A multi-objective optimization perspective in Data envelopment analysis

Data Envelopment Analysis (DEA) is traditionally employed to evaluate the relative efficiency of Decision Making Units (DMUs) and to identify projection paths from inefficient units toward the efficient frontier. Classical approaches generally interpret this transition as a shortest-path problem, frequently based on distance minimization criteria. However, multiple alternative efficient transformation strategies may coexist. This work proposes the interpretation of DEA efficiency recovery as a multimodal multi-objective optimization problem. Two optimization formulations are investigated: a norm-based formulation minimizing the $L_1$, $L_2$, and $L_{\infty}$ distances, and a five-objective formulation minimizing the individual changes associated with each decision variable. The optimization process is performed using a synthetic benchmark. The resulting Pareto sets and Pareto fronts are analyzed through parallel-coordinate visualizations. The results demonstrate that several efficient solutions may coexist within similar objective-space quality levels while requiring substantially different decision-space adaptations.