Aggregation or Selection? Clustering Many Objectives for Vehicle Routing Problem with Demand Responsive Transport

This paper discusses a dimensionality reduction procedure to tackle a many-objective formulation of a Vehicle Routing Problem with a Demand Responsive Transport (VRPDRT). The problem formulation presents eight objective functions that aim to reduce the operating costs while meeting passenger needs and providing a high-quality service. Two different dimensionality reduction-based approaches, aggregation and feature selection are employed to transform the many-objective formulation into a bi-objective one. The reduction, applied during the search evolution, follows a hierarchical clustering technique in which the objective functions' similarity and conflict are explored. The proposed approaches are compared with a classic version of MOEA/D that solves the problem in its original formulation. Moreover, different dimensionality reduction frequencies are tested to assess the impact on the algorithms' performance. When comparing the outcomes in the original objective space, the results show that the aggregation approach outperforms the feature selection method, regardless of the dimensionality reduction frequency. Furthermore, while there is no statistical difference between the MOEA/D and the aggregation approach and the MOEA/D outperforms the feature selection approaches.