This paper addresses the question of time-domain-constrained data clustering, a problem which deals with data labelled with the time they are obtained and imposing the condition that clusters need to be contiguous in time (the time-domain constraint). The objective is to obtain a partitioning of a multivariate time series into internally homogeneous segments with respect to a statistical model given in each cluster. In this paper, time-domain-constrained data clustering is formulated as an unrestricted bi-level optimization problem. The clustering problem is stated at the upper level model and at the lower level the statistical models are adjusted to the set of clusters determined in the upper level. This formulation is sufficiently general to allow these statistical models to be used as black boxes. A hybrid technique based on combining a generic population-based optimization algorithm and Nelder–Mead simplex search is used to solve the bi-level model. The capability of the proposed approach is illustrated using simulations of synthetic signals and a novel application for survival analysis. This application shows that the proposed methodology is a useful tool to detect changes in the hidden structure of historical data. Finally, the performance of the hybridizations of particle swarm optimization, genetic algorithms and simulated annealing with Nelder–Mead simplex search are tested on a pattern recognition problem of text identification. 
Hybrid meta-heuristic optimization algorithms for time-domain-constrained data clustering