Online clustering reduction based on parametric and non-parametric correlation for a many-objective vehicle routing problem with demand responsive transport

Renan S. Mendes*, Victoria Lush, Elizabeth F. Wanner, Flávio V.C. Martins, João F.M. Sarubbi, Kalyanmoy Deb

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number114467
JournalExpert Systems with Applications
Early online date16 Dec 2020
Publication statusPublished - 15 May 2021

Bibliographical note

Funding 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.

Publisher Copyright:
© 2020 Elsevier Ltd

Copyright 2021 Elsevier B.V., All rights reserved.


  • Cluster analysis
  • Dimensionality reduction techniques
  • Kendall's correlation
  • Many-objective optimization
  • Pearson's correlation
  • Vehicle routing problem with a demand responsive transport


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