Domain reduction techniques for global NLP and MINLP optimization

Puranik, Yash; Sahinidis, Nikolaos V.

doi:10.1007/s10601-016-9267-5

Cited by 55 publications

(39 citation statements)

References 180 publications

(223 reference statements)

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“…Preprocessing ideas for gas network problems can be found in [38], including more complex procedures like pressure and flow propagation heuristics. For a broader overview of different preprocessing ideas for mixed-integer nonlinear programs, see the review article [41]. However, we cannot use most of the mentioned ideas as is since they are tailored towards nominal problems without uncertainty.…”

Section: Appendix A: Reducing Model Size By Preprocessingmentioning

confidence: 99%

“…Since the problems in (A5) are LPs, we also call this the LP-based relaxation preprocessing approach. In the literature, this type of preprocessing strategy is also known as feasibility-based bounds tightening; see [41]. We remark that in case of demand uncertainty, the problems (A5) contain description of the uncertainty set.…”

Section: Bounds Due To Linear Relaxationsmentioning

confidence: 99%

See 1 more Smart Citation

Decomposable robust two‐stage optimization: An application to gas network operations under uncertainty

2019

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We study gas network problems with compressors and control valves under uncertainty that can be formulated as two‐stage robust optimization problems. Uncertain data are present in the physical parameters of the pipes as well as in the overall demand. We show how to exploit the special decomposable structure of the problem to reformulate the two‐stage problem as a single‐stage robust optimization problem. The right‐hand side of the single‐stage problem can be precomputed by solving a series of optimization problems and multiple elements of the right‐hand side can be combined into one optimization task. The practical feasibility and effectiveness of our approach is demonstrated with benchmarks on several gas network instances, among them a realistic model of the Greek natural gas network. Overall, aggregation and preprocessing allow us to quickly solve large gas network instances under uncertainty for the price of slightly more conservative solutions.

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Section: Appendix A: Reducing Model Size By Preprocessingmentioning

confidence: 99%

Section: Bounds Due To Linear Relaxationsmentioning

confidence: 99%

Decomposable robust two‐stage optimization: An application to gas network operations under uncertainty

2019

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“…The application of GO algorithms using deterministic mathematical models allows to obtain a solution for a given global optimality tolerance. As is well known from a computational point of view, the calculation of good lower and upper bounds is crucial for the success of any GO algorithm [23]. Sherali et al [24] proposed an improved method to develop tight linear relaxations to calculate global lower bounds for a design problem associated with the water distribution network.…”

Section: Cost Itemmentioning

confidence: 99%

Membrane-Based Processes: Optimization of Hydrogen Separation by Minimization of Power, Membrane Area, and Cost

Arias

Scenna

et al. 2018

Processes

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This work deals with the optimization of two-stage membrane systems for H2 separation from off-gases in hydrocarbons processing plants to simultaneously attain high values of both H2 recovery and H2 product purity. First, for a given H2 recovery level of 90%, optimizations of the total annual cost (TAC) are performed for desired H2 product purity values ranging between 0.90 and 0.95 mole fraction. One of the results showed that the contribution of the operating expenditures is more significant than the contribution of the annualized capital expenditures (approximately 62% and 38%, respectively). In addition, it was found that the optimal trade-offs existing between process variables (such as total membrane area and total electric power) depend on the specified H2 product purity level. Second, the minimization of the total power demand and the minimization of the total membrane area were performed for H2 recovery of 90% and H2 product purity of 0.90. The TAC values obtained in the first and second cases increased by 19.9% and 4.9%, respectively, with respect to that obtained by cost minimization. Finally, by analyzing and comparing the three optimal solutions, a strategy to systematically and rationally provide ‘good’ lower and upper bounds for model variables and initial guess values to solve the cost minimization problem by means of global optimization algorithms is proposed, which can be straightforward applied to other processes.

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“…OBBT solves a sequence of convex minimization and maximization problems on the variables that appear in nonconvex terms. The solutions to these problems tighten domains of the variables and the associated relaxation to the nonconvex terms [42,4,16,37]. Recent work has observed the effectiveness of applying OBBT in various applications [13,54,39].…”

Section: Introductionmentioning

confidence: 99%

An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs

Nagarajan

Wang

et al. 2019

J Glob Optim

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In this work, we develop an adaptive, multivariate partitioning algorithm for solving nonconvex, Mixed-Integer Nonlinear Programs (MINLPs) with polynomial functions to global optimality. In particular, we present an iterative algorithm that exploits piecewise, convex relaxation approaches via disjunctive formulations to solve MINLPs that is different than conventional spatial branch-and-bound approaches. The algorithm partitions the domains of variables in an adaptive and non-uniform manner at every iteration to focus on productive areas of the search space. Furthermore, domain reduction techniques based on sequential, optimization-based bound-tightening and piecewise relaxation techniques, as a part of a presolve step, are integrated into the main algorithm. Finally, we demonstrate the effectiveness of the algorithm on well-known benchmark problems (including Pooling and Blending instances) from MINLPLib and compare our algorithm with state-of-the-art global optimization solvers. With our novel approach, we solve several largescale instances, some of which are not solvable by state-of-the-art solvers. We also succeed in reducing the best known optimality gap for a hard, generalized pooling problem instance.

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Domain reduction techniques for global NLP and MINLP optimization

Cited by 55 publications

References 180 publications

Decomposable robust two‐stage optimization: An application to gas network operations under uncertainty

Decomposable robust two‐stage optimization: An application to gas network operations under uncertainty

Membrane-Based Processes: Optimization of Hydrogen Separation by Minimization of Power, Membrane Area, and Cost

An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs

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