Kill-web absorption resilience depends on whether directed mission paths remain available after disruption. This study addresses how to allocate a limited fortification budget to mission-function nodes so that an adaptive interdictor must incur the greatest possible cost to disconnect all valid mission paths. We formulate Mission-Path Cut Fortification ( MPCF), which maximizes the post-fortification minimum node-cut cost. Node-capacity splitting converts the interdiction response for a fixed fortification set into an equivalent maximum-flow minimum-cut problem. A compact mixed-integer linear program provides the primary exact solution, and an independent cut-generation formulation cross-checks the optimum in cut space. Across 135 graph-budget pairs from 45 prespecified synthetic networks, the mean optimality gaps of MPCF-Greedy and PathFrequency are 2.76% and 9.50%, respectively. Across 810 combinations under six role-composition profiles, the two exact formulations obtain identical objective values; MPCF-Greedy has a mean gap of 1.98%, whereas the best non-MPCF method under each profile has a mean gap of 8.11%–10.12%. Exact optimization also agrees with exhaustive enumeration on 72 small fortification instances and 72 capacity-interdiction instances, and cut-space verification agrees on 30 public-network instances. These results show that mission-path fortification benefits from joint optimization of the protected node set and the adaptive minimum-cut response.

Resilience optimization in adversarial Multi-Agent Mission Systems (MAMSs) requires a decision mechanism whose objective is explicitly aligned with the resilience metric, not merely resilience measurement. This paper proposes a net-effectiveness-based evaluation–optimization framework for bilateral temporal adversarial operational-loop networks (BTAR), turning resilience evaluation into a reusable world model and reward source for decision-making. We model bilateral confrontation as a heterogeneous temporal network and quantify resilience through the integral of net effectiveness, which captures temporal and adversarial dynamics beyond static topological indicators. We then formulate resilience enhancement as a fixed-dimensional, size-agnostic, cost-aware Markov decision process and solve it with a hierarchically decoupled reinforcement learning architecture: an upper-level PPO policy learns when and for which chains to trigger selective replanning, while a lower-level greedy routine selects concrete replacement nodes. In this way, the optimization objective remains aligned with the evaluation metric through a metric-aligned reward. Experiments on a reproducible multi-scale, multi-style scenario pool show that the learned policy improves $R_{\mathrm{total}}$ from $0.3673$ to $1.1696$, reaching $96.8\%$ of an idealized oracle benchmark ($1.2082$), while slightly outperforming the always-replan rule ($1.1482$) with a lower trigger rate. Under nonzero replanning cost, retraining yields a cost-aware policy whose trigger rate drops to $21.2\%$ and whose cost-adjusted resilience at the target cost setting increases by $+0.15$, surpassing the greedy oracle benchmark in the high-cost regime. These results show that coupling net-effectiveness evaluation with hierarchical RL yields a deployable, size-agnostic, and cost-aware resilience optimizer.

Maintaining end-to-end connectivity under disruption is a central problem in systems resilience. This study examines how limited protection resources can increase the minimum node-removal cost required to disconnect a specified service. Mission-Path Cut Fortification (MPCF) models a directed service as a functional graph and treats protection as a finite increase in node-removal cost. Node splitting yields a compact mixed-integer linear program, and an independent cut-generation formulation verifies its optimal value. On 45 synthetic graphs, mean minimum-cut values are 33.62 for MPCF-Exact and MPCF-CG, 32.30 for MPCF-Greedy, 30.41 for PathFrequency, and 27.38 without fortification. Graph-level analyses treat budgets as repeated measurements, and a 90-graph extension reproduces the paired effects for the nine designated methods. Further experiments assess heterogeneous fortification costs and effectiveness. Scaling to 1000 nodes identifies the computational limits of both exact formulations through stopping times and optimality bounds. Ten source–sink cases from public transport and telecommunications networks demonstrate applicability to empirical path topologies. Partial-capacity analysis shows that complete-disconnection and residual-capacity criteria can favor different fortification sets. The findings support joint node-set selection for resistance to complete disconnection and show that the service criterion should be specified before resources are allocated.