The imperialist competitive algorithm (ICA), inspired by sociopolitical behavior in the real world, is a new optimization algorithm. The ICA shows great potential to solve complex optimization problems. In order to improve the ICA’s exploration ability and speed up its convergence, two improved schemes are proposed in this paper. The first scheme presents a new possession probability in the imperialistic competition phase. Inspired by geopolitics, not only the power of the empire but also the distance between the imperialists are taken into account in calculating the new possession probability. The second scheme introduces the wavelet mutation operator into the original ICA so as to improve its exploration ability. The improved ICAs (IICAs) are tested on several benchmark functions and then used to design the optimum parameters of tuned mass damper and tune the parameters of a fractional order PID controller of an automatic voltage regulator (AVR) system. Results show that the IICAs outperform the original ICA in terms of solution quality and convergence speed.