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Conceptual comparison of population based metaheuristics for engineering problems.

Adekanmbi O, Green P - ScientificWorldJournal (2015)

Bottom Line: Several extensions of differential evolution have been adopted in solving constrained and nonconstrained multiobjective optimization problems, but in this study, the third version of generalized differential evolution (GDE) is used for solving practical engineering problems.GDE3 metaheuristic modifies the selection process of the basic differential evolution and extends DE/rand/1/bin strategy in solving practical applications.The performance of the metaheuristic is investigated through engineering design optimization problems and the results are reported.

View Article: PubMed Central - PubMed

Affiliation: Department of Finance and Information Management, Durban University of Technology, P.O. Box 101112, Scottsville, Pietermaritzburg 3209, South Africa.

ABSTRACT
Metaheuristic algorithms are well-known optimization tools which have been employed for solving a wide range of optimization problems. Several extensions of differential evolution have been adopted in solving constrained and nonconstrained multiobjective optimization problems, but in this study, the third version of generalized differential evolution (GDE) is used for solving practical engineering problems. GDE3 metaheuristic modifies the selection process of the basic differential evolution and extends DE/rand/1/bin strategy in solving practical applications. The performance of the metaheuristic is investigated through engineering design optimization problems and the results are reported. The comparison of the numerical results with those of other metaheuristic techniques demonstrates the promising performance of the algorithm as a robust optimization tool for practical purposes.

No MeSH data available.


The GDE3 algorithm [29].
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Related In: Results  -  Collection


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alg1: The GDE3 algorithm [29].

Mentions: The whole GDE3 is presented in Algorithm 1. Parts that are new compared to previous GDE versions are framed in Algorithm 1. Without these parts, the algorithm is identical to GDE1. GDE3 can be seen as a combination of GDE2 and Pareto Differential Evolution Approach (PDEA). GDE3 is similar to differential evolution for multiobjective optimization (DEMO) except that DEMO does not contain constraint handling nor recede to basic DE in the case of a single objective because DEMO modifies the basic DE and does not consider weak dominance in the selection. Moreover, GDE3 has an improved diversity maintenance compared to DEMO. There are no constraints to be evaluated when K = 0 and M = 1, and the selection is simply(1)xi,G+1=ui,G,if  fui,G≤fxi,G,xi,G,otherwise.This is the same as for the basic DE algorithm. The size of the population does not increase since this requires that xi,G and ui,G do not dominate each other even weakly, but in the case of a single objective, the reverse is the case. GDE3 performs the sorting of the vector by calculating the crowding distance of the vector. The selection process based on crowding distance gives GDE3 an advantage over NSGAII. In the case of comparing feasible, incomparable, and nondominating solutions, both offspring and parent vectors are saved for the population of the next generation [4]. There is no need to remove elements, since the population size does not increase. Hence, GDE3 is identical to basic DE in this case. GDE3 improves the ability to handle multiobjective optimization problems by giving a better distributed set of solutions and are less sensitive to the selection of control parameter values compared to the earlier GDE versions. As a result, this procedure reduces the computational costs of the metaheuristic and improves its efficiency. Readers interested in GDE3 should refer to the texts by [30, 31].


Conceptual comparison of population based metaheuristics for engineering problems.

Adekanmbi O, Green P - ScientificWorldJournal (2015)

The GDE3 algorithm [29].
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4383342&req=5

alg1: The GDE3 algorithm [29].
Mentions: The whole GDE3 is presented in Algorithm 1. Parts that are new compared to previous GDE versions are framed in Algorithm 1. Without these parts, the algorithm is identical to GDE1. GDE3 can be seen as a combination of GDE2 and Pareto Differential Evolution Approach (PDEA). GDE3 is similar to differential evolution for multiobjective optimization (DEMO) except that DEMO does not contain constraint handling nor recede to basic DE in the case of a single objective because DEMO modifies the basic DE and does not consider weak dominance in the selection. Moreover, GDE3 has an improved diversity maintenance compared to DEMO. There are no constraints to be evaluated when K = 0 and M = 1, and the selection is simply(1)xi,G+1=ui,G,if  fui,G≤fxi,G,xi,G,otherwise.This is the same as for the basic DE algorithm. The size of the population does not increase since this requires that xi,G and ui,G do not dominate each other even weakly, but in the case of a single objective, the reverse is the case. GDE3 performs the sorting of the vector by calculating the crowding distance of the vector. The selection process based on crowding distance gives GDE3 an advantage over NSGAII. In the case of comparing feasible, incomparable, and nondominating solutions, both offspring and parent vectors are saved for the population of the next generation [4]. There is no need to remove elements, since the population size does not increase. Hence, GDE3 is identical to basic DE in this case. GDE3 improves the ability to handle multiobjective optimization problems by giving a better distributed set of solutions and are less sensitive to the selection of control parameter values compared to the earlier GDE versions. As a result, this procedure reduces the computational costs of the metaheuristic and improves its efficiency. Readers interested in GDE3 should refer to the texts by [30, 31].

Bottom Line: Several extensions of differential evolution have been adopted in solving constrained and nonconstrained multiobjective optimization problems, but in this study, the third version of generalized differential evolution (GDE) is used for solving practical engineering problems.GDE3 metaheuristic modifies the selection process of the basic differential evolution and extends DE/rand/1/bin strategy in solving practical applications.The performance of the metaheuristic is investigated through engineering design optimization problems and the results are reported.

View Article: PubMed Central - PubMed

Affiliation: Department of Finance and Information Management, Durban University of Technology, P.O. Box 101112, Scottsville, Pietermaritzburg 3209, South Africa.

ABSTRACT
Metaheuristic algorithms are well-known optimization tools which have been employed for solving a wide range of optimization problems. Several extensions of differential evolution have been adopted in solving constrained and nonconstrained multiobjective optimization problems, but in this study, the third version of generalized differential evolution (GDE) is used for solving practical engineering problems. GDE3 metaheuristic modifies the selection process of the basic differential evolution and extends DE/rand/1/bin strategy in solving practical applications. The performance of the metaheuristic is investigated through engineering design optimization problems and the results are reported. The comparison of the numerical results with those of other metaheuristic techniques demonstrates the promising performance of the algorithm as a robust optimization tool for practical purposes.

No MeSH data available.