Son Nguyen Van

Cuong Van Duc, Minh Nguyen Dinh Tuan, Tam Vu Duc et al.

Designing effective heuristics for NP-hard combinatorial optimization problems remains a challenging and expertise-intensive task. Existing applications of large language models (LLMs) primarily rely on one-shot code synthesis, yielding brittle heuristics that underutilize the models' capacity for iterative reasoning. We propose ReVEL: Multi-Turn Reflective LLM-Guided Heuristic Evolution via Structured Performance Feedback, a hybrid framework that embeds LLMs as interactive, multi-turn reasoners within an evolutionary algorithm (EA). The core of ReVEL lies in two mechanisms: (i) performance-profile grouping, which clusters candidate heuristics into behaviorally coherent groups to provide compact and informative feedback to the LLM; and (ii) multi-turn, feedback-driven reflection, through which the LLM analyzes group-level behaviors and generates targeted heuristic refinements. These refinements are selectively integrated and validated by an EA-based meta-controller that adaptively balances exploration and exploitation. Experiments on standard combinatorial optimization benchmarks show that ReVEL consistently produces heuristics that are more robust and diverse, achieving statistically significant improvements over strong baselines. Our results highlight multi-turn reasoning with structured grouping as a principled paradigm for automated heuristic design.

Cuong Van Duc, Thai Tran Quoc, Minh Nguyen Dinh Tuan et al.

Detecting student misconceptions in open-ended responses is a longstanding challenge, demanding semantic precision and logical reasoning. We propose MiRAGE - Misconception Detection with Retrieval-Guided Multi-Stage Reasoning and Ensemble Fusion, a novel framework for automated misconception detection in mathematics. MiRAGE operates in three stages: (1) a Retrieval module narrows a large candidate pool to a semantically relevant subset; (2) a Reasoning module employs chain-of-thought generation to expose logical inconsistencies in student solutions; and (3) a Reranking module refines predictions by aligning them with the reasoning. These components are unified through an ensemble-fusion strategy that enhances robustness and interpretability. On mathematics datasets, MiRAGE achieves Mean Average Precision scores of 0.82/0.92/0.93 at levels 1/3/5, consistently outperforming individual modules. By coupling retrieval guidance with multi-stage reasoning, MiRAGE reduces dependence on large-scale language models while delivering a scalable and effective solution for educational assessment.

Son Nguyen Van, Hoai Nguyen Xuan

The Poisson process, especially the nonhomogeneous Poisson process (NHPP), is an essentially important counting process with numerous real-world applications. Up to date, almost all works in the literature have been on the estimation of NHPPs with infinite data using non-data driven binning methods. In this paper, we formulate the problem of estimation of NHPPs from finite and limited data as a learning generalization problem. We mathematically show that while binning methods are essential for the estimation of NHPPs, they pose a threat of overfitting when the amount of data is limited. We propose a framework for regularized learning of NHPPs with two new adaptive and data-driven binning methods that help to remove the ad-hoc tuning of binning parameters. Our methods are experimentally tested on synthetic and real-world datasets and the results show their effectiveness.