Limits...
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 final nondominated solutions and fronts found by MMEA-RA. (a) The result with the lowest γ-metric and (b) all the 10 fronts in 10 runs.
© Copyright Policy - open-access
Related In: Results  -  Collection


getmorefigures.php?uid=PMC4385692&req=5

fig8: The final nondominated solutions and fronts found by MMEA-RA. (a) The result with the lowest γ-metric and (b) all the 10 fronts in 10 runs.

Mentions: Figure 8 shows the final nondominated solutions and fronts obtained by MMEA-RA on the test case. Figure 8(a) is the result with the lowest γ-metric obtained in 10 runs while Figure 8(b) is all the 10 fronts in 10 runs. It can be seen that the nondominated fronts with the lowest γ-metric are very close to the Pareto front, especially when f1 tends to 0 and f2 tends to 1. It can also be noted that the nondominated solutions in every run have some small fluctuations around the Pareto front.


A novel multiobjective evolutionary algorithm based on regression analysis.

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

The final nondominated solutions and fronts found by MMEA-RA. (a) The result with the lowest γ-metric and (b) all the 10 fronts in 10 runs.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig8: The final nondominated solutions and fronts found by MMEA-RA. (a) The result with the lowest γ-metric and (b) all the 10 fronts in 10 runs.
Mentions: Figure 8 shows the final nondominated solutions and fronts obtained by MMEA-RA on the test case. Figure 8(a) is the result with the lowest γ-metric obtained in 10 runs while Figure 8(b) is all the 10 fronts in 10 runs. It can be seen that the nondominated fronts with the lowest γ-metric are very close to the Pareto front, especially when f1 tends to 0 and f2 tends to 1. It can also be noted that the nondominated solutions in every run have some small fluctuations around the Pareto front.

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