The paper is focused on univariate relaxation and coordinate exchange with improved multistart algorithms. The effectiveness of these algorithm are shown for searching of D-optimal designs with continuous and 3-level discrete parameters in 3-15 dimensions with 10 to 300 runs (45 to 4500 optimization parameters) and for optimization of Latin hypercube designs according to several criteria. The optimized designs are compared on many metamodeling test problems. For the case of second order local polynomial approximation, the use of MSE-optimal Latin hypercube designs and modified Gaussian weighting function is proposed. Optimized experimental designs are available in public Internet pages.