AI 中文总结
针对态势与维持分配（PSA）问题，提出CEV优化器及RobustCEV扩展，在印太基地环境实验中验证其相比贪心基线、朴素优化器可显著提升对抗不确定性下的态势效率。
AI 中文摘要
预承诺态势是指在冲突场景解决前将军事资产分配至战区地点的过程，是联合作战规划中关键且尚未得到形式化解决的问题。当前实践依赖贪心启发式算法，该算法仅最大化价值而忽略地理覆盖，且在结构上易受针对高战略价值地点的对手攻击。本文针对态势与维持分配（PSA）问题，提出了一种场景加权的对抗鲁棒态势优化引擎，将其建模为关于资产、战区地点和时间步的有限马尔可夫决策过程。我们引入了复合期望值（CEV）优化器，该优化器通过在威胁场景分布上最大化场景加权的期望态势效率来部署资产；还引入了RobustCEV扩展，其会针对贝叶斯对手进行迭代，该对手会根据观察到的部署更新其目标分布。在印太地区基地环境下开展的三项实验中，实验设置为20项资产和5个战区地点，我们证明：（1）贪心基线因地理覆盖不足导致态势效率永久损失25.1%，在价值相关的对抗威胁下，场景加权战备度崩溃达57.3%；（2）当威胁分布带有地理信号时，CEV优化器相比贪心方法最多可恢复19.8%的效率，且5至20个精心挑选的场景足以捕捉大部分增益；（3）当自适应对手采用欺骗性威胁先验时，RobustCEV扩展相比朴素优化器最多可恢复158%的效率。所有发现均通过配对t检验（采用Bonferroni校正）和两级方差分解验证，证实报告的性能差距是部署策略的结构属性，而非采样假象。
英文摘要
Pre-commitment posture, the assignment of military assets to theater locations before conflict scenarios resolve, is a critical and formally unsolved problem in joint operational planning. Current practice relies on greedy heuristics that maximize value and ignore geographic coverage and are structurally vulnerable to adversaries that target high-strategic value locations. This paper presents a scenario-weighted adversarially robust posture optimization engine for the Posture and sustainability allocation (PSA) problem, modeled as a finite-horizon Markov Decision Process over assets, theater locations, and time steps. We introduce the Composite Expected Value (CEV) optimizer, which places assets by maximizing scenario-weighted expected posture efficiency over a distribution of threat scenarios, and the RobustCEV extension, which iterates against a Bayesian adversary that updates its targeting distribution in response to observed placement. Across three experiments in an Indo-Pacific basing environment with 20 assets and 5 theater locations, we demonstrate that: (1) the greedy baseline incurs a permanent 25.1% posture efficiency penalty due to geographic under-coverage and a 57.3% scenario-weighted readiness collapse under value-correlated adversarial threat; (2) the CEV optimizer recovers up to 19.8% efficiency over greedy when the threat distribution carries a geographic signal, with a curated set of 5 to 20 scenarios sufficient to capture the majority of this gain; and (3) the RobustCEV extension recovers up to 158% efficiency relative to a naive optimizer when an adaptive adversary employs a deceptive threat prior. All findings are validated using paired t-tests with Bonferroni correction and two-level variance decomposition, confirming that the performance gaps reported are structural properties of placement strategies rather than sampling artifacts.
