<p>This paper presents a novel parametric optimization framework for achieving optical on-orbit inspection missions in geostationary Earth orbit (GEO) while satisfying multiple mission constraints. To better represent real-world scenarios, the effects of perturbations in GEO are examined. Additionally, multiple constraints are incorporated into the problem, including the imaging distance and solar angle, observation duration, time interval of maneuvers, impulse magnitude, and the mission deadline. To address these constraints, we employ parametric methods and propose a novel impulse division and replanning (IDR) method, which forms the basis of the optimization framework to minimize fuel consumption and mission duration. The optimization framework is then solved using the parallel particle swarm optimization (PPSO) algorithm, and its effectiveness is demonstrated through a set of instances. The simulations, which compare the proposed IDR method with the penalty function method of velocity increments (PFV), show improved performance in terms of reduced constraint violations and lower fuel costs.</p>