A Scalable Solution Methodology for Mixed-Integer Linear Programming Problems Arising in Automation

Bragin, Mikhail A.; Luh, Peter B.; Yan, Bing; Sun, Xiaojun

doi:10.1109/tase.2018.2835298

Cited by 57 publications

(104 citation statements)

References 46 publications

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“…SLR thus satisfies high computational efficiency requirement because of much improved convergence over standard LR, and low communication requirements because subsystems are not required to communicate with each other. The method has been shown to outperform other previous methods including coordination methods such as ADMM [24].…”

Section: Surrogate Lagrangian Relaxation Methodsmentioning

confidence: 95%

“…All major difficulties of standard LR such as high computational effort required to solve all subproblems, zigzagging of multipliers and the requirement of the knowledge of the optimal dual value, have been overcome within our recent surrogate Lagrangian relaxation (SLR) [23][24]49]. Within the method, it is not necessary to spend the effort to optimally subproblems.…”

Section: Surrogate Lagrangian Relaxation Methodsmentioning

confidence: 99%

“…In Example 2, a generalized assignment problem with 20 machines and 1600 jobs is considered to demonstrate capability of DA-SLR to solve largescale optimization problems fast with near-optimal performance. Because of difficulties associated with other methods as reviewed in Literature Review, subsection II.B and space limitations, comparison of DA-SLR is performed against its sequential version -SLR [23] only, which, in turn, has been shown to outperform other previous coordination methods in [24]. The DA-SLR method is implemented using IBM ILOG CPLEX Optimization Studio Version: 12.7.1.0 on a PC with 3.10GHz Intel(R) Xeon(R) CPU and 32G RAM.…”

Section: Numerical Testingmentioning

confidence: 99%

“…Some the above difficulties have been overcome within subgradient incremental methods [14,15], Alternate Direction Method of Multipliers (ADMM) [16][17][18][19][20][21], surrogate subgradient method [22], and surrogate Lagrangian relaxation (SLR) [23][24]49]. The distributed and asynchronous incremental subgradient method [15] for optimizing convex dual functions consisting of a large number of components, which arise within Lagrangian relaxation framework with a large number of subproblems, overcomes the synchronization difficulty.…”

Section: Introductionmentioning

confidence: 99%

“…Our recent SLR method [23,24,49] has overcome major convergence difficulties of standard Lagrangian Relaxation such as high computational effort, zigzagging of multipliers, and the need to know the optimal dual value for convergence. In [49], it has been demonstrated that the method is capable of efficiently coordinating thousands of subsystems.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Asynchronous Coordination of Distributed Mixed-Integer Linear Subsystems via Surrogate Lagrangian Relaxation

Bragin¹,

Luh²,

Yan³

2020

Preprint

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With the emergence of Internet of Things that allows communications and local computations, and with the vision of Industry 4.0, a foreseeable transition is from centralized system planning and operation toward decentralization with interacting components and subsystems, e.g., self-optimizing factories. In this paper, a new “price-based” decomposition and coordination methodology is developed to efficiently coordinate subsystems such as machines and parts, which are described by Mixed-Integer Linear Programming (MILP) formulations, in a distributed and asynchronous way. To ensure low communication requirements, exchanges between the “coordinator” and subsystems are limited to “prices” (Lagrangian multipliers) broadcast by the coordinator, and to subsystem solutions sent to the coordinator. Asynchronous coordination, however, may lead to convergence difficulties since the order in which subsystem solutions arrive at the coordinator is not predefined as a result of uncertainties in communication and solving times. Under realistic assumptions of finite communication and solve times, convergence of our method is proved by innovatively extending Lyapunov Stability Theory. Numerical testing of generalized assignment problems through simulation demonstrates that the method converges fast and provides near-optimal results, paving the way for self-optimizing factories in the future.

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Section: Surrogate Lagrangian Relaxation Methodsmentioning

confidence: 95%

Section: Surrogate Lagrangian Relaxation Methodsmentioning

confidence: 99%

Section: Numerical Testingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Asynchronous Coordination of Distributed Mixed-Integer Linear Subsystems via Surrogate Lagrangian Relaxation

Bragin¹,

Luh²,

Yan³

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Operations of Microgrids with Meshed Topology Under Uncertainty

Bragin,

Yan,

Kumar

et al. 2024

Microgrids

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A simulation‐based integrated virtual testbed for dynamic optimization in smart manufacturing systems

Sun

Bragin

et al. 2022

J Adv Manuf & Process

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In a manufacturing system, production control-related decision-making activities occur at different levels. At the process level, one of the main control activities is to tune the parameters of individual manufacturing equipment. At the system level, the main activity is to coordinate production resources and to route parts to appropriate workstations based on their processing requirement, priority indices, and control policy. At the factory level, the goal is to plan and schedule the processing of parts at different operations for the entire system in order to optimize certain objectives. Note that the results of such activities at different levels are closely coupled and affect the overall performance of the manufacturing system as a whole. Therefore, it is important to systematically integrate these control and optimization activities into one unified platform to ensure the goal of each individual activity is aligned with the overall performance of the system. In this paper, we develop a simulation-based virtual testbed that implements dynamic optimization, automatic information exchange, and decision-making from the process-level, system-level, and factory-level of a manufacturing system into an integrated computation environment. This is demonstrated by connecting a Python-based numerical computation program, discrete-event simulation software (Simul8), and an optimization solver (CPLEX) via a third-party master program. The application of this simulation-based virtual testbed is illustrated by a case study in a machining shop.

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A Scalable Solution Methodology for Mixed-Integer Linear Programming Problems Arising in Automation

Cited by 57 publications

References 46 publications

Asynchronous Coordination of Distributed Mixed-Integer Linear Subsystems via Surrogate Lagrangian Relaxation

Asynchronous Coordination of Distributed Mixed-Integer Linear Subsystems via Surrogate Lagrangian Relaxation

Operations of Microgrids with Meshed Topology Under Uncertainty

A simulation‐based integrated virtual testbed for dynamic optimization in smart manufacturing systems

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