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.

Neural Information Processing Systems http://nips.cc/

Interpretability has become a well-recognized goal for machine learning models.

In this paper, we propose to factorize the selection of a variable subset into decisions on selection of each variable, under our LNS framework. To represent such action factorization, we employ the bipartite GCN as the destroy operator, as shown in Figure A.1. MLP module that computes probabilities of selecting each variable in parallel.Figure A.1: Illustration of our LNS framework with the bipartite GCN based destroy operator. Our RL algorithm for training LNS policies is depicted by the pseudo code in Algorithm 1. The architecture of the neural network is displayed in the upper half of Figure A.2, which MLPs by a parameter-sharing MLP, as shown in the lower half of Figure A.2. S. / D. V ariable features ( V) Normalized reduced cost. 1 S. Normalized objective coefficient. 1 S. Normalized LP age. 1 S. Equality of solution value and lower bound, 0 or 1. 1 S. Equality of solution value and upper bound, 0 or 1 . 1 S. Fractionality of solution value. 1 S. One-hot encoding of simplex basis status (i.e., lower, basic, upper).

However, the combinatorial number of variable subsets prevents direct application of typical RL algorithms.

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We sincerely thank all of you for the detailed, thoughtful, and constructive comments and feedback. We added a table of racial composition data for all networks. We incorporated all the recommendations. We improve clarity of Th. 1 by adding "In this formulation, there are two sets of variables: a) We will provide a head-to-head comparison with Table 1. We will release the code and a "readme" file with instructions, detailing the sequence of the runs.

There are other approaches (e.g., [ Here, if all team members play strategies according to an NE minimizing the adversary's utility, the Eq.(1c) ensures that binary variable This space is represented by Eq.(1), which involves nonlinear terms in Eq.(1a) Section 3.4 shows that our techniques can significantly reduce the time The procedure of CRM is shown in Algorithm 2, which is illustrated in Appendix A. A collection N of subsets of players is a binary collection if: 1. { i | i N } N ; Eqs.(1b)-(1g), (3), and (4) is the space of NEs. Example 1 provides an example of N .