DeCODe: a community-based algorithm for generating high-quality decompositions of optimization problems

Allman, Andrew; Tang, Wen; Daoutidis, Pródromos

doi:10.1007/s11081-019-09450-5

Cited by 23 publications

(25 citation statements)

References 41 publications

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“…We highlight that the proposed modularity measure and MIQP formulation can be used in other applications that go beyond manufacturing. For instance, these tools can be used to identify optimal configurations for control architectures and optimal decomposition strategies for optimization problems . In this context, constraints on the number and size of modules can be used to create balanced configurations (e.g., to handle computational load balancing issues).…”

Section: Modeling Extensions and Other Applicationsmentioning

confidence: 99%

“…The argument behind this measure is that modular organizations that arise in natural systems are nonrandom. This measure is intuitive and has seen many interesting applications; for instance, this measure has been shown to provide a flexible and powerful tool for the analysis and design of control architectures and for the decomposition of large‐scale optimization problems . A powerful generalization of Newman's measure has been proposed in Reference and here it was shown that systems of high modularity are extremum points of a Hamiltonian function.…”

Section: Introductionmentioning

confidence: 98%

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Modularity measures: Concepts, computation, and applications to manufacturing systems

Shao

Zavala

2020

AIChE Journal

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We propose a measure to quantify the modularity of industrial production (manufacturing) systems and optimization formulations to compute it. From a manufacturing perspective, we argue that a system is deemed modular if: (a) the equipment units that comprise it form clusters (modules) of dense connectivity (i.e., difficult module assembly tasks are performed off-site), (b) connectivity between modules is sparse (i.e., easy assembly tasks are performed on-site), (c) the number of modules is small, and (d) the module dimensions facilitate transportation. We show that the measure proposed satisfies these requirements and that it can be computed by solving a convex mixed-integer quadratic program. We provide a discussion on advantages and disadvantages of alternative modularity measures used in different scientific and engineering communities. Our results seek to highlight conceptual and computational challenges that arise from the need to define and quantify modularity in a manufacturing context.

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Section: Modeling Extensions and Other Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Modularity measures: Concepts, computation, and applications to manufacturing systems

Shao

Zavala

2020

AIChE Journal

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“…RAC-ADMM is an algorithm that is applied to solve convex problems (1). The algorithm addresses equality and inequality constraints separately, with the latter converted into equalities using slack variables, s:…”

Section: The Algorithmmentioning

confidence: 99%

“…Problem (1) naturally arises from applications such as machine and statistical learning, image processing, portfolio management, tensor decomposition, matrix completion or decomposition, manifold optimization, data clustering and many other problems of practical importance. To solve problem (1), we consider in particular a randomly assembled multi-block and cyclic alternating direction method of multipliers (RAC-ADMM), a novel algorithm with which we hope to mitigate the problem of slow convergence and divergence issues of the classical alternating direction method of multipliers (ADMM) when applied to problems with cross-block coupled variables.…”

Section: Introductionmentioning

confidence: 99%

Managing randomization in the multi-block alternating direction method of multipliers for quadratic optimization

Mihić

Zhu

2020

Math. Prog. Comp.

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The Alternating Direction Method of Multipliers (ADMM) has gained a lot of attention for solving large-scale and objective-separable constrained optimization. However, the two-block variable structure of the ADMM still limits the practical computational efficiency of the method, because one big matrix factorization is needed at least once even for linear and convex quadratic programming. This drawback may be overcome by enforcing a multi-block structure of the decision variables in the original optimization problem. Unfortunately, the multi-block ADMM, with more than two blocks, is not guaranteed to be convergent. On the other hand, two positive developments have been made: first, if in each cyclic loop one randomly permutes the updating order of the multiple blocks, then the method converges in expectation for solving any system of linear equations with any number of blocks. Secondly, such a randomly permuted ADMM also works for equality-constrained convex quadratic programming even when the objective function is not separable. The goal of this paper is twofold. First, we add more randomness into the ADMM by developing a randomly assembled cyclic ADMM (RAC-ADMM) where the decision variables in each block are randomly assembled. We discuss the theoretical properties of RAC-ADMM and show when random assembling helps and when it hurts, and develop a criterion to guarantee that it converges almost surely. Secondly, using the theoretical guidance on RAC-ADMM, we conduct multiple numerical tests on solving both randomly generated and large-scale benchmark quadratic optimization problems, which include continuous, and binary graph-partition and quadratic assignment, and selected machine learning problems. Our numerical tests show that the RAC-ADMM, with a variable-grouping strategy, could significantly improve the computation efficiency on solving most quadratic optimization problems.

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“…The special issue then turns its attention to the area of problem decomposition, where Allman et al (2019) discuss the automated use of graph community detection in the context of identifying promising, and often non-intuitive, decompositions for complex optimization models. Their algorithm, dubbed DeCODe, has been implemented in a tool that is offered freely for academic use.…”

Section: Recent Advances From This Special Issuementioning

confidence: 99%

A preface to the special issue on enterprise-wide optimization

Gounaris

Grossmann

2019

Optim Eng

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DeCODe: a community-based algorithm for generating high-quality decompositions of optimization problems

Cited by 23 publications

References 41 publications

Modularity measures: Concepts, computation, and applications to manufacturing systems

Modularity measures: Concepts, computation, and applications to manufacturing systems

Managing randomization in the multi-block alternating direction method of multipliers for quadratic optimization

A preface to the special issue on enterprise-wide optimization

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