EFFECT OF THE REGION COLLAPSE PARAMETER ON CONVERGENCE RATE OF LJ OPTIMIZATION PROCEDURE

摘要

The use of a multi-pass procedure with a relatively small number of randomly chosen points in the LJ optimization procedure yields faster convergence than the use of a very large number of points in a single pass. The efficiency is increased by choosing the region size at the beginning of a pass, over which the randomly chosen candidates for variables are chosen, to be the range over which the variables have changed during the previous pass. To avoid the possibility of region collapse when the change during a pass in some variable is very small, a region collapse parameter ε is introduced, so that if the calculated region size is less than ε, then the region size is put equal to ε at the beginning of the subsequent pass. This parameter has a very significant effect on the convergence rate, especially near the optimum. Three optimization problems are used to illustrate the effect of ε and to test the viability of using a progressively smaller value for ε as the number of passes increases.