arXiv subjects

Geunyeong Byeon

Publications and source records attributed to Geunyeong Byeon.

11 recordsLinked to original sources

arXiv2025

Disjunctive Benders Decomposition

We propose an enhancement to Benders decomposition (BD) that generates valid inequalities for the convex hull of the Benders reformulation, addressing the limitation that classical BD cuts are typically tight only for the continuous relaxation. Our method integrates disjunctive programming with BD and introduces a routine that leverages existing cut-generating oracles as-is to construct convex hull inequalities. For mixed-binary linear programs, the approach removes the need to solve the master problem as a mixed-integer program, even with separable subproblems. It builds on a unified normalization framework for cut-generating programs, encompassing norm-based, reverse polar, and right-hand-side normalization, and enabling the design of new normalization schemes with streamlined analysis of supporting cuts. Computational results on large-scale instances show substantial reductions in branch-and-bound nodes often by orders of magnitude, while consistently outperforming commercial solvers on selected problem classes.

math.OC↗

arXiv2025

A GPU-Accelerated Distributed Algorithm for Optimal Power Flow in Distribution Systems

We propose a GPU-accelerated distributed optimization algorithm for controlling multi-phase optimal power flow in active distribution systems with dynamically changing topologies. To handle varying network configurations and enable adaptable decomposition, we advocate a componentwise decomposition strategy. However, this approach can lead to a prolonged computation time mainly due to the excessive iterations required for achieving consensus among a large number of fine-grained components. To overcome this, we introduce a technique that segregates equality constraints from inequality constraints, enabling GPU parallelism to reduce per-iteration time by orders of magnitude, thereby significantly accelerating the overall computation. Numerical experiments on IEEE test systems ranging from 13 to 8500 buses demonstrate the superior scalability of the proposed approach compared to its CPU-based counterparts.

cs.DC↗

arXiv2025

FIRM: Federated Image Reconstruction using Multimodal Tomographic Data

We propose a federated algorithm for reconstructing images using multimodal tomographic data sourced from dispersed locations, addressing the challenges of traditional unimodal approaches that are prone to noise and reduced image quality. Our approach formulates a joint inverse optimization problem incorporating multimodality constraints and solves it in a federated framework through local gradient computations complemented by lightweight central operations, ensuring data decentralization. Leveraging the connection between our federated algorithm and the quadratic penalty method, we introduce an adaptive step-size rule with guaranteed sublinear convergence and further suggest its extension to augmented Lagrangian framework. Numerical results demonstrate its superior computational efficiency and improved image reconstruction quality.

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arXiv2025

Comparative Analysis of Two-Stage Distributionally Robust Optimization over 1-Wasserstein and 2-Wasserstein Balls

This paper investigates advantages of using 2-Wasserstein ambiguity sets over 1-Wasserstein sets in two-stage distributionally robust optimization with right-hand side uncertainty. We examine the worst-case distributions within 1- and 2-Wasserstein balls under both unrestricted and nonnegative orthant supports, highlighting a pathological behavior arising in 1-Wasserstein balls. Closed-form solutions for a single-scenario newsvendor problem illustrate that 2-Wasserstein balls enable more informed decisions. Additionally, a penalty-based dual interpretation suggests that 2-Wasserstein balls may outperform 1-Wasserstein balls across a broader range of Wasserstein radii, even with general support sets.

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arXiv2024

Linearized Optimal Power Flow for Multiphase Radial Networks with Delta Connections

This paper proposes a linear approximation of the alternating current optimal power flow problem for multiphase distribution networks with voltage-dependent loads connected in both wye and delta configurations. We establish a set of linear equations that exactly describes the relationship between power changes at a bus and the corresponding values from a delta-connected device under specific assumptions necessary for a widely accepted linear model. Numerical studies on IEEE test feeders demonstrate that the proposed linear model provides solutions with reasonable error bounds efficiently, as compared with an exact nonconvex formulation and a convex conic relaxation. Our experiments reveal that modeling delta-connected, voltage-dependent loads as if they are wye-connected can lead to significantly different voltage profiles. We also investigate the limitations of the proposed linear approximation stemming from the underlying assumptions, while emphasizing its robust performance in practical situations.

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arXiv2024

Two-Stage Distributionally Robust Conic Linear Programming over 1-Wasserstein Balls

This paper studies two-stage distributionally robust conic linear programming under constraint uncertainty over type-1 Wasserstein balls. We present optimality conditions for the dual of the worst-case expectation problem, which characterizes worst-case uncertain parameters for its inner maximization problem. This condition offers an alternative proof, a counter-example, and an extension to previous works. Additionally, the condition highlights the potential advantage of a specific distance metric for out-of-sample performance, as exemplified in a numerical study on a facility location problem with demand uncertainty. A cutting-plane-based algorithm and a variety of algorithmic enhancements are proposed with a finite convergence proof under less stringent assumptions.

