The resulting nonconvex optimization problem is solved by a primal-dual interior-point algorithm, which is based on a full-space primal-dual approach to achieve feasibility and optimality simultaneously.
With this problem formulation, it follows (from Sylvester's law of inertia [35]) that we need m ≥ rank(D B ) to achieve feasibility in the constraint (i.e., having at least as many non-zero singular values of Σ as non-zero eigenvalues in D B ).
Swapping two jobs in a schedule, for example, is conceptually rather simple and easily implemented in an activity list encoding, whereas in a direct binary encoding of a schedule, potentially, many different variables must be modified and it can be difficult to achieve feasibility again.
Besides, the IRR of the 1G + 2G biorefinery is more sensitive with respect to the price of ethanol, and an increase of 11.5% in this value would be enough to achieve feasibility.
Minimizing CO2 emission, while achieving economic feasibility in CO2 utilization for producing valuable chemicals is a challenging problem, as reported in recent studies.
The designed scheme of relaxation factor control can avoid overcharge and over discharge of energy storage, reducing the frequency of charge-discharge of lithium battery, achieving the feasibility and effectiveness of energy management strategy.
The overall success rate in achieving our feasibility criteria was 98.4 %.
However, the path to achieving economic feasibility is likely to require strain optimization through using available tools and technologies in the fields of systems and synthetic biology.
To achieve fabrication feasibility of a designed Halbach magnet array, two design schemes are combined with the isoparametric projection method.
