On interval-subgradient and no-good cuts

d'Ambrosio, Claudia; Frangioni, Antonio; Liberti, Leo; Lodi, Andrea

doi:10.1016/j.orl.2010.05.010

Cited by 23 publications

(21 citation statements)

References 25 publications

(21 reference statements)

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“…In the case where an integer solution found by CPLEX at the root node appears in the tabu list, CPLEX stops and no new integer feasible solution is provided to FP 4 . In such a case, we amend problem (9) with a no-good cut [17] which excludes the solution and we call CPLEX again. Avoid cycling when solving (9) by rounding.…”

Section: Fp Variants and Preliminary Resultsmentioning

confidence: 99%

“…Note that while (18) could seem to require that each g for ∈ C be a differentiable function, this is only assumed for the sake of notational simplicity: notoriously, subgradients of nondifferentiable convex functions can be used as well (e.g. [17]). …”

Section: Addressing the Convex Minlp (9)mentioning

confidence: 99%

“…The interesting part is that, of course,x i violates (20), and therefore (20) provides-at least in theory-a convenient globalization mechanism. No-good cuts [17] were originally introduced in [4] with the name of "canonical" cuts and recently used within the context of MINLP [17,32]. If x are binary variables and · is the L 1 norm, we can take ε = 1 and reformulate (20) linearly as…”

Section: Example 2 Inmentioning

confidence: 99%

“…For general integer variables, an exact linear reformulation is given, for example, in [17] and involves adding 2p new continuous variables, p new binary variables and adding 3p + 1 linear equations to the problem. Thus, the size of such a reformulation could rapidly become prohibitive in the context of an iterative method like FP.…”

Section: Example 2 Inmentioning

confidence: 99%

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A storm of feasibility pumps for nonconvex MINLP

et al. 2012

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One of the foremost difficulties in solving Mixed-Integer Nonlinear Programs, either with exact or heuristic methods, is to find a feasible point. We address this issue with a new feasibility pump algorithm tailored for nonconvex Mixed-Integer Nonlinear Programs. Feasibility pumps are algorithms that iterate between solving a continuous relaxation and a mixed-integer relaxation of the original problems. Such approaches currently exist in the literature for Mixed-Integer Linear Programs and convex Mixed-Integer Nonlinear Programs: both cases exhibit the distinctive property that the continuous relaxation can be solved in polynomial time. In nonconvex Mixed-Integer Nonlinear Programming such a property does not hold, and therefore special care has to be exercised in order to allow feasibility pump algorithms to rely only on local optima of the continuous relaxation. Based on a new, high level view of feasibility pump algorithms as a special case of the well-known successive projection method, we show that many possible different variants of the approach can be developed, depending on how several different (orthogonal) implementation choices are taken. A remarkable twist of feasibility pump algorithms is that, unlike most previous successive projection methods from the literature, projection is "naturally" taken in two different norms in the two different subproblems. To cope with this issue while retaining the local convergence properties of standard successive projection methods we propose the introduction of appropriate norm constraints in the subproblems; these actually seem to significantly improve the practical performance of the approach. We present extensive computational results on the MINLPLib, showing the effectiveness and efficiency of our algorithm.

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Section: Fp Variants and Preliminary Resultsmentioning

confidence: 99%

Section: Addressing the Convex Minlp (9)mentioning

confidence: 99%

Section: Example 2 Inmentioning

confidence: 99%

Section: Example 2 Inmentioning

confidence: 99%

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A storm of feasibility pumps for nonconvex MINLP

et al. 2012

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“…Cutting planes developed for MINLP include those based on: pseudo-convex MINLP problems , outer approximation of convex terms and linearization of other convex underestimators (Tawarmalani and Sahinidis, 2005;, multi-term quadratic expressions (Bao et al, 2009;Luedtke et al, 2012;, multilinear functions (Rikun, 1997;Belotti et al, 2010b;Qualizza et al, 2012), optimizing convex quadratic functions over nonconvex sets (Bienstock and Michalka, 2014), and other cutting plane classes based on nonlinear functional forms (D'Ambrosio et al, 2010;Richard and Tawarmalani, 2010). A review on cutting plane methods for MINLP can be found in Nowak (2005); multivariable and multiterm relaxations are typically favoured for MINLP because the tightest convex relaxation of each individual is not typically equivalent to the tightest possible relaxation of the entire MINLP (Westerlund et al, 2011).…”

Section: Cutting Planesmentioning

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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Evaluating demand response opportunities for power systems resilience using MILP and MINLP Formulations

et al. 2019

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While peak shaving is commonly used to reduce power costs, chemical process facilities that can reduce power consumption on demand during emergencies (e.