A cellular genetic algorithm (CGA) is a decentralized form of GA where individuals in a population are usually arranged in a 2D grid and interactions among individuals are restricted to a set neighborhood. In this paper, we extend the notion of cellularity to memetic algorithms (MA), a configuration termed cellular memetic algorithm (CMA). In addition, we propose adaptive mechanisms that tailor the amount of exploration versus exploitation of local solutions carried out by the CMA. We systematically benchmark this adaptive mechanism and provide evidence that the resulting adaptive CMA outperforms other methods both in the quality of solutions obtained and the number of function evaluations for a range of continuous optimization problems.