Local search is a common method for solving combinatorial optimisation problems. We focus on general-purpose local search solvers that accept as input a constraint model -- a declarative description of a problem consisting of a set of decision variables under a set of constraints. Existing approaches typically take as input models written in solver-independent constraint modelling languages like MiniZinc. The Athanor solver we describe herein differs in that it begins from a specification of a problem in the abstract constraint specification language Essence, which allows problems to be described without commitment to low-level modelling decisions through its support for a rich set of abstract types. The advantage of proceeding from Essence is that the structure apparent in a concise, abstract specification of a problem can be exploited to generate high quality neighbourhoods automatically, avoiding the difficult task of identifying that structure in an equivalent constraint model. Based on the twin benefits of neighbourhoods derived from high level types and the scalability derived by searching directly over those types, our empirical results demonstrate strong performance in practice relative to existing solution methods.

Peptide therapeutics, a major class of medicines, have achieved remarkable success across diseases such as diabetes and cancer, with landmark examples such as GLP-1 receptor agonists revolutionizing the treatment of type-2 diabetes and obesity. Despite their success, designing peptides that satisfy multiple conflicting objectives, such as target binding affinity, solubility, and membrane permeability, remains a major challenge. Classical drug development and structure-based design are ineffective for such tasks, as they fail to optimize global functional properties critical for therapeutic efficacy. Existing generative frameworks are largely limited to continuous spaces, unconditioned outputs, or single-objective guidance, making them unsuitable for discrete sequence optimization across multiple properties. To address this, we present PepTune, a multi-objective discrete diffusion model for the simultaneous generation and optimization of therapeutic peptide SMILES. Built on the Masked Discrete Language Model (MDLM) framework, PepTune ensures valid peptide structures with state-dependent masking schedules and penalty-based objectives. To guide the diffusion process, we propose a Monte Carlo Tree Search (MCTS)-based strategy that balances exploration and exploitation to iteratively refine Pareto-optimal sequences. MCTS integrates classifier-based rewards with search-tree expansion, overcoming gradient estimation challenges and data sparsity inherent to discrete spaces. Using PepTune, we generate diverse, chemically-modified peptides optimized for multiple therapeutic properties, including target binding affinity, membrane permeability, solubility, hemolysis, and non-fouling characteristics on various disease-relevant targets. In total, our results demonstrate that MCTS-guided discrete diffusion is a powerful and modular approach for multi-objective sequence design in discrete state spaces.

The Hierarchical Directed Capacitated Arc Routing Problem (HDCARP) is an extension of the Capacitated Arc Routing Problem (CARP), where the arcs of a graph are divided into classes based on their priority. The traversal of these classes is determined by either precedence constraints or a hierarchical objective, resulting in two distinct HDCARP variants. To the best of our knowledge, only one matheuristic has been proposed for these variants, but it performs relatively slowly, particularly for large-scale instances (Ha et al., 2024). In this paper, we propose a fast heuristic to efficiently address the computational challenges of HDCARP. Furthermore, we incorporate Reinforcement Learning (RL) into our heuristic to effectively guide the selection of local search operators, resulting in a hybrid algorithm. We name this hybrid algorithm as the Hybrid Reinforcement Learning and Heuristic Algorithm for Directed Arc Routing (HRDA). The hybrid algorithm adapts to changes in the problem dynamically, using real-time feedback to improve routing strategies and solution's quality by integrating heuristic methods. Extensive computational experiments on artificial instances demonstrate that this hybrid approach significantly improves the speed of the heuristic without deteriorating the solution quality. Our source code is publicly available at: https://github.com/HySonLab/ArcRoute

The growing necessity for enhanced processing capabilities in edge devices with limited resources has led us to develop effective methods for improving high-performance computing (HPC) applications. In this paper, we introduce LASP (Lightweight Autotuning of Scientific Application Parameters), a novel strategy designed to address the parameter search space challenge in edge devices. Our strategy employs a multi-armed bandit (MAB) technique focused on online exploration and exploitation. Notably, LASP takes a dynamic approach, adapting seamlessly to changing environments. We tested LASP with four HPC applications: Lulesh, Kripke, Clomp, and Hypre. Its lightweight nature makes it particularly well-suited for resource-constrained edge devices. By employing the MAB framework to efficiently navigate the search space, we achieved significant performance improvements while adhering to the stringent computational limits of edge devices. Our experimental results demonstrate the effectiveness of LASP in optimizing parameter search on edge devices.

