<scp>MINLP</scp>Solver Software

Bussieck, Michael R.; Vigerske, Stefan

doi:10.1002/9780470400531.eorms0527

Cited by 100 publications

(61 citation statements)

References 48 publications

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“…We refer the reader to the reviews of Floudas and co-workers [55,60] for background on the state-of-the-art in global optimization, to the recent review of Bussieck and Vigerske [36] for detailed descriptions of generic MINLP solver software, and to an array of excellent texts [51,52,68,105,125,133]. Hereafter, we narrow our focus to the contributions most relevant to this paper.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Automatic reformulations, while common in MIP solver software, are relatively rare in MIQCQP solver software [36]. GloMIQO represents a major effort to elucidate special structure within MIQCQP via reformulations, but we can only review MIQCQP formulation strategies that are external to any solver; GloMIQO is on the leading edge of integrating reformulation techniques that can be implemented generically and applied universally.…”

Section: Literature Reviewmentioning

confidence: 99%

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GloMIQO: Global mixed-integer quadratic optimizer

2012

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This paper introduces the Global Mixed-Integer Quadratic Optimizer, GloMIQO, a numerical solver addressing mixed-integer quadratically-constrained quadratic programs (MIQCQP) to ε-global optimality. The algorithmic components are presented for: reformulating user input, detecting special structure including convexity and edge-concavity, generating tight convex relaxations, partitioning the search space, bounding the variables, and finding good feasible solutions. To demonstrate the capacity of GloMIQO, we extensively tested its performance on a test suite of 399 problems of diverse size and structure. The test cases are taken from process networks applications, computational geometry problems, GLOBALLib, MINLPLib, and the Bonmin test set. We compare the performance of GloMIQO with respect to four state-of-the-art global optimization solvers: BARON 10.1.2,

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Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

GloMIQO: Global mixed-integer quadratic optimizer

2012

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“…Automatic reformulations, while common in MIP, are relatively rare in MINLP (Bussieck and Vigerske, 2010). Recommendations made to modelers (i.e., nonautomatic reformulations) often include: using linear formulations if possible (Harjunkoski et al, 1996); using convex functional forms if possible ; dissaggregating terms (Tawarmalani et al, 2002;Tawarmalani and Sahinidis, 2002b); adding redundant constraints into the model formulation (Karuppiah and Grossmann, 2006;Ahmetović and Grossmann, 2011;Ruiz and Grossmann, 2011b).…”

Section: Reformulations and Other Preprocessing Methodsmentioning

confidence: 99%

“…Global optimization solver software for MINLP has been covered most completely by Bussieck and Vigerske (2010); the book of Belotti et al (2013b) and the review of D'Ambrosio and Lodi (2013) also discuss several software implementations for MINLP. We augment their work with Table 11, which documents algorithmic advances for each of several deterministic global optimization codes for MINLP.…”

Section: Global Optimization Algorithms and Software For Minlp Modelsmentioning

confidence: 99%

Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

Boukouvala

Misener

Floudas

2016

European Journal of Operational Research

193

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This manuscript reviews recent advances in deterministic global optimization for Mixed-Integer Nonlinear Programming (MINLP), as well as Constrained DerivativeFree Optimization (CDFO). This work provides a comprehensive and detailed literature review in terms of significant theoretical contributions, algorithmic developments, software implementations and applications for both MINLP and CDFO. Both research areas have experienced rapid growth, with a common aim to solve a wide range of real-world problems. We show their individual prerequisites, formulations and applicability, but also point out possible points of interaction in problems which contain hybrid characteristics. Finally, an inclusive and complete test suite is provided for both MINLP and CDFO algorithms, which is useful for future benchmarking.

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“…We briefly mention several code bases; complete treatment of numerical optimization software is in the review of Bussieck and Vigerske [32].…”

Section: Problem Definition and Literature Reviewmentioning

confidence: 99%

A Framework for Globally Optimizing Mixed-Integer Signomial Programs

Misener

Floudas

2013

J Optim Theory Appl

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Mixed-integer signomial optimization problems have broad applicability in engineering. Extending the Global Mixed-Integer Quadratic Optimizer, GloMIQO[1], this manuscript documents a computational framework for deterministically addressing mixed-integer signomial optimization problems to ε-global optimality. This framework generalizes the GloMIQO strategies of (1) reformulating user input, (2) detecting special mathematical structure, and (3) globally optimizing the mixed-integer nonconvex program. Novel contributions of this paper include: flattening an expression tree towards term-based data structures; introducing additional nonconvex terms to interlink expressions; integrating a dynamic implementation of the reformulationlinearization technique into the branch-and-cut tree; designing term-based underestimators that specialize relaxation strategies according to variable bounds in the current tree node. Computational results are presented along with comparison of the computational framework to several state-of-the-art solvers.

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MINLPSolver Software

Cited by 100 publications

References 48 publications

GloMIQO: Global mixed-integer quadratic optimizer

GloMIQO: Global mixed-integer quadratic optimizer

Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

A Framework for Globally Optimizing Mixed-Integer Signomial Programs

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