One of the simplest ways of optimizing a problem without knowledge of its gradient, is to iteratively and randomly pick a sequence of candidate solutions that improve on the fitness. This paper shows mathematically that to exhaust the optimum of a problem, the search-range from which the candidate solutions are picked, must be decreased during an optimization run. A simple technique for doing t...

A Bayesian nonparametric method for unimodal densities on the real line is provided by considering a class of species sampling mixture models containing random densities that are unimodal and not necessarily symmetric. This class of densities generalize the model considered by Brunner (1992), in which the Dirichlet process is replaced by a more general class of species sampling models. A novel ...

In this paper, a meta-optimization algorithm, based on Local Unimodal Sampling (LUS), has been applied to tune selected parameters of QuantumInspired Evolutionary Algorithm for numerical optimization problems coded in real numbers. Tuning of the following two parameters has been considered: crossover rate and contraction factor. Performance landscapes of the algorithm meta-fitness have been app...

We study, to the best of our knowledge, the first Bayesian algorithm for unimodal Multi–Armed Bandit (MAB) problems with graph structure. In this setting, each arm corresponds to a node of a graph and each edge provides a relationship, unknown to the learner, between two nodes in terms of expected reward. Furthermore, for any node of the graph there is a path leading to the unique node providin...

We introduce a new complete metric in the space V2 of unimodal Cmaps of the interval, with two maps close if they are close in the C-metric and differ only on a small interval containing their critical points. We identify all structurally stable maps in the sense of this metric. They are maps for which either (1) the trajectory of the critical point is attracted to a topologically attracting (a...

There are errors in S1 Text and S2 Text that affect the code script. The corrected S1 Text fixes an error in creating Fig. 9. The corrected S2 Text fixes an error that masked the location of a needed function. Please find the corrected files here. S1 Text. PlosOneMRDSAnalysis.txt. A R script file that will replicate the results found in this manuscript. (TXT) S2 Text. Two.Piece.Normal.txt. A R ...