Hydrocracking is carried out in a multiphase trickle-bed reactor. The reactions that occur in this reactor are the cracking of high molecular weight hydrocarbons into lower molecular weight hydrocarbons followed by their hydrogenation. In a typical hydrocracker, many reactions occur simultaneously. It would be cumbersome to keep track of all of the individual reactions (literally thousands) at the molecular level. This problem is avoided by lumping the reactants together on the basis of a property like the carbon number, etc. The different lumps in the hydrocarbon mixture are characterized by the carbon number (number of carbon atoms in a molecule) or molecular weight of the components or their boiling point. A discrete lumping approach is used to model the evolution of the weight fraction distribution with time using one of these variables as the characteristic parameter. A complete description of the behavior of the lumps would necessitate consideration of all possible reactions the lumps undergo. This can be a large number. However, in a realistic situation only some of these reactions will be dominant or significant. The rate constants of these fast reactions are significantly higher than those of the slow reactions, which can be approximated to be zero. We discuss a technique based on genetic algorithm and sequential quadratic programming to determine the significant reactions and their corresponding rate constants. We consider two choices of characteristic variables (i) carbon number (or molecular weight) and (ii) true boiling point. It is shown that for the latter choice multiple solutions exist for the choice of the important reactions and their rate constants. These solutions identically satisfy the evolution of the weight fraction distribution equation. When considering the carbon number as the characteristic variable, the important reactions and their rate constants are identified uniquely. The method proposed is verified using simulated as well as experimental data.