We use a technique from engineering (Xia and Moog, in IEEE Trans. Autom. Contr. 48(2):330-336, 2003; Jeffrey and Xia, in Tan, W.Y., Wu, H. (Eds.), Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention, 2005) to investigate the algebraic identifiability of a popular three-dimensional HIV/AIDS dynamic model containing six unknown parameters. We find that not all six parameters in the model can be identified if only the viral load is measured, instead only four parameters and the product of two parameters (N and lambda) are identifiable. We introduce the concepts of an identification function and an identification equation and propose the multiple time point (MTP) method to form the identification function which is an alternative to the previously developed higher-order derivative (HOD) method (Xia and Moog, in IEEE Trans. Autom. Contr. 48(2):330-336, 2003; Jeffrey and Xia, in Tan, W.Y., Wu, H. (Eds.), Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention, 2005). We show that the newly proposed MTP method has advantages over the HOD method in the practical implementation. We also discuss the effect of the initial values of state variables on the identifiability of unknown parameters. We conclude that the initial values of output (observable) variables are part of the data that can be used to estimate the unknown parameters, but the identifiability of unknown parameters is not affected by these initial values if the exact initial values are measured with error. These noisy initial values only increase the estimation error of the unknown parameters. However, having the initial values of the latent (unobservable) state variables exactly known may help to identify more parameters. In order to validate the identifiability results, simulation studies are performed to estimate the unknown parameters and initial values from simulated noisy data. We also apply the proposed methods to a clinical data set to estimate HIV dynamic parameters. Although we have developed the identifiability methods based on an HIV dynamic model, the proposed methodologies are generally applicable to any ordinary differential equation systems.

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In this article, we propose a penalized likelihood method to estimate time-varying parameters in standard linear state space models. The time-varying parameter is modeled as a smoothing spline and then expressed as a state space model. The maximum likelihood method is used to estimate the smoothing parameter. The proposed method is assessed by a simulation study and applied to virological response data from an HIV-infected patient receiving antiretroviral treatment.

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No-wait flow shop scheduling problems (NWFSPs) are widespread in practical applications. The authors propose a quantum-inspired cuckoo co-evolutionary algorithm for the NWFSP to minimize the makespan. There are three algorithm components: quantum solution construction, quantum population evolution, and an improved neighbourhood local search. They generate initial solutions, search solutions, and improve solution qualities, respectively. Parameters of the proposed algorithm are calibrated statistically. The proposal with calibrated parameters is compared with three existing algorithms on Reeves and Taillard benchmark instances with middle scales. Experimental results show that the proposal outperforms the compared algorithms. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

In this paper, we consider single machine group scheduling with non-periodical maintenance and deteriorating effects. Non-periodical maintenance, which has unfixed maintaining interval or the number of jobs in each group is unfixed, results in a variable number of groups. Deteriorating effects lead to longer processing times of which the deterioration index depends on job grouping. This problem is of significance in different production settings and is much more difficult than and general that other simpler single machine group scheduling problems. Making use of historical processing times, we construct the actual processing time model for jobs. We prove that the problem under study is NP-hard. By transforming the optimization objective, properties are discovered and two batchbased heuristics are presented for small size problems. To further improve the effectiveness for large size problems, an iterated greedy algorithm is proposed being its main advantages simplicity and effectiveness. The proposed methods are evaluated over a large number of random instances with calibrated parameters and components. Comprehensive computational and statistical analyses demonstrate the superiority of the methods proposed over adapted existing approaches.