DPb-MOPSO: A Novel Dynamic Pareto bi-level Multi-Objective Particle
Swarm Optimization Algorithm
Abstract
Particle swarm optimization system based on the distributed architecture
over multiple sub-swarms has shown its efficiency for static
optimization and has not been studied to solve dynamic multi-objective
problems (DMOPs). When solving DMOP, tracking the best solutions over
time and ensuring good exploitation and exploration are the main
challenging tasks. This study proposes a novel 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 a 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 of the objective function due to time-varying parameters. A
response strategy consisting in re-evaluate all unimproved solutions and
replacing them with newly generated ones is also implemented. Inverted
generational distance, mean inverted generational distance, and
hypervolume difference metrics are used to assess the DPb-MOPSO
performances. All quantitative results are analyzed using Friedman’s
analysis of variance while the Lyapunov theorem is used for stability
analysis. Compared with several multi-objective evolutionary algorithms,
the DPb-MOPSO is robust in solving 21 complex problems over a range of
changes in both the Pareto optimal set and Pareto optimal front. For 13
UDF and ZJZ functions, DPb-MOPSO can solve 8/13 and 7/13 on IGD and HVD
with moderate changes. For the 8 FDA and dMOP benchmarks, DPb-MOPSO was
able to resolve 4/8 with severe change on MIGD, and 5/8 for moderate and
slight changes. However, for the 3 kind of environmental changes,
DPb-MOPSO assumes 4/8 of the solving function on IGD and HVD metrics.