Decomposition-Based Algorithms Using Pareto Adaptive Scalarizing Methods

Decomposition-based algorithms have become increasingly popular for evolutionary multiobjective optimization. However, the effect of scalarizing methods used in these algorithms is still far from being well understood. This paper analyzes a family of frequently used scalarizing methods, the L p meth...

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Bibliographic Details
Published in:IEEE transactions on evolutionary computation 2016-12, Vol.20 (6), p.821-837
Main Authors: Wang, Rui, Zhang, Qingfu, Zhang, Tao
Format: Article
Language:English
Subjects:
Adaptive algorithms
Approximation algorithms
Chebyshev approximation
Decomposition
Evolutionary algorithms
Evolutionary computation
Geometry
Linear programming
multiobjective evolutionary algorithm based on decomposition (MOEA/D)
multiobjective optimization
Pareto optimization
Pareto optimum
scalarizing method
Scalars
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Summary:Decomposition-based algorithms have become increasingly popular for evolutionary multiobjective optimization. However, the effect of scalarizing methods used in these algorithms is still far from being well understood. This paper analyzes a family of frequently used scalarizing methods, the L p methods, and shows that the p value is crucial to balance the selective pressure toward the Pareto optimal and the algorithm robustness to Pareto optimal front (PF) geometries. It demonstrates that an L p method that can maximize the search ability of a decomposition-based algorithm exists and guarantees that, given some weight, any solution along the PF can be found. Moreover, a simple yet effective method called Pareto adaptive scalarizing (PaS) approximation is proposed to approximate the optimal p value. In order to demonstrate the effectiveness of PaS, we incorporate PaS into a state-of-the-art decomposition-based algorithm, i.e., multiobjective evolutionary algorithm based on decomposition (MOEA/D), and compare the resultant MOEA/D-PaS with some other MOEA/D variants on a set of problems with different PF geometries and up to seven conflicting objectives. Experimental results demonstrate that the PaS is effective.
ISSN:1089-778X
1941-0026
DOI:10.1109/TEVC.2016.2521175