Guillem Rodríguez-Corominas

arXiv2026

From Hand-Crafted to LLM-Based Variation Operators in Metaheuristics: A Tutorial

Large language models (LLMs) are increasingly being employed as variation operators in metaheuristics, generating or modifying candidate solutions, heuristics, or programs inside iterative search loops. This shift reframes variation as a model call conditioned on different types of information. We introduce an operator-level framework with two descriptors: (1) the type of prompt-conditioning information at variation time (\texttt{Numeric}, \texttt{Symbolic}, \texttt{Linguistic}), and (2) artifact persistence, identifying what survives the model call (\texttt{Transient}, \texttt{Amortized}, \texttt{Transfer}). The tutorial shows how to classify, build, and select these operators through a worked build template, a method survey, an evidence table, and a cost-aware decision guide.

cs.NE↗

arXiv2026

Construct, Merge, Solve & Adapt with Reinforcement Learning for the min-max Multiple Traveling Salesman Problem

The Multiple Traveling Salesman Problem (mTSP) extends the Traveling Salesman Problem to m tours that start and end at a common depot and jointly visit all customers exactly once. In the min-max variant, the objective is to minimize the longest tour, reflecting workload balance. We propose a hybrid approach, Construct, Merge, Solve & Adapt with Reinforcement Learning (RL-CMSA), for the symmetric single-depot min-max mTSP. The method iteratively constructs diverse solutions using probabilistic clustering guided by learned pairwise q-values, merges routes into a compact pool, solves a restricted set-covering MILP, and refines solutions via inter-route remove, shift, and swap moves. The q-values are updated by reinforcing city-pair co-occurrences in high-quality solutions, while the pool is adapted through ageing and pruning. This combination of exact optimization and reinforcement-guided construction balances exploration and exploitation. Computational results on random and TSPLIB instances show that RL-CMSA consistently finds (near-)best solutions and outperforms a state-of-the-art hybrid genetic algorithm under comparable time limits, especially as instance size and the number of salesmen increase.

cs.AI↗