Group Search Optimiser (GSO) is a new swarm intelligence optimiser algorithm inspired by animal social behaviours. In this paper, we proposed two variants of GSO to improve its search capability, and applied them to solving non-linear equations. Producers in the GSO are like the eyes of animals, which determine the i¾food' position and the movement direction of scroungers. However, due to the random sample mechanism, the computational efficiency is poor. To improve its search efficiency, a new GSO based on quadratic interpolation method (QIGSO) is proposed, in which the estimated position with quadratic interpolation theory is used to replace the random point in each iteration to increase the speed of convergence. Furthermore, the steepest gradient descent method is also incorporated into QIGSO (QIGSO_SDO) to improve the local search capability. Numerical simulation and a special problem about radar detection are used to test the proposed two variants.