The use of simulated annealing for finding optimal population designs

The development of functions for MATLAB and S-PLUS that can be used for the evaluation of specific population pharmacokinetic designs has been described recently. These functions are based on the evaluation of an approximation of the population Fisher information matrix. Optimisation of the design of the population experiment can be made on the basis of D-optimal design techniques, where the determinant of the population Fisher information matrix is maximised. This maximisation is complex due to the convoluted nature of the surface of the determinant. Four optimisation algorithms (simplex, non-adaptive random search, non-adaptive random search followed by simplex and simulated annealing) are compared in their ability to optimise the sampling times for various design structures for three examples of population pharmacokinetic models. In all cases, despite more computing time, simulated annealing was superior to the other methods for finding optimal designs with greater benefits being seen over the other algorithms for the more complex designs.