arXiv subjects

Mikhail A. Bragin

Publications and source records attributed to Mikhail A. Bragin.

9 recordsLinked to original sources

arXiv2025

Accelerating Level-Value Adjustment for the Polyak Stepsize

The Polyak stepsize has been widely used in subgradient methods for non-smooth convex optimization. However, calculating the stepsize requires the optimal value, which is generally unknown. Therefore, dynamic estimations of the optimal value are usually needed. In this paper, to guarantee convergence, a series of level values is constructed to estimate the optimal value successively. This is achieved by developing a decision-guided procedure that involves solving a novel, easy-to-solve linear constraint satisfaction problem referred to as the ``Polyak Stepsize Violation Detector'' (PSVD). Once a violation is detected, the level value is recalculated. We rigorously establish the convergence for both the level values and the objective function values. Furthermore, with our level adjustment approach, calculating an approximate subgradient in each iteration is sufficient for convergence. A series of empirical tests of convex optimization problems with diverse characteristics demonstrates the practical advantages of our approach over existing methods.

math.OC↗

arXiv2024

Reforming Quantum Microgrid Formation

This letter introduces a novel compact and lossless quantum microgrid formation (qMGF) approach to achieve efficient operational optimization of the power system and improvement of resilience. This is achieved through lossless reformulation to ensure that the results are equivalent to those produced by the classical MGF by exploiting graph-theory-empowered quadratic unconstrained binary optimization (QUBO) that avoids the need for redundant encoding of continuous variables. Additionally, the qMGF approach utilizes a compact formulation that requires significantly fewer qubits compared to other quantum methods thereby enabling a high-accuracy and low-complexity deployment of qMGF on near-term quantum computers. Case studies on real quantum processing units (QPUs) empirically demonstrated that qMGF can achieve the same high accuracy as classic results with a significantly reduced number of qubits.

quant-ph↗

arXiv2023

Toward Efficient Transportation Electrification of Heavy-Duty Trucks: Joint Scheduling of Truck Routing and Charging

The timely transportation of goods to customers is an essential component of economic activities. However, heavy-duty diesel trucks used for goods delivery significantly contribute to greenhouse gas emissions within many large metropolitan areas, including Los Angeles, New York, and San Francisco. To reduce GHG emissions by facilitating freight electrification, this paper proposes Joint Routing and Charging scheduling for electric trucks. The objective of the associated optimization problem is to minimize the cost of transportation, charging, and tardiness. A large number of possible combinations of road segments as well as a large number of combinations of charging decisions and charging durations leads to a combinatorial explosion in the possible decisions electric trucks can make. The resulting mixed-integer linear programming problem is thus extremely challenging because of the combinatorial complexity even in the deterministic case. Therefore, a Surrogate Level-Based Lagrangian Relaxation (SLBLR) method is employed to decompose the overall problem into significantly less complex truck subproblems. In the coordination aspect, each truck subproblem is solved independently of other subproblems based on the values of Lagrangian multipliers. In addition to serving as a means of guiding and coordinating trucks, multipliers can also serve as a basis for transparent and explanatory decision-making by trucks. Testing results demonstrate that even small instances cannot be solved using the off-the-shelf solver CPLEX after several days of solving. The SLBLR method, on the other hand, can obtain near-optimal solutions within a few minutes for small cases, and within 30 minutes for large ones. Furthermore, it has been demonstrated that as battery capacity increases, the total cost decreases significantly; moreover, as the charging power increases, the number of trucks required decreases as well.

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arXiv2023

Survey on Lagrangian Relaxation for MILP: Importance, Challenges, Historical Review, Recent Advancements, and Opportunities

Operations in areas of importance to society are frequently modeled as Mixed-Integer Linear Programming (MILP) problems. While MILP problems suffer from combinatorial complexity, Lagrangian Relaxation has been a beacon of hope to resolve the associated difficulties through decomposition. Due to the non-smooth nature of Lagrangian dual functions, the coordination aspect of the method has posed serious challenges. This paper presents several significant historical milestones (beginning with Polyak's pioneering work in 1967) toward improving Lagrangian Relaxation coordination through improved optimization of non-smooth functionals. Finally, this paper presents the most recent developments in Lagrangian Relaxation for fast resolution of MILP problems. The paper also briefly discusses the opportunities that Lagrangian Relaxation can provide at this point in time.

math.OC↗

arXiv2023

Toward Robust Manufacturing Scheduling: Stochastic Job-Shop Scheduling

Manufacturing plays a significant role in economic development, production, exports, and job creation, which ultimately contribute to improving the quality of life. The presence of manufacturing defects is, however, inevitable leading to products being discarded, i.e. scrapped. In some cases, defective products can be repaired through rework. Scrap and rework cause a longer completion time, which can contribute to orders being shipped late. Moreover, the presence of uncertainties and combinatorial complexity significantly increases the difficulty of complex manufacturing scheduling. This paper tackles this challenge, exemplified by a case study on stochastic job-shop scheduling in low-volume, high-variety manufacturing contexts. To ensure on-time delivery, high-quality solutions are required, and near-optimal solutions must be obtained within strict time constraints to ensure smooth operations on the job-shop floor. To efficiently solve the stochastic job-shop scheduling (JSS) problem, a recently-developed Surrogate "Level-Based" Lagrangian Relaxation is used to reduce computational effort while efficiently exploiting the geometric convergence potential inherent to Polyak's stepsizing formula thereby leading to fast convergence. Numerical testing demonstrates that the new method is two orders of magnitude faster as compared to commercial solvers.

