A Twinkling Technique for Brownian Moves in Optimization Processes
Mounib Mekhilef · 1999
Abstract This paper outlines a computational method for constructing displacements subspaces in optimization processes. In the first section, we present the research field. The second section is devoted to the mathematical formulation of the twinkling technique. The basic idea is that moving the state vector according to random subspaces while generating a new point is better than displacements in the whole optimization space. We then provide in the third section two different problems. We have made the choice to study the behavior of this technique on non specific areas to show that this efficiency is not problem dependent. The first case concerns the general NP-hard problem by the means of the travel salesman problem, the second problem deals with a continuous problem built in a random space. The following section is devoted to some numerical results. We discuss the results and give some orientations for the determination of the optimal subspace dimension. The second part is devoted to the study of the distribution law on the convergence. We compare three laws, the first one is the uniform distribution, the second the normal gaussian and finally we discuss the circular selection of the parameters.