Dimensionality reduction approach for many-objective vehicle routing problem with demand responsive transport

Abstract

Demand Responsive Transport (DRT) systems emanate as a substitute to face the problem of volatile, or even inconstant, demand, occurring in popular urban transport systems. This paper is focused in the Vehicle Routing Problem with Demand Responsive Transport (VRPDRT), a type of transport which enables passengers to be taken to their destination, as a shared service, trying to minimize the company costs and offer a quality service taking passengers on their needs. A manyobjective approach is applied in VRPDRT in which seven different objective functions are used. To solve the problem through traditional multiobjective algorithms, the work proposes the usage of cluster analysis to perform the dimensionaly reduction task. The seven functions are then aggregated resulting in a bi-objective formulation and the algorithms NSGA-II and SPEA 2 are used to solve the problem. The results show that the algorithms achieve statistically different results and NSGA-II reaches a greater number of non-dominated solutions when compared to SPEA 2. Furthermore, the results are compared to an approach proposed in literature that uses another way to reduce the dimensionality of the problem in a two-objective formulation and the cluster analysis procedure is proven to be a competitive methodology in that problem. It is possbile to say that the behavior of the algorithm is modified by the way the dimensionality reduction of the problem is made.