\(X\)-evolve: Solution space evolution powered by large language models

• URL: http://arxiv.org/abs/2508.07932v1
• Date: Mon, 11 Aug 2025 12:47:59 GMT
• Title: \(X\)-evolve: Solution space evolution powered by large language models
• Authors: Yi Zhai, Zhiqiang Wei, Ruohan Li, Keyu Pan, Shuo Liu, Lu Zhang, Jianmin Ji, Wuyang Zhang, Yu Zhang, Yanyong Zhang,
• Abstract summary: We introduce (X)-evolve, a paradigm-shifting method that instead evolves solution spaces (X) (sets of individual solutions)<n>A score-based search algorithm then efficiently explores this parametrically defined space, guided by feedback from objective function scores.
• Score: 16.586197761629744
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: While combining large language models (LLMs) with evolutionary algorithms (EAs) shows promise for solving complex optimization problems, current approaches typically evolve individual solutions, often incurring high LLM call costs. We introduce \(X\)-evolve, a paradigm-shifting method that instead evolves solution spaces \(X\) (sets of individual solutions) - subsets of the overall search space \(S\). In \(X\)-evolve, LLMs generate tunable programs wherein certain code snippets, designated as parameters, define a tunable solution space. A score-based search algorithm then efficiently explores this parametrically defined space, guided by feedback from objective function scores. This strategy enables broader and more efficient exploration, which can potentially accelerate convergence at a much lower search cost, requiring up to two orders of magnitude fewer LLM calls than prior leading methods. We demonstrate \(X\)-evolve's efficacy across three distinct hard optimization problems. For the cap set problem, we discover a larger partial admissible set, establishing a new tighter asymptotic lower bound for the cap set constant (\(C \ge 2.2203\)). In information theory, we uncover a larger independent set for the 15-vertex cycle graph (\(\mathcal{C}_{15}^{\boxtimes 5}\), size 19,946), thereby raising the known lower bound on its Shannon capacity. Furthermore, for the NP-hard online bin packing problem, we generate heuristics that consistently outperform standard strategies across established benchmarks. By evolving solution spaces, our method considerably improves search effectiveness, making it possible to tackle high-dimensional problems that were previously computationally prohibitive.

