We employed a hybrid genetic algorithm (HGA) technique (GA coupled with the local optimization algorithm (LOA)) and a model-free (isoconversional) method of analysis coupled with LOA to obtain the optimized kinetics triplet values for catalytic (ZSM-5) and noncatalytic decomposition of a waste low-density polyethylene (LDPE) sample. Catalytic decomposition starts and completes at much lower temperatures but continues for a wider range of temperatures indicating a slower process in comparison to the noncatalytic decomposition one. Contrary to the single peak observed for noncatalytic decomposition of LDPE, ZSM-5 catalyzed decomposition shows multiple peaks indicating the existence of multistep reactions. The same is also supported by the isoconversional method of analysis showing the variation of activation energy with conversion. Both of the methods employed in the present study give almost the same optimized kinetics triplet values, which predict the experimental thermogravimetric analysis (TGA) data well indicating the fact that either of the two methods can effectively be used for pyrolysis kinetics analysis. The isoconversional method coupled with LOA should be the preferred one as this approach additionally helps in understanding the different reaction steps taking place during pyrolysis from the variation of activation energy with conversion.