Ant Colony Optimization (ACO) is a meta-heuristic algorithm that has been successfully applied to various Combinatorial Optimization Problems (COPs).

Bayesian Optimization (BO) is a powerful method for tackling expensive black-box optimization problems.

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Hyperparameter tuning is a challenging problem especially when the system itself involves uncertainty. Due to noisy function evaluations, optimization under uncertainty can be computationally expensive. In this paper, we present a novel Bayesian optimization framework tailored for hyperparameter tuning under uncertainty, with a focus on optimizing a scale- or precision-type parameter in stochastic models. The proposed method employs a statistical surrogate for the underlying random variable, enabling analytical evaluation of the expectation operator. Moreover, we derive a closed-form expression for the optimizer of the random acquisition function, which significantly reduces computational cost per iteration. Compared with a conventional one-dimensional Monte Carlo-based optimization scheme, the proposed approach requires 40 times fewer data points, resulting in up to a 40-fold reduction in computational cost. We demonstrate the effectiveness of the proposed method through two numerical examples in computational engineering.

Multi-objective discrete optimization problems, such as molecular design, pose significant challenges due to their vast and unstructured combinatorial spaces. Traditional evolutionary algorithms often get trapped in local optima, while expert knowledge can provide crucial guidance for accelerating convergence. Large language models (LLMs) offer powerful priors and reasoning ability, making them natural optimizers when expert knowledge matters. However, closed-source LLMs, though strong in exploration, cannot update their parameters and thus cannot internalize experience. Conversely, smaller open models can be continually fine-tuned but lack broad knowledge and reasoning strength. We introduce Multi-LLM Collaborative Co-evolution (MCCE), a hybrid framework that unites a frozen closed-source LLM with a lightweight trainable model. The system maintains a trajectory memory of past search processes; the small model is progressively refined via reinforcement learning, with the two models jointly supporting and complementing each other in global exploration. Unlike model distillation, this process enhances the capabilities of both models through mutual inspiration. Experiments on multi-objective drug design benchmarks show that MCCE achieves state-of-the-art Pareto front quality and consistently outperforms baselines. These results highlight a new paradigm for enabling continual evolution in hybrid LLM systems, combining knowledge-driven exploration with experience-driven learning.

Augmented reality (AR) applications for construction monitoring rely on real-time environmental tracking to visualize architectural elements. However, construction sites present significant challenges for traditional tracking methods due to featureless surfaces, dynamic changes, and drift accumulation, leading to misalignment between digital models and the physical world. This paper proposes a BIM-aware drift correction method to address these challenges. Instead of relying solely on SLAM-based localization, we align ``as-built" detected planes from the real-world environment with ``as-planned" architectural planes in BIM. Our method performs robust plane matching and computes a transformation (TF) between SLAM (S) and BIM (B) origin frames using optimization techniques, minimizing drift over time. By incorporating BIM as prior structural knowledge, we can achieve improved long-term localization and enhanced AR visualization accuracy in noisy construction environments. The method is evaluated through real-world experiments, showing significant reductions in drift-induced errors and optimized alignment consistency. On average, our system achieves a reduction of 52.24% in angular deviations and a reduction of 60.8% in the distance error of the matched walls compared to the initial manual alignment by the user.