Guillem Rodríguez Corominas

Guillem Rodríguez Corominas, Maria J. Blesa, Christian Blum

In this paper, we propose an acceleration of the exact k-means++ algorithm using geometric information, specifically the Triangle Inequality and additional norm filters, along with a two-step sampling procedure. Our experiments demonstrate that the accelerated version outperforms the standard k-means++ version in terms of the number of visited points and distance calculations, achieving greater speedup as the number of clusters increases. The version utilizing the Triangle Inequality is particularly effective for low-dimensional data, while the additional norm-based filter enhances performance in high-dimensional instances with greater norm variance among points. Additional experiments show the behavior of our algorithms when executed concurrently across multiple jobs and examine how memory performance impacts practical speedup.

Guillem Rodríguez-Corominas, Maria J. Blesa, Christian Blum

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.

Mariella Dimiccoli, Lluís Garrido, Guillem Rodriguez-Corominas et al.

Recently, transfer subspace learning based approaches have shown to be a valid alternative to unsupervised subspace clustering and temporal data clustering for human motion segmentation (HMS). These approaches leverage prior knowledge from a source domain to improve clustering performance on a target domain, and currently they represent the state of the art in HMS. Bucking this trend, in this paper, we propose a novel unsupervised model that learns a representation of the data and digs clustering information from the data itself. Our model is reminiscent of temporal subspace clustering, but presents two critical differences. First, we learn an auxiliary data matrix that can deviate from the initial data, hence confer more degrees of freedom to the coding matrix. Second, we introduce a regularization term for this auxiliary data matrix that preserves the local geometrical structure present in the high-dimensional space. The proposed model is efficiently optimized by using an original Alternating Direction Method of Multipliers (ADMM) formulation allowing to learn jointly the auxiliary data representation, a nonnegative dictionary and a coding matrix. Experimental results on four benchmark datasets for HMS demonstrate that our approach achieves significantly better clustering performance then state-of-the-art methods, including both unsupervised and more recent semi-supervised transfer learning approaches.