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Yu-Chen Shu

Publications and source records attributed to Yu-Chen Shu.

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Nurse Scheduling Problem via PyQUBO

The nurse scheduling problem is a critical optimization challenge in healthcare management. It aims to balance staffing demands, nurse satisfaction, and patient care quality. Corresponding to the constraints inherent in this scheduling problem, we detail the mathematical formulation step-by-step. We then utilize a quantum-inspired technique, the simulated annealing algorithm, and a quadratic unconstrained binary optimization model to optimize workload and increase nurse preferences. Numerical experiments are implemented to show the capacity of our proposed techniques. Our findings indicate a promising direction for future research, with potential applications extending beyond nurse scheduling to other complex optimization problems.

math.OC

Optimal estimation for the Fujino-Morley interpolation error constants

The quantitative estimation for the interpolation error constants of the Fujino-Morley interpolation operator is considered. To give concrete upper bounds for the constants, which is reduced to the problem of providing lower bounds for eigenvalues of bi-harmonic operators, a new algorithm based on the finite element method along with verified computation is proposed. In addition, the quantitative analysis for the variation of eigenvalues upon the perturbation of the shape of triangles is provided. Particularly, for triangles with longest edge length less than one, the optimal estimation for the constants is provided. An online demo with source codes of the constants calculation is available at http://www.xfliu.org/onlinelab/.

math.NA