Concurrently, we introduce the associated optimisation algorithm, which is inspired by GECO [25]--the latter does not always lead to good encodings (e.g., Sec.

We argue that this problem is in fact twofold.

The Maximum Clique Problem (MCP) is a foundational NP-hard problem with wide-ranging applications, yet no single algorithm consistently outperforms all others across diverse graph instances. This underscores the critical need for instance-aware algorithm selection, a domain that remains largely unexplored for the MCP. To address this gap, we propose a novel learning-based framework that integrates both traditional machine learning and graph neural networks. We first construct a benchmark dataset by executing four state-of-the-art exact MCP solvers on a diverse collection of graphs and extracting their structural features. An evaluation of conventional classifiers establishes Random Forest as a strong baseline and reveals that connectivity and topological features are key predictors of performance. Building on these insights, we develop GAT-MLP, a dual-channel model that combines a Graph Attention Network (GAT) to encode local graph structure with a Multilayer Perceptron (MLP) to model global features. Extensive experiments demonstrate that GAT-MLP achieves superior and consistent performance, significantly outperforming all baseline methods. Our results highlight the effectiveness of the dual-channel architecture and the promise of graph neural networks for combinatorial algorithm selection, achieving 90.43% accuracy in choosing the optimal solver. Code and models are available at: https://anonymous.4open.science/r/GAT-MLP-7E5F.

When people reason about cause and effect, they often consider many competing "what if" scenarios before deciding which explanation fits best. Analogously, advanced language models capable of causal inference can consider multiple interventions and counterfactuals to judge the validity of causal claims. Crucially, this type of reasoning is less like a single calculation and more like an internal dialogue between alternative hypotheses. In this paper, we make this dialogue explicit through a dual-agent debate framework where one model provides a structured causal inference, and the other critically examines this reasoning for logical flaws. When disagreements arise, agents attempt to persuade each other, challenging each other's logic and revising their conclusions until they converge on a mutually agreed answer. To take advantage of this deliberative process, we specifically use reasoning language models, whose strengths in both causal inference and adversarial debate remain under-explored relative to standard large language models. We evaluate our approach on the CLadder dataset, a benchmark linking natural language questions to formally defined causal graphs across all three rungs of Pearl's ladder of causation. With Qwen3 and DeepSeek-R1 as debater agents, we demonstrate that multi-agent debate improves DeepSeek-R1's overall accuracy in causal inference from 78.03% to 87.45%, with the counterfactual category specifically improving from 67.94% to 80.04% accuracy. Similarly, Qwen3's overall accuracy improves from 84.16% to 89.41%, and counterfactual questions from 71.53% to 80.35%, showing that strong models can still benefit greatly from debate with weaker agents. Our results highlight the potential of reasoning models as building blocks for multi-agent systems in causal inference, and demonstrate the importance of diverse perspectives in causal problem-solving.

Background/Objectives: Efficient task allocation in hospital emergency departments (EDs) is critical for operational efficiency and patient care quality, yet the complexity of staff coordination poses significant challenges. This study proposes a simulation-based framework for modeling doctors and nurses as intelligent agents guided by computational trust mechanisms. The objective is to explore how trust-informed coordination can support decision making in ED management. Methods: The framework was implemented in Unity, a 3D graphics platform, where agents assess their competence before undertaking tasks and adaptively coordinate with colleagues. The simulation environment enables real-time observation of workflow dynamics, resource utilization, and patient outcomes. We examined three scenarios - Baseline, Replacement, and Training - reflecting alternative staff management strategies. Results: Trust-informed task allocation balanced patient safety and efficiency by adapting to nurse performance levels. In the Baseline scenario, prioritizing safety reduced errors but increased patient delays compared to a FIFO policy. The Replacement scenario improved throughput and reduced delays, though at additional staffing cost. The training scenario forstered long-term skill development among low-performing nurses, despite short-term delays and risks. These results highlight the trade-off between immediate efficiency gains and sustainable capacity building in ED staffing. Conclusions: The proposed framework demonstrates the potential of computational trust for evidence-based decision support in emergency medicine. By linking staff coordination with adaptive decision making, it provides hospital managers with a tool to evaluate alternative policies under controlled and repeatable conditions, while also laying a foundation for future AI-driven personalized decision support.