This article explores an approach to addressing the Close Enough Traveling Salesman Problem (CETSP). The objective is to streamline the mathematical formulation by introducing reformu-lations that approximate the Euclidean distances and simplify the objective function. Additionally, the use of convex sets in the constraint design offers computational benefits. The proposed methodology is empirically validated on real-world CETSP instances, with the aid of computational strategies such as a fragmented CPLEX-based approach. Results demonstrate its effectiveness in managing computational resources without compromising solution quality. Furthermore, the article analyzes the behavior of the proposed mathematical formulations, providing comprehensive insights into their performance.

Developing algorithms for real-life problems that perform well in practice highly depends on the availability of realistic data for testing. Obtaining real-life data for optimization problems in health care, however, is often difficult. This is especially true for any patient related optimization problems, e.g., for patient-to-room assignment, due to data privacy policies. Furthermore, obtained real-life data usually cannot be published which prohibits reproducibility of results by other researchers. Therefore, often artificially generated instances are used. We use these insights to develop a configurable instance generator for PRA with an easy-to-use graphical user interface. Configurability is in this case especially important as we observed in an extensive analysis of real-life data that, e.g., the probability distribution for patients' age and length of stay depends on the respective ward. Introduction The development of algorithms for real-world optimization problems that perform well in practice heavily relies on the availability of realistic data for testing.

A recent trend in the mathematical optimization literature is to embed trained machine learning predictors into a larger optimization model. The m ost common application is for a practitioner to train a machine learning predictor as a sur rogate for a more complicated subsystem that cannot be directly embedded into an optimiza tion model, for example, because it does not have an algebraic form or because it is non -differentiable. L opez-Flores et al. (2024) provide a review of the field.

Despite the impressive advancements in modern machine learning, achieving robustness in Domain Generalization (DG) tasks remains a significant challenge. In DG, models are expected to perform well on samples from unseen test distributions (also called domains), by learning from multiple related training distributions. Most existing approaches to this problem rely on single-valued predictions, which inherently limit their robustness. We argue that set-valued predictors could be leveraged to enhance robustness across unseen domains, while also taking into account that these sets should be as small as possible. We introduce a theoretical framework defining successful set prediction in the DG setting, focusing on meeting a predefined performance criterion across as many domains as possible, and provide theoretical insights into the conditions under which such domain generalization is achievable. We further propose a practical optimization method compatible with modern learning architectures, that balances robust performance on unseen domains with small prediction set sizes. We evaluate our approach on several real-world datasets from the WILDS benchmark, demonstrating its potential as a promising direction for robust domain generalization.

Federated learning (FL) has emerged as a promising paradigm for distributed machine learning, enabling collaborative training of a global model across multiple local devices without requiring them to share raw data. Despite its advancements, FL is limited by factors such as: (i) privacy risks arising from the unprotected transmission of local model updates to the fusion center (FC) and (ii) decreased learning utility caused by heterogeneity in model quantization resolution across participating devices. Prior work typically addresses only one of these challenges because maintaining learning utility under both privacy risks and quantization heterogeneity is a non-trivial task. In this paper, our aim is therefore to improve the learning utility of a privacy-preserving FL that allows clusters of devices with different quantization resolutions to participate in each FL round. Specifically, we introduce a novel stochastic quantizer (SQ) that is designed to simultaneously achieve differential privacy (DP) and minimum quantization error. Notably, the proposed SQ guarantees bounded distortion, unlike other DP approaches. To address quantization heterogeneity, we introduce a cluster size optimization technique combined with a linear fusion approach to enhance model aggregation accuracy. Numerical simulations validate the benefits of our approach in terms of privacy protection and learning utility compared to the conventional LaplaceSQ-FL algorithm.

Visualization techniques are a critical means of shedding light on the behavior of metaheuristic numerical optimization algorithms. Conventional methods such as convergence analysis, trajectory visualizations, and fitness landscape analysis provide valuable insights into aspects like convergence speed, diversity, and solution quality. However, these approaches often fail to capture the structural dynamics of the search process, particularly in high-dimensional or complex spaces. Existing methods rarely address the location of the solution candidates in the search space, which can reveal crucial information about the exploratory and exploitative strategies of an algorithm. We propose ClustOpt, a novel representation and visualization methodology for metaheuristic numerical population-based optimization algorithms, that focuses on clustering solution candidates explored by optimization algorithms.

