This paper compares various optimization techniques and objective functions to obtain optimum rocket engine performances. This research proposes a modular optimization framework that provides an optimum design for Gas Generator (GG) and Staged Combustion (SC) Liquid Propellant Rocket Engines. This process calculates the ideal rocket engine performance by applying seven different optimization techniques: Simulated Annealing (SA), Nelder Mead (NM), Cuckoo Search Algorithm (CSA), Particle Swarm Optimization (PSO), Pigeon-Inspired Optimization (PIO), Genetic Algorithm (GA) and a novel hybrid GA-PSO technique named GA-Swarm. This new technique combines the superior search capability of GA with the efficient constraint matching capability of PSO. This research also compares objective functions to determine the most suitable function for GG and SC cycle rocket engines. Three single objective functions are used to minimize the Gross Lift-Off Weight and to maximize Specific Impulse and the Thrust-to-Weight ratio. A fourth multiobjective function is used to simultaneously maximize both Specific Impulse and Thrust-to-Weight ratio. This framework is validated against a pump-fed rocket, and results are within 1% of the actual rocket engine mass. The results of this research indicate that PSO and GA-Swarm produce optimum results for all objective functions. Finally, the most suitable objective function to use while comparing these two cycles is the Gross Lift-Off Weight.