In recent years, the utilization of Low Earth Orbit (LEO) satellite constellations has gained significant traction as a cost-effective solution for a wide array of applications. These applications span communication, military operations, and persistent surveillance, all benefiting from the broad coverage that LEO constellations offer. However, the practical implementation of any satellite constellation necessitates adherence to specific requirements and criteria. These criteria, while crucial, can often present conflicting design challenges when optimizing the constellation.This research undertakes a comprehensive examination and exposition of the key design criteria for three distinct mission types: remote sensing, communication, and navigation. Subsequently, a hybrid optimization approach, employing a Genetic Algorithm (GA) coupled with Sequential Quadratic Programming (SQP) – denoted as GA-SQP – is utilized to perform a constrained optimization of all three constellation types. It includes number of satellites, and orbit attitude of satellites.This optimization assumes an equal number of satellites and a uniform deployment altitude across the constellations, the large scale optimization problem will be solved.This large-scale optimization problem, encompassing approximately 96 variables, introduces significant challenges related to solution convergence and the reliable extraction of optimal parameters, challenges that this study endeavors to address.Following the optimization process, a comparative performance evaluation of the resulting satellite constellations is conducted. The results reveal that the optimized communication constellation achieves 65% coverage of the designated target area within a 24-hour period. In contrast, the optimized navigation constellation provides 6% coverage, and the optimized remote sensing constellation achieves 3% coverage within the same timeframe.