Algorithms and Applications to Weighted Rank-one Binary Matrix Factorization

Binary matrix factorization via collaborative neurodynamic optimization

Binary matrix factorization is an important tool for dimension reduction for high-dimensional datasets with binary attributes and has been successfully applied in numerous areas. This paper presents a collaborative neurodynamic optimization approach to binary matrix factorization based on the original combinatorial optimization problem formulation and quadratic unconstrained binary optimization problem reformulations. The proposed approach employs multiple discrete Hopfield networks operating concurrently in search of local optima. In addition, a particle swarm optimization rule is used to reinitialize neuronal states iteratively to escape from local minima toward better ones. Experimental results on eight benchmark datasets are elaborated to demonstrate the superior performance of the proposed approach against six baseline algorithms in terms of factorization error. Additionally, the viability of the proposed approach is demonstrated for pattern discovery on three datasets.

Surgical scheduling by Fuzzy model considering inpatient beds shortage under uncertain surgery durations

Operating Room (OR) management has been among the mainstream of hospital management research, as ORs are commonly considered as one of the most critical and expensive resources. The complicated connection and interplay between ORs and their upstream and downstream units has recently attracted research attention to focus more on allocating medical resources efficiently for the sake of a balanced coordination. As a critical step, surgical scheduling in the presence of uncertain surgery durations is pivotal but rather challenging since a patient cannot be hospitalized if a recovery bed will not be available to accommodate the admission. To tackle the challenge, we propose an overflow strategy that allows patients to be assigned to an undesignated department if the designated one is full. It has been proved that overflow strategy can successfully alleviate the imbalance of capacity utilization. However, some studies indicate that implementation of the overflow strategy exacerbates the readmission rate as well as the length of stay (LOS). To rigorously examine the overflow strategy and explore its optimal solution, we propose a Fuzzy model for surgical scheduling by explicitly considering downstream shortage, as well as the uncertainty of surgery duration and patient LOS. To solve the Fuzzy model, a hybrid algorithm (so-called GA-P) is developed, stemming from Genetic Algorithm (GA). Extensive numerical results demonstrate the plausible efficiency of the GA-P algorithm, especially for large-scale scheduling problems (e.g., comprehensive hospitals). Additionally, it is shown that the overflow cost plays a critical role in determining the efficiency of the overflow strategy; viz., benefits from the overflow strategy can be reduced as the overflow cost increases, and eventually almost vanishes when the cost becomes sufficiently large. Finally, the Fuzzy model is tested to be effective in terms of simplicity and reliability, yet without cannibalizing the patient admission rate.