Global search methods for nonlinear optimisation: a new probabilistic-stochastic approach

Abstract

In this work the problem of overcoming local minima in the solution of nonlinear optimisation problems is addressed. As a first step, the existing nonlinear local and global optimisation methods are reviewed so as to identify their advantages and disadvantages. Then, the major capabilities of a number of successful methods such as genetic, deterministic global optimisation methods and simmulated annealing, are combined to develop an alternative global optimisation approach based on a Stochastic-Probabilistic heuristic. The capabilities, in terms of robustness and efficiency, of this new approach are validated through the solution of a number of nonlinear optimisation problems. A well know evolutionary technique (Differential Evolution) is also considered for the solution of these case studies offering a better insight of the possibilities of the method proposed here.