Constraint Programming and its high-level modeling languages have long been recognized for their potential to achieve the holy grail of problem-solving. However, the complexity of modeling languages, the large number of global constraints, and the art of creating good models have often hindered non-experts from choosing CP to solve their combinatorial problems. While generating an expert-level model from a natural-language description of a problem would be the dream, we are not yet there. We propose a tutoring system called CP-Model-Zoo, exploiting expert-written models accumulated through the years. CP-Model-Zoo retrieves the closest source code model from a database based on a user's natural language description of a combinatorial problem. It ensures that expert-validated models are presented to the user while eliminating the need for human data labeling. Our experiments show excellent accuracy in retrieving the correct model based on a user-input description of a problem simulated with different levels of expertise.

In serial batch (s-batch) scheduling, jobs are grouped in batches and processed sequentially within their batch. This paper considers multiple parallel machines, nonidentical job weights and release times, and sequence-dependent setup times between batches of different families. Although s-batch has been widely studied in the literature, very few papers have taken into account a minimum batch size, typical in practical settings such as semiconductor manufacturing and the metal industry. The problem with this minimum batch size requirement has been mostly tackled with dynamic programming and meta-heuristics, and no article has ever used constraint programming (CP) to do so. This paper fills this gap by proposing, three CP models for s-batching with minimum batch size: (i) an Interval Assignment model that computes and bounds the size of the batches using the presence literals of interval variables of the jobs. The computational experiments on standard cases compare the three CP models with two existing mixed-integer programming (MIP) models from the literature. The results demonstrate the versatility of the proposed CP models to handle multiple variations of s-batching; and their ability to produce, in large instances, better solutions than the MIP models faster. Introduction In the current and highly competitive landscape of the manufacturing industry, companies are under growing pressure to minimize production costs and reduce cycle times. One effective strategy to improve efficiency is to process similar tasks, called jobs, together in groups known as batches [1]. There are two main ways to process these batches. In parallel batching (p-batch), all jobs in a batch are processed simultaneously [2]. In contrast, in serial batching (s-batch), jobs in a batch are processed sequentially one after another [3]. The benefits of p-batching are obvious since it saves time by processing multiple jobs at once. Similarly, s-batching is especially useful when grouping similar jobs can prevent repetitive machine setups, which are time-consuming and costly [4]. Serial batching appears in many industries, including metal processing [5], additive manufacturing (3D printing) [5, 6], paint [7] and pharmaceutical production [8], chemical manufacturing [9], and semiconductor manufacturing [10, 11].

Large language models (LLMs) are increasingly expected to go beyond simple factual queries toward Deep Research--tasks that require decomposing questions into sub-problems, coordinating multi-step reasoning, and synthesizing evidence from diverse sources. We formalize Deep Research tasks with verifiable answers as Hierarchical Constraint Satisfaction Problems (HCSPs), which are fundamentally different from single-constraint, multi-hop, or flat CSP formulations. However, existing benchmarks (e.g., Natural Questions, HotpotQA) fail to capture this complexity, while recent synthetic datasets often introduce shortcut reasoning, knowledge leakage, or lack sufficient structural depth. To address this gap, we introduce InfoSeek, a scalable framework for synthesizing complex Deep Research tasks. InfoSeek uses a dual-agent system to recursively build a Research Tree from large-scale webpages, blurring intermediate nodes into valid sub-problems, and converting these trees into natural language questions that require traversing the full hierarchy. It also enables rapid scaling, yielding over 50K training examples, a curated test set, and reasoning trajectories generated via reject sampling. Experiments show that models trained on InfoSeek consistently outperform strong baselines. On a challenging benchmark BrowseComp-Plus, 3B LLMs optimized with InfoSeek surpass much larger 32B models and lightweight commercial APIs (e.g., Gemini2.5-Flash), while achieving performance comparable to stronger APIs (e.g., Gemini2.5-Pro). By preserving meta-information such as intermediate steps and retrieval labels, InfoSeek further supports advanced optimization strategies, including compound reward design and trajectory-level exploration. We provide our codes and datasets in this repository.Figure 1: Performance comparison on the BrowseComp-Plus benchmark. InfoSeeker-3B, a compact LLM trained with the InfoSeek dataset, significantly outperforms Qwen3-32B and achieves performance on par with leading commercial LLMs (ordered in API prices), highlighting the strong potential of InfoSeek for advancing Deep Research tasks.

