Biological systems with both protein-protein and protein-gene interactions can be modeled by differential equations for concentrations of the proteins with time-delay terms because of the time needed for DNA transcription to mRNA and translation of mRNA to protein. Values of some parameters in the mathematical model can not be measured owing to the difficulty of experiments. Also values of some parameters obtained in a normal stress condition can be changed under pathological stress stimuli. Thus it is important to find the effective way of determining parameters values. One approach is to use optimization algorithms. Here we construct an optimal system used to find optimal parameters in the equations with nonnegative time delays and apply this optimization result to the Nuclear factor-${kappa}B$ pathway.