1. CONSTRAINT ORDINAL OPTIMIZATION

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 n_m designs, which meet all the m constraints.  Finally we order the n_m 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].

2. VECTOR ORDINAL OPTIMIZATION

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].