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arXiv2024

Distributionally Robust Decentralized Volt-Var Control with Network Reconfiguration

This paper presents a decentralized volt-var optimization (VVO) and network reconfiguration strategy to address the challenges arising from the growing integration of distributed energy resources, particularly photovoltaic (PV) generation units, in active distribution networks. To reconcile control measures with different time resolutions and empower local control centers to handle intermittency locally, the proposed approach leverages a two-stage distributionally robust optimization; decisions on slow-responding control measures and set points that link neighboring subnetworks are made in advance while considering all plausible distributions of uncertain PV outputs. We present a decomposition algorithm with an acceleration scheme for solving the proposed model. Numerical experiments on the IEEE 123 bus distribution system are given to demonstrate its outstanding out-of-sample performance and computational efficiency, which suggests that the proposed method can effectively localize uncertainty via risk-informed proactive timely decisions.

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arXiv2023

A GPU-based Distributed Algorithm for Linearized Optimal Power Flow in Distribution Systems

We propose a GPU-based distributed optimization algorithm, aimed at controlling optimal power flow in multi-phase and unbalanced distribution systems. Typically, conventional distributed optimization algorithms employed in such scenarios rely on parallel execution with multiple CPUs. However, this often leads to significant computation time primarily due to the need for optimization solvers to solve subproblems for every iteration of the algorithms. To address this computational challenge, we propose a distributed optimization algorithm that eliminates solver dependencies and harnesses GPU acceleration. The central idea involves decomposing networks to yield subproblems with closed-form solutions based on matrix operations that GPU can efficiently handle. We demonstrate the computational performance of our approach through numerical experiments on four IEEE test instances ranging from 13 to 8500 buses. Our results affirm the scalability and superior speed of our GPU-based approach compared to the CPU-based counterpart.

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arXiv2021

Benders Subproblem Decomposition for Bilevel Problems with Convex Follower

Bilevel optimization formulates hierarchical decision-making processes that arise in many real-world applications such as in pricing, network design, and infrastructure defense planning. In this paper, we consider a class of bilevel optimization problems where the upper-level problem features some integer variables while the lower-level problem enjoys strong duality. We propose a dedicated Benders decomposition method for solving this class of bilevel problems, which decomposes the Benders subproblem into two more tractable, sequentially solvable problems that can be interpreted as the upper and the lower-level problems. We show that the Benders subproblem decomposition carries over to an interesting extension of bilevel problems, which connects the upper-level solution with the lower level dual solution, and discuss some special cases of bilevel problems that allow sequence-independent subproblem decomposition. Several novel schemes for generating numerically stable cuts, finding a good incumbent solution, and accelerating the search tree are discussed. A computational study demonstrates the computational benefits of the proposed method over a state-of-the-art bilevel-tailored branch-and-cut method, a commercial solver, and the standard Benders method on standard test cases and the motivating applications in sequential energy markets.

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arXiv2019

Unit Commitment With Gas Network Awareness

Recent changes in the fuel mix for electricity generation and, in particular, the increase in Gas-Fueled Power Plants (GFPP), have created significant interdependencies between the electrical power and natural gas transmission systems. However, despite their physical and economic couplings, these networks are still operated independently, with asynchronous market mechanisms. This mode of operation may lead to significant economic and reliability risks in congested environments as revealed by the 2014 polar vortex event experienced by the northeastern United States. To mitigate these risks, while preserving the current structure of the markets, this paper explores the idea of introducing gas network awareness into the standard unit commitment model. Under the assumption that the power system operator has some (or full) knowledge of gas demand forecast and the gas network, the paper proposes a tri-level mathematical program where natural gas zonal prices are given by the dual solutions of natural-gas flux conservation constraints and commitment decisions are subject to bid-validity constraints that ensure the economic viability of the committed GFPPs. This tri-level program can be reformulated as a single-level Mixed-Integer Second-Order Cone program which can then be solved using a dedicated Benders decomposition. The approach is validated on a case study for the Northeastern United States [1] that can reproduce the gas and electricity price spikes experienced during the early winter of 2014. The results on the case study demonstrate that gas awareness in unit commitment is instrumental in avoiding the peaks in electricity prices while keeping the gas prices to reasonable levels.

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arXiv2018

Communication-Constrained Expansion Planning for Resilient Distribution Systems

Distributed generation and remotely controlled switches have emerged as important technologies to improve the resiliency of distribution grids against extreme weather-related disturbances. Therefore it becomes impor- tant to study how best to place them on the grid in order to meet a resiliency criteria, while minimizing costs and capturing their dependencies on the associated communication systems that sustains their distributed operations. This paper introduces the Optimal Resilient Design Problem for Distribution and Communi- cation Systems (ORDPDC) to address this need. The ORDPDC is formulated as a two-stage stochastic mixed-integer program that captures the physical laws of distribution systems, the communication connec- tivity of the smart grid components, and a set of scenarios which specifies which components are affected by potential disasters. The paper proposes an exact branch-and-price algorithm for the ORDPDC which features a strong lower bound and a variety of acceleration schemes to address degeneracy. The ORDPDC model and branch-and-price algorithm were evaluated on a variety of test cases with varying disaster inten- sities and network topologies. The results demonstrate the significant impact of the network topologies on the expansion plans and costs, as well as the computational benefits of the proposed approach.

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