Some transformation techniques with applications in global optimization

Lundell, Andreas; Westerlund, Joakim; Westerlund, Tapio

doi:10.1007/s10898-007-9223-4

Cited by 57 publications

(39 citation statements)

References 8 publications

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“…GloMIQO and this framework are equivalent when there are no signomial terms in MISO (c m, s = 0 ∀ s, m). Other relevant codes include αBB [27,[33][34][35][36]; BARON [31,37,38]; Couenne [39,40]; LINDO [41,42]; SCIP [43][44][45][46][47]; and SGO [48][49][50][51]. Observe that αBB, ANTIGONE, BARON, Couenne, LINDO, SCIP, and SGO all admit more functional forms than this computational framework; as with GloMIQO, our focus is careful analysis of special mathematical structure for specific problem classes.…”

Section: Problem Definition and Literature Reviewmentioning

confidence: 99%

“…The complementary horizontal, term-based data structures easily admit multivariable relaxations that are specifically designed for particular functional forms. For example, beyond the convex, bilinear, trilinear, fractional, fractional trilinear, univariate concave, and general nonconvex terms as introduced by Adjiman et al [33,34], underestimators have been introduced or improved for: fractional terms [31,36,54]; trilinear terms [55,56]; quadrilinear terms [57]; odd degree monomials [58]; signomial terms [8,48,50]; low-dimensional edge-concave terms [59][60][61][62]; submodular functions [63]; and interesting products [36,[64][65][66][67].…”

Section: Problem Definition and Literature Reviewmentioning

confidence: 99%

“…The αBB methodology adapts its approach to the special mathematical structure of each nonconvex term; the ideologically similar SGO algorithm underestimates individual terms with a special emphasis on signomial forms [48][49][50][51].…”

Section: Flattening the Expression Treementioning

confidence: 99%

“…The MISO framework transforms a factorable programming tree into a flattened expression tree to capitalize on the development of tight convex underestimators for specific classes of nonlinear terms (e.g., [8,31,36,48,50,[54][55][56][57][58][59][60][61][62][63][64][65][66][67]). This hybrid approach reformulates towards multivariable terms with specialized underestimators while maintaining a tree-like representation of powers that cannot be distributed and convex operators that can be exploited by dynamic cut generation.…”

Section: Flattening the Expression Treementioning

confidence: 99%

“…For the remaining under-and over-estimators, the framework uses the exponential transformation [8,48,50]. But exponential transformation-based relaxations do not produce the convex hull and may be less effective than other relaxations.…”

Section: Adding Nonconvex Terms For Advanced Rltmentioning

confidence: 99%

See 4 more Smart Citations

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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Section: Problem Definition and Literature Reviewmentioning

confidence: 99%

Section: Problem Definition and Literature Reviewmentioning

confidence: 99%

Section: Flattening the Expression Treementioning

confidence: 99%

Section: Flattening the Expression Treementioning

confidence: 99%

Section: Adding Nonconvex Terms For Advanced Rltmentioning

confidence: 99%

See 3 more Smart Citations

A Framework for Globally Optimizing Mixed-Integer Signomial Programs

Misener

Floudas

2013

J Optim Theory Appl

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A new AC OPF tool for sub‐transmission networks considering distribution switching actions and load‐transferring capability

Tavakkoli

Amjady

2019

Int Trans Electr Energ Syst

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In practical power systems, in order to study the results of optimal power flow (OPF) for a sub‐transmission network (STN), the downstream primary distribution network is usually modeled as constant load. However, in practical distribution grids, the operators are constantly transferring load from one primary distribution feeder to another one because of, eg, congestion problems or maintenance plans. Considering distribution switching actions can improve the performance of sub‐transmission OPF tool that typically aims at reducing the operation cost of STN. This paper presents a new sub‐transmission Alternating Current (AC) OPF (ST‐AC‐OPF) considering load transferring (LT) between primary distribution feeders implemented through distribution maneuvers. The proposed OPF tool is tested on an illustrative practical example as well as on a real‐world Tehran STN. The numerical results show that the proposed model can obtain a more optimal operating point than conventional ST‐AC‐OPF in terms of the operation cost and load shedding.

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Global Optimization of Mixed-Integer Signomial Programming Problems

Lundell¹,

Westerlund²

2011

Mixed Integer Nonlinear Programming

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Some transformation techniques with applications in global optimization

Cited by 57 publications

References 8 publications

A Framework for Globally Optimizing Mixed-Integer Signomial Programs

A Framework for Globally Optimizing Mixed-Integer Signomial Programs

A new AC OPF tool for sub‐transmission networks considering distribution switching actions and load‐transferring capability

Global Optimization of Mixed-Integer Signomial Programming Problems

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