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DPb-MOPSO: A Dynamic Pareto bi-level Multi-objective Particle Swarm Optimization Algorithm

Aboud, Ahlem; Rokbani, Nizar; Fdhila, Raja; Qahtani, Abdulrahman M.; Almutiry, Omar; Dhahri, Habib; Hussain, Amir; Alimi, Adel M.


Ahlem Aboud

Nizar Rokbani

Raja Fdhila

Abdulrahman M. Qahtani

Omar Almutiry

Habib Dhahri

Adel M. Alimi


Particle Swarm Optimization (PSO) system based on the distributed architecture over multiple sub-swarms is very efficient for static multi-objective optimization but has not been considered for solving dynamic multi-objective problems (DMOPs). Tracking the most effective solutions over time and ensuring good exploitation and exploration are the main challenges of solving DMOP. This study proposes a Dynamic Pareto bi-level Multi-Objective Particle Swarm Optimization (DPb-MOPSO) algorithm including two parallel optimization levels. At the first level, all solutions are managed in a single search space. When a dynamic change is successfully detected in the objective values, the Pareto ranking operator is used to enable multiple sub-swarm’ subdivisions and processing which drives the second level of enhanced exploitation. A dynamic handling strategy based on random detectors is used to track the changes in the objective function due to time-varying parameters. A response strategy consisting in reevaluating all unimproved solutions and replacing them with newly generated ones is also implemented. The DPb-MOPSO system is tested on DMOPs with different types of time-varying Pareto Optimal Set (POS) and Pareto Optimal Front (POF). Inverted generational distance (IGD), mean inverted generational distance (MIGD), hypervolume difference (HVD), Robust IGD (RIGD), and Robust General Distance (RGD) metrics are used to assess the DPb-MOPSO performance. Quantitative results are analyzed using Friedman’s analysis of variance, and the Wilcoxon sum ranks test, while the stability is analyzed using Lyapunov’s theorem. The DPb-MOPSO is more robust than several dynamic multi-objective evolutionary algorithms in solving 21 complex problems over a range of changes in both the POS and POF. On IGD and HVD, DPb-MOPSO can solve 8/13 and 8/13 of the 13 UDF and ZJZ functions with moderate changes. DPb-MOPSO can resolve 7/8 FDA and DMOP benchmarks with severe changes to the MIGD, and 6/8 with moderate changes. DPb-MOPSO assumes 7/8, 6/8, and 5/8 for solving FDA, and dMOP functions on IGD and 6/8, 5/8, and 5/8 on HVD metrics considering severe, moderate, and slight environmental changes respectively. Also, it is the winner for solving 8 DMOPs based on RIGD, and RGD metrics.

Journal Article Type Article
Acceptance Date Aug 31, 2022
Online Publication Date Sep 16, 2022
Publication Date 2022-11
Deposit Date Nov 3, 2022
Publicly Available Date Sep 17, 2023
Journal Applied Soft Computing
Print ISSN 1568-4946
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 129
Article Number 109622
Keywords Dynamic multi-objective optimization problem, Dynamic particle swarm optimization, Detectors, Dynamic response, Friedman analysis of variance, Wilcoxon test, Lyapunov theorem
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DPb-MOPSO: A Dynamic Pareto Bi-level Multi-objective Particle Swarm Optimization Algorithm (supplementary data) (1.4 Mb)

DPb-MOPSO: A Dynamic Pareto Bi-level Multi-objective Particle Swarm Optimization Algorithm (accepted version) (1.4 Mb)

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