We study GCS-TSP, a new variant of the Traveling Salesman Problem (TSP) defined over a Graph of Convex Sets (GCS) -- a powerful representation for trajectory planning that decomposes the configuration space into convex regions connected by a sparse graph. In this setting, edge costs are not fixed but depend on the specific trajectory selected through each convex region, making classical TSP methods inapplicable. We introduce GHOST, a hierarchical framework that optimally solves the GCS-TSP by combining combinatorial tour search with convex trajectory optimization. GHOST systematically explores tours on a complete graph induced by the GCS, using a novel abstract-path-unfolding algorithm to compute admissible lower bounds that guide best-first search at both the high level (over tours) and the low level (over feasible GCS paths realizing the tour). These bounds provide strong pruning power, enabling efficient search while avoiding unnecessary convex optimization calls. We prove that GHOST guarantees optimality and present a bounded-suboptimal variant for time-critical scenarios. Experiments show that GHOST is orders-of-magnitude faster than unified mixed-integer convex programming baselines for simple cases and uniquely handles complex trajectory planning problems involving high-order continuity constraints and an incomplete GCS.

Efficient coordination of multiple robots for coverage of large, unknown environments is a significant challenge that involves minimizing the total coverage path length while reducing inter-robot conflicts. In this paper, we introduce a Multi-robot Connectivity-Aware Planner (Multi-CAP), a hierarchical coverage path planning algorithm that facilitates multi-robot coordination through a novel connectivity-aware approach. The algorithm constructs and dynamically maintains an adjacency graph that represents the environment as a set of connected subareas. Critically, we make the assumption that the environment, while unknown, is bounded. This allows for incremental refinement of the adjacency graph online to ensure its structure represents the physical layout of the space, both in observed and unobserved areas of the map as robots explore the environment. We frame the task of assigning subareas to robots as a Vehicle Routing Problem (VRP), a well-studied problem for finding optimal routes for a fleet of vehicles. This is used to compute disjoint tours that minimize redundant travel, assigning each robot a unique, non-conflicting set of subareas. Each robot then executes its assigned tour, independently adapting its coverage strategy within each subarea to minimize path length based on real-time sensor observations of the subarea. We demonstrate through simulations and multi-robot hardware experiments that Multi-CAP significantly outperforms state-of-the-art methods in key metrics, including coverage time, total path length, and path overlap ratio. Ablation studies further validate the critical role of our connectivity-aware graph and the global tour planner in achieving these performance gains.

This study presents Neural Focused Ant Colony Optimization (NeuFACO), a non-autoregressive framework for the Traveling Salesman Problem (TSP) that combines advanced reinforcement learning with enhanced Ant Colony Optimization (ACO). NeuFACO employs Proximal Policy Optimization (PPO) with entropy regularization to train a graph neural network for instance-specific heuristic guidance, which is integrated into an optimized ACO framework featuring candidate lists, restricted tour refinement, and scalable local search. By leveraging amortized inference alongside ACO stochastic exploration, NeuFACO efficiently produces high-quality solutions across diverse TSP instances.

A.2 Proof of Theorem 1 To prove Theorem 1, we assume that G Proof of Lemma 1. Let's first rewrite Equation (4) as null null By Lemma 1, linearity of expectation and knowing that each RWT is independent from the other tours by the Strong Markov Property, Theorem 1 holds. MHM-GNN can recover edge-based models where representations don't use graph-wide However, on Rent the Runway we see the raw features achieving the highest performance. That is, structural information does not seem to be relevant to this specific task. All hyperparameters were chosen to minimize training loss. For k = 5, we used a minibatch of size 5 in all datasets.

Prompt design is a critical factor in the effectiveness of Large Language Models (LLMs), yet remains largely heuristic, manual, and difficult to scale. This paper presents the first comprehensive evaluation of Automatic Prompt Optimization (APO) methods for real-world, high-stakes multiclass classification in a commercial setting, addressing a critical gap in the existing literature where most of the APO frameworks have been validated only on benchmark classification tasks of limited complexity. We introduce APE-OPRO, a novel hybrid framework that combines the complementary strengths of APE and OPRO, achieving notably better cost-efficiency, around $18\%$ improvement over OPRO, without sacrificing performance. We benchmark APE-OPRO alongside both gradient-free (APE, OPRO) and gradient-based (ProTeGi) methods on a dataset of ~2,500 labeled products. Our results highlight key trade-offs: ProTeGi offers the strongest absolute performance at lower API cost but higher computational time as noted in~\cite{protegi}, while APE-OPRO strikes a compelling balance between performance, API efficiency, and scalability. We further conduct ablation studies on depth and breadth hyperparameters, and reveal notable sensitivity to label formatting, indicating implicit sensitivity in LLM behavior. These findings provide actionable insights for implementing APO in commercial applications and establish a foundation for future research in multi-label, vision, and multimodal prompt optimization scenarios.

Tours of electric vehicle factories have quickly become the hottest ticket in Beijing, with tens of thousands of people signing up each month for the chance to win a free visit. Chinese smartphone giant Xiaomi, which has reinvented itself as an EV maker in recent years, started offering the one-hour tours in January to visitors interested in seeing its factory up close and getting a race car experience in a Xiaomi EV. As Chinese EV brands expand from competing on low prices to promoting premium features and sleek designs, they are increasingly putting their factories in the spotlight. At least two Chinese EV brands, Xiaomi and Nio, offer regular tours for the general public this year, and three more automakers have announced plans to follow suit. "More and more Chinese EVs are using factory tours as an important channel of communication between the brand and the outside world. It offers a chance to not only see the production line up close, but also experience the human side of the brand," says Freya Zhang, a research analyst at the investment consulting firm Tech Buzz China, who has been organizing tours for foreign investors to visit Chinese electric vehicle startups for two years.

Planning a trip takes time and often its more of a hassle than you'd like. If you don't feel like spending hours researching, you can simply outsource the first draft of your holiday plans to ChatGPT. The chatbot suggests travel destinations, creates daily plans, compares means of transport, reminds you of charging devices, and even virtually packs your suitcase. But how reliable are these suggestions? And can it actually save you money?