Humans often find good solutions to combinatorial optimization problems that are computationally hard even for advanced computer algorithms. In the Euclidean traveling salesman problems (TSP), people rapidly produce tours that are near-optimal, despite severe limits on time and computation. What makes a tour human-like, and how might such solutions be learned? Here we address these questions through a large-scale behavioral and computational investigation of human performance in Euclidean TSP. We sampled a broad space of TSP instances, collected human solutions, and compared them with neural policies based on Pointer Networks, which are recurrent neural networks with an attention-based pointing mechanism that define probability distributions over valid tours. We trained these networks under multiple objectives, including reinforcement learning (RL), supervised learning from optimal tours, supervised learning from human tours, and RL fine-tuning after optimal-supervised pretraining. Human tours were not identical to optimal tours, but occupied a near-optimal geometric basin: they shared many structural properties with optimal solutions while preserving systematic human-specific deviations. The best account of human tours was not direct imitation of optimal tours, but a model pretrained on optimal tours, fine-tuned by RL, and decoded through $\text{Best-of-}N$ sampling. These findings suggest that human-like solutions may emerge from a combination of structured supervised learning, RL, and test-time search, echoing computational principles underlying many modern artificial intelligence systems.
Retrieval-augmented question answering depends on selecting evidence passages that jointly support answer generation. However, many RAG pipelines rely on top-\(k\) ranking, where passages are selected mainly by individual relevance scores, even though multi-hop questions often require complementary evidence satisfying multiple information requirements. Recent LLM-based selectors address this by treating retrieval as set selection, but using an LLM for this intermediate stage can be costly and difficult to scale. In this work, we formulate evidence selection as a Quadratic Unconstrained Binary Optimization (QUBO) problem. Given a question, candidate passages, and decomposed information requirements, our method constructs an energy function that balances relevance, requirement coverage, support strength, redundancy, complementarity, and compactness. Low-energy solutions correspond to compact evidence subsets that cover the needed requirements while avoiding unnecessary or repetitive context. The selected passages are then passed to a downstream language model for answer generation, separating combinatorial evidence selection from semantic answer generation. We evaluate the proposed QUBO selector on HotpotQA and compare it with LLM-based set selectors and non-LLM baselines including BM25, relevance top-\(k\), maximal marginal relevance, hybrid lexical--semantic ranking, greedy coverage, and random selection. The QUBO selector achieves competitive exact-match and token-F1 performance relative to LLM-based selectors while providing a solver-compatible formulation for structured evidence selection. These results suggest that multi-hop evidence selection can be cast as discrete optimization, opening a path toward RAG pipelines where LLMs are reserved for semantic processing and answer generation, while context selection is handled by Ising/QUBO-compatible solvers.