Global optimization by multilevel partition

Partition-based algorithms, such as the DIRECT algorithm, are popular algorithms for solving global optimization problems. However, these algorithms often have an eventually inefficient behavior due to much more costs requirement to obtain a solution with higher accuracy. In this paper, we present a...

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Vydáno v:	Journal of global optimization Ročník 61; číslo 1; s. 47 - 69
Hlavní autoři:	Liu, Qunfeng, Zeng, Jinping
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Boston Springer US 01.01.2015 Springer Springer Nature B.V
Témata:	Accuracy Algorithms Analysis Computer Science Construction Construction costs Differential equations Mathematical models Mathematical optimization Mathematics Mathematics and Statistics Multilevel Operations Research/Decision Theory Optimization Optimization algorithms Partial differential equations Partitions Real Functions Strategy Studies Global optimization DIRECT algorithm Partition-based algorithm Multigrid algorithm
ISSN:	0925-5001, 1573-2916
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Abstract	Partition-based algorithms, such as the DIRECT algorithm, are popular algorithms for solving global optimization problems. However, these algorithms often have an eventually inefficient behavior due to much more costs requirement to obtain a solution with higher accuracy. In this paper, we present an algorithm framework for bound constrained global optimization problems based on a multilevel partition strategy. This multilevel partition strategy can be regarded as a combination of the basic partition strategy and the multigrid algorithm, which is one of the best algorithms to solve partial differential equation. Our basic idea is to combine the multigrid algorithm with the partition-based algorithm to improve the eventually inefficient behavior of the partition-based algorithm. First, we provide a general framework of the partition-based algorithms which include the DIRECT algorithm as a special case. Then we present a strategy to build the subproblem at the coarse level. This strategy is easy to implement and brings no more computational costs. Under mild conditions, we show that the sequence generated by the proposed global optimization algorithm framework converges to the global optimum. Finally, we employ the original DIRECT algorithm to build a specific global optimization algorithm based on multilevel partition and compare it with the original DIRECT algorithm. Our numerical results show that obtained algorithm improves significantly the eventually inefficient behavior of the original DIRECT algorithm when the required accuracy is high.
AbstractList	Partition-based algorithms, such as the DIRECT algorithm, are popular algorithms for solving global optimization problems. However, these algorithms often have an eventually inefficient behavior due to much more costs requirement to obtain a solution with higher accuracy. In this paper, we present an algorithm framework for bound constrained global optimization problems based on a multilevel partition strategy. This multilevel partition strategy can be regarded as a combination of the basic partition strategy and the multigrid algorithm, which is one of the best algorithms to solve partial differential equation. Our basic idea is to combine the multigrid algorithm with the partition-based algorithm to improve the eventually inefficient behavior of the partition-based algorithm. First, we provide a general framework of the partition-based algorithms which include the DIRECT algorithm as a special case. Then we present a strategy to build the subproblem at the coarse level. This strategy is easy to implement and brings no more computational costs. Under mild conditions, we show that the sequence generated by the proposed global optimization algorithm framework converges to the global optimum. Finally, we employ the original DIRECT algorithm to build a specific global optimization algorithm based on multilevel partition and compare it with the original DIRECT algorithm. Our numerical results show that obtained algorithm improves significantly the eventually inefficient behavior of the original DIRECT algorithm when the required accuracy is high. Partition-based algorithms, such as the DIRECT algorithm, are popular algorithms for solving global optimization problems. However, these algorithms often have an eventually inefficient behavior due to much more costs requirement to obtain a solution with higher accuracy. In this paper, we present an algorithm framework for bound constrained global optimization problems based on a multilevel partition strategy. This multilevel partition strategy can be regarded as a combination of the basic partition strategy and the multigrid algorithm, which is one of the best algorithms to solve partial differential equation. Our basic idea is to combine the multigrid algorithm with the partition-based algorithm to improve the eventually inefficient behavior of the partition-based algorithm. First, we provide a general framework of the partition-based algorithms which include the DIRECT algorithm as a special case. Then we present a strategy to build the subproblem at the coarse level. This strategy is easy to implement and brings no more computational costs. Under mild conditions, we show that the sequence generated by the proposed global optimization algorithm framework converges to the global optimum. Finally, we employ the original DIRECT algorithm to build a specific global optimization algorithm based on multilevel partition and compare it with the original DIRECT algorithm. Our numerical results show that obtained algorithm improves significantly the eventually inefficient behavior of the original DIRECT algorithm when the required accuracy is high.[PUBLICATION ABSTRACT]
Audience	Academic
Author	Zeng, Jinping Liu, Qunfeng
Author_xml	– sequence: 1 givenname: Qunfeng surname: Liu fullname: Liu, Qunfeng email: liuqf@dgut.edu.cn organization: School of Computing, Dongguan University of Technology – sequence: 2 givenname: Jinping surname: Zeng fullname: Zeng, Jinping organization: School of Computing, Dongguan University of Technology
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Cites_doi	10.1007/BF00941892 10.1023/A:1017930332101 10.1137/1.9781611971309 10.1023/A:1008382309369 10.1137/1.9780898719505 10.1007/s10898-009-9515-y 10.1007/s10898-006-9029-9 10.1093/bioinformatics/bth175 10.1007/s10898-008-9332-8 10.1090/S0025-5718-1977-0431719-X 10.2514/6.2002-5573 10.1109/ICNN.1995.488968 10.1145/1570256.1570323 10.1109/MHS.1995.494215
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Snippet	Partition-based algorithms, such as the DIRECT algorithm, are popular algorithms for solving global optimization problems. However, these algorithms often have...
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SubjectTerms	Accuracy Algorithms Analysis Computer Science Construction Construction costs Differential equations Mathematical models Mathematical optimization Mathematics Mathematics and Statistics Multilevel Operations Research/Decision Theory Optimization Optimization algorithms Partial differential equations Partitions Real Functions Strategy Studies
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Title	Global optimization by multilevel partition
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