The limited sensors in mass-produced automatic transmissions introduce a significant challenge for performing gearshifts with multiple clutches. To tackle this challenge, this study proposes an integrated surrogate-assisted multi-objective optimization (ISAMO) framework to obtain the optimal control profiles. An optimization-oriented gearshift control strategy coordinated with engine torque reduction is proposed for the gearshift process with four active clutches. A multi-objective optimization problem is formulated to determine the optimal parameters of the proposed control strategy. To mitigate the excessive computation required by the iterative simulation of the physical model in the multi-objective optimization process, we construct a surrogate model to substitute for the physical model based on a radial basis function neural network (RBFNN) and an adaptive sampling method. The RBFNN surrogate model is used in conjunction with the non-dominated sorting genetic algorithm (NSGA-II) to obtain the Pareto optimal set. The improved radar chart evaluation method is adopted to determine an optimal trade-off solution in the Pareto optimal set. The shift transitions of the optimal trade-off solution are simulated and analyzed. Results validate the effectiveness of the proposed ISAMO framework in improving optimization efficiency without sacrificing accuracy.