Generalization of the Apollonius theorem for simplices and related problems

The Apollonius theorem gives the length of a median of a triangle in terms of the lengths of its sides. The straightforward generalization of this theorem obtained for m-simplices in the n-dimensional Euclidean space for n greater than or equal to m is given. Based on this, generalizations of properties related to the medians of a triangle are presented. In addition, applications of the generalized Apollonius' theorem and the related to the medians results, are given for obtaining: (a) the minimal spherical surface that encloses a given simplex or a given bounded set, (b) the thickness of a simplex that it provides a measure for the quality or how well shaped a simplex is, and (c) the convergence and error estimates of the root-finding bisection method applied on simplices

Tuning PSO Parameters Through Sensitivity Analysis

In this paper, a first analysis of the Particle Swarm Optimization (PSO) method's parameters, using Design of Experiments (DOE) techniques, is performed, and important settings as well as interactions among the parameters, are investigated (screening)

Particle Swarm Optimizers for Pareto Optimization with Enhanced Archiving Techniques

During the last decades, numerous heuristic search methods for solving multi-objective optimization problems have been developed. Population oriented approaches such as evolutionary algorithms and particle swarm optimization can be distinguished into the class of archive-based algorithms and algorithms without archive. While the latter may lose the best solutions found so far, archive based algorithms keep track of these solutions. In this article a new particle swarm optimization technique, called DOPS, for multiobjective optimization problems is proposed. DOPS integrates well-known archiving techniques from evolutionary algorithms into particle swarm optimization. Modifications and extensions of the archiving techniques are empirically analyzed and several test functions are used to illustrate the usability of the proposed approach. A statistical analysis of the obtained results is presented. The article concludes with a discussion of the obtained results as well as ideas for further research

Neural network-based colonoscopic diagnosis using on-line learning and differential evolution

In this paper, on-line training of neural networks is investigated in the context of computer-assisted colonoscopic diagnosis. A memory-based adaptation of the learning rate for the on-line back-propagation (BP) is proposed and used to seed an on-line evolution process that applies a differential evolution (DE) strategy to (re-) adapt the neural network to modified environmental conditions. Our approach looks at on-line training from the perspective of tracking the changing location of an approximate solution of a pattern-based, and thus, dynamically changing, error function. The proposed hybrid strategy is compared with other standard training methods that have traditionally been used for training neural networks off-line. Results in interpreting colonoscopy images and frames of video sequences are promising and suggest that networks trained with this strategy detect malignant regions of interest with accuracy