Global Optimization of Mixed-Integer Signomial Programming Problems

Lundell, Andreas; Westerlund, Tapio

doi:10.1007/978-1-4614-1927-3_12

Cited by 13 publications

(6 citation statements)

References 15 publications

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“…Like aBB [4,5,10,50,93] and SGO [89][90][91][92], ANTIGONE emphasizes term-based underestimators [105]. ANTIGONE therefore begins by reformulating the user-defined MINLP Fig.…”

Section: Reformulating User Inputmentioning

confidence: 99%

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ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations

2014

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“…Like aBB [4,5,10,50,93] and SGO [89][90][91][92], ANTIGONE emphasizes term-based underestimators [105]. ANTIGONE therefore begins by reformulating the user-defined MINLP Fig.…”

Section: Reformulating User Inputmentioning

confidence: 99%

“…SCIP [1,3,18,19,145]; SGO [89][90][91][92]. ANTIGONE performs equivalently to GloMIQO [102,104,107] when all nonlinearities in MINLP are quadratic.…”

Section: Introductionmentioning

confidence: 99%

ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations

2014

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“…There are different strategies for selecting the grid points for piecewise linear approximations. 62,63 A systematic approach to determine the optimal number of the initial Figure 9. Steps of the OAGO-N algorithm for solving large-scale case study.…”

Section: Large-scale Case Studymentioning

confidence: 99%

Energy optimization of water supply system scheduling: Novel MINLP model and efficient global optimization algorithm

Shi

You

2016

AIChE Journal

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This article is concerned with global optimization of water supply system scheduling with pump operations to minimize total energy cost. The scheduling problem is first formulated as a non-convex mixed-integer nonlinear programming (MINLP) problem, accounting for flow rates in pipes, operation profiles of pumps, water levels of tanks, and customer demand. Binary variables denote on-off switch operations for pumps and flow directions in pipes, and nonlinear terms originate from characteristic functions for pumps and hydraulic functions for pipes. The proposed MINLP model is verified with EPANET, which is a leading software package for water distribution system modeling. We further develop a novel global optimization algorithm for solving the non-convex MINLP problem. To demonstrate the applicability of the proposed model and the efficiency of the tailored global optimization algorithm, we present results of two case studies with up to 4 tanks, 5 pumps, 5 check valves, and 21 pipes.

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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 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%

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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Global Optimization of Mixed-Integer Signomial Programming Problems

Cited by 13 publications

References 15 publications

ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations

ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations

Energy optimization of water supply system scheduling: Novel MINLP model and efficient global optimization algorithm

A Framework for Globally Optimizing Mixed-Integer Signomial Programs

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