In unsupervised combinatorial optimization (UCO), during training, one aims to have continuous decisions that are promising in a probabilistic sense for each training instance, which enables end-to-end training on initially discrete and non-differentiable problems. At the test time, for each test instance, starting from continuous decisions, derandomization is typically applied to obtain the final deterministic decisions. Researchers have developed more and more powerful test-time derandomization schemes to enhance the empirical performance and the theoretical guarantee of UCO methods. However, we notice a misalignment between training and testing in the existing UCO methods. Consequently, lower training losses do not necessarily entail better post-derandomization performance, even for the training instances without any data distribution shift. Empirically, we indeed observe such undesirable cases. We explore a preliminary idea to better align training and testing in UCO by including a differentiable version of derandomization into training. Our empirical exploration shows that such an idea indeed improves training-test alignment, but also introduces nontrivial challenges into training.

Recent neural heuristics for the Vehicle Routing Problem (VRP) primarily rely on node coordinates as input, which may be less effective in practical scenarios where real cost metrics-such as edge-based distances-are more relevant. To address this limitation, we introduce EFormer, an Edge-based Transformer model that uses edge as the sole input for VRPs. Our approach employs a precoder module with a mixed-score attention mechanism to convert edge information into temporary node embeddings. We also present a parallel encoding strategy characterized by a graph encoder and a node encoder, each responsible for processing graph and node embeddings in distinct feature spaces, respectively. This design yields a more comprehensive representation of the global relationships among edges. In the decoding phase, parallel context embedding and multi-query integration are used to compute separate attention mechanisms over the two encoded embeddings, facilitating efficient path construction. We train EFormer using reinforcement learning in an autoregressive manner. Extensive experiments on the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) reveal that EFormer outperforms established baselines on synthetic datasets, including large-scale and diverse distributions. Moreover, EFormer demonstrates strong generalization on real-world instances from TSPLib and CVRPLib. These findings confirm the effectiveness of EFormer's core design in solving VRPs.

Adversarial attacks in machine learning have been extensively reviewed in areas like computer vision and NLP, but research on tabular data remains scattered. This paper provides the first systematic literature review focused on adversarial attacks targeting tabular machine learning models. We highlight key trends, categorize attack strategies and analyze how they address practical considerations for real-world applicability. Additionally, we outline current challenges and open research questions. By offering a clear and structured overview, this review aims to guide future efforts in understanding and addressing adversarial vulnerabilities in tabular machine learning.

The Susceptible-Infected-Susceptible (SIS) model is a widely used model for the spread of information and infectious diseases, particularly non-immunizing ones, on a graph. Given a highly contagious disease, a natural question is how to best vaccinate individuals to minimize the disease's extinction time. While previous works showed that the problem of optimal vaccination is closely linked to the NP-hard Spectral Radius Minimization (SRM) problem, they assumed that the graph is known, which is often not the case in practice. In this work, we consider the problem of minimizing the extinction time of an outbreak modeled by an SIS model where the graph on which the disease spreads is unknown and only the infection states of the vertices are observed. To this end, we split the problem into two: learning the graph and determining effective vaccination strategies. We propose a novel inclusion-exclusion-based learning algorithm and, unlike previous approaches, establish its sample complexity for graph recovery. We then detail an optimal algorithm for the SRM problem and prove that its running time is polynomial in the number of vertices for graphs with bounded treewidth. This is complemented by an efficient and effective polynomial-time greedy heuristic for any graph. Finally, we present experiments on synthetic and real-world data that numerically validate our learning and vaccination algorithms.

In many applications, including underwater robotics, the coverage problem requires an autonomous vehicle to systematically explore a defined area while minimizing redundancy and avoiding obstacles. This paper investigates coverage path planning strategies to enhance the efficiency of underwater gliders, particularly in maximizing the probability of detecting a radioactive source while ensuring safe navigation. We evaluate three path-planning approaches: the Traveling Salesman Problem (TSP), Minimum Spanning Tree (MST), and Optimal Control Problem (OCP). Simulations were conducted in MATLAB, comparing processing time, uncovered areas, path length, and traversal time. Results indicate that OCP is preferable when traversal time is constrained, although it incurs significantly higher computational costs. Conversely, MST-based approaches provide faster but less optimal solutions. These findings offer insights into selecting appropriate algorithms based on mission priorities, balancing efficiency and computational feasibility.

