Combined bound-grid-factor constraints for enhancing RLT relaxations for polynomial programs

Polynomial programs, Reformulation-linearization technique (RLT), Grid-factor constraints, Factorable programs, BARON, Cutting planes, Valid inequalities, Global optimization,

Harmonized decision modeling process for smart grid component allocation

This article presents a harmonized decision modeling framework for smart grid component allocation. The harmonized decision modeling process is intended to realize a decision support system for the smart grid system analysis. The traditional decision modeling processes have mainly stresses the economic feasibility of smart grid systems. However, the mathematical programming-based decision models for component allocation in smart grid systems are often designed without the enough consideration on the operational circumstances of component, and it reduces the utility of the solution. Our framework considers the operational circumstances of the system and the feasibility in terms of solving process for achieving a practical decision. As a case study, we present a component allocation of Phasor Measurement Units (PMUs) in smart grid systems. With the obtained results, the advantages gained from the harmonized decision modeling process are assessed and discussed.This proceeding was published in Proceedings of the 24th International Conference on Flexible Automation & Intelligent Manufacturing (2014): 901–908, doi:10.14809/faim.2014.0901. Posted with permission.</p

Enhancing RLT-based relaxations for polynomial programming problems via a new class of v-semidefinite cuts

In this paper, we propose to enhance Reformulation-Linearization Technique (RLT)-based linear programming (LP) relaxations for polynomial programming problems by developing cutting plane strategies using concepts derived from semidefinite programming. Given an RLT relaxation, we impose positive semidefiniteness on suitable dyadic variable-product matrices, and correspondingly derive implied semidefinite cuts. In the case of polynomial programs, there are several possible variants for selecting such particular variable-product matrices on which positive semidefiniteness restrictions can be imposed in order to derive implied valid inequalities. This leads to a new class of cutting planes that we call v-semidefinite cuts. We explore various strategies for generating such cuts, and exhibit their relative effectiveness towards tightening the RLT relaxations and solving the underlying polynomial programming problems in conjunction with an RLT-based branch-and-cut scheme, using a test-bed of problems from the literature as well as randomly generated instances. Our results demonstrate that these cutting planes achieve a significant tightening of the lower bound in contrast with using RLT as a stand-alone approach, thereby enabling a more robust algorithm with an appreciable reduction in the overall computational effort, even in comparison with the commercial software BARON and the polynomial programming problem solver GloptiPoly

Prediction of emergency department patient disposition decision for proactive resource allocation for admission.

We investigate the capability of information from electronic health records of an emergency department (ED) to predict patient disposition decisions for reducing boarding delays through the proactive initiation of admission processes (e.g., inpatient bed requests, transport, etc.). We model the process of ED disposition decision prediction as a hierarchical multiclass classification while dealing with the progressive accrual of clinical information throughout the ED caregiving process. Multinomial logistic regression as well as machine learning models are built for carrying out the predictions. Utilizing results from just the first set of ED laboratory tests along with other prior information gathered for each patient (2.5 h ahead of the actual disposition decision on average), our model predicts disposition decisions with positive predictive values of 55.4%, 45.1%, 56.9%, and 47.5%, while controlling false positive rates (1.4%, 1.0%, 4.3%, and 1.4%), with AUC values of 0.97, 0.95, 0.89, and 0.84 for the four admission (minor) classes, i.e., intensive care unit (3.6% of the testing samples), telemetry unit (2.2%), general practice unit (11.9%), and observation unit (6.6%) classes, respectively. Moreover, patients destined to intensive care unit present a more drastic increment in prediction quality at triage than others. Disposition decision classification models can provide more actionable information than a binary admission vs. discharge prediction model for the proactive initiation of admission processes for ED patients. Observing the distinct trajectories of information accrual and prediction quality evolvement for ED patients destined to different types of units, proactive coordination strategies should be tailored accordingly for each destination unit