This article proposes a computational trajectory optimization framework for solving the problem of multiobjective automatic parking motion planning. Constrained automatic parking maneuver problem is usually difficult to solve because of some practical limitations and requirements. This problem becomes more challenging when multiple objectives are required to be optimized simultaneously. The designed approach employs a swarm intelligent algorithm to produce the tradeoff front along the objective space. In order to enhance the local search ability of the algorithm, a gradient operation is utilized to update the solution. In addition, since the evolutionary process tends to be sensitive with respect to the flight control parameters, a novel adaptive parameter controller is designed and incorporated in the algorithm framework such that the proposed method can dynamically balance the exploitation and exploration. The performance of using the designed multiobjective strategy is validated and analyzed by performing a number of simulation and experimental studies. The results indicate that the present approach can provide reliable solutions and it can outperform other existing approaches investigated in this article.