Related papers

• AdaEvolve: Adaptive LLM Driven Zeroth-Order Optimization [61.535567824938205]
  We introduce AdaEvolve, a framework that reformulates LLM-driven evolution as a hierarchical adaptive optimization problem.<n>AdaEvolve consistently outperforms the open-ended baselines across 185 different open-ended optimization problems.
  arXiv  Detail & Related papers  (2026-02-23T18:45:31Z)
• K-Search: LLM Kernel Generation via Co-Evolving Intrinsic World Model [57.440609834690385]
  Existing approaches treat Large Language Models (LLMs) as rapid code generators within evolutionary loops.<n>We propose Search via Co-Evolving World Model and build K-Search based on this method.<n>We evaluate K-Search on diverse, complex kernels FlashInfer, including GQA, MLA, and MoE kernels.
  arXiv  Detail & Related papers  (2026-02-22T11:06:22Z)
• DRAGON: LLM-Driven Decomposition and Reconstruction Agents for Large-Scale Combinatorial Optimization [40.88623618289683]
  Large Language Models (LLMs) have recently shown promise in addressing optimization problems (COPs) through prompt-based strategies.<n>We propose DRAGON, which combines the strengths of metaheuristic design and LLM reasoning.<n>By continuously interacting with the optimization environment and leveraging an adaptive experience memory, the agents iteratively learn from feedback.
  arXiv  Detail & Related papers  (2026-01-10T09:31:40Z)
• Model-Based and Sample-Efficient AI-Assisted Math Discovery in Sphere Packing [51.30643063554434]
  A leading technique for upper bounds, the three-point method, reduces the problem to solving large, high-precision semidefinite programs (SDPs)<n>We formulate SDP construction as a sequential decision process, the SDP game, in which a policy assembles SDP formulations from a set of admissible components.<n>We obtain new state-of-the-art upper bounds in dimensions $4-16$, showing that model-based search can advance computational progress in longstanding geometric problems.
  arXiv  Detail & Related papers  (2025-12-04T14:11:52Z)
• Efficient QAOA Architecture for Solving Multi-Constrained Optimization Problems [3.757262277494307]
  This paper proposes a novel combination of constraint encoding methods for the Quantum Approximate Optimization Ansatz.<n>One-hot constraints are enforced through $XY$-mixers that restrict the search space to the feasible sub-space naturally.<n>Since $XY$-mixers restrict the search space, specific state vector entries are always zero and can be omitted from the simulation, saving valuable memory and computing resources.
  arXiv  Detail & Related papers  (2025-06-03T17:46:53Z)
• Q-VLM: Post-training Quantization for Large Vision-Language Models [73.19871905102545]
  We propose a post-training quantization framework of large vision-language models (LVLMs) for efficient multi-modal inference.<n>We mine the cross-layer dependency that significantly influences discretization errors of the entire vision-language model, and embed this dependency into optimal quantization strategy.<n> Experimental results demonstrate that our method compresses the memory by 2.78x and increase generate speed by 1.44x about 13B LLaVA model without performance degradation.
  arXiv  Detail & Related papers  (2024-10-10T17:02:48Z)
• Large Language Model-Aided Evolutionary Search for Constrained Multiobjective Optimization [15.476478159958416]
  We employ a large language model (LLM) to enhance evolutionary search for solving constrained multi-objective optimization problems. Our aim is to speed up the convergence of the evolutionary population.
  arXiv  Detail & Related papers  (2024-05-09T13:44:04Z)
• Accelerating Cutting-Plane Algorithms via Reinforcement Learning Surrogates [49.84541884653309]
  A current standard approach to solving convex discrete optimization problems is the use of cutting-plane algorithms. Despite the existence of a number of general-purpose cut-generating algorithms, large-scale discrete optimization problems continue to suffer from intractability. We propose a method for accelerating cutting-plane algorithms via reinforcement learning.
  arXiv  Detail & Related papers  (2023-07-17T20:11:56Z)
• Learning Proximal Operators to Discover Multiple Optima [66.98045013486794]
  We present an end-to-end method to learn the proximal operator across non-family problems. We show that for weakly-ized objectives and under mild conditions, the method converges globally.
  arXiv  Detail & Related papers  (2022-01-28T05:53:28Z)
• Nonequilibrium Monte Carlo for unfreezing variables in hard combinatorial optimization [1.1783108699768]
  We introduce a quantum-inspired family of nonlocal Nonequilibrium Monte Carlo (NMC) algorithms by developing an adaptive gradient-free strategy. We observe significant speedup and robustness over both specialized solvers and generic solvers.
  arXiv  Detail & Related papers  (2021-11-26T17:45:32Z)
• Two-Stage Stochastic Optimization via Primal-Dual Decomposition and Deep Unrolling [86.85697555068168]
  Two-stage algorithmic optimization plays a critical role in various engineering and scientific applications. There still lack efficient algorithms, especially when the long-term and short-term variables are coupled in the constraints. We show that PDD-SSCA can achieve superior performance over existing solutions.
  arXiv  Detail & Related papers  (2021-05-05T03:36:00Z)
• Towards Optimally Efficient Tree Search with Deep Learning [76.64632985696237]
  This paper investigates the classical integer least-squares problem which estimates signals integer from linear models. The problem is NP-hard and often arises in diverse applications such as signal processing, bioinformatics, communications and machine learning. We propose a general hyper-accelerated tree search (HATS) algorithm by employing a deep neural network to estimate the optimal estimation for the underlying simplified memory-bounded A* algorithm.
  arXiv  Detail & Related papers  (2021-01-07T08:00:02Z)
• Online Model Selection for Reinforcement Learning with Function Approximation [50.008542459050155]
  We present a meta-algorithm that adapts to the optimal complexity with $tildeO(L5/6 T2/3)$ regret. We also show that the meta-algorithm automatically admits significantly improved instance-dependent regret bounds.
  arXiv  Detail & Related papers  (2020-11-19T10:00:54Z)
• Evolutionary Algorithm and Multifactorial Evolutionary Algorithm on Clustered Shortest-Path Tree problem [2.578242050187029]
  Clustered Shortest-Path Tree Problem (CluSPT) is an NP-hard problem. To enhance the performance of the search process, two approaches are proposed.
  arXiv  Detail & Related papers  (2020-10-19T08:37:18Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.