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 compared with typical approaches outside this field. This paper conducts such a systematic theoretical comparison on problem classes with different degrees of conflict. With OneMaxMin$_k$ depicting $k\in[0..n]$ degrees of conflict, we show the difficulties of two typical non-MOEA approaches, the scalarization (weighted-sum) and {the} $ε-$constraint approach. We prove that for any set of weights, the set of optima formed by {the} scalarization approach cannot cover its full Pareto front for $k>2$. Although constrained problems constructed from $ε-$constraint approach ensure the full coverage, general ways (via exterior or nonparameter penalty functions) to solve these constrained problems encounter difficulties. The nonparameter penalty function way cannot guarantee the full coverage, and the exterior way covers the Pareto front with expected $O(\max\{k,1\}n\ln n)$ number of function evaluations, but only with careful settings of $ε$ and $r$ ($r>1/(ε+1-\lceil ε\rceil)$). In contrast, MOEAs efficiently solve OneMaxMin$_k$ without careful designs. We prove the same expected runtime of $O(\max\{k,1\}n\ln n)$ for the (G)SEMO, MOEA/D, NSGA-II, and SMS-EMOA. Our brief discussions on a bi-objective LeadingOnes variant with different degrees of conflict show similar findings.

翻译：多目标进化算法（MOEAs）领域常强调其在具有冲突目标的优化问题中的广泛应用，然而，该领域外典型方法相较于MOEAs的理论性能差异仍属未知。本文针对具有不同冲突程度的问题类别展开系统性理论比较。通过定义描述$k\in[0..n]$冲突程度的OneMaxMin$_k$问题，我们揭示了两类典型非MOEA方法——标量化（加权求和）法与$\varepsilon$约束法的局限性。证明表明：对任意权重集合，标量化法形成的最优解集在$k>2$时无法覆盖完整帕累托前沿；尽管基于$\varepsilon$约束法构建的约束问题可保证全覆盖，但通过外部惩罚函数或无需参数惩罚函数求解此类约束问题均存在困难——无需参数惩罚函数法无法保证全覆盖，而外部法虽能以期望$O(\max\{k,1\}n\ln n)$次函数评估覆盖帕累托前沿，却需精心设置$\varepsilon$与$r$参数（满足$r>1/(\varepsilon+1-\lceil\varepsilon\rceil)$）。相比之下，MOEAs无需精细设计即可高效求解OneMaxMin$_k$问题：我们证明(G)SEMO、MOEA/D、NSGA-II与SMS-EMOA均具有相同的期望运行时间$O(\max\{k,1\}n\ln n)$。对具有不同冲突程度的双目标LeadingOnes变体问题的简要讨论揭示了类似发现。