparameter penalty function way cannot construct the set of optima whose
function values are the Pareto front, and the exterior way helps (with expected
runtime of $O(n\ln n)$ for the randomized local search algorithm for reaching
any Pareto front point) but with careful settings of $\epsilon$ and $r$
($r>1/(\epsilon+1-\lceil \epsilon \rceil)$).
  In constrast, the generally analyzed MOEAs can efficiently solve
OneMaxMin$_k$ without above careful designs. We prove that (G)SEMO, MOEA/D,
NSGA-II, and SMS-EMOA can cover the full Pareto front in $O(\max\{k,1\}n\ln n)$
expected number of function evaluations, which is the same asymptotic runtime
as the exterior way in $\epsilon$-constraint approach with careful settings. As
a side result, our results also give the performance analysis of solving a
constrained problem via multiobjective way.
