Composite spherical shell panels are commonly used for the lightweight design of thin-walled structures in the structure, architecture, aerospace engineering. Depending on the shell panel length, thickness, curvature, and stacking sequence, the load-deflection response under lateral load can be either a completely stable equilibrium path or an unstable snap-through path. In this work, the response of simply supported cross-ply composite spherical shell panels subjected to lateral static loads is studied and optimized. The spherical shell exhibiting snap-through response is optimized to (a) maximize the load required to initiate snap-through and (b) minimize the unstable region. Meanwhile, the spherical shell exhibiting continuous response is optimized to (a) maximize the softening-hardening load and (b) minimize the shell weight. The decision variables for both constraint multi-objective optimization (CMOO) problems include layup sequence, thickness, and the radius of curvature to side length ratio. The nonlinear governing equations are derived based on Kirchhoff–Love hypotheses for thin shells and Hamilton’s principle. A novel semi-analytical method is presented based on Bernstein polynomials combined with a fast iterative approach to compute the objective features of the responses. Benefiting from the high efficiency and robustness of the proposed approach, the CMOO problems are solved by the metaheuristic Multi-Objective Artificial Hummingbird Algorithm (MOAHA). Composite spherical shell panels with various geometry and lamination configurations are considered to validate the performance of the proposed method. The optimization of geometric parameters (shell curvature and thickness) in addition to the staking sequence provide a high degree of tailoring of the shell performance to meet various objectives. These parameters are taken as design variables that must be optimized to achieve some objectives and satisfy arbitrary nonlinear constraints