manufacturing process planners

Abstract: Engineering design frequently involves redesigning a prior solution to adapt to changes in context, such as material prices or system requirements. Redesign often leverages simulators too complex and/or computationally intensive for traditional numerical solvers, which lack engineering knowledge and context, to ensure global solution quality. Large language models (LLMs) can interpret semantic information, including engineering knowledge about the system and changes in context, to help guide search, and recent studies have shown that incorporating this knowledge into optimization can improve search performance. However, how best to combine LLMs with numerical solvers in redesign remains unclear. We develop and test an integrated LLM-optimization approach for redesign and compare three methods for leveraging LLMs (warm start, variable fixing and ReAct) and four black-box solvers (Bayesian optimization, genetic algorithms, mesh adaptive direct search and random search) on an electric vehicle battery pack cost minimization case study across four types of redesign scenarios. We find that the integrated approach can match feasible design discovery of the numerical-solver baselines with 80% fewer simulator evaluations while tripling the fraction of runs that find near-optimal solutions. We find that the best LLM-solver integration approach and the way the prior solution is leveraged depend on the structure of the design requirement change, and that the benefit of increasing LLM model size grows with the extent to which the LLM controls the search. These results show clear potential for LLMs in redesign tasks for guiding or replacing numerical solvers.

Abstract: The mechanical properties of a metallic alloy are set by its microstructure and texture: the size and shape of its grains and the orientation of their crystals. That structure is in turn set by a recipe, the alloy composition together with the processing parameters. Alloy development runs this chain forwards, tuning the structure until a target property is met. Running it backwards, from an optimized structure to the recipe that would produce it, still relies on expert knowledge. We ask whether this backwards step can be learned. On an in-house dataset of 107 magnesium alloy extrusion conditions across 14 alloys, each with optical micrographs and an X-ray texture measurement, we compare three descriptors of microstructure and texture: conventional grain and texture statistics, a vision embedding from a pretrained image encoder, and a graph neural network on the grain network. Each is paired with prediction heads for two tasks: the alloy composition given the process (Task A), and the process parameters given the composition (Task B). Under 5-fold cross-validation, the conventional descriptors identify the correct alloy for 65% of held-out conditions, against 17% for always guessing the most common alloy, while the learned embeddings stay below 30%. The process parameters are recoverable but noisier: compared with using the composition alone, the microstructure roughly halves the temperature error. Because only a few alloys were cast and only a few press settings were used, both answers are discrete, and heads that pick from these known options, while respecting their order, worked better than heads that predict a free value.

Abstract: The job shop scheduling problem is a challenging combinatorial optimization problem, and recent reinforcement learning approaches using graph neural networks have shown promise for learning scheduling policies directly from problem instances. However, training on large instances remains computationally expensive, and generalization across instance sizes remains challenging. This paper studies curriculum learning for graph neural network-based reinforcement learning in the job shop scheduling problem by comparing it with single-size training across three target sizes: 20 x 20, 25 x 25, and 30 x 30. In the curriculum setting, the policy is first trained on smaller instances and then progressively adapted to larger target sizes, allowing scheduling behavior learned in earlier stages to support learning on larger instances. Models are evaluated on unseen instances from 8 x 8 to 30 x 30 using the optimality gap, considering both generalization across all evaluation sizes and specialization on the target size. Results show that curriculum learning consistently reduces wall-clock training time, with larger benefits as the target size increases. The strongest advantage is observed at 30 x 30, where curriculum learning reduces the mean optimality gap across all evaluation sizes by approximately 8.1 percentage points, reduces the target-size mean optimality gap by approximately 8.6 percentage points, and saves approximately 50 hours of training time.

Abstract: Multi-Fidelity optimization (MFO) has received extensive attentions in engineering design, which resorts to augmenting the small number of expensive high-fidelity (HF) samples by a large number of low-fidelity (LF) but cheap samples to improve the optimization performance. A key factor that influences the effectiveness of MFO is how to adaptively assign samples for HF and LF simulations in the iteration process. To address such sample assignment issue in MFO, we propose a new infill criterion named as Filter-GEI, which imposes an adaptive filter function on top of the generalized expected improvement (GEI) acquisition function. In particular, by taking the correlations between HF and LF models into account, the Filter-GEI can efficiently allocate HF and LF samples to achieve a good balance in between the local and global search. Furthermore, considering parallel computing, the Filter-GEI infills multiple HF and LF samples in each iteration, which can further improve its efficiency as computing power increases. Through tests on five mathematical toy problems and one engineering problem for the turbine blade design, the effectiveness of the proposed algorithm has been well demonstrated.

Abstract: We study packings of annuli ("rings") of a common width into a disk, where a ring may nest inside the hole of a strictly larger one, a selection-oriented relative of the Recursive Circle Packing Problem. The two natural objectives, cardinality and contact area, genuinely diverge. For superincreasing radii (each exceeding the sum of all smaller ones) we prove that the descending greedy maximizes every positive, increasing, superadditive objective. Our main structural theorem shows more: the placement rule is irrelevant - any choice among feasible containers yields the lexicographically maximal feasible set, for containers of arbitrary shape and in every dimension. Both hypotheses are sharp: placement irrelevance holds for at most three rings and fails at four, and twin instances rule out every rule that is a function of the observable state. Write $ρ=\max_i(\sum_{j>i}r_j)/r_i$ for the violation of superincreasingness. The additive relaxation has universal threshold exactly $ρ=1$. In the geometric model we prove, with no tangency idealization, that the rigid four-ring family has infimum exactly the Tribonacci constant $T\approx1.83929$. Yet $T$ is not the global threshold: an explicit golden family breaks placement obliviousness at $ρ=\varphi+3\varepsilon$ for every small $\varepsilon>0$, proving $τ\le\varphi<T$ for the geometric threshold $τ$ and refuting the natural Tribonacci-threshold conjecture. The matching bound $τ\ge\varphi$ remains conjectural; we prove it for pair profiles and outside an explicit heavy region. We also give a phase diagram for this divergence and split hardness into a geometric layer and a combinatorial (subset-sum) layer, of which superincreasingness eliminates exactly the latter. The main theorems carry complete written proofs; every computer-assisted closure carries an epistemic label and a script in the verification map.

Abstract: The 11/6 worst-case constant of the Wang-Sitters rounding scheme, which a companion note establishes, can naturally be attributed to the freedom in Step 3, where an arbitrary valid slot matching is permitted. We show that eliminating that freedom does not improve the constant. A minimum-makespan completion oracle still has worst-case constant exactly 11/6 against the optimum; both natural 7/4 statements about it are false; and restricting Step 1 to vertices of the relaxation does not help. The loss therefore cannot be attributed solely to the freedom in Step 3. We also record what structure survives: a reduction confining every overload to two shapes, a seven-machine instance defeating the natural two-phase repair, and a strict 7/4 bound on the generalized three-path family.