<p>This paper addresses the task assignment problem for a geodesic dome phased array antenna (GDPAA), which is described as an optimization problem to obtain the maximum measurement performance. Several critical challenges arise in this task allocation, including the high dimensionality of decision variables, multiple conflicting objectives, and the lack of an analytical expression for the objective function. To solve these challenges, this work proposes a high-dimensional combinatorial Bayesian optimization approach for this task scheduling. A random dimension reduction method is used to simplify the decision variables to handle large-scale tasks. With the consideration on the time complexity of the construction of the classical surrogate model for Bayesian optimization, a probabilistic surrogate model is built to describe the relationship between the measurement task and the GDPAA’s performance. The new strategy accelerates the algorithm convergence. An experiment is conducted to show the merit of effectiveness of the proposed method. Compared to reinforcement learning, particle swarm optimization, and other methods, the proposed approach achieves superior measurement performance with reduced computational time.</p>