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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

The evolution of the average γ-metric of the nondominated solutions in three algorithms for T1.
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fig7: The evolution of the average γ-metric of the nondominated solutions in three algorithms for T1.

Mentions: The evolution of the average γ-metric of the nondominated solutions for the test case is shown in Figure 7. It should be noted that the solutions of all three algorithms are stable when the iteration generation is more than 300. After the solutions are stable, the convergence values of the three algorithms are small than 0.1. Because we adopt the average of the minimum Euclidean distance of each solution from chosen solutions as the metric γ, the smaller the convergence values, the better the convergence metric γ. As is shown by Figure 7, among the three algorithms, MEMA-RA has best convergence performance and NSGA-II and RM-MEDA follow.


A novel multiobjective evolutionary algorithm based on regression analysis.

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

The evolution of the average γ-metric of the nondominated solutions in three algorithms for T1.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig7: The evolution of the average γ-metric of the nondominated solutions in three algorithms for T1.
Mentions: The evolution of the average γ-metric of the nondominated solutions for the test case is shown in Figure 7. It should be noted that the solutions of all three algorithms are stable when the iteration generation is more than 300. After the solutions are stable, the convergence values of the three algorithms are small than 0.1. Because we adopt the average of the minimum Euclidean distance of each solution from chosen solutions as the metric γ, the smaller the convergence values, the better the convergence metric γ. As is shown by Figure 7, among the three algorithms, MEMA-RA has best convergence performance and NSGA-II and RM-MEDA follow.

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