To explore the full search space we removed the additional inequalities and ran the optimization again using the previously calculated values as starting point. The optimization needed 12 iterations (5.31 seconds). The results are given in Table . In contrast to the first example studied in Subsection 5.1 the solution with and without additional inequalites differ more. The objective value in the second run is around 7.08% smaller. The difference in the product streams is very small. The results show that in an optimal solution less is withdrawn in the side product streams than in the bottom and distillate stream. We again compare the results of the new approach to results obtained with an external optimization routine and Aspen Plus R as simulation software. As specifications that are varied by the external optimizer we used the reboiler duty QR (4.4 to 5 kW), the total molar flow rates of the product streams A, B, C (24.5 to 25.5 mol/h) and the four split ratios v s,1 , v s,2 , l s,1 , l s,2 . All of them are limited by 0.1 from below and 0.95 from above, except for v s,2 the lower bound was set to 0.2. The external optimization routine needed 189 iterations which took 11.77 hours. Both results, the one obtained with the new approach and with Aspen Plus R as simulation software, are shown in Table . Again we list the product streams, the heat duties and the split ratios. Both solutions are similar. The split ratios only differ slightly this time. The maximal violation of the purity specification for the solution calculated with Aspen Plus R is 0.01%. The new approach found a solution with a reboiler duty that is 1.73% smaller.