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A novel multiobjective evolutionary algorithm based on regression analysis.

Song Z, Wang M, Dai G, Vasile M - ScientificWorldJournal (2015)

Bottom Line: The result shows that MMEA-RA outperforms RM-MEDA and NSGA-II on the test instances with variable linkages.At the same time, MMEA-RA has higher efficiency than the other two algorithms.A few shortcomings of MMEA-RA have also been identified and discussed in this paper.

View Article: PubMed Central - PubMed

Affiliation: School of Computer, China University of Geosciences, Wuhan 430074, China.

ABSTRACT
As is known, the Pareto set of a continuous multiobjective optimization problem with m objective functions is a piecewise continuous (m - 1)-dimensional manifold in the decision space under some mild conditions. However, how to utilize the regularity to design multiobjective optimization algorithms has become the research focus. In this paper, based on this regularity, a model-based multiobjective evolutionary algorithm with regression analysis (MMEA-RA) is put forward to solve continuous multiobjective optimization problems with variable linkages. In the algorithm, the optimization problem is modelled as a promising area in the decision space by a probability distribution, and the centroid of the probability distribution is (m - 1)-dimensional piecewise continuous manifold. The least squares method is used to construct such a model. A selection strategy based on the nondominated sorting is used to choose the individuals to the next generation. The new algorithm is tested and compared with NSGA-II and RM-MEDA. The result shows that MMEA-RA outperforms RM-MEDA and NSGA-II on the test instances with variable linkages. At the same time, MMEA-RA has higher efficiency than the other two algorithms. A few shortcomings of MMEA-RA have also been identified and discussed in this paper.

No MeSH data available.


Related in: MedlinePlus

Individual solutions should be scattered around the PS in the decision space in a successful MOEA.
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fig1: Individual solutions should be scattered around the PS in the decision space in a successful MOEA.

Mentions: The population in the decision space in a MOEA for (1) will hopefully approximate the PS and is uniformly scattered around the PS as the search goes on. Therefore, we can envisage the points in the population as independent observations of a random vector ξ ∈ Rn whose centroid is the PS of (1). Since the PS is a (m − 1)-dimensional piecewise continuous manifold, ξ can be naturally described by (2)ξ=ζ+ε,where ζ is uniformly distributed over a piecewise continuous (m − 1)-dimensional manifold, and ε is an n-dimensional zero-mean noise vector. Figure 1 illustrates the basic idea.


A novel multiobjective evolutionary algorithm based on regression analysis.

Song Z, Wang M, Dai G, Vasile M - ScientificWorldJournal (2015)

Individual solutions should be scattered around the PS in the decision space in a successful MOEA.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4385692&req=5

fig1: Individual solutions should be scattered around the PS in the decision space in a successful MOEA.
Mentions: The population in the decision space in a MOEA for (1) will hopefully approximate the PS and is uniformly scattered around the PS as the search goes on. Therefore, we can envisage the points in the population as independent observations of a random vector ξ ∈ Rn whose centroid is the PS of (1). Since the PS is a (m − 1)-dimensional piecewise continuous manifold, ξ can be naturally described by (2)ξ=ζ+ε,where ζ is uniformly distributed over a piecewise continuous (m − 1)-dimensional manifold, and ε is an n-dimensional zero-mean noise vector. Figure 1 illustrates the basic idea.

Bottom Line: The result shows that MMEA-RA outperforms RM-MEDA and NSGA-II on the test instances with variable linkages.At the same time, MMEA-RA has higher efficiency than the other two algorithms.A few shortcomings of MMEA-RA have also been identified and discussed in this paper.

View Article: PubMed Central - PubMed

Affiliation: School of Computer, China University of Geosciences, Wuhan 430074, China.

ABSTRACT
As is known, the Pareto set of a continuous multiobjective optimization problem with m objective functions is a piecewise continuous (m - 1)-dimensional manifold in the decision space under some mild conditions. However, how to utilize the regularity to design multiobjective optimization algorithms has become the research focus. In this paper, based on this regularity, a model-based multiobjective evolutionary algorithm with regression analysis (MMEA-RA) is put forward to solve continuous multiobjective optimization problems with variable linkages. In the algorithm, the optimization problem is modelled as a promising area in the decision space by a probability distribution, and the centroid of the probability distribution is (m - 1)-dimensional piecewise continuous manifold. The least squares method is used to construct such a model. A selection strategy based on the nondominated sorting is used to choose the individuals to the next generation. The new algorithm is tested and compared with NSGA-II and RM-MEDA. The result shows that MMEA-RA outperforms RM-MEDA and NSGA-II on the test instances with variable linkages. At the same time, MMEA-RA has higher efficiency than the other two algorithms. A few shortcomings of MMEA-RA have also been identified and discussed in this paper.

No MeSH data available.


Related in: MedlinePlus