Public Abstract

DE-SC0023361: New Abstractions and Randomized Algorithms for Multiscale Stochastic Optimization

Award Status: Active

Institution: Southern Methodist University, Dallas, TX
UEI: D33QGS3Q3DJ3
DUNS: 001981133

Most Recent Award Date: 07/01/2024
Number of Support Periods: 3
PM: Lee, Steven

Current Budget Period: 09/01/2024 - 08/31/2025
Current Project Period: 09/01/2022 - 08/31/2025
PI: Gangammanavar, Harsha

Supplement Budget Period: N/A

Public Abstract

This project is in the broad area of computational mathematics for sustainability; specifically, it proposes to investigate new modeling abstractions, randomized algorithms, and statistical verification and validation tools necessary for Multiscale Stochastic Mixed-Integer Optimization (MSMIO) problems, as those that arise in the management of the power grid under intermittent renewable power. The proposed mathematical and computational tools generalize existing multistage stochastic programming paradigms to tackle significantly more complex hierarchical multiscale problems. The MSMIO problems pose several challenges because their complexity grows exponentially with the number of epochs in the problem horizon, layers in the hierarchy, and realizations of random variables. This complexity is further exacerbated by the fact that every epoch in every layer must manage constrained optimization problems. As such, MSMIO problems may not be fully instantiated with data at any instant; their solutions may only be estimated. Yet, such problems arise in several applications relevant to the DOE, including power systems operations. Therefore, they require meticulously developed randomized algorithms. Our principal goal is to study randomization-based computational algorithms and new analysis techniques, enabling us to support near-optimal decisions for problems far beyond our capabilities today. The four principal methodological thrusts of the proposed research are founded on the principles of stochastic programming. In the first thrust, we will develop graph-based abstractions of the MSMIO problem class. In the second thrust, we propose to design solution methods based on the decomposition-coordination concepts and different randomization techniques. We will develop analytical and computational tools to assess the performance of our randomized algorithms in our third verification and validation-focused thrust. Finally, in the fourth thrust, we will undertake an implementation of the randomized algorithms that is compatible with a high-performance computing environment. The resulting software will be publicly available.

This project is in the broad area of computational mathematics for sustainability; specifically, it proposes to investigate new modeling abstractions, randomized algorithms, and statistical verification and validation tools necessary for Multiscale Stochastic Mixed-Integer Optimization (MSMIO) problems, as those that arise in the management of the power grid under intermittent renewable power. The proposed mathematical and computational tools generalize existing multistage stochastic programming paradigms to tackle significantly more complex hierarchical multiscale problems. The MSMIO problems pose several challenges because their complexity grows exponentially with the number of epochs in the problem horizon, layers in the hierarchy, and realizations of random variables. This complexity is further exacerbated by the fact that every epoch in every layer must manage constrained optimization problems. As such, MSMIO problems may not be fully instantiated with data at any instant; their solutions may only be estimated. Yet, such problems arise in several applications relevant to the DOE, including power systems operations. Therefore, they require meticulously developed randomized algorithms. Our principal goal is to study randomization-based computational algorithms and new analysis techniques, enabling us to support near-optimal decisions for problems far beyond our capabilities today.

The four principal methodological thrusts of the proposed research are founded on the principles of stochastic programming. In the first thrust, we will develop graph-based abstractions of the MSMIO problem class. In the second thrust, we propose to design solution methods based on the decomposition-coordination concepts and different randomization techniques. We will develop analytical and computational tools to assess the performance of our randomized algorithms in our third verification and validation-focused thrust. Finally, in the fourth thrust, we will undertake an implementation of the randomized algorithms that is compatible with a high-performance computing environment. The resulting software will be publicly available.