A new algorithm to identify all global maximizers based on simulated annealing

• Autor(es): Pereira, Ana I. ; Fernandes, Edite M.G.P.
• Data: 2005
• Identificador Persistente: http://hdl.handle.net/10198/4734
• Origem: Biblioteca Digital do IPB
• Assunto(s): Multi-global optimization; Simulated annealing
• Tipo de Documento: Artigo
• Idioma: Inglês

Descrição

In this paper we consider the problem of finding all the global maximizers of a given nonlinear optimization problem. This type of problem appears, for example, in the phase-shift analysis of experimental data on scattering in nuclear and elementary particle physics and in a local reduction method for solving semi-infinite programming problems. The simulated annealing (SA) method is a stochastic method and it is well documented in the literature. Its most important property, as a global optimizer, is that asymptotic convergence to a global solution can be proven. However, in general, the SA algorithm finds just one global optimum. The function stretching technique carries out a two-step transformation of the objective function aiming to eliminate local optima while preserving the global ones. We propose a new algorithm which combines the SA algorithm with a function stretching, to generate a sequence of nonlinear maximization problems that are defined whenever a new maximizer is identified. To find all global maximizers, we apply the SA algorithm to this sequence of maximization problems. Results of numerical experiments with a set of well-known test problems in the global optimization literature show that the proposed method is effective. We also compare the performance of our algorithm with other multi-local solvers.