A comparison between simultaneous and hierarchical approaches to solve a multi-objective location-routing problem

Aydin Teymourifar*, Ana Maria Rodrigues, José Soeiro Ferreira

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

4 Citations (Scopus)


This paper deals with a multi-objective location-routing problem (MO-LRP) and follows the idea of sectorization to simplify the solution approaches. The MO-LRP consists of sectorization, sub-sectorization, and routing sub-problems. In the sectorization sub-problem, a subset of potential distribution centres (DCs) is opened and a subset of customers is assigned to each of them. Each DC and the customers assigned to it form a sector. Afterward, in the sub-sectorization stage customers of each DC are divided into different sub-sector. Then, in the routing sub-problem, a route is determined and a vehicle is assigned to meet demands. To solve the problem, we design two approaches, which adapt the sectorization, sub-sectorization and routing sub-problems with the non-dominated sorting genetic algorithm (NSGA-II) in two different manners. In the first approach, NSGA-II is used to find non-dominated solutions for all sub-problems, simultaneously. The second one is similar to the first one but it has a hierarchical structure, such that the routing sub-problem is solved with a solver for binary integer programming in MATLAB optimization toolbox after solving sectorization and sub-sectorization sub-problem with NSGA-II. Four benchmarks are used and based on a comparison between the obtained results it is shown that the first approach finds more non-dominated solutions. Therefore, it is concluded that the simultaneous approach is more effective than the hierarchical approach for the defined problem in terms of finding more non-dominated solutions.
Original languageEnglish
Title of host publicationAIRO Springer Series
EditorsClaudio Gentile, Giuseppe Stecca, Paolo Ventura
PublisherSpringer Nature
Number of pages13
ISBN (Print)9783030630720
Publication statusPublished - 2021
Externally publishedYes

Publication series

NameAIRO Springer Series
ISSN (Print)2523-7047
ISSN (Electronic)2523-7055


  • Binary integer programming
  • Evolutionary algorithm
  • Location-routing problems
  • Non-dominated sorting genetic algorithm
  • Routing
  • Sectorization


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