Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

ND-Tree-based update: a Fast Algorithm for the Dynamic Non-Dominance Problem

Abstract : In this paper we propose a new method called ND-Tree-based update (or shortly ND-Tree) for the dynamic non-dominance problem, i.e. the problem of online update of a Pareto archive composed of mutually non-dominated points. It uses a new ND-Tree data structure in which each node represents a subset of points contained in a hyperrectangle defined by its local approximate ideal and nadir points. By building subsets containing points located close in the objective space and using basic properties of the local ideal and nadir points we can efficiently avoid searching many branches in the tree. ND-Tree may be used in multiobjective evolutionary algorithms and other multiobjective metaheuristics to update an archive of potentially non-dominated points. We prove that the proposed algorithm has sub-linear time complexity under mild assumptions. We experimentally compare ND-Tree to the simple list, Quad-tree, and M-Front methods using artificial and realistic benchmarks with up to 10 objectives and show that with this new method substantial reduction of the number of point comparisons and computational time can be obtained. Furthermore, we apply the method to the non-dominated sorting problem showing that it is highly competitive to some recently proposed algorithms dedicated to this problem.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [32 references]  Display  Hide  Download
Contributor : Gestionnaire Hal-Su Connect in order to contact the contributor
Submitted on : Friday, November 16, 2018 - 2:21:24 PM
Last modification on : Tuesday, March 23, 2021 - 9:28:02 AM
Long-term archiving on: : Sunday, February 17, 2019 - 2:05:30 PM


Publication funded by an institution


  • HAL Id : hal-01900840, version 1
  • ARXIV : 1603.04798


Andrzej Jaszkiewicz, Thibaut Lust. ND-Tree-based update: a Fast Algorithm for the Dynamic Non-Dominance Problem. 2018. ⟨hal-01900840⟩