Performance profile assessment of electromagnetism-like algorithms for global optimization

This paper introduces a modification on the movement force vector of the Birbil and Fang's electromagnetism-like algorithm for solving global optimization problems with bounded variables. The proposed movement vector combines the total force exerted on each point of the population, at the current iteration, with the rate of change in the force vector of a previous iteration. Several widely used benchmark problems were solved to compare the proposed modification with the original algorithm. A performance profile assessment shows the efficiency and robustness of the proposed modification

Self-adaptive penalties in the electromagnetism-like algorithm for constrained global optimization problems

A well-known approach for solving constrained optimization problems is based on penalty functions. A penalty technique transforms the constrained problem into an unconstrained problem by penalizing the objective function when constraints are violated and then minimizing the penalty function using methods for unconstrained problems. In this paper, we analyze the implementation of a self-adaptive penalty approach, within the electromagnetism-like population-based algorithm, in which the constraints that are more difficult to be satisfied will have relatively higher penalty values. The penalties depend upon the level of constraint violation scaled by the average of the objective function values. Numerical results obtained with a collection of well-known global optimization problems are presented and a comparison with other stochastic methods is also reported

A new electromagnetism-like algorithm with a population shrinking strategy

The Electromagnetism-like (EM) algorithm, developed by Birbil and Fang [31 is a population-based stochastic global optimization algorithm that uses an attraction-repulsion mechanism to move sample points toward optimality. In order to improve the accuracy of the solutions the EM algorithm incorporates a random local search. In this paper we propose: a new local search procedure based on a pattern search method, and a population shrinking strategy to improve efficiency. The proposed method is applied to some test problems and compared with the original EM algorithm.info:eu-repo/semantics/publishedVersio

Numerical experiments with a population shrinking strategy within an electromagnetism-like algorithm

This paper extends our previous work done with a modified Electromagnetism-like (EM) algorithm to a benchmark global optimization collection of test problems. The EM algorithm is a population-based stochastic method that uses an attractionrepulsion mechanism to move sample points towards optimality. The modifications include a local search based on the original pattern search method of Hooke and Jeeves and a shrinking strategy that aims to reduce the population size as the iterative process progresses. Performance profiles are used to compare the proposed modifications with the original EM algorithm considering the average number of function evaluations and the best function value

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

A stochastic augmented Lagrangian equality constrained-based algorithm for global optimization

This paper presents a numerical study of a stochastic augmented Lagrangian algorithm to solve continuous constrained global optimization problems. The algorithm approximately solves 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 mechanism to move points towards optimality. A comparison with another stochastic technique is also reported.Fundação para a Ciência e a Tecnologia (FCT

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

Mutation-based artificial fish swarm algorithm for bound constrained global optimization

The herein presented mutation-based artificial fish swarm (AFS) algorithm includes mutation operators to prevent the algorithm to falling into local solutions, diversifying the search, and to accelerate convergence to the global optima. Three mutation strategies are introduced into the AFS algorithm to define the trial points that emerge from random, leaping and searching behaviors. Computational results show that the new algorithm outperforms other well-known global stochastic solution methods.Fundação para a Ciência e a Tecnologia (FCT

Resolução de problemas de optimização global através da função Lagrangeana aumentada

Neste trabalho, é apresentado uma estratégia baseada na função Lagrangeana aumentada para resolver problemas com restrições contínuos de optimização global. Este tipo de problemas de optimização global é muito importante e é frequentemente encontrado em diversas aplicações da engenharia. O método resolve aproximadamente uma sequência de subproblemas, com limites nas variáveis, em que a função objectivo penaliza a violação das restrições de igualdade e de desigualdade. A função objectivo é uma função Lagrangeana aumentada e depende de um parâmetro positivo da penalidade, assim como dos vectores dos multiplicadores de Lagrange associados às restrições da igualdade e do desigualdade. A actualização do vector dos multiplicadores é feita através da fórmula de actualização baseada nas condições de primeira ordem, e a do parâmetro da penalidade é feita de acordo com o valor da violação das restrições. Os valores do parâmetro da penalidade e do vector dos multiplicadores são fundamentais para promover a convergência global dos métodos baseados na função Lagrangeana aumentada. Cada subproblema é resolvido por um método estocástico de optimização global, baseado em populações, que se designa por algoritmo Electromagnético (EM). Este método simula a teoria do electromagnetismo da física considerando cada ponto da população como uma partícula que tem uma carga eléctrica associada. O algoritmo EM começa com uma população de pontos gerados aleatoriamente na região admissível e usa um mecanismo do atracção-repulsão para mover a população de pontos até à optimalidade. A carga de cada ponto está relacionada com o valor da função de avaliação e determina a magnitude de atracção de um ponto sobre a população. Quanto melhor for o valor da função de avaliação, maior é a magnitude de atracção. No final de cada iteração do algoritmo EM é realizada uma pesquisa local na vizinhança do melhor ponto da população encontrado até ao momento. Neste estudo, são apresentados e comparados três procedimentos diferentes de pesquisa local para realçar o desempenho do algoritmo EM, que está incorporado na estratégia baseada na função Lagrangeana aumentada. Para avaliar o desempenho de cada um dos algoritmos são apresentados os resultados da sua aplicação num conjunto de problem

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