Modified movement force vector in an electromagnetism-like mechanism for global optimization

This paper presents an algorithm for solving global optimization problems with bounded variables. The algorithm is a modification of the electromagnetism-like mechanism proposed by Birbil and Fang [An electromagnetism-like mechanism for global optimization, J. Global Optim. 25 (2003), pp. 263–282]. The differences are mainly on the local search procedure and on the force vector used to move each point in the population. Several widely-used benchmark problems were solved in a performance evaluation of the new algorithm when compared with the original one. A comparison with other stochastic methods is also included. The algorithm seems appropriate for large dimension problems

Implementation of a fixing strategy and parallelization in a recent global optimization method

Electromagnetism-like Mechanism (EM) heuristic is a population-based stochastic global optimization method inspired by the attraction-repulsion mechanism of the electromagnetism theory. EM was originally proposed for solving continuous global optimization problems with bound constraints and it has been shown that the algorithm performs quite well compared to some other global optimization methods. In this work, we propose two extensions to improve the performance of the original algorithm: First, we introduce a fixing strategy that provides a mechanism for not being trapped in local minima, and thus, improves the effectiveness of the search. Second, we use the proposed fixing strategy to parallelize the algorithm and utilize a cooperative parallel search on the solution space. We then evaluate the performance of our study under three criteria: the quality of the solutions, the number of function evaluations and the number of local minima obtained. Test problems are generated by an algorithm suggested in the literature that builds test problems with varying degrees of difficulty. Finally, we benchmark our results with that of the Knitro solver with the multistart option set

A modified electromagnetism-like algorithm based on a pattern search method

The Electromagnetism-like (EM) algorithm, developed by Birbil and Fang [2] is a population-based stochastic global optimization algorithm that uses an attraction-repulsion mechanism to move sample points towards optimality. A typical EM algorithm for solving continuous bound constrained optimization problems performs a local search in order to gather information for a point, in the population. Here, we propose a new local search procedure based on the original pattern search method of Hooke and Jeeves, which is simple to implement and does not require any derivative information. The proposed method is applied to different test problems from the literature and compared with the original EM algorithm.(undefined

Numerical study of augmented lagrangian algorithms for constrained global optimization

To cite this article: Ana Maria A.C. Rocha & Edite M.G.P. Fernandes (2011): Numerical study of augmented Lagrangian algorithms for constrained global optimization, Optimization, 60:10-11, 1359-1378This article presents a numerical study of two augmented Lagrangian algorithms to solve continuous constrained global optimization problems. The algorithms approximately solve a sequence of bound constrained subproblems whose objective function penalizes equality and inequality constraints violation and depends on the Lagrange multiplier vectors and a penalty parameter. Each subproblem is solved by a population-based method that uses an electromagnetism-like (EM) mechanism to move points towards optimality. Three local search procedures are tested to enhance the EM algorithm. Benchmark problems are solved in a performance evaluation of the proposed augmented Lagrangian methodologies. A comparison with other techniques presented in the literature is also reported

Hybrid optimization coupling electromagnetism and descent search for engineering problems

In this paper, we present a new stochastic hybrid technique for constrained global optimization. It is a combination of the electromagnetism-like (EM) mechanism with an approximate descent search, which is a derivative-free procedure with high ability of producing a descent direction. Since the original EM algorithm is specifically designed for solving bound constrained problems, the approach herein adopted for handling the constraints of the problem relies on a simple heuristic denoted by feasibility and dominance rules. The hybrid EM method is tested on four well-known engineering design problems and the numerical results demonstrate the effectiveness of the proposed approach

A new competitive implementation of the electromagnetism-like algorithm for global optimization

The Electromagnetism-like (EM) algorithm is a population- based stochastic global optimization algorithm that uses an attraction- repulsion mechanism to move sample points towards the optimal. In this paper, an implementation of the EM algorithm in the Matlab en- vironment as a useful function for practitioners and for those who want to experiment a new global optimization solver is proposed. A set of benchmark problems are solved in order to evaluate the performance of the implemented method when compared with other stochastic methods available in the Matlab environment. The results con rm that our imple- mentation is a competitive alternative both in term of numerical results and performance. Finally, a case study based on a parameter estimation problem of a biology system shows that the EM implementation could be applied with promising results in the control optimization area.Acknowledgments This work has been supported by FCT (Funda¸c˜ao para a Ciˆencia e Tecnologia, Portugal) in the scope of the project PEst-UID/CEC/00319/2013

On Challenging Techniques for Constrained Global Optimization

This chapter aims to address the challenging and demanding issue of solving a continuous nonlinear constrained global optimization problem. We propose four stochastic methods that rely on a population of points to diversify the search for a global solution: genetic algorithm, differential evolution, artificial fish swarm algorithm and electromagnetism-like mechanism. The performance of different variants of these algorithms is analyzed using a benchmark set of problems. Three different strategies to handle the equality and inequality constraints of the problem are addressed. An augmented Lagrangian-based technique, the tournament selection based on feasibility and dominance rules, and a strategy based on ranking objective and constraint violation are presented and tested. Numerical experiments are reported showing the effectiveness of our suggestions. Two well-known engineering design problems are successfully solved by the proposed methods. © Springer-Verlag Berlin Heidelberg 2013.Fundação para a Ciência e a Tecnologia (Foundation for Science and Technology), Portugal for the financial support under fellowship grant: C2007-UMINHO-ALGORITMI-04. The other authors acknowledge FEDER COMPETE, Programa Operacional Fatores de Competitividade (Operational Programme Thematic Factors of Competitiveness) and FCT for the financial support under project grant: FCOMP-01-0124-FEDER-022674info:eu-repo/semantics/publishedVersio

An electromagnetism-like method for the maximum set splitting problem

In this paper, an electromagnetism-like approach (EM) for solving the maximum set splitting problem (MSSP) is applied. Hybrid approach consisting of the movement based on the attraction-repulsion mechanisms combined with the proposed scaling technique directs EM to promising search regions. Fast implementation of the local search procedure additionally improves the efficiency of overall EM system. The performance of the proposed EM approach is evaluated on two classes of instances from the literature: minimum hitting set and Steiner triple systems. The results show, except in one case, that EM reaches optimal solutions up to 500 elements and 50000 subsets on minimum hitting set instances. It also reaches all optimal/best-known solutions for Steiner triple systems

On charge effects to the electromagnetism-like algorithm

This paper presents modifications of the electromagnetism-like (EM) algorithm for solving global optimization problems with box constraints. The modifications are concerned with the charges associated with each point in the population. The purpose here is to improve efficiency and solution accuracy by exploring the attraction-repulsion mechanism of the EM algorithm. Several widely used benchmark problems were solved in a performance evaluation of the new algorithm when compared with the original one. The modified algorithm has also been compared with other heuristic population-based methods