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A suitable choice of the representation of candidate solutions is crucial for the efficiency of evolutionary algorithms and related metaheuristics. We focus on problems in permutation spaces, which are at the core of numerous practical applications of such algorithms, e.g., in scheduling and transportation. Inversion vectors (also called Lehmer codes) are an alternative representation of the permutation space $S_n$ compared to the classical encoding as a vector of $n$ unique entries. In particular, they do not require any constraint handling. Using rigorous mathematical runtime analyses, we compare the efficiency of inversion vector encodings to the classical representation and give theory-guided advice on their choice. Moreover, we link the effect of local changes in the inversion code space to classical measures on permutations like the number of inversions. Finally, through experimental studies on linear ordering and quadratic assignment problems, we demonstrate the practical efficiency of inversion vector encodings.

AAAI 2026

Theoretical and Empirical Analysis of Lehmer Codes to Search Permutation Spaces with Evolutionary Algorithms

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We are pleased to announce the Fortieth AAAI Conference on Artificial Intelligence (AAAI-26), which will be held in Singapore EXPO from January 20 to January 27, 2026.

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We are pleased to announce the Fortieth AAAI Conference on Artificial Intelligence (AAAI-26), which will be held in Singapore EXPO from January 20 to January 27, 2026.

Multiphase flow systems, with their complex dynamics, field discontinuities, and interphase interactions, pose significant computational challenges for traditional numerical solvers. While neural operators offer efficient alternatives, they often struggle to achieve high-resolution numerical accuracy in these systems. This limitation primarily stems from the inherent spatial heterogeneity and the scarcity of high-quality training data in multiphase flows.
In this work, we propose the Interface Information-Aware Neural Operator (IANO), a novel framework that explicitly incorporates interface topology to enhance the prediction accuracy even in low-data regimes. The IANO architecture introduces two key components: 1) An interface-aware multiple function encoding mechanism jointly models multiple physical fields and interface topology, thus capturing the high-frequency physical features at the interface.
2) A geometry-aware positional encoding mechanism further establishes the relationship between interface topology, physical variables, and spatial positions, making it to achieve pointwise super-resolution prediction in a more refined spatial space. Experimental results demonstrate that IANO outperforms baselines by $\sim$10\% in accuracy for multiphase flow simulations while maintaining robustness under data-scarce and noise-perturbed conditions.

Cross-Field Interface-Aware Neural Operators for Multiphase Flow Simulation

Recently, Interleaved-modal Chain-of-Thought (ICoT) reasoning has achieved remarkable success by leveraging both multimodal inputs and outputs, attracting increasing attention. While achieving promising performance, current ICoT methods still suffer from two major limitations: (1) Static Visual Thought Positioning, which statically inserts visual information at fixed steps, resulting in inefficient and inflexible reasoning; and (2) Broken Visual Thought Representation, which involves discontinuous and semantically incoherent visual tokens. To address these limitations, we introduce Interleaved-modal Chain-of-Thought reasoning with Dynamic and Precise Visual Thoughts (DaP-ICoT), which incorporates two key components: (1) Dynamic Visual Thought Integration adaptively introduces visual inputs based on reasoning needs, reducing redundancy and improving efficiency. (2) Precise Visual Thought Guidance ensures visual semantically coherent and contextually aligned representations. Experiments across multiple benchmarks and models demonstrate that DaP-ICoT achieves state-of-the-art performance. In addition, DaP-ICoT significantly reduces the number of inserted images, leading to a 72.6% decrease in token consumption, enabling more efficient ICoT reasoning.

