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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Bibliographic Details
Published in:Journal of global optimization Vol. 61; no. 1; pp. 47 - 69
Main Authors: Liu, Qunfeng, Zeng, Jinping
Format: Journal Article
Language:English
Published: Boston Springer US 01.01.2015
Springer
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-014-0152-8