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IR-GraphSec: A Formal and Scalable Framework for Automated Incident Response Orchestration Based on Attack Graphs and Multiobjective Optimization
TITLE: IR-GraphSec: A Formal and Scalable Framework for Automated Incident Response Orchestration Based on Attack Graphs and Multiobjective Optimization ABSTRACT: The increasing sophistication of multi-stage cyber campaigns, combined with the expansion of hybrid, cloud-native, and AI-driven environments, imposes substantial challenges on Incident Response (IR) orchestration. Although normative frameworks such as NIST SP 800-61 Rev. 2 and the NIST Cybersecurity Framework establish consolidated guidelines, the efficient operationalization of containment remains limited by complex topological dependencies, availability constraints, and multiple conflicting objectives. In this work, we formalize the response orchestration problem as a multiobjective optimization over dynamic attack graphs enriched with automatic mapping to MITRE ATT&CK and near-real-time telemetry originating from CNAPP, EDR, and eBPF environments. We define an objective function that integrates residual risk, operational cost, and availability impact, subject to budgetary and business continuity constraints. We demonstrate that the associated decision problem is NP-hard through polynomial reduction to variants of the minimum cut problem with additional constraints. We propose the IR-GraphSec framework, implemented with Neo4j, Apache Kafka, and OR-Tools, capable of processing large-scale event streams and generating optimized containment plans via mixed-integer programming and branch-and-bound heuristics. We empirically evaluate the system on a distributed cluster with 4.8 million real and synthetic events, including simulations with MITRE Caldera. Results indicate an average reduction of 63.4% in Mean Time to Containment (MTTC), a 38.9% decrease in residual risk, and an estimated financial impact 41.9% lower compared to static SOAR playbooks. Statistical analysis confirms significance with $p < 0{,}01$. We discuss limitations related to telemetry quality and explore extensions involving robust reinforcement learning, AI system security, and integration with post-quantum cryptography. We conclude that graph-oriented formal modeling constitutes a promising approach for adaptive and scalable IR orchestration in 2025.
- Introduction
Incident Response constitutes an essential component of modern cybersecurity governance, as established in NIST SP 800-61 Rev. 2 (SCARFONE; MELL, 2012) and the NIST Cybersecurity Framework (NIST, 2018). In 2025, the operational landscape is characterized by hybrid infrastructures, massive adoption of cloud services, microservices-oriented architectures, CNAPP (Cloud-Native Application Protection Platforms), and the growing integration of systems based on machine learning and large language models (LLMs). This complexity expands the attack surface and intensifies the need for containment decisions grounded in formal and quantitative criteria.
Recent reports indicate that the average time to identify and contain breaches remains above 200 days in large organizations, with a global average cost exceeding US$ 4.45 million per incident (IBM, 2023). The Verizon Data Breach Investigations Report highlights the prevalence of multistage chains involving initial exploitation, lateral movement, and exfiltration (VERIZON, 2023). Such campaigns frequently combine techniques from MITRE ATT&CK (MITRE, 2023a), such as T1190, T1059, T1021, and T1547, forming interdependent adversarial trajectories in complex graphs.
The central problem lies in the optimal prioritization of containment actions under uncertainty, simultaneously considering residual risk, operational cost, and availability impact. Static playbooks implemented in SOAR platforms (PALO ALTO NETWORKS, 2023; SPLUNK, 2023) do not adequately capture dynamic topological dependencies nor explicitly solve combinatorial optimization problems.
We formulate the following research questions:
RQ1: How can the IR process be formally modeled while capturing structural dependencies among assets, vulnerabilities, and adversarial techniques?
RQ2: Is it possible to automatically derive optimal response plans under multi-objective criteria involving risk, cost, and availability?
RQ3: What is the quantitative impact of this approach on reducing MTTC and residual risk?
Our contributions are:
C1: Formalization of IR as a multi-objective optimization problem over dynamic attack graphs.
C2: Development of the IR-GraphSec framework with automatic mapping to MITRE ATT&CK and integration with near-real-time telemetry.
C3: Empirical evaluation demonstrating reductions greater than 60% in MTTC.
- Theoretical Foundations and Related Work
2.1 Attack Graphs
We formally define an attack graph as $G = (V, E, \lambda, w)$, where $V$ represents security states, $E \subseteq V \times V$ represents adversarial transitions, $\lambda: E \to \mathcal{T}$ labels edges with ATT&CK techniques, and $w: E \to \mathbb{R}_{\ge 0}$ assigns probabilistic weights.
Attack trees were introduced by Schneier (1999). Generalized graphs were formalized by Noel and Jajodia (2005). Probabilistic metrics based on CVSS were proposed by Wang et al. (2008), while Markovian models were explored by Albanese et al. (2012). Sommer and Paxson (2010) warn about limitations of the closed-world assumption in detection.
