In this paper, we introduce and apply Operations Research Question Answering (ORQA), a new benchmark, to assess the generalization capabilities of Large Language Models (LLMs) in the specialized technical domain of Operations Research (OR). This benchmark is designed to evaluate whether LLMs can emulate the knowledge and reasoning skills of OR experts when given diverse and complex optimization problems. The dataset, crafted by OR experts, presents real-world optimization problems that require multistep reasoning to build their mathematical models. Our evaluations of various open-source LLMs, such as LLaMA 3.1, DeepSeek, and Mixtral reveal their modest performance, indicating a gap in their aptitude to generalize to specialized technical domains. This work contributes to the ongoing discourse on LLMs’ generalization capabilities, providing insights for future research in this area. The dataset and evaluation code are publicly available.

Math Word Problem (MWP) is a crucial NLP task aimed at providing solutions for given mathematical descriptions. A notable sub-category of MWP is the Linear Programming Word Problem (LPWP), which holds significant relevance in real-world decision-making and operations research. While the recent rise of generative large language models (LLMs) has brought more advanced solutions to LPWPs, existing evaluation methodologies for this task still diverge from human judgment and face challenges in recognizing mathematically equivalent answers. In this paper, we introduce a novel evaluation metric rooted in graph edit distance, featuring benefits such as permutation invariance and more accurate program equivalence identification. Human evaluations empirically validate the superior efficacy of our proposed metric when particularly assessing LLM-based solutions for LPWP.

This paper presents a Simple and effective unsupervised adaptation method for Robust Object Detection (SimROD). To overcome the challenging issues of domain shift and pseudo-label noise, our method integrates a novel domain-centric data augmentation, a gradual self-labeling adaptation procedure, and a teacher-guided fine-tuning mechanism. Using our method, target domain samples can be leveraged to adapt object detection models without changing the model architecture or generating synthetic data. When applied to image corruptions and high-level cross-domain adaptation benchmarks, our method outperforms prior baselines on multiple domain adaptation benchmarks. SimROD achieves new state-of-the-art on standard real-to-synthetic and cross-camera setup benchmarks. On the image corruption benchmark, models adapted with our method achieved a relative robustness improvement of 15-25% AP50 on Pascal-C and 5-6% AP on COCO-C and Cityscapes-C. On the cross-domain benchmark, our method outperformed the best baseline performance by up to 8% and 4% AP50 on Comic and Watercolor respectively.1

In this paper, we consider the resource allocation in two-tier wireless systems in which small-cell base stations harvest energy from renewable sources in addition to the conventional power grid. Moreover, we assume that each cell has access to an energy storage system with a limited battery capacity. We introduce new mechanisms that enable an efficient allocation of the available energy over time across the network. In doing so, we take into account the time-varying fading channel, the inter-cell interference and the fluctuations of harvested energy. In particular, we propose convergent offline algorithms to maximize the network energy efficiency while satisfying an average sum-rate constraint at each cell. Furthermore, we extend the resource allocation scheme by enabling an energy cooperation between the cells. By cooperating, they can exchange their harvested energy through a smart-grid power infrastructure. Using numerical simulations, we verify the convergence of the proposed algorithms and analyze the efficacy of the resource allocation and energy cooperation schemes.

To support the surge in wireless data traffic, the spectrum and energy efficiencies of cellular networks should be largely increased. Heterogeneous two-tier architecture has been identified as one key solution. However, small-cell deployment raises questions about the resulting energy efficiency and interference mitigation. Therefore, we propose an energy-efficient and cognitive spectrum sharing scheme between primary macrocell and secondary small cells. Specifically, the small cells allocate their transmission power to maximize their total energy efficiency while respecting some interference constraints imposed by macrocell users. We solve this centralized optimization in two steps. First, assuming that the small-cell transmissions are noninterfering, the solution of this nonconvex optimization is characterized using a convex parametric approach. Using this characterization, we derive an algorithm based on Newton method, which converges to a global optimal solution. Second, when the small-cell transmissions are not necessarily orthogonal, we derive an algorithm, which converges at least to a local optimum, using the minorization-maximization principle and Newton method. Through simulations, we validate the convergence of these algorithms and compare their performance with existing schemes. We also analyze the effects of the interference and of the number of users on the energy efficiency.

