Constraint Ordinal Optimization (COO) can deal with constraint optimization problem. First, the objective function based on value is converted to based on order. Then a constraint optimization problem with m constraints can be tackled through m iterations. We randomly sample N designs. Order the designs by the first constraint function value, and select the top n1 designs. Then we order the n1 designs by the second constraint function value, and select the top n2 designs. This procedure iterates until we get nm designs, which meet all the m constraints. Finally we order the nm designs by the objective function, and select the top n designs as the result. We can estimate the alignment probability of COO. Details please consult [Li, D., Lee, L.H., and Ho, Y.C., "Constraint Ordinal Optimization", Information Sciences, Vol.148, pp.201-220, 2002].
Vector Ordinal Optimization (VOO) can deal with multi-objective optimization problem. If we consider all the m constraints in a constraint optimization problem equally important, it can be converted to a multi-objective optimization problem with m+1 objective functions. And VOO can be applied. Details please consult [Zhao, Q.C., Ho, Y.C., and Jia, Q.S., "Vector Ordinal Optimization", submitted to Automatica, 2003].กก