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This study focuses on investigating how grid-stiffened composite shells behave under external hydrostatic pressure. The critical buckling load is calculated using the first-order shear deformation theory (FSDT) and the Ritz method. Various factors, including shell thickness, angle of helical stiffeners, rib section area, and the number of stiffeners, are examined to understand their impact on the buckling load. To optimize the design, three multi-objective optimization algorithms are employed: Nondominated Sorting Genetic Algorithm II (NSGAII), Multiobjective Particle Swarm Optimization (MOPSO), and a hybrid method that combines NSGAII and MOPSO. The hybrid method intelligently divides the population into two groups and uses NSGAII and MOPSO to efficiently explore and exploit the solution space. The results yield a Pareto optimal front that showcases diverse solutions across different regions, providing decision-makers with the flexibility to select the solution that best fits their preferences. The solutions obtained through these algorithms are compared based on their diversity and distribution throughout the Pareto front. [ABSTRACT FROM AUTHOR]