In this work, we investigate the robust energy-efficient transmission for the cognitive uplink wireless system. Precisely, we propose an optimization framework for maximizing the sum energy efficiency while taking into account the uncertainty of the channel between the primary and secondary users. Here, we assume that the base station has multiple antennas and employs a zero-forcing receive filter to eliminate the inter-user interference. We handle the intractability of the probabilistic interference constraints by approximating them with convex and linear surrogate constraints. Despite the non-convexity of the utility function, we propose a parametric convex programming approach to derive an optimal algorithm based on Newton method. Through numerical simulations, we show the convergence and effectiveness of the proposed method and analyze the effect of channel uncertainty on the energy efficiency of the cognitive uplink system.

We investigate the trade-off between performance and energy efficiency in cooperative cognitive underlay systems. By cooperating, cognitive base stations mitigate the interference and serve their users more effectively at the cost of spending more power. With a flexible cooperation scheme, we thus jointly optimize the clustering and the beamforming to minimize the overall power consumption while satisfying the secondary users' quality of service and respecting the primary users' interference limits. We formulate this problem as a mixed-integer nonlinear program and decompose it into a master problem and a beamforming subproblem. Then, we derive an iterative algorithm based on the generalized Benders decomposition method to find an optimal solution. Moreover, we propose simple techniques to speed up its convergence. When the clusters are fixed and non-overlapping, we also propose a decentralized algorithm with limited signaling schemes using the alternating direction method of multipliers. In contrast to previous works, our distributed algorithm handles the total interference power constraints coupling the cognitive base stations. Through simulations, we analyze the effectiveness and convergence of the proposed algorithms and show the benefits of the cooperation in cognitive wireless networks.

We consider the energy-efficient design of transmit beamforming in the downlink of a cognitive multi-cell wireless system. In this system, multiple secondary cells minimize their total transmit power while satisfying given SINR requirements for the secondary users. At the same time, the secondary base stations are not allowed to exceed aggregate interference temperature limits to the users of a primary system. We propose a distributed optimization framework to decompose this multi-cell problem into parallel single-cell beamforming subproblems. As a result, the cognitive cells independently compute their beamformers using only local channel information. Moreover, they coordinate their inter-cell interference as well as the interference temperature to the primary users by exchanging some signaling information through a backhaul. This coordination is achieved through a consensus-based optimization. In contrast to classical decomposition methods, our approach is based on the alternating direction method of multipliers. Therefore, it leverages the augmented Lagrangian technique to accelerate the interference coordination between the secondary cells, thanks to the quadratic penalty terms that are added in the objective function with the standard pricing terms. Numerical results are provided to verify the effectiveness of this distributed algorithm.

We investigate the joint optimization of power allocation and transceiver weights in multiple-input multiple-output(MIMO) two-way multihop networks. The objective is to maximize the minimum weighted signal-to-interference-plus noise power ratio (SINR) of the multihop links while satisfying general linear power constraints at the transmit nodes. First, we derive a distributed power allocation algorithm by extending the notion of link SINR metric and analyze its convergence and optimality. Using that result, we propose an alternating optimization algorithm for solving the more complex MIMO transceiver weights optimization. We compare its performance against those of centralized and conventional schemes through numerical simulations. Our results show that the proposed algorithm provides considerable improvement to the end-to-end rate of multihop networks. In fact, it achieves, with low complexity and low coordination overhead, a rate performance close to an upper-bound that was obtained from a centralized optimization with a relaxed power constraint.

We propose a new cross-layer approach to mitigate interference in multihop networks. Precisely, we cancel all adjacent node interference in a multihop path by MIMO two-way relay scheme and jointly optimize the routing and power allocation to mitigate the interference from far nodes. We model and efficiently solve this optimization problem using a geometric programming framework. Our simulation results showed that this cross-layer approach provided significant end-to-end capacity gain and outperformed conventional multihop schemes. Also, a number of hops ranging from 2 to 6 was optimal in interference-limited regime. Finally, single hop MIMO routing was shown to provide higher capacity only in very high SNR scenarios.