Survival analysis is an important problem in healthcare because it models the relationship between an individual's covariates and the onset time of an event of interest (e.g., death). It is important for survival models to be well-calibrated (i.e., for their predicted probabilities to be close to ground-truth probabilities) because badly calibrated systems can result in erroneous clinical decisions. Existing survival models are typically calibrated at the population level only, and thus run the risk of being poorly calibrated for one or more minority subpopulations. We propose a model called GRADUATE that achieves multicalibration by ensuring that all subpopulations are well-calibrated too. GRADUATE frames multicalibration as a constrained optimization problem, and optimizes both calibration and discrimination in-training to achieve a good balance between them. We mathematically prove that the optimization method used yields a solution that is both near-optimal and feasible with high probability. Empirical comparisons against state-of-the-art baselines on real-world clinical datasets demonstrate GRADUATE's efficacy. In a detailed analysis, we elucidate the shortcomings of the baselines vis-a-vis GRADUATE's strengths.

This paper leverages the recently introduced concept of algorithm footprints to investigate the interplay between algorithm configurations and problem characteristics. Performance footprints are calculated for six modular variants of the CMA-ES algorithm (modCMA), evaluated on 24 benchmark problems from the BBOB suite, across two-dimensional settings: 5-dimensional and 30-dimensional. These footprints provide insights into why different configurations of the same algorithm exhibit varying performance and identify the problem features influencing these outcomes. Our analysis uncovers shared behavioral patterns across configurations due to common interactions with problem properties, as well as distinct behaviors on the same problem driven by differing problem features. The results demonstrate the effectiveness of algorithm footprints in enhancing interpretability and guiding configuration choices.

This paper considers the problem of cost-aware downlink sum-rate maximization via joint optimal radio access technologies (RATs) assignment and power allocation in next-generation heterogeneous wireless networks (HetNets). We consider a future HetNet comprised of multi-RATs and serving multi-connectivity edge devices (EDs), and we formulate the problem as mixed-integer non-linear programming (MINP) problem. Due to the high complexity and combinatorial nature of this problem and the difficulty to solve it using conventional methods, we propose a hierarchical multi-agent deep reinforcement learning (DRL)-based framework, called DeepRAT, to solve it efficiently and learn system dynamics. In particular, the DeepRAT framework decomposes the problem into two main stages; the RATs-EDs assignment stage, which implements a single-agent Deep Q Network (DQN) algorithm, and the power allocation stage, which utilizes a multi-agent Deep Deterministic Policy Gradient (DDPG) algorithm. Using simulations, we demonstrate how the various DRL agents efficiently interact to learn system dynamics and derive the global optimal policy. Furthermore, our simulation results show that the proposed DeepRAT algorithm outperforms existing state-of-the-art heuristic approaches in terms of network utility. Finally, we quantitatively show the ability of the DeepRAT model to quickly and dynamically adapt to abrupt changes in network dynamics, such as EDs mobility.

This paper presents a leaderless cooperative guidance strategy for simultaneous time-constrained interception of a stationary target when the interceptors exchange information over switched dynamic graphs. We specifically focus on scenarios when the interceptors lack radial acceleration capabilities, relying solely on their lateral acceleration components. This consideration aligns with their inherent kinematic turn constraints. The proposed strategy explicitly addresses the complexities of coupled 3D engagements, thereby mitigating performance degradation that typically arises when the pitch and yaw channels are decoupled into two separate, mutually orthogonal planar engagements. Moreover, our formulation incorporates modeling uncertainties associated with the time-to-go estimation into the derivation of cooperative guidance commands to ensure robustness against inaccuracies in dynamic engagement scenarios. To optimize control efficiency, we analytically derive the lateral acceleration components in the orthogonal pitch and yaw channels by solving an instantaneous optimization problem, subject to an affine constraint. We show that the proposed cooperative guidance commands guarantee consensus in time-to-go values within a predefined time, which can be prescribed as a design parameter, regardless of the interceptors' initial configurations. We provide simulations to attest to the efficacy of the proposed method.