Proportionality is an attractive fairness concept that has been applied to a range of problems including the facility location problem, a classic problem in social choice.

The difficulty and expense of obtaining large-scale human responses make Large Language Models (LLMs) an attractive alternative and a promising proxy for human behavior. However, prior work shows that LLMs often produce homogeneous outputs that fail to capture the rich diversity of human perspectives and behaviors. Thus, rather than trying to capture this diversity with a single LLM agent, we propose a novel framework to construct a set of agents that collectively capture the diversity of a given human population. Each agent is an LLM whose behavior is steered by conditioning on a small set of human demonstrations (task-response pairs) through in-context learning. The central challenge is therefore to select a representative set of LLM agents from the exponentially large space of possible agents. We tackle this selection problem from the lens of submodular optimization. In particular, we develop methods that offer different trade-offs regarding time complexity and performance guarantees. Extensive experiments in crowdsourcing and educational domains demonstrate that our approach constructs agents that more effectively represent human populations compared to baselines. Moreover, behavioral analyses on new tasks show that these agents reproduce the behavior patterns and perspectives of the students and annotators they are designed to represent.

Quantum annealing offers a promising paradigm for solving NP-hard combinatorial optimization problems, but its practical application is severely hindered by two challenges: the complex, manual process of translating problem descriptions into the requisite Quadratic Unconstrained Binary Optimization (QUBO) format and the scalability limitations of current quantum hardware. To address these obstacles, we propose a novel end-to-end framework, LLM-QUBO, that automates this entire formulation-to-solution pipeline. Our system leverages a Large Language Model (LLM) to parse natural language, automatically generating a structured mathematical representation. To overcome hardware limitations, we integrate a hybrid quantum-classical Benders' decomposition method. This approach partitions the problem, compiling the combinatorial complex master problem into a compact QUBO format, while delegating linearly structured sub-problems to classical solvers. The correctness of the generated QUBO and the scalability of the hybrid approach are validated using classical solvers, establishing a robust performance baseline and demonstrating the framework's readiness for quantum hardware. Our primary contribution is a synergistic computing paradigm that bridges classical AI and quantum computing, addressing key challenges in the practical application of optimization problem. This automated workflow significantly reduces the barrier to entry, providing a viable pathway to transform quantum devices into accessible accelerators for large-scale, real-world optimization challenges.

As urban aerial mobility (UAM) infrastructure development accelerates globally, cities like Shenzhen are planning large-scale vertiport networks (e.g., 1,200+ facilities by 2026). Existing planning frameworks remain inadequate for this complexity due to historical limitations in data granularity and real-world applicability. This paper addresses these gaps by first proposing the Capacitated Dynamic Maximum Covering Location Problem (CDMCLP), a novel optimization framework that simultaneously models urban-scale spatial-temporal demand, heterogeneous user behaviors, and infrastructure capacity constraints. Building on this foundation, we introduce an Integrated Planning Recommendation System that combines CDMCLP with socio-economic factors and dynamic clustering initialization. This system leverages adaptive parameter tuning based on empirical user behavior to generate practical planning solutions. Validation in a Chinese center city demonstrates the effectiveness of the new optimization framework and recommendation system. Under the evaluation and optimization of CDMCLP, the quantitative performance of traditional location methods are exposed and can be improved by 38\%--52\%, while the recommendation system shows user-friendliness and the effective integration of complex elements. By integrating mathematical rigor with practical implementation considerations, this hybrid approach bridges the gap between theoretical location modeling and real-world UAM infrastructure planning, offering municipalities a pragmatic tool for vertiport network design.

The rapid development of urban low-altitude unmanned aerial vehicle (UAV) economy poses new challenges for dynamic site selection of UAV landing points and supply stations. Traditional deep reinforcement learning methods face computational complexity bottlenecks, particularly with standard attention mechanisms, when handling large-scale urban-level location problems. This paper proposes GeoHopNet, a Hopfield-augmented sparse spatial attention network specifically designed for dynamic UAV site location problems. Our approach introduces four core innovations: (1) distance-biased multi-head attention mechanism that explicitly encodes spatial geometric information; (2) K-nearest neighbor sparse attention that reduces computational complexity from $O(N^2)$ to $O(NK)$; (3) a modern Hopfield external memory module; and (4) a memory regularization strategy. Experimental results demonstrate that GeoHopNet extends the boundary of solvable problem sizes. For large-scale instances with 1,000 nodes, where standard attention models become prohibitively slow (over 3 seconds per instance) and traditional solvers fail, GeoHopNet finds high-quality solutions (0.22\% optimality gap) in under 0.1 seconds. Compared to the state-of-the-art ADNet baseline on 100-node instances, our method improves solution quality by 22.2\% and is 1.8$\times$ faster.

