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The Ring Loading Problem (AlphaEvolve problem 61)

The Ring Loading Problem (AlphaEvolve problem 61). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

MSC 90C27 · Combinatorial optimizationMSC 90B10 · Deterministic network models in operations research

Editorial MSC2020 classification. Original article codes and source evidence are recorded in the literature directory.

Licensed source statementAs of Repository at commit 8f44745 (2026-07-11); the repository records AlphaEvolve results, not current research statusSource & evidence ↓
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Problem statement

Let CC be the infimum of all reals α\alpha for which the following statement holds: for all positive integers mm and nonnegative reals u1,…,umu_1, \ldots, u_m and v1,…,vmv_1, \ldots, v_m with ui+vi≤1u_i + v_i \leq 1, there exist z1,…,zmz_1, \ldots, z_m such that for every kk, we have zk∈{vk,−uk}z_k \in \{v_k, -u_k\}, and

∣∑i=1kzi−∑i=k+1mzi∣≤α.\left|\sum_{i=1}^k z_i - \sum_{i=k+1}^m z_i\right|\leq \alpha.

Obtain upper and lower bounds on CC that are as strong as possible.

Lean 4

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Background

Repository result category: world record — AlphaEvolve improved on the best known result recorded at the time. See Section 6.41 in "Mathematical Exploration and Discovery at Scale " paper: arXiv:2511.02864. Experiment notebook.

Progress & source assessment

The repository page records no bounds for this problem.

References
  1. [1]Georgiev, Bogdan; Gómez-Serrano, Javier; Tao, Terence; Wagner, Adam Zsolt. Repository of problems accompanying “Mathematical exploration and discovery at scale” (arXiv:2511.02864), github.com/google-deepmind/alphaevolve_repository_of_problems (commit 8f44745, 11 July 2026). — The Ring Loading Problem (AlphaEvolve problem 61) linkApache-2.0 (repository license); problem pages reproduced with attribution.

Recorded progress

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Discussion

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