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Zuluaga, Luis F.

Publications and source records attributed to Zuluaga, Luis F..

6 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Quantum Interior Point Methods for Semidefinite Optimization

We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact search direction and is not guaranteed to explore only feasible points; the second scheme uses a nullspace representation of the Newton linear system to ensure feasibility even with inexact search directions. The second is a novel scheme that might seem impractical in the classical world, but it is well-suited for a hybrid quantum-classical setting. We show that both schemes converge to an optimal solution of the semidefinite optimization problem under standard assumptions. By comparing the theoretical performance of classical and quantum interior point methods with respect to various input parameters, we show that our second scheme obtains a speedup over classical algorithms in terms of the dimension of the problem n , but has worse dependence on other numerical parameters.

Augustino, Brandon↗
DOE OSTI2023

On relaxations of the max k -cut problem formulations

Here, a tight continuous relaxation is a crucial factor in solving mixed integer formulations of many NP-hard combinatorial optimization problems. The (weighted) max k-cut problem is a fundamental combinatorial optimization problem with multiple notorious mixed integer optimization formulations. In this paper, we explore four existing mixed integer optimization formulations of the max k-cut problem. Specifically, we show that the continuous relaxation of a binary quadratic optimization formulation of the problem is: (i) stronger than the continuous relaxation of two mixed integer linear optimization formulations and (ii) at least as strong as the continuous relaxation of a mixed integer semidefinite optimization formulation. We also conduct a set of experiments on multiple sets of instances of the max k-cut problem using state-of-the-art solvers that empirically confirm the theoretical results in item (i). Furthermore, these numerical results illustrate the advances in the efficiency of global non-convex quadratic optimization solvers and more general mixed integer nonlinear optimization solvers. As a result, these solvers provide a promising option to solve combinatorial optimization problems. Our codes and data are available on GitHub.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A Heuristic Approach to the Post-disturbance and Stochastic Pre-disturbance Microgrid Formation Problem

Microgrid formation is a potential solution in post-disaster electric grid recovery efforts. Recent works propose distribution level microgrid formation models using mixed-integer linear programming techniques. However, these models can only be solved for small and medium size power systems due to their computational intractability. In this article we introduce a heuristic approach that allows to approximately solve the post-disturbance microgrid formation problem for medium to large, more realistic, instances. Furthermore, the proposed approach allows to approximately solve the pre-disturbance microgrid formation problem (a stochastic version of the post-disturbance problem), in which the aim is to allocate extra generation capacity to the network to immunize it, as best as possible, against an uncertain cascading failure. Our results are illustrated by solving versions of the problem on ten test cases with up to 3012 buses.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

Stochastic risk-sensitive market integration for renewable energy: Application to ocean wave power plants

With the expected increase of intermittent renewable energy resources on the electric power grid, short-term reserve markets can prove to be a critical reliability asset. This paper introduces and tests a potential market structure that includes a short-term reserve market for renewable resources where the realized energy is drawn within the bounds of the hourly capacity offered. The study presents a risk-aware stochastic model that determines, based on the day-ahead offer derived using a classic newsvendor formula, the best intraday offers for a renewable energy power plant. The stochastic approach takes into account the uncertainties of energy production and market prices. The proposed risk-sensitive model aims to maximize the renewable power plant's revenues and minimize potential risks of loss in a multi-product multi-timescale market setup. To demonstrate the effectiveness of the proposed formulation, we study the case of a hypothetical 750-kW wave power plant coupled with energy storage. The study shows that the risk of profit loss is not uniformly distributed across the risk-aversion factor space. We also find that the introduction of the short-term reserve market results in a wider range of conditional value at risk while inducing 5% profit increase and a lower profit reduction across the risk range. In addition, the study reveals that the short-term reserve market is profitable for both the system operator and the wave energy power plant considered.

24 POWER TRANSMISSION AND DISTRIBUTION↗