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.
Two-Stage Robust Optimization (2RO) with discrete uncertainty is challenging, often rendering exact solutions prohibitive. Scenario reduction alleviates this issue by selecting a small, representative subset of scenarios to enable tractable computation. However, existing methods are largely problem-agnostic, operating solely on the uncertainty set without consulting the feasible region or recourse structure. In this paper, we introduce PRISE, a problem-driven sequential lookahead heuristic that constructs reduced scenario sets by evaluating the marginal impact of each scenario. While PRISE yields high-quality scenario subsets, each selection step requires solving multiple subproblems, making it computationally expensive at scale. To address this, we propose NeurPRISE, a neural surrogate model built on a GNN-Transformer backbone that encodes the per-scenario structure via graph convolution and captures cross-scenario interactions through attention. NeurPRISE is trained via imitation learning with a gain-aware ranking objective, which distills marginal gain information from PRISE into a learned scoring function for scenario ranking and selection. Extensive results on three 2RO problems show that NeurPRISE consistently achieves competitive regret relative to comprehensive methods, maintains strong calability with varying numbers of scenarios, and delivers 17-200x speedup over PRISE. NeurPRISE also exhibits strong zero-shot generalization, effectively handling instances with larger problem scales (up to 5x), more scenarios (up to 4x), and distribution shifts.