摘要
Among the different difficulties plaguing the optimal planning and management of water resources, the presence of several and conflicting interests is one of the most intriguing, as this imposes to formulate multi-objective optimization problems, whose resolution yields to a set of Pareto efficient solutions. Both classical and evolutionary multi-objective optimization algorithms can efficiently deal with a reduced number of objectives (usually not more than three), while the majority of the real-world applications requires the designer to handle a much larger number of interests, leading to the so-called many-objective optimization problems. It is then common practice to simply reduce the dimensionality of the objective vector by removing the objectives considered to be redundant. To improve such approach, this study proposes to aggregate, rather than remove, the objectives in few variables, with respect to which the optimization problem is then solved. In particular, the aggregation is obtained via Non-negative Sparse Principal Component Analysis (NSPCA), a feature extraction technique that provides linear combinations of the objectives, while explaining the variance in the data with few combinations and imposing a non-negative constraint on the obtained coefficients. This novel method is demonstrated on a regional environmental planning problem, characterized by four conflicting objectives.