Gradient subspace approximation: a direct search method for memetic computing

The hybridization of evolutionary algorithms and local search techniques as, e.g., mathematical programming techniques, also referred to as memetic algorithms, has caught the interest of many researchers in the recent past. Reasons for this include that the resulting algorithms are typically robust and reliable since they take the best of both worlds. However, one crucial drawback of such hybrids is the relatively high cost of the local search techniques since many of them require the gradient or even the Hessian at each candidate solution. Here, we propose an alternative way to compute search directions by exploiting the neighborhood information. That is, for a given point within a population $$\mathcal{P}$$P, the neighboring solutions in $$\mathcal{P}$$P are used to compute the most greedy search direction out of the given data. The method is hence particularly interesting for the usage within population-based search strategies since the search directions come ideally for free in terms of additional function evaluations. In this study, we analyze the novel method first as a stand-alone algorithm and show further on its benefit as a local searcher within differential evolution.