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On Tchebycheff Decomposition Approaches for Multiobjective Evolutionary Optimization
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DOI：10.1109/TEVC.2017.2704118.png)
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摘要
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Tchebycheff decomposition represents one of the most widely used decomposition approaches that can convert a multiobjective optimization problem into a set of scalar optimization subproblems. Nevertheless, the geometric properties of the subproblem objective functions in Tchebycheff decomposition have not been explicitly studied. This paper proposes a Tchebycheff decomposition with l(p)-norm constraint on direction vectors in which the subproblem objective functions are endowed with clear geometric property. Especially, the Tchebycheff decomposition with l(2)-norm constraint on direction vectors is taken as an example to illustrate its advantage. A new unary R-2 indicator is also introduced to approximate the hyper-volume metric and justify the efficiency of the proposed Tchebycheff decomposition. A resultant Tchebycheff decomposition-based multiobjective evolutionary algorithm (MOEA) with l(2)-norm constraint and a new population update strategy is proposed to solve multiobjective optimization problems. The experimental results on both benchmark and real-world multiobjective optimization problems show that the proposed algorithm is capable of obtaining high quality solutions compared with other state-of-the-art MOEAs.
Keyword:
R-2 metric
maximal fitness improvement
multiobjective evolutionary algorithm based on decomposition (MOEA/D)
population update strategy
Tchebycheff decomposition
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