Testing Nelder-Mead based repulsion algorithms for multiple roots of nonlinear systems via a two-level factorial design of experiments

This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.Fundação para a Ciência e Tecnologia (FCT

Recherches sur la cinétique des transformations bactériennes

info:eu-repo/semantics/publishe

Stability analysis of the multi-objective multi-guided particle swarm optimizer

At present particle swarm optimizers (PSO) designed for multi-objective optimization have undergone no form of theoretical stability analysis. This paper derives the sufficient and necessary conditions for order-1 and order-2 stability of the recently proposed multi-guided PSO (MGPSO), which was designed specifically for multi-objective optimization. The paper utilizes a recently published theorem for performing stability analysis on PSO variants, which requires minimal modeling assumptions. It is vital for PSO practitioners to know the actual criteria for particle stability of the given PSO variant being used, as it been shown that particle stability has a considerable impact on PSO’s performance. This paper empirically validates its theoretical findings by comparing the derived stability criteria against those of an assumption free MGPSO algorithm. It was found that the derived criteria for order-1 and order-2 stability are an accurate predictor of the unsimplified MGPSO’s particle behavior.http://link.springer.combookseries/5582019-10-03hj2018Computer Scienc