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Results for “generalized disjunctive programming”

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24 records · Page 2

Optimization Model and Algorithm for Capacity Planning and Operation of Reliable and Carbon-neutral Power Systems with High Penetration of Renewable Generation

In this work, we propose a Generalized Disjunctive Programming (GDP) model that optimizes both long-term capacity planning (such as the number and size of dispatchable/renewable generators, batteries, and transmission lines) and hourly operation (such as on/off schedules of dispatchable generators, power output from each generator, and power flow) to maximize power system reliability while minimizing total cost and CO2 emissions.

Cho, Seolhee↗

Superstructure Optimization for Brine Valorization from Brackish Water Desalination

This poster presents preliminary results from a superstructure optimization framework developed to identify cost-optimal brine valorization configurations for brackish water desalination plants across diverse U.S. regional feed chemistries. The study uses brackish groundwater compositions from Arizona, California, Florida, New Mexico, and Texas. Using Pyomo Generalized Disjunctive Programming (GDP) within the WaterTAP modeling environment, the optimization framework simultaneously evaluates thousands of candidate treatment configurations, spanning nanofiltration, reverse osmosis, and chemical precipitation, to minimize the levelized cost of water (LCOW) while meeting water recovery targets and product recovery constraints. Results across eight representative feed clusters demonstrate water recovery rates of 57–87% and net LCOW values ranging from -$0.032/m³ (net revenue-positive) to $0.80/m. Notably, no single process configuration was optimal across all feed types, underscoring the necessity of feed-specific optimization. Products targeted include calcium carbonate (CaCO₃) at $0.01/kg and sodium chloride (NaCl) at $0.10/kg, both at 95% purity, with product revenues offsetting treatment costs in several scenarios. The work advances NAWI's process systems engineering capabilities for multi-configuration screening.

58 GEOSCIENCES↗

Optimal Membrane Cascade Design for Critical Mineral Recovery Through Logic-based Superstructure Optimization

Critical minerals and rare earth elements play an important role in our climate change initiatives, particularly in applications related with energy storage. Here, we use discrete optimization approaches to design a process for the recovery of Lithium and Cobalt from battery recycling, through membrane separation. Our contribution involves proposing a Generalized Disjunctive Programming (GDP) model for the optimal design of a multistage diafiltration cascade for Li-Co separation. By solving the resulting nonconvex mixed-integer nonlinear program model to global optimality, we investigated scalability and solution quality variations with changes in the number of stages and elements per stage. Results demonstrate the computational tractability of the nonlinear GDP formulation for design of membrane separation processes while opening the door for decom-position strategies for multicomponent separation cascades. Future work aims to extend the GDP formulation to account for stage installation and explore various decomposition techniques to enhance solution efficiency.

Ovalle, Daniel↗

Compressing branch-and-bound trees

A branch-and-bound (BB) tree certifies a dual bound on the value of an integer program. In this work, we introduce the tree compression problem (TCP): Given a BB tree T that certifies a dual bound, can we obtain a smaller tree with the same (or stronger) bound by either (1) applying a different disjunction at some node in T or (2) removing leaves from T? Here we believe such post-hoc analysis of BB trees may assist in identifying helpful general disjunctions in BB algorithms. We initiate our study by considering computational complexity and limitations of TCP. We then conduct experiments to evaluate the compressibility of realistic branch-and-bound trees generated by commonly-used branching strategies, using both an exact and a heuristic compression algorithm.

97 MATHEMATICS AND COMPUTING↗

Primate translational vestibuloocular reflexes. II. Version and vergence responses to fore-aft motion

To maintain binocular fixation on near targets during fore-aft translational disturbances, largely disjunctive eye movements are elicited the amplitude and direction of which should be tuned to the horizontal and vertical eccentricities of the target. The eye movements generated during this task have been investigated here as trained rhesus monkeys fixated isovergence targets at different horizontal and vertical eccentricities during 10 Hz fore-aft oscillations. The elicited eye movements complied with the geometric requirements for binocular fixation, although not ideally. First, the corresponding vergence angle for which the movement of each eye would be compensatory was consistently less than that dictated by the actual fixation parameters. Second, the eye position with zero sensitivity to translation was not straight ahead, as geometrically required, but rather exhibited a systematic dependence on viewing distance and vergence angle. Third, responses were asymmetric, with gains being larger for abducting and downward compared with adducting and upward gaze directions, respectively. As frequency was varied between 4 and 12 Hz, responses exhibited high-pass filter properties with significant differences between abduction and adduction responses. As a result of these differences, vergence sensitivity increased as a function of frequency with a steeper slope than that of version. Despite largely undercompensatory version responses, vergence sensitivity was closer to ideal. Moreover, the observed dependence of vergence sensitivity on vergence angle, which was varied between 2.5 and 10 MA, was largely linear rather than quadratic (as geometrically predicted). We conclude that the spatial tuning of eye velocity sensitivity as a function of gaze and viewing distance follows the general geometric dependencies required for the maintenance of foveal visual acuity. However, systematic deviations from ideal behavior exist that might reflect asymmetric processing of abduction/adduction responses perhaps because of different functional dependencies of version and vergence eye movement components during translation.

NASA Program Biomedical Research and Countermeasur↗