Cellular Genetic Algorithms (cGAs) have attracted the attention of researchers due to their high performance, ease of implementation and massive parallelism. Maintaining an adequate balance between exploitative and explorative search is essential when studying evolutionary optimization techniques. In this respect, cGAs inherently possess a number of structural configuration parameters that are able to sustain diversity during evolution. In this study, the internal reconfiguration of the lattice is proposed to constantly or adaptively control the exploration-exploitation trade-off. Genetic operators are characterized in their simplest form since algorithmic performance is assessed on implemented reconfiguration mechanisms. Moreover, internal reconfiguration allows the adjacency of individuals to be maintained. Hence, any improvement in performance is only a consequence of topological changes. Two local selection methods presenting opposite selection pressures are used in order to evaluate the influence of the proposed techniques. Problems ranging from continuous to real world and combinatorial are tackled. Empirical results are supported statistically in terms of efficiency and efficacy.