The accelerating uptake of battery-electric vehicles demands infrastructure planning tools that are both data-rich and geographically scalable. Whereas most prior studies optimise charging locations for single cities, state-wide and national networks must reconcile the conflicting requirements of dense metropolitan cores, car-dependent exurbs, and power-constrained rural corridors. We present DOVA-PATBM (Deployment Optimisation with Voronoi-oriented, Adaptive, POI-Aware Temporal Behaviour Model), a geo-computational framework that unifies these contexts in a single pipeline. The method rasterises heterogeneous data (roads, population, night lights, POIs, and feeder lines) onto a hierarchical H3 grid, infers intersection importance with a zone-normalised graph neural network centrality model, and overlays a Voronoi tessellation that guarantees at least one five-port DC fast charger within every 30 km radius. Hourly arrival profiles, learned from loop-detector and floating-car traces, feed a finite M/M/c queue to size ports under feeder-capacity and outage-risk constraints. A greedy maximal-coverage heuristic with income-weighted penalties then selects the minimum number of sites that satisfy coverage and equity targets. Applied to the State of Georgia, USA, DOVA-PATBM (i) increases 30 km tile coverage by 12 percentage points, (ii) halves the mean distance that low-income residents travel to the nearest charger, and (iii) meets sub-transmission headroom everywhere -- all while remaining computationally tractable for national-scale roll-outs. These results demonstrate that a tightly integrated, GNN-driven, multi-resolution approach can bridge the gap between academic optimisation and deployable infrastructure policy.

The facility location problem (FLP) is a classical combinatorial In real cities, facility layout tends to deviate from residential demands optimization challenge aimed at strategically laying out facilities for corresponding services, leading to costly travel [12, 13]. to maximize their accessibility. In this paper, we propose a reinforcement Therefore, optimizing accessibility by strategically locating urban learning method tailored to solve large-scale urban facilities is crucial for creating more sustainable and inclusive cities. FLP, capable of producing near-optimal solutions at superfast inference In fact, facility location problem (FLP) is a classic combinatorial speed. We distill the essential swap operation from local optimization (CO) problem [2, 8], which is notoriously challenging search, and simulate it by intelligently selecting edges on a graph due to the NP-hardness inherent in selecting urban regions to of urban regions, guided by a knowledge-informed graph neural place facilities from candidate regions [5]. As both and are network, thus sidestepping the need for heavy computation typically large in urban contexts, designing a reliable algorithm that of local search. Extensive experiments on four US cities with different delivers satisfactory solutions within reasonable timeframes is difficult.

The extended Weber location problem is a classical optimization problem that has inspired some new works in several machine learning scenarios recently. However, most existing algorithms may get stuck due to the singularity at the data points when the power of the cost function $1\leqslant q<2$, such as the widely-used iterative Weiszfeld approach. In this paper, we establish a de-singularity subgradient approach for this problem. We also provide a complete proof of convergence which has fixed some incomplete statements of the proofs for some previous Weiszfeld algorithms. Moreover, we deduce a new theoretical result of superlinear convergence for the iteration sequence in a special case where the minimum point is a singular point. We conduct extensive experiments in a real-world machine learning scenario to show that the proposed approach solves the singularity problem, produces the same results as in the non-singularity cases, and shows a reasonable rate of linear convergence. The results also indicate that the $q$-th power case ($1

Algorithms with predictions have attracted much attention in the last years across various domains, including variants of facility location, as a way to surpass traditional worst-case analyses. We study the $k$-facility location mechanism design problem, where the $n$ agents are strategic and might misreport their location. Unlike previous models, where predictions are for the $k$ optimal facility locations, we receive $n$ predictions for the locations of each of the agents. However, these predictions are only "mostly" and "approximately" correct (or MAC for short) -- i.e., some $\delta$-fraction of the predicted locations are allowed to be arbitrarily incorrect, and the remainder of the predictions are allowed to be correct up to an $\varepsilon$-error. We make no assumption on the independence of the errors. Can such predictions allow us to beat the current best bounds for strategyproof facility location? We show that the $1$-median (geometric median) of a set of points is naturally robust under corruptions, which leads to an algorithm for single-facility location with MAC predictions. We extend the robustness result to a "balanced" variant of the $k$ facilities case. Without balancedness, we show that robustness completely breaks down, even for the setting of $k=2$ facilities on a line. For this "unbalanced" setting, we devise a truthful random mechanism that outperforms the best known result of Lu et al. [2010], which does not use predictions. En route, we introduce the problem of "second" facility location (when the first facility's location is already fixed). Our findings on the robustness of the $1$-median and more generally $k$-medians may be of independent interest, as quantitative versions of classic breakdown-point results in robust statistics.

Industries frequently adjust their facilities network by opening new branches in promising areas and closing branches in areas where they expect low profits. In this paper, we examine a particular class of facility location problems. Our objective is to minimize the loss of sales resulting from the removal of several retail stores. However, estimating sales accurately is expensive and time-consuming. To overcome this challenge, we leverage Monte Carlo Tree Search (MCTS) assisted by a surrogate model that computes evaluations faster. Results suggest that MCTS supported by a fast surrogate function can generate solutions faster while maintaining a consistent solution compared to MCTS that does not benefit from the surrogate function.