The paper presents a method for generating hard problem instances by treating instance creation as an optimization problem, using solver runtime as the objective. Leveraging the Nevergrad platform, the authors generate challenging instances for four NP‑hard problems—satisfiability, traveling salesperson, Hamiltonian cycle, and non‑permutation flow‑shop scheduling—that outperform random draws and rival curated benchmark sets. The approach requires only a solver, an instance encoder, and a compute budget, and it can uncover structural insights such as phase‑transition behavior in SAT.
arXiv:2609.37356v1 Announce Type: new Abstract: Generating optimization instances that are both feasible and computationally challenging is crucial for benchmarking solvers and training learning-base...
arXiv:2609.13443v1 Announce Type: cross Abstract: We demonstrate that training LLMs with RL does not improve performance equally across a dataset. RL shows large improvements on easy problems that an...
arXiv:2610.35595v1 Announce Type: new Abstract: LLMs now prove hard theorems in Lean. Can they also design algorithms and prove their correctness and efficiency? LLM-guided design of optimisation heu...
arXiv:2608.29397v1 Announce Type: new Abstract: Tool-use benchmarks generally evaluate whether an agent completes a workflow using appropriate tools and valid arguments. However, feasibility alone is...
The paper introduces OSCAR, an LLM‑based framework that translates business descriptions into accurate optimization models while verifying and improving them through a simulator, coder, and reviewer. OSCAR uses a cost‑ordered escalation strategy to select among LLMs of varying price and capability, achieving 95–100% accuracy on benchmark problems with local, open‑weight models. The framework also provides competitive guarantees and token‑cost advantages over existing LLMs like Codex and Claude Code.
arXiv:2602. 14772v2 Announce Type: replace Abstract: The Winner Determination Problem (WDP) in combinatorial auctions is NP-hard, and no existing method reliably predicts which instances will defeat fast greedy heuristics.
The paper investigates how algorithms for hard combinatorial optimization problems converge to trivial solutions, focusing on finite-size behavior rather than asymptotic limits. By analyzing large-graph asymptotics and running numerical experiments on problems like maximum independent set and maximum K‑SAT, the authors show that convergence to theoretically predicted bounds is surprisingly slow. In the intermediate regime of high constraint density, local algorithms actually outperform their asymptotic predictions, highlighting a gap between finite-regime performance and asymptotic theory.
The paper presents a method for reliably scheduling operator execution in real‑time inference on small devices, achieving exact peak‑memory predictions and certified optimality. By profiling the generated program and modeling its memory usage, the authors can permute statements to match the modeled peak, guaranteeing bitwise‑identical results on CPUs and characterizing GPU limitations. They also provide efficient lower‑bound traps and analyze selective recomputation, showing it is NP‑hard in general but can reduce peak memory on certain architectures.
The paper investigates how optimization algorithms for hard combinatorial problems converge to trivial solutions. By combining rigorous large‑graph asymptotics with numerical experiments on maximum independent set and maximum K‑SAT, the authors show that convergence to the theoretically predicted bounds is extremely slow, especially in the intermediate regime of high constraint density. This reveals a significant gap between finite‑size performance and asymptotic expectations, indicating that practical algorithm design remains essential even when theory predicts inevitable failure.
arXiv:2605. 25246v3 Announce Type: replace Abstract: Large language models (LLMs) are increasingly used for optimization modeling and solver-code generation, yet practical operations research and optimization problems often require a harder capability: designing scalable algorithms that exploit problem structure and outperform direct formulation-and-solve baselines.
Probabilistic Focal Search (PFS) augments traditional Focal Search by probabilistically choosing between the standard heuristic-guided expansion and expanding the minimum‑f node in OPEN. This strategy advances the lower bound, enlarges the FOCAL frontier, and can dramatically reduce node expansions—up to 90% in some benchmarks such as N‑Puzzle and TSP—especially when long f_min plateaus delay useful FOCAL admissions. An anytime variant, APFS, outperforms other tested anytime algorithms on the Generalized Covering TSP, and the same probabilistic scheduler transfers to Dynamic Potential Search as Probabilistic Dynamic Potential Search (PDPS), though its effectiveness varies by domain and bound.
FrugalEvo introduces a cost‑aware evolutionary framework that pairs a high‑cost, powerful LLM with a cheaper LLM to explore and refine program solutions, respectively. It incorporates a cache‑efficient evolution process that maximizes prefix reuse across steps and defines a Budget‑Aware Area Under the Curve (BA‑AUC) metric to evaluate solution quality within a fixed cost budget. Across ten mathematical and systems optimization tasks, FrugalEvo matches or surpasses state‑of‑the‑art baselines in final solution quality and achieves higher BA‑AUC on nine tasks, while delivering new state‑of‑the‑art performance on circle packing for costs as low as $0.55 to $1.68.