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Advisor(s)
Abstract(s)
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.
Description
Keywords
Multi-global optimization Simulated annealing
Citation
Pereira, Ana I.; Fernandes, Edite M.G.P. (2005). A new algorithm to identify all global maximizers based on simulated annealing. In the 6th World Congress on Structural and Multidisciplinary Optimization. Rio de Janeiro - Brazil.
Publisher
International Society for Structural and Multidisciplinary Optimization