Data Envelopment Analysis (DEA) is a nonparametric methodology for estimating technical efficiency of a set of Decision Making Units (DMUs) from a dataset of inputs and outputs. This paper is devoted to computational aspects of DEA models under the application of the Principle of Least Action. This principle guarantees that the efficient closest targets are determined as benchmarks for each assessed unit. Usually, these models have been addressed in the literature by applying unsatisfactory techniques, based fundamentally on combinatorial NP-hard problems. Recently, some heuristics have been developed to partially solve these DEA models. This paper improves the heuristic methods used in previous works by applying a combination of metaheuristics and an exact method. Also, a parameterized scheme of metaheuristics is developed in order to implement metaheuristics and hybridations/combinations, adapting them to the particular problem proposed here. In this scheme, some parameters are used to study several types of metaheuristics, like Greedy Random Adaptative Search Procedure, Genetic Algorithms or Scatter Search. The exact method is included inside the metaheuristic to solve the particular model presented in this paper. A hyperheuristic is used on top of the parameterized scheme in order to search, in the space of metaheuristics, for metaheuristics that provide solutions close to the optimum. The method is competitive with exact methods, obtaining fitness close to the optimum with low computational time.