It is difficult to prove the optimality of a mixture design in the region with complex constraints, however, it is relatively easy to negate the optimality of the design. In this paper, we construct a set of dense lattice points in the experimental region with complex constraint. It can not only be used to evaluate the optimization
of a design, but also to compare the advantages of multiple local optimal designs. As an alternative set of points, the densely covered set of lattice points can produce the local optimal design in the constrained region. This method is effective through case analysis.