Stochastic Multi-Objective Optimization (SMOO) is critical for decision-making trading off multiple potentially conflicting objectives in uncertain environments. SMOO aims at identifying the Pareto frontier, which contains all mutually non-dominating decisions. The problem is highly intractable due to the embedded probabilistic inference, such as computing the marginal, posterior probabilities, or expectations. Existing methods, such as scalarization, sample average approximation, and evolutionary algorithms, either offer arbitrarily loose approximations or may incur prohibitive computational costs. We propose XOR-SMOO, a novel algorithm that with probability $1-δ$, obtains $γ$-approximate Pareto frontiers ($γ>1$) for SMOO by querying an SAT oracle poly-log times in $γ$ and $δ$. A $γ$-approximate Pareto frontier is only below the true frontier by a fixed, multiplicative factor $γ$. Thus, XOR-SMOO solves highly intractable SMOO problems (\#P-hard) with only queries to SAT oracles while obtaining tight, constant factor approximation guarantees. Experiments on real-world road network strengthening and supply chain design problems demonstrate that XOR-SMOO outperforms several baselines in identifying Pareto frontiers that have higher objective values, better coverage of the optimal solutions, and the solutions found are more evenly distributed. Overall, XOR-SMOO significantly enhanced the practicality and reliability of SMOO solvers.

翻译：随机多目标优化（SMOO）对于在不确定环境中权衡多个潜在冲突目标的决策至关重要。SMOO 旨在识别包含所有互不支配决策的帕累托前沿。由于嵌入的概率推理（如计算边际概率、后验概率或期望），该问题高度棘手。现有方法，如标量化、样本均值近似和进化算法，要么提供任意宽松的近似，要么可能产生过高的计算成本。我们提出 XOR-SMOO，一种新颖算法，通过查询 SAT 甲骨文（次数在 $γ$ 和 $δ$ 的多对数范围内），能以概率 $1-δ$ 获得 SMOO 的 $γ$ 近似帕累托前沿（$γ>1$）。$γ$ 近似帕累托前沿仅以固定的乘法因子 $γ$ 低于真实前沿。因此，XOR-SMOO 在仅查询 SAT 甲骨文的条件下，解决了高度棘手的 SMOO 问题（#P 困难），同时获得紧致的常数因子近似保证。在真实世界的道路网络加固和供应链设计问题上的实验表明，XOR-SMOO 在识别具有更高目标值、更优最优解覆盖度且解分布更均匀的帕累托前沿方面，优于多个基线方法。总体而言，XOR-SMOO 显著增强了 SMOO 求解器的实用性和可靠性。