Layer fusion techniques are critical to improving the inference efficiency of deep neural networks (DNN) for deployment. Fusion aims to lower inference costs by reducing data transactions between an accelerator's on-chip buffer and DRAM. This is accomplished by grouped execution of multiple operations like convolution and activations together into single execution units - fusion groups. However, on-chip buffer capacity limits fusion group size and optimizing fusion on whole DNNs requires partitioning into multiple fusion groups. Finding the optimal groups is a complex problem where the presence of invalid solutions hampers traditional search algorithms and demands robust approaches. In this paper we incorporate Explainable AI, specifically Graph Explanation Techniques (GET), into layer fusion. Given an invalid fusion group, we identify the operations most responsible for group invalidity, then use this knowledge to recursively split the original fusion group via a greedy tree-based algorithm to minimize DRAM access. We pair our scheme with common algorithms and optimize DNNs on two types of layer fusion: Line-Buffer Depth First (LBDF) and Branch Requirement Reduction (BRR). Experiments demonstrate the efficacy of our scheme on several popular and classical convolutional neural networks like ResNets and MobileNets. Our scheme achieves over 20% DRAM Access reduction on EfficientNet-B3.

In this paper, we delve into the utilization of the negative momentum technique in constrained minimax games. From an intuitive mechanical standpoint, we introduce a novel framework for momentum buffer updating, which extends the findings of negative momentum from the unconstrained setting to the constrained setting and provides a universal enhancement to the classic game-solver algorithms. Additionally, we provide theoretical guarantee of convergence for our momentum-augmented algorithms with entropy regularizer. We then extend these algorithms to their extensive-form counterparts. Experimental results on both Normal Form Games (NFGs) and Extensive Form Games (EFGs) demonstrate that our momentum techniques can significantly improve algorithm performance, surpassing both their original versions and the SOTA baselines by a large margin.

We introduce HunyuanProver, an language model finetuned from the Hunyuan 7B for interactive automatic theorem proving with LEAN4. To alleviate the data sparsity issue, we design a scalable framework to iterative synthesize data with low cost. Besides, guided tree search algorithms are designed to enable effective ``system 2 thinking`` of the prover. HunyuanProver achieves state-of-the-art (SOTA) performances on major benchmarks. Specifically, it achieves a pass of 68.4% on the miniF2F-test compared to 65.9%, the current SOTA results. It proves 4 IMO statements (imo_1960_p2, imo_1962_p2}, imo_1964_p2 and imo_1983_p6) in miniF2F-test. To benefit the community, we will open-source a dataset of 30k synthesized instances, where each instance contains the original question in natural language, the converted statement by autoformalization, and the proof by HunyuanProver.

In this work, we aim to develop an MLLM that understands and solves questions by learning to create each intermediate step of the reasoning involved till the final answer. To this end, we propose Collective Monte Carlo Tree Search (CoMCTS), a new learning-to-reason method for MLLMs, which introduces the concept of collective learning into ``tree search'' for effective and efficient reasoning-path searching and learning. The core idea of CoMCTS is to leverage collective knowledge from multiple models to collaboratively conjecture, search and identify effective reasoning paths toward correct answers via four iterative operations including Expansion, Simulation and Error Positioning, Backpropagation, and Selection. Using CoMCTS, we construct Mulberry-260k, a multimodal dataset with a tree of rich, explicit and well-defined reasoning nodes for each question. With Mulberry-260k, we perform collective SFT to train our model, Mulberry, a series of MLLMs with o1-like step-by-step Reasoning and Reflection capabilities. Extensive experiments demonstrate the superiority of our proposed methods on various benchmarks. Code will be available at https://github.com/HJYao00/Mulberry

Parallelization and External Memory (PEM) techniques have significantly enhanced the capabilities of search algorithms when solving large-scale problems. Previous research on PEM has primarily centered on unidirectional algorithms, with only one publication on bidirectional PEM that focuses on the meet-in-the-middle (MM) algorithm. Building upon this foundation, this paper presents a framework that integrates both uni- and bi-directional best-first search algorithms into this framework. We then develop a PEM variant of the state-of-the-art bidirectional heuristic search (BiHS) algorithm BAE* (PEM-BAE*). As previous work on BiHS did not focus on scaling problem sizes, this work enables us to evaluate bidirectional algorithms on hard problems. Empirical evaluation shows that PEM-BAE* outperforms the PEM variants of A* and the MM algorithm, as well as a parallel variant of IDA*. These findings mark a significant milestone, revealing that bidirectional search algorithms clearly outperform unidirectional search algorithms across several domains, even when equipped with state-of-the-art heuristics.

In minimax optimization, the extragradient (EG) method has been extensively studied because it outperforms the gradient descent-ascent method in convex-concave (C-C) problems. Yet, stochastic EG (SEG) has seen limited success in C-C problems, especially for unconstrained cases. Motivated by the recent progress of shuffling-based stochastic methods, we investigate the convergence of shuffling-based SEG in unconstrained finite-sum minimax problems, in search of convergent shuffling-based SEG. Our analysis reveals that both random reshuffling and the recently proposed flip-flop shuffling alone can suffer divergence in C-C problems. However, with an additional simple trick called anchoring, we develop the SEG with flip-flop anchoring (SEG-FFA) method which successfully converges in C-C problems. We also show upper and lower bounds in the strongly-convex-strongly-concave setting, demonstrating that SEG-FFA has a provably faster convergence rate compared to other shuffling-based methods.