Table 1 Hierarchical optimization framework based on four objectives for AVTD

The objectives of the outer optimization problem are as follows:

1

To eliminate the viral biomass growth rate (VBGR) of HV cells as much as possible under the target treatment

2

To maximize the ATP production rate for treated HV cells and perturbed HT cells during treatment

3

To evaluate the fuzzy similarity between the metabolic patterns of treated HV cells and perturbed HT cells and those of HT cells

4

To evaluate the fuzzy dissimilarity between the metabolic patterns of treated HV cells and perturbed HT cells and those of HV cells

The objectives of the inner optimization problem, which is subject to a constraint-based model, are as follows:

1

To conduct FBA and solve UFD problems for the treated HV cells

2

To conduct FBA and solve UFD problems for the perturbed HT cells