A deterministic technique for fast surrogate-assisted multi-objective design optimization of antennas in highly-dimensional parameters spaces has been discussed. In this two-stage approach, the initial approximation of the Pareto set representing the best compromise between conflicting objectives is obtained using a bisection algorithm which finds new Pareto-optimal designs by dividing the line segments interconnecting previously found optimal points, and executing poll-type search that involves Pareto ranking. The initial Pareto front is generated at the level of the coarsely-discretized EM model of the antenna. In the second stage of the algorithm, the high-fidelity Pareto designs are obtained through optimization of corrected local-approximation models. The considered optimization method is verified using a 17-variable uniplanar antenna operating in ultra-wideband frequency range. The method is compared to three state-of-the-art surrogate-assisted multi-objective optimization algorithms.