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A Simulated Annealing Algorithm for D-Optimal Design for 2-Way and 3-Way Polynomial Regression with Correlated Observations

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  • Chang Li
  • Daniel C. Coster

Abstract

Much of the previous work in D-optimal design for regression models with correlated errors focused on polynomial models with a single predictor variable, in large part because of the intractability of an analytic solution. In this paper, we present a modified, improved simulated annealing algorithm, providing practical approaches to specifications of the annealing cooling parameters, thresholds, and search neighborhoods for the perturbation scheme, which finds approximate D-optimal designs for 2-way and 3-way polynomial regression for a variety of specific correlation structures with a given correlation coefficient. Results in each correlated-errors case are compared with traditional simulated annealing algorithm, that is, the SA algorithm without our improvement. Our improved simulated annealing results had generally higher D-efficiency than traditional simulated annealing algorithm, especially when the correlation parameter was well away from 0.

Suggested Citation

  • Chang Li & Daniel C. Coster, 2014. "A Simulated Annealing Algorithm for D-Optimal Design for 2-Way and 3-Way Polynomial Regression with Correlated Observations," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-6, March.
    • Handle: RePEc:hin:jnljam:746914
    DOI: 10.1155/2014/746914
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    Cited by:

    1. Stephen J. Walsh & John J. Borkowski, 2022. "Improved G -Optimal Designs for Small Exact Response Surface Scenarios: Fast and Efficient Generation via Particle Swarm Optimization," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    2. Saeid Pooladsaz & Mahboobeh Doosti-Irani, 2020. "An algorithm for finding efficient test-control block designs with correlated observations," Computational Statistics, Springer, vol. 35(2), pages 821-836, June.

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