Transmitting antenna positioning or transmitter placement is a well-known NP-hard optimization problem pertinent to communication systems. Furthermore, it is of practical importance to yield an optimal location of transmitters to ensure low sensitivity with respect to potential uncertainties. Notwithstanding, incorporating uncertainties in the optimization problem can highly increase the computational expenses. This paper aims at the development of a new reducedcost algorithm for a multi-objective robust transmitter placement under uncertainties. Toward this end, a new hybrid surrogate-metaheuristic approach is developed using Grey Wolf Optimizer (GWO) and the Kriging surrogate in a mathematical framework of a robust dual-surface model. The proposed algorithm is also able to analyze the sensitivity of the obtained optimal results. The latter is achieved by obtaining the bootstrapped confidence regions without extra simulation experiments. The paper investigates the performance of the proposed algorithm for robust optimal placing of two, three, and four transmitters, under uncertainties concerning the transmitting antenna gain. The results demonstrate the utility and the efficiency of the proposed method in rendering the robust optimal design and analyzing the sensitivity of the transmitter placement problem under practically acceptable computational efforts.