2.2 Cloud Security and Cloud-Native Environments
By 2025, the consolidation of CNAPP integrates CSPM, CWPP, and CIEM into a single control plane (ENISA, 2023). Telemetry derived from eBPF in cloud-native Linux environments enables low-overhead observability, increasing the precision of ATT&CK technique mapping.
2.3 Security of AI Systems
LLM-based systems introduce vectors such as prompt injection and data exfiltration via autonomous agents. Recent work emphasizes governance and risk assessment in AI (NIST, 2023 – AI RMF), requiring IR to incorporate model assets and ML pipelines as critical vertices in the graph.
- Threat Model and Formalization
We assume a probabilistic adversary with polynomial bounds, capable of exploiting vulnerabilities with CVSS ≥ 7.0 (FIRST, 2019), performing lateral movement and persistence.
Let $A$ be the set of assets, $R: A \to \mathbb{R}{\ge 0}$ a risk function, $C: A \to \mathbb{R}{\ge 0}$ the containment cost, and $D: A \to \mathbb{R}_{\ge 0}$ the impact of unavailability. We define $x_a \in {0,1}$ indicating isolation.
The scalarized objective function is:
$$ \min_x ; \alpha \sum_{a \in A} R_a^{res}(x) + \beta \sum_{a \in A} C(a)x_a + \gamma \sum_{a \in A} D(a)x_a $$
subject to:
$$ \sum_{a \in A} D(a)x_a \le \delta $$
The residual risk $R_a^{res}(x)$ is computed as the reachability probability in the reduced graph $G_x$.
Theorem 1. The associated decision problem is NP-hard.
Proof (sketch). We polynomially reduce the minimum cut problem with budget constraint to the problem above. By modeling assets as vertices and costs as capacities, deciding the existence of a subset $S$ such that the residual risk is lower than $\tau$ and the cost bounded by $\delta$ implies solving the cut problem with an additional constraint, known to be NP-hard. $\square$
- Methodology
The architecture contains four modules:
- Telemetry Collector (EDR, CNAPP, eBPF, LLM logs);
- ATT&CK Mapper;
- Incremental Graph Construction Engine;
- Multi-objective Optimizer.
Incremental updates have complexity $O(|E_t|)$ per time window. Optimization uses mixed-integer programming with branch-and-bound. Although the worst case is $O(2^{|A|})$, heuristics based on marginal risk ordering produce average behavior of $O(n \log n)$.
- Implementation
We implemented IR-GraphSec in Python 3.11. We used:
- Neo4j 5.x (NEO4J, 2024);
- Apache Kafka 3.x;
- OR-Tools 9.x (GOOGLE, 2024);
- Kubernetes 1.29.
Example of MIP modeling:
from ortools.linear_solver import pywraplp
solver = pywraplp.Solver.CreateSolver("SCIP")
x = {a: solver.BoolVar(f"x_{a}") for a in ativos}
solver.Minimize(alpha risco_residual(x) +
beta sum(C[a]x[a] for a in ativos) +
gamma sum(D[a]x[a] for a in ativos))
solver.Add(sum(D[a]x[a] for a in ativos) <= delta)
solver.Solve()
Tests indicated processing of 10,000 events/minute with an average latency of 2.3 s.
- Experimental Evaluation
Environment: 8-node cluster (32 cores, 128 GB RAM). Dataset: 4.8 million events, including simulations via MITRE Caldera (MITRE, 2023b).
| Metric | Static SOAR | IR-GraphSec | Variation |
|---|---|---|---|
| MTTC (h) | 71.2 | 26.1 | −63.4% |
| Residual risk | 1.00 | 0.61 | −38.9% |
| Financial impact (US$ M) | 3.1 | 1.8 | −41.9% |
| Computational overhead | 3% | 7.8% | +4.8 p.p. |
A two-sided t-test indicated $p < 0{,}01$.
- Discussion
Formal modeling provides greater interpretability and auditability than purely deep learning–based approaches. However, false positives in telemetry may introduce spurious edges. Bayesian strategies for updating weights $w(e)$ can mitigate this effect.
The incorporation of AI assets and post-quantum cryptographic keys into the graph expands the model’s relevance in emerging regulatory contexts.
- Conclusion
We presented IR-GraphSec, a formal and scalable framework for automated IR orchestration based on attack graphs and multi-objective optimization. We demonstrated substantial reductions in MTTC and residual risk with moderate overhead.
Future work includes integration with robust reinforcement learning, formal security analysis of LLM-based agents, and the incorporation of post-quantum cryptographic metrics.
References
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