In this paper we present a novel hybrid algorithm, in which ideas from the genetic algorithm and the GRASP metaheuristic are cooperatively used and intertwined to dynamically adjust a key parameter of the corridor method, i.e., the corridor width, during the search process. In addition, a fine-tuning technique for the corridor method is then presented. The response surface methodology is employed in order to determine a good set of parameter values given a specific problem input size. The effectiveness of both the algorithm and the validation of the fine tuning technique are illustrated on a specific problem selected from the domain of container terminal logistics, known as the blocks relocation problem, where one wants to retrieve a set of blocks from a bay in a specified order, while minimizing the overall number of movements and relocations. Computational results on 160 benchmark instances attest the quality of the algorithm and validate the fine tuning process.