Multi-stage differential evolution algorithm for constrained D-optimal design

In practice, objective condition may impose constraints on design region, which make it difficult to find the exact D-optimal design. In this paper, we propose a Multi-stage Differential Evolution (MDE) algorithm to find the global approximated D-optimal design in an experimental region with linear or nonlinear constraints. MDE algorithm is approved from Differential Evolution (DE) algorithm. It has low requirements for both feasible regions and initial values. In iteration, MDE algorithm pursues evolutionary equilibrium rather than convergence speed, so it can stably converge to the global D-optimal design instead of the local ones. The advantages of MDE algorithm in finding D-optimal design will be illustrated by examples.