Multi-Robot Motion Planning (MRMP) involves generating collision-free trajectories for multiple robots operating in a shared continuous workspace. While discrete multi-agent path finding (MAPF) methods are broadly adopted due to their scalability, their coarse discretization severely limits trajectory quality. In contrast, continuous optimization-based planners offer higher-quality paths but suffer from the curse of dimensionality, resulting in poor scalability with respect to the number of robots. This paper tackles the limitations of these two approaches by introducing a novel framework that integrates discrete MAPF solvers with constrained generative diffusion models. The resulting framework, called Discrete-Guided Diffusion (DGD), has three key characteristics: (1) it decomposes the original nonconvex MRMP problem into tractable subproblems with convex configuration spaces, (2) it combines discrete MAPF solutions with constrained optimization techniques to guide diffusion models capture complex spatiotemporal dependencies among robots, and (3) it incorporates a lightweight constraint repair mechanism to ensure trajectory feasibility. The proposed method sets a new state-of-the-art performance in large-scale, complex environments, scaling to 100 robots while achieving planning efficiency and high success rates.

Failure-Directed Search (FDS) is a significant complete generic search algorithm used in Constraint Programming (CP) to efficiently explore the search space, proven particularly effective on scheduling problems. This paper analyzes FDS's properties, showing that minimizing the size of its search tree guided by ranked branching decisions is closely related to the Multi-armed bandit (MAB) problem. Building on this insight, MAB reinforcement learning algorithms are applied to FDS, extended with problem-specific refinements and parameter tuning, and evaluated on the two most fundamental scheduling problems, the Job Shop Scheduling Problem (JSSP) and Resource-Constrained Project Scheduling Problem (RCPSP). The resulting enhanced FDS, using the best extended MAB algorithm and configuration, performs 1.7 times faster on the JSSP and 2.1 times faster on the RCPSP benchmarks compared to the original implementation in a new solver called OptalCP, while also being 3.5 times faster on the JSSP and 2.1 times faster on the RCPSP benchmarks than the current state-of-the-art FDS algorithm in IBM CP Optimizer 22.1. Furthermore, using only a 900-second time limit per instance, the enhanced FDS improved the existing state-of-the-art lower bounds of 78 of 84 JSSP and 226 of 393 RCPSP standard open benchmark instances while also completely closing a few of them.

Procedural Content Generation for 3D game levels faces challenges in balancing spatial coherence, navigational functionality, and adaptable gameplay progression across multi-floor environments. This paper introduces a novel framework for generating such levels, centered on the offline, LLM-assisted construction of reusable databases for architectural components (facilities and room templates) and gameplay mechanic elements. Our multi-phase pipeline assembles levels by: (1) selecting and arranging instances from the Room Database to form a multi-floor global structure with an inherent topological order; (2) optimizing the internal layout of facilities for each room based on predefined constraints from the Facility Database; and (3) integrating progression-based gameplay mechanics by placing components from a Mechanics Database according to their topological and spatial rules. A subsequent two-phase repair system ensures navigability. This approach combines modular, database-driven design with constraint-based optimization, allowing for systematic control over level structure and the adaptable pacing of gameplay elements. Initial experiments validate the framework's ability in generating diverse, navigable 3D environments and its capability to simulate distinct gameplay pacing strategies through simple parameterization. This research advances PCG by presenting a scalable, database-centric foundation for the automated generation of complex 3D levels with configurable gameplay progression.

