Jianghan Zhu, Cong Zhang, Ni Zhang, Yifan Yang, Yew Soon Ong, Zhiguang Cao
Automatic operator design (AOD) has increasingly adopted large language models (LLMs) to generate problem-specific search and variation operators for multi-objective combinatorial optimization (MOCO). Yet most methods evolve the operators while leaving the process that discovers them fixed. This limits adaptation as new Pareto trade-offs and operator interactions change where and how the search should proceed. We introduce HEMO, which makes the AOD harness itself a self-evolving optimization target. HEMO maintains a persistent harness state and updates one module at a time, revising the logic that determines which experience to retrieve, which operators to improve, which parents to select, and how to formulate the orchestration of search steps. Downstream solution quality and runtime guide these updates, while a discounted UCB scheduler directs adaptation toward promising modules as their utility changes. A persistent memory filesystem preserves candidate outcomes and diagnostic feedback across harness states, enabling successive states to build on accumulated optimization experience. Experiments across eight MOCO tasks and two structurally distinct evolutionary backbones demonstrate strong performance against conventional evolutionary, neural, and LLM-based AOD baselines, together with effective transfer to related tasks. HEMO extends automatic operator design beyond evolving individual operators to improving the search process that discovers them.
Ni Zhang, Zhiqin Zhang, Ling Pan, Hoong Chuin Lau, Zhiguang Cao
Traditional neural solvers for solving vehicle routing problems (VRPs) often suffer from limited solution diversity, motivating the development of Generative Flow Network (GFlowNet)-based models. However, the effectiveness of these models is frequently constrained by insufficient flow expansion in high-reward regions, limiting their ability to distribute probability across promising solution routes. Deeper exploration could yield superior results. Diffusion models, in contrast, provide stronger structural guidance for exploration. These two paradigms are naturally complementary: GFlowNet can supply edge-level signals for diffusion to embed, while diffusion can guide broader exploration. Leveraging this synergy, we propose Diffusion-Enhanced GFlowNet (DEG), a novel framework that integrates GFlowNet with a diffusion model to encourage richer flow expansion toward high-reward regions and derive higher-quality solutions. Specifically, DEG exploits GFlowNet's inherent diversity to generate edge-specific backward signals, applies the stochastic noise schedule of diffusion to perturb these signals, and then denoises them within the GFlowNet paradigm. To further improve scalability, we introduce a specialized decoder capable of dynamically adapting to diverse problem scales. Extensive experimental evaluations on synthetic and real-world datasets, including instances with up to 10,000 nodes, demonstrate that DEG consistently achieves favorable performance compared to baseline methods.
Kuan Xu, Jianming Wang, Ni Zhang, Yaoxin Wu, Yong Wang, Zhiguang Cao
Large language models (LLMs) enable algorithm discovery for combinatorial optimization problems (COPs) through iterative program generation and evaluation. A central challenge is how to organize search to discover better algorithms within a limited budget. Our key insight is that past search trajectories and their recorded outcomes form an experience world, which can be used to facilitate the COP solving through replay. We introduce Dream-COP, in which a \emph{policy agent} learns executable policies through \emph{dreaming} in this experience world to guide a \emph{discovery agent} in generating and refining COP programs. Specifically, policy replay provides feedback on the quality of the programs revealed and the search steps used, to guide policy selection more effectively. Across five COPs, \textsc{Dream} discovers better algorithms than fixed exploration in both heuristic component design and complete solver generation. Particularly, it matches the optimal values on KP and reduces the gap on OBPP from 2.112\% to 1.199\% while using 42.5\% fewer search requests. Moreover, the learned exploration policies transfer effectively across different COPs with the assitance of the experience world.