math.OC↗

arXiv2023

Novel Quality Measure and Efficient Resolution of Convex Hull Pricing for Unit Commitment

Electricity prices determined by economic dispatch that do not consider fixed costs may lead to significant uplift payments. However, when fixed costs are included, prices become non-monotonic with respect to demand, which can adversely impact market transparency. To overcome this issue, convex hull (CH) pricing has been introduced for unit commitment with fixed costs. Several CH pricing methods have been presented, and a feasible cost has been used as a quality measure for the CH price. However, obtaining a feasible cost requires a computationally intensive optimization procedure, and the associated duality gap may not provide an accurate quality measure. This paper presents a new approach for quantifying the quality of the CH price by establishing an upper bound on the optimal dual value. The proposed approach uses Surrogate Lagrangian Relaxation (SLR) to efficiently obtain near-optimal CH prices, while the upper bound decreases rapidly due to the convergence of SLR. Testing results on the IEEE 118-bus system demonstrate that the novel quality measure is more accurate than the measure provided by a feasible cost, indicating the high quality of the upper bound and the efficiency of SLR.

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arXiv2023

Surrogate Lagrangian Relaxation: A Path To Retrain-free Deep Neural Network Pruning

Network pruning is a widely used technique to reduce computation cost and model size for deep neural networks. However, the typical three-stage pipeline significantly increases the overall training time. In this paper, we develop a systematic weight-pruning optimization approach based on Surrogate Lagrangian relaxation, which is tailored to overcome difficulties caused by the discrete nature of the weight-pruning problem. We prove that our method ensures fast convergence of the model compression problem, and the convergence of the SLR is accelerated by using quadratic penalties. Model parameters obtained by SLR during the training phase are much closer to their optimal values as compared to those obtained by other state-of-the-art methods. We evaluate our method on image classification tasks using CIFAR-10 and ImageNet with state-of-the-art MLP-Mixer, Swin Transformer, and VGG-16, ResNet-18, ResNet-50 and ResNet-110, MobileNetV2. We also evaluate object detection and segmentation tasks on COCO, KITTI benchmark, and TuSimple lane detection dataset using a variety of models. Experimental results demonstrate that our SLR-based weight-pruning optimization approach achieves a higher compression rate than state-of-the-art methods under the same accuracy requirement and also can achieve higher accuracy under the same compression rate requirement. Under classification tasks, our SLR approach converges to the desired accuracy $3\times$ faster on both of the datasets. Under object detection and segmentation tasks, SLR also converges $2\times$ faster to the desired accuracy. Further, our SLR achieves high model accuracy even at the hard-pruning stage without retraining, which reduces the traditional three-stage pruning into a two-stage process. Given a limited budget of retraining epochs, our approach quickly recovers the model's accuracy.

cs.NE↗

arXiv2023

Surrogate "Level-Based" Lagrangian Relaxation for Mixed-Integer Linear Programming

Mixed-Integer Linear Programming (MILP) plays an important role across a range of scientific disciplines and within areas of strategic importance to society. The MILP problems, however, suffer from combinatorial complexity. Because of integer decision variables, as the problem size increases, the number of possible solutions increases super-linearly thereby leading to a drastic increase in the computational effort. To efficiently solve MILP problems, a "price-based" decomposition and coordination approach is developed to exploit 1. the super-linear reduction of complexity upon the decomposition and 2. the geometric convergence potential inherent to Polyak's stepsizing formula for the fastest coordination possible to obtain near-optimal solutions in a computationally efficient manner. Unlike all previous methods to set stepsizes heuristically by adjusting hyperparameters, the key novel way to obtain stepsizes is purely decision-based: a novel "auxiliary" constraint satisfaction problem is solved, from which the appropriate stepsizes are inferred. Testing results for large-scale Generalized Assignment Problems (GAP) demonstrate that for the majority of instances, certifiably optimal solutions are obtained. For stochastic job-shop scheduling as well as for pharmaceutical scheduling, computational results demonstrate the two orders of magnitude speedup as compared to Branch-and-Cut (B&C). The new method has a major impact on the efficient resolution of complex Mixed-Integer Programming (MIP) problems arising within a variety of scientific fields.

math.OC↗

arXiv2021

Distributed and Asynchronous Operational Optimization of Networked Microgrids

Smart programmable microgrids (SPM) is an emerging technology for making microgrids more software-defined and less hardware-independent such that converting distributed energy resources (DERs) to networked community microgrids becomes affordable, autonomic, and secure. As one of the cornerstones of SPM, this paper pioneers a concept of software-defined operation optimization for networked microgrids, where operation objectives, grid connection, and DER participation will be defined by software and plug-and-play, and can be quickly reconfigured, based on the development of modularized and tightened models and a novel asynchronous price-based decomposition-and-coordination method. Key contributions include: (1) design the architecture of the operational optimization of networked microgrids which can be readily implemented to ensure the programmability of islanded microgrids in solving the distributed optimization models, (2) realize a novel discrete model of droop controller, and (3) introduce a powerful distributed and asynchronous method Distributed and Asynchronous Surrogate Lagrangian Relaxation (DA-SLR) to efficiently coordinate microgrids asynchronously. Two case studies are tested to demonstrate the efficiency of developed DA-SLR, and specifically, the testing results show the superiority of DA-SLR as compared to previous methods such as ADMM.

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