Let’s Think with Images Efficiently! An Interleaved-Modal Chain-of-Thought Reasoning Framework with Dynamic and Precise Visual Thoughts

The MOEA/D is the most popular decomposition-based evolutionary algorithm to solve multi-objective optimization problems. However, among the two common decomposition approaches, weighted-sum and Tchebycheff, the existing theoretical research almost exclusively focus on the latter one. In this first complete mathematical runtime analysis for the MOEA/D using the original weighted-sum decomposition, we show that this variant of the algorithm solves the classic ONEMINMAX benchmark considerably faster than both the MOEA/D with Tchebycheff decomposition and many other classic algorithms such as the NSGA-II, NSGA-III, SMS-EMOA, and SPEA2. More precisely, we show that already a logarithmic number of subproblems suffices for the algorithm to be efficient, and then typically $O(n \log^2 n)$ function evaluations suffice to compute the full Pareto front. This beats the other algorithms by a factor of $\Theta(n / \log n)$. For a second benchmark, the ONEJUMPZEROJUMP problem, we show a speed-up by a factor of $\Theta(n)$. Overall, this work shows that a further development of the weighted-sum approach might be fruitful.

Superior Runtime Guarantees for the MOEA/D Multi-Objective Optimizer via Weighted-Sum Decomposition

We propose a multi-agent multi-armed bandit (MA-MAB) framework to ensure fair outcomes across agents while maximizing overall system performance. For example, in a ridesharing setting where a central dispatcher assigns drivers to distinct geographic regions, utilitarian welfare (the sum of driver earnings) can be highly skewed—some drivers may receive no rides. We instead measure fairness by Nash social welfare, i.e., the product of individual rewards. A key challenge in this setting is decision-making under limited information about arm rewards (geographic regions). To address this, we introduce a novel probing mechanism that strategically gathers information about selected arms before assignment. In the offline setting, where reward distributions are known, we exploit submodularity to design a greedy probing algorithm with a constant-factor approximation guarantee. In the online setting, we develop a probing-based algorithm that achieves sublinear regret while preserving Nash social welfare. Extensive experiments on synthetic and real-world datasets demonstrate that our approach outperforms baseline methods in both fairness and efficiency.

Fair Algorithms with Probing for Multi-Agent Multi-Armed Bandits

The powerful generalization capabilities of Vision-Language-Action (VLA) models are bottlenecked by their heavy reliance on massive, redundant, and unevenly valued datasets, hindering their widespread application. Existing model-centric optimization paths, whether through model compression (which often leads to performance degradation) or policy distillation (where the output is model-dependent and lacks versatility), have failed to fundamentally address this data-level challenge. To this end, we propose a fundamentally different, data-centric generative data distillation framework, FT-NCFM. Our framework employs a self-contained FT (Fact-Tracing) engine that combines causal attribution with programmatic contrastive verification to assess the intrinsic value of samples. This evaluation guides an NCFM adversarial game to synthesize a model-agnostic, information-dense, reusable data asset. Experimental results on several mainstream VLA benchmarks show that using just 5% of our distilled coreset, we can train models that achieve over 90% of the task success rate of models trained on the full dataset, while reducing training time by 75.4%. Our work demonstrates that intelligent data distillation is a highly promising new path for building efficient, high-performance VLA models. Code and datasets will be made available upon acceptance.

FT-NCFM: An Influence-Aware Data Distillation Framework for Efficient VLA Models

Recent advancements in bidirectional heuristic search have yielded significant theoretical insights and novel algorithms.
While most previous work has concentrated on optimal search methods, this paper focuses on bounded-suboptimal bidirectional search, where a bound on the suboptimality of the solution cost is specified. We build upon the state-of-the-art optimal bidirectional search algorithm, BAE*, designed for consistent heuristics, and introduce several variants of BAE* specifically tailored for the bounded-suboptimal context. Through experimental evaluation, we compare the performance of these new variants against other bounded-suboptimal bidirectional algorithms as well as the standard weighted A* algorithm. Our results demonstrate that each algorithm excels under distinct conditions, highlighting the strengths and weaknesses of each approach.

