Combined mutation differential evolution to solve systems of nonlinear equations

This paper presents a differential evolution heuristic to compute a solution of a system of nonlinear equations through the global optimization of an appropriate merit function. Three different mutation strategies are combined to generate mutant points. Preliminary numerical results show the effectiveness of the presented heuristic.Fundação para a Ciência e a Tecnologia (FCT

Solving systems of nonlinear equations by harmony search

In this paper, we aim to analyze the performance of some variants of the harmony search (HS) metaheuristic when solving systems of nonlinear equations through the global optimization of an appropriate merit function. The HS metaheuristic draws its inspiration from an artistic process, the improvisation process of musicians seeking a wonderful harmony. A new differential best HS algorithm, based on an improvisation operator that mimics the best harmony and uses a differential variation, is proposed. Computational experiments involving a well-known set of small-dimensional problems are presented.Fundação para a Ciência e a Tecnologia (FCT

Solving nonlinear equations by a tabu search strategy

Solving systems of nonlinear equations is a problem of particular importance since they emerge through the mathematical modeling of real problems that arise naturally in many branches of engineering and in the physical sciences. The problem can be naturally reformulated as a global optimization problem. In this paper, we show that a metaheuristic, called Directed Tabu Search (DTS) [16], is able to converge to the solutions of a set of problems for which the fsolve function of MATLAB® failed to converge. We also show the effect of the dimension of the problem in the performance of the DTS.Fundação para a Ciência e a Tecnologia (FCT

Nonmonotone hybrid tabu search for Inequalities and equalities: an experimental study

The main goal of this paper is to analyze the behavior of nonmonotone hybrid tabu search approaches when solving systems of nonlinear inequalities and equalities through the global optimization of an appropriate merit function. The algorithm combines global and local searches and uses a nonmonotone reduction of the merit function to choose the local search. Relaxing the condition aims to call the local search more often and reduces the overall computational effort. Two variants of a perturbed pattern search method are implemented as local search. An experimental study involving a variety of problems available in the literature is presented.Fundação para a Ciência e a Tecnologia (FCT

Solving systems of inequalities and equalities by a nonmonotone hybrid tabu search method

Series : AIP Conference Proceedings, Vol. 1479This paper presents a derivative-free nonmonotone hybrid tabu search to compute a solution of overdetermined systems of inequalities and equalities through the global optimization of an appropriate merit function. The proposed algorithm combines global and local searches aiming to reduce computational effort. Preliminary numerical results show the effectiveness of the combined heuristic.Fundação para a Ciência e a Tecnologia (FCT

Combining global tabu search with local search for solving systems of equalities and inequalities

This papers aims at providing a combined strategy for solving systems of equalities and inequalities. The combined strategy uses two types of steps: a global search step and a local search step. The global step relies on a tabu search heuristic and the local step uses a deterministic search known as Hooke and Jeeves. The choice of step, at each iteration, is based on the level of reduction of the l2-norm of the error function observed in the equivalent system of equations, compared with the previous iterationFundação para a Ciência e a Tecnologia (FCT

On metaheuristics for solving the parameter estimation problem in dynamic systems: A comparative study

This paper presents an experimental study that aims to compare the practical performance of well-known metaheuristics for solving the parameter estimation problem in a dynamic systems context. The metaheuristics produce good quality approximations to the global solution of a finite small-dimensional nonlinear programming problem that emerges from the application of the sequential numerical direct method to the parameter estimation problem. Using statistical hypotheses testing, significant differences in the performance of the metaheuristics, in terms of the average objective function values and average CPU time, are determined. Furthermore, the best obtained solutions are graphically compared in relative terms by means of the performance profiles. The numerical comparisons with other results in the literature show that the tested metaheuristics are effective in achieving good quality solutions with a reduced computational effort.The authors would like to acknowledge the financial support of CIDEM, R&D Unit, funded by the Portuguese Foundation for the Development of Science and Technology (FCT), Ministry of Science, Technology and Higher Education, under the Project UID/EMS/0615/2016, and of COMPETE: POCI-01-0145-FEDER-007043 and FCT within the Projects UID/CEC/00319/2013 and UID/MAT/00013/2013.info:eu-repo/semantics/publishedVersio

Finding multiple roots of systems of nonlinear equations by a hybrid harmony search-based multistart method

A multistart (MS) clustering technique to compute multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function is presented. The search procedure that is invoked to converge to a root, starting from a randomly generated point inside the search space, is a new variant of the harmony search (HS) metaheuristic. The HS draws its inspiration from an artistic process, the improvisation process of musicians seeking a wonderful harmony. The new hybrid HS algorithm is based on an improvisation operator that mimics the best harmony and uses the idea of a differential variation, borrowed from the differential evolution algorithm. Computational experiments involving a benchmark set of small and large dimensional problems with multiple roots are presented. The results show that the proposed hybrid HS-based MS algorithm is effective in locating multiple roots and competitive when compared with other metaheuristics.FCT - Fuel Cell Technologies Program(UID/EMS/0615/2016). The authors are grateful to the anonymous referees for their helpful suggestions to improve the paper. This research has been supported by CIDEM (Centre for Research & Development in Mechanical Engineering, Portugal), by COMPETE POCI-01-0145-FEDER-007043 and FCT (Foundation for Science and Technology, Portugal) within the projects UID/EMS/0615/2016 and UID/CEC/00319/2013

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

Solving Systems of Inequalities and Equalities by a Nonmonotone Hybrid Tabu Search Method

Abstract. This paper presents a derivative-free nonmonotone hybrid tabu search to compute a solution of overdetermined systems of inequalities and equalities through the global optimization of an appropriate merit function. The proposed algorithm combines global and local searches aiming to reduce computational effort. Preliminary numerical results show the effectiveness of the combined heuristic