This study provides insights into the optimal operation of one of the most important refinery units, namely, the crude distillation unit (CDU). A steady state model based on (C+3) iteration variables is used to simulate an industrial column. The model is first tuned using some industrial data. The elitist non-dominated sorting genetic algorithm (NSGAII) is used to solve a few meaningful multi-objective optimization problems. It is observed that current plant operation is sub-optimal and more profit can be realized for the same amount of energy cost using the optimal operating conditions found. Also, it was found that profit can be increased keeping the product properties within acceptable limits. The procedure used is quite general and can be applied to other CDUs.