Multi-stage differential evolution algorithm for constrained D-optimal design

Xinfeng Zhang; Zhibin Zhu; Chongqi Zhang; Xinfeng Zhang; Zhibin Zhu; Chongqi Zhang

doi:10.3934/math.2021179

AIMS Mathematics

2021, Volume 6, Issue 3: 2956-2969. doi: 10.3934/math.2021179

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Research article

Multi-stage differential evolution algorithm for constrained D-optimal design

1.
School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China
2.
Undergraduate School of Medical Business, Guangdong Pharmaceutical University, Guangzhou 510006, China

Received: 25 October 2020 Accepted: 17 December 2020 Published: 08 January 2021
MSC : 62K05, 62K99

In practice, objective condition may impose constraints on design region, which make it difficult to find the exact D-optimal design. In this paper, we propose a Multi-stage Differential Evolution (MDE) algorithm to find the global approximated D-optimal design in an experimental region with linear or nonlinear constraints. MDE algorithm is approved from Differential Evolution (DE) algorithm. It has low requirements for both feasible regions and initial values. In iteration, MDE algorithm pursues evolutionary equilibrium rather than convergence speed, so it can stably converge to the global D-optimal design instead of the local ones. The advantages of MDE algorithm in finding D-optimal design will be illustrated by examples.
- experimental design,
- D-optimal design,
- constrained experimental region,
- multi-stage differential evolution algorithm
Citation: Xinfeng Zhang, Zhibin Zhu, Chongqi Zhang. Multi-stage differential evolution algorithm for constrained D-optimal design[J]. AIMS Mathematics, 2021, 6(3): 2956-2969. doi: 10.3934/math.2021179

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Abstract

In practice, objective condition may impose constraints on design region, which make it difficult to find the exact D-optimal design. In this paper, we propose a Multi-stage Differential Evolution (MDE) algorithm to find the global approximated D-optimal design in an experimental region with linear or nonlinear constraints. MDE algorithm is approved from Differential Evolution (DE) algorithm. It has low requirements for both feasible regions and initial values. In iteration, MDE algorithm pursues evolutionary equilibrium rather than convergence speed, so it can stably converge to the global D-optimal design instead of the local ones. The advantages of MDE algorithm in finding D-optimal design will be illustrated by examples.

References

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