Advancing AI systems in scientific domains like physics, materials science, and engineering calls for reasoning over complex, multi-physics phenomena while respecting governing principles. Although Large Language Models (LLMs) and existing preference optimization techniques perform well on standard benchmarks, they often struggle to differentiate between physically valid and invalid reasoning. This shortcoming becomes critical in high-stakes applications like metal joining, where seemingly plausible yet physically incorrect recommendations can lead to defects, material waste, equipment damage, and serious safety risks. To address this challenge, we introduce PKG-DPO, a novel framework that integrates Physics Knowledge Graphs (PKGs) with Direct Preference Optimization (DPO) to enforce physical validity in AI-generated outputs. PKG-DPO comprises three key components A) hierarchical physics knowledge graph that encodes cross-domain relationships, conservation laws, and thermodynamic principles. B) A physics reasoning engine that leverages structured knowledge to improve discrimination between physically consistent and inconsistent responses. C) A physics-grounded evaluation suite designed to assess compliance with domain-specific constraints. PKG-DPO achieves 17% fewer constraint violations and an 11% higher Physics Score compared to KG-DPO (knowledge graph-based DPO). Additionally, PKG-DPO demonstrates a 12\% higher relevant parameter accuracy and a 7% higher quality alignment in reasoning accuracy. While our primary focus is on metal joining, the framework is broadly applicable to other multi-scale, physics-driven domains, offering a principled approach to embedding scientific constraints into preference learning.

The Profiled V ehicle Routing Problem (PVRP) extends the classical VRP by incorporating vehicle-client-specific preferences and constraints, reflecting real-world requirements such as zone restrictions and service-level preferences. While recent reinforcement-learning solvers have shown promising performance, they require retraining for each new profile distribution, suffer from poor representation ability, and struggle to generalize to out-of-distribution instances. In this paper, we address these limitations by introducing U nified Solver for Profiled R outing (USPR), a novel framework that natively handles arbitrary profile types. USPR introduces on three key innovations: (i) Profile Embeddings (PE) to encode any combination of profile types; (ii) Multi-Head Profiled Attention (MHP A), an attention mechanism that models rich interactions between vehicles and clients; (iii) Profile-aware Score Reshaping (PSR), which dynamically adjusts decoder logits using profile scores to improve generalization. Empirical results on diverse PVRP benchmarks demonstrate that USPR achieves state-of-the-art results among learning-based methods while offering significant gains in flexibility and computational efficiency. We make our source code publicly available to foster future research.

We address the problem of data scarcity in harmful text classification for guardrailing applications and introduce GRAID (Geometric and Reflective AI-Driven Data Augmentation), a novel pipeline that leverages Large Language Models (LLMs) for dataset augmentation. GRAID consists of two stages: (i) generation of geometrically controlled examples using a constrained LLM, and (ii) augmentation through a multi-agentic reflective process that promotes stylistic diversity and uncovers edge cases. This combination enables both reliable coverage of the input space and nuanced exploration of harmful content. Using two benchmark data sets, we demonstrate that augmenting a harmful text classification dataset with GRAID leads to significant improvements in downstream guardrail model performance.

Enabling neural networks to learn complex logical constraints and fulfill symbolic reasoning is a critical challenge. Bridging this gap often requires guiding the neural network's output distribution to move closer to the symbolic constraints. While diffusion models have shown remarkable generative capability across various domains, we employ the powerful architecture to perform neuro-symbolic learning and solve logical puzzles. Our diffusion-based pipeline adopts a two-stage training strategy: the first stage focuses on cultivating basic reasoning abilities, while the second emphasizes systematic learning of logical constraints. To impose hard constraints on neural outputs in the second stage, we formulate the diffusion reasoner as a Markov decision process and innovatively fine-tune it with an improved proximal policy optimization algorithm. We utilize a rule-based reward signal derived from the logical consistency of neural outputs and adopt a flexible strategy to optimize the diffusion reasoner's policy. We evaluate our methodology on some classical symbolic reasoning benchmarks, including Sudoku, Maze, pathfinding and preference learning. Experimental results demonstrate that our approach achieves outstanding accuracy and logical consistency among neural networks.