In this paper, we address an online dimensionality reduction approach to deal with a many-objective formulation of a Vehicle Routing Problem with a Demand Responsive Transport (VRPDRT). The problem relates to a mode of transport similar to available carpooling services in which passengers are transported from their origin to their destination sharing the same vehicle. The goal is to reduce the operating/riding costs while meeting passenger needs and providing high-quality service. Due to the complexity and conflicting characteristics of the problem, an evolutionary approach based on a dimensionality reduction technique is applied to solve the VRPDRT in which eight different objective functions are used. The performance of the proposed approaches – OnCLτ-MOEA/D and OnCLρ-MOEA/D – are compared to an a priori cluster dimensionality reduction with Pearson's and τ of Kendall correlation coefficients using a realistic data set containing distances and travel time for Belo Horizonte, Brazil. The online and offline versions of the algorithms are also compared with a baseline approach, a classic version of MOEA/D. Results show that the online cluster-based approach achieves a better spread of solutions, when compared to its a priori versions. Moreover, there is no difference between the results obtained from the online Cluster-based approach and the original MOEA/D. It shows that the proposed dimensionality reduction is an effective technique presenting a positive effect on the search efficiency, computational cost, and in the application of usual visualization techniques.
Bibliographical noteFunding Information:
Flávio Martins, Elizabeth Wanner, and João Sarubbi would like to thank the support from the Brazilian funding agencies: CAPES, FAPEMIG and CNPq. Flávio Martins also acknowledges the support from Michigan State University (MSU) (under Koenig Endowed Chair grant of Prof. Kalyanmoy Deb) for his visit to MSU.
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- Cluster analysis
- Dimensionality reduction techniques
- Kendall's correlation
- Many-objective optimization
- Pearson's correlation
- Vehicle routing problem with a demand responsive transport