Bidirectional Bounded-Suboptimal Heuristic Search with Consistent Heuristics

Recent progress in two-view geometry increasingly emphasizes enforcing smoothness and global consistency priors when estimating motion fields between pairs of images. However, in complex real-world scenes, characterized by extreme viewpoint and scale changes as well as pronounced depth discontinuities, the motion field often exhibits diverse and heterogeneous motion patterns. Most existing methods lack targeted modeling strategies and fail to explicitly account for this variability, resulting in estimated motion fields that diverge from their true underlying structure and distribution. We observe that Mixture-of-Experts (MoE) can assign dedicated experts to motion sub-fields, enabling a divide-and-conquer strategy for heterogeneous motion patterns. Building on this insight, we re-architect motion field modeling in two-view geometry with GeoMoE, a streamlined framework. Specifically, we first devise a Probabilistic Prior-Guided Decomposition strategy that exploits inlier probability signals to perform a structure-aware decomposition of the motion field into heterogeneous sub-fields, sharply curbing outlier-induced bias. Next, we introduce an MoE-Enhanced Bi-Path Rectifier that enhances each sub-field along spatial-context and channel-semantic paths and routes it to a customized expert for targeted modeling, thereby decoupling heterogeneous motion regimes, suppressing cross-sub-field interference and representational entanglement, and yielding fine-grained motion-field rectification. With this minimalist design, GeoMoE outperforms prior state-of-the-art methods in relative pose and homography estimation and shows strong generalization.

GeoMoE: Divide-and-Conquer Motion Field Modeling with Mixture-of-Experts for Two-View Geometry

Text-only training provides an attractive approach to address data scarcity challenges in zero-shot image captioning (ZIC), avoiding the expense of collecting paired image-text annotations. However, although these approaches perform well within training domains, they suffer from poor cross-domain generalization, often producing hallucinated content when encountering novel visual environments. Retrieval-based methods attempt to mitigate this limitation by leveraging external knowledge, but they can paradoxically exacerbate hallucination when retrieved captions contain entities irrelevant to the inputs. We introduce the concept of $\textbf{\emph{negative entities}}$—objects that appear in generated caption but are absent from the input—and propose Negative Entity Suppression (NES) to tackle this challenge. NES seamlessly integrates three stages: (1) it employs synthetic images to ensure consistent image-to-text retrieval across both training and inference; (2) it filters negative entities from retrieved content to enhance accuracy; and (3) it applies attention-level suppression using identified negative entities to further minimize the impact of hallucination-prone features. Evaluation across multiple benchmarks demonstrates that NES maintains competitive in-domain performance while improving cross-domain transfer and reducing hallucination rates, achieving new state-of-the-art results in ZIC. Our code is available at: https://anonymous.4open.science/r/NES-CB86

Negative Entity Suppression for Zero-Shot Captioning with Synthetic Images

Distributed online convex optimization (D-OCO), where multiple agents within a network collaboratively learn optimal decisions in real-time, arises naturally in applications such as federated learning, sensor networks, and multi-agent control. In this paper, we study D-OCO under unknown, time- and agent-varying feedback delays. While recent work has addressed delayed feedback (Nguyen, Kim Thang,
and Trystram 2024), existing algorithms assume prior knowledge of the cumulative delay over agents and still suffer from suboptimal dependence on both the delay and network parameters. To overcome these limitations, we propose a novel algorithm that achieves an improved regret bound of $\widetilde{\mathcal{O}}\Big(\sqrt{N^3d_{\text{tot},T}} + \sqrt{\frac{N^{5/2}T}{\sqrt{1-\sigma_2}}}\Big)$, where $d_{\text{tot}}$ denotes the average total delay across agents, $N$ is the number of agents, and $1 - \sigma_2$ is the spectral gap of the network. We also show that the dependence on $T$, $d_{\text{tot}}$ and $\sigma_2$ is tight by providing a matching lower bound. Our approach builds upon recent advances in D-OCO (Wan et al. 2024), but crucially incorporates an adaptive learning rate mechanism via a decentralized communication protocol. This enables each agent to estimate delays locally using a gossip-based strategy without the prior knowledge of the total delay. We further extend our framework to the strongly convex setting and derive sharper regret bounds. Experimental results validate the effectiveness of our approach, showing improvements over existing benchmark algorithms.

Decentralized Online Convex Optimization with Unknown Feedback Delays

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.

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Cross-Field Interface-Aware Neural Operators for Multiphase Flow Simulation

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