Inspired by Fisher's geometric approach to study beneficial mutations, we analyse probabilities of beneficial mutation and crossover recombination of strings in a general Hamming space with arbitrary finite alphabet. Mutations and recombinations that reduce the distance to an optimum are considered as beneficial. Geometric and combinatorial analysis is used to derive closed-form expressions for transition probabilities between spheres around an optimum giving a complete description of Markov evolution of distances from an optimum over multiple generations. This paves the way for optimization of parameters of mutation and recombination operators. Here we derive optimality conditions for mutation and recombination radii maximizing the probabilities of mutation and crossover into the optimum. The analysis highlights important differences between these evolutionary operators. While mutation can potentially reach any part of the search space, the probability of beneficial mutation decreases with distance to an optimum, and the optimal mutation radius or rate should also decrease resulting in a slow-down of evolution near the optimum. Crossover recombination, on the other hand, acts in a subspace of the search space defined by the current population of strings. However, probabilities of beneficial and deleterious crossover are balanced, and their characteristics, such as variance, are translation invariant in a Hamming space, suggesting that recombination may complement mutation and boost the rate of evolution near the optimum.

The job shop scheduling problem is an NP-hard combinatorial optimization problem relevant to manufacturing and timetabling. Traditional approaches use priority dispatching rules based on simple heuristics. Recent work has attempted to replace these with deep learning models, particularly graph neural networks (GNNs), that learn to assign priorities from data. However, training such models requires customizing numerous factors: graph representation, node features, action space, and reward functions. The lack of modular libraries for experimentation makes this research time-consuming. This work introduces JobShopLib, a modular library that allows customizing these factors and creating new components with its reinforcement learning environment. We trained several dispatchers through imitation learning to demonstrate the environment's utility. One model outperformed various graph-based dispatchers using only individual operation features, highlighting the importance of feature customization. Our GNN model achieved near state-of-the-art results on large-scale problems. These results suggest significant room for improvement in developing such models. JobShopLib provides the necessary tools for future experimentation.

With the technological advancements of the last couple of decades, machine learning (ML) and artificial intelligence (AI) play an important part in automated decision-making pipelines [1-3]. Even though these tools are generally created by optimising with respect to their accuracy and performance, there are other important aspects that should be considered, such as their fairness, robustness, and privacy [4]. One of these aspects, fairness, becomes even more crucial when AI-based tools are used for decision-making tasks such as checking whether accepting a credit application is profitable and risk-free, if an applicant is worthy of a job position, or if a defendant has a higher risk of committing a crime again.

Instruction subsets (ISs) are heuristics that can shrink the size of the inductive programming (IP) search space by tens of orders of magnitude. Here, we extend the IS approach by introducing instruction and solution probabilities as additional heuristics. Instruction probability reflects the expectation of an instruction occurring in a solution, based on the frequency of instruction occurrence in a large code sample. The solution probability for a partial or complete program is simply the product of all constituent instruction probabilities, including duplicates. We treat the minimum solution probabilities observed in code sample program units of different sizes as solution probability thresholds. These thresholds are used to prune the search space as partial solutions are constructed, thereby eliminating any branches containing unlikely combinations of instructions. The new approach has been evaluated using a large sample of human code. We tested two formulations of instruction probability: one based on instruction occurrence across the entire code sample and another that measured the distribution separately for each IS. Our results show that both variants produce substantial further reductions in the IP search space size of up to tens of orders of magnitude, depending on solution size. In combination with IS, reductions of over 100 orders of magnitude can be achieved. We also carried out cross-validation testing to show that the heuristics should work effectively with unseen code. The approach is described and the results and some ideas for future work are discussed.

We present a suite of scalable algorithms for minimizing feedback arcs in large-scale weighted directed graphs, with the goal of revealing biologically meaningful feedforward structure in neural connectomes. Using the FlyWire Connectome Challenge dataset, we demonstrate the effectiveness of our ranking strategies in maximizing the total weight of forward-pointing edges. Our methods integrate greedy heuristics, gain-aware local refinements, and global structural analysis based on strongly connected components. Experiments show that our best solution improves the forward edge weight over previous top-performing methods. All algorithms are implemented efficiently in Python and validated using cloud-based execution on Google Colab Pro+.