The q-Gradient Method for Continuous Global Optimization

Here, we present an extension of the classical steepest descent method for solving global continuous optimization problems. To this end, we apply the concept of Jackson’s derivative to compute the negative of the q-gradient of the objective function, used as the search direction. The use of Jackson’s derivative has shown to be an effective mechanism for escaping from local minima. The q-gradient algorithm is complemented with strategies for selecting the parameter q and to compute the step length. These strategies are implemented in a way such that the search process gradually shifts from global in the beginning to local as the algorithm converges. For testing this new approach, we considered a set of multimodal test functions and compared our results with those obtained by Evolutionary Algorithms (EAs) widely used in optimizing multidimensional and multimodal functions. Overall, the q-gradient method performs well against the EAs arriving in forth position in a direct comparison with them, for the dimensions 10 and 30.