We study the deterministic global optimization of trained Gaussian process posterior mean functions over hyperrectangular domains. Although the posterior mean function has a compact closed-form representation, its global optimization is challenging because it remains nonlinear and nonconvex. Existing exact deterministic approaches become increasingly difficult to scale as the number of training data points grows, leading to approximation-based methods that improve tractability by optimizing a modified (inexact) objective. In this work, we propose PALM-Mean, a piecewise-analytic lower-bounding framework embedded in reduced-space spatial branch-and-bound. At each node, kernel terms that are locally important are replaced by a sign-aware piecewise-linear relaxation in an appropriate scalar distance variable, while the remaining terms are bounded analytically in closed form. We show this hybrid approach yields a valid lower bound for the posterior mean, while limiting the size of the branch-and-bound subproblems. We establish validity of the node lower bounds and $\varepsilon$-global convergence of the resulting algorithm. Computational results on synthetic benchmarks and real-world application problems show that PALM-Mean improves scalability relative to representative general-purpose deterministic global solvers, particularly as the number of training data points increases.

We present NeuroLKH, a novel algorithm that combines deep learning with the strong traditional heuristic Lin-Kernighan-Helsgaun (LKH) for solving Traveling Salesman Problem. Specifically, we train a Sparse Graph Network (SGN) with supervised learning for edge scores and unsupervised learning for node penalties, both of which are critical for improving the performance of LKH. Based on the output of SGN, NeuroLKH creates the edge candidate set and transforms edge distances to guide the searching process of LKH. Extensive experiments firmly demonstrate that, by training one model on a wide range of problem sizes, NeuroLKH significantly outperforms LKH and generalizes well to much larger sizes. Also, we show that NeuroLKH can be applied to other routing problems such as Capacitated Vehicle Routing Problem (CVRP), Pickup and Delivery Problem (PDP), and CVRP with Time Windows (CVRPTW).

In this paper, we focus on computing an NE that optimizes a given objective function.

Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. Unlike binary matrix factorization based on standard arithmetic, BMF employs the Boolean OR and AND operations for the matrix product, which improves interpretability and reduces the approximation error. It is also used in role mining and computer vision. In this paper, we first propose algorithms for BMF that perform alternating optimization (AO) of the factor matrices, where each subproblem is solved via integer programming (IP). We then design different approaches to further enhance AO-based algorithms by selecting an optimal subset of rank-one factors from multiple runs. To address the scalability limits of IP-based methods, we introduce new greedy and local-search heuristics. We also construct a new C++ data structure for Boolean vectors and matrices that is significantly faster than existing ones and is of independent interest, allowing our heuristics to scale to large datasets. We illustrate the performance of all our proposed methods and compare them with the state of the art on various real datasets, both with and without missing data, including applications in topic modeling and imaging.

Rapid post-disaster road damage assessment is critical for effective emergency response, yet traditional optimization methods suffer from excessive computational time and require domain knowledge for algorithm design, making them unsuitable for time-sensitive disaster scenarios. This study proposes an attention-based encoder-decoder model (AEDM) for rapid drone routing decision in post-disaster road damage assessment. The method employs deep reinforcement learning to determine high-quality drone assessment routes without requiring algorithmic design knowledge. A network transformation method is developed to convert link-based routing problems into equivalent node-based formulations, while a synthetic road network generation technique addresses the scarcity of large-scale training datasets. The model is trained using policy optimization with multiple optima (POMO) with multi-task learning capabilities to handle diverse parameter combinations. Experimental results demonstrate two key strengths of AEDM: it outperforms commercial solvers by 20--71\% and traditional heuristics by 23--35\% in solution quality, while achieving rapid inference (1--2 seconds) versus 100--2,000 seconds for traditional methods. The model exhibits strong generalization across varying problem scales, drone numbers, and time constraints, consistently outperforming baseline methods on unseen parameter distributions and real-world road networks. The proposed method effectively balances computational efficiency with solution quality, making it particularly suitable for time-critical disaster response applications where rapid decision-making is essential for saving lives. The source code for AEDM is publicly available at https://github.com/PJ-HTU/AEDM-for-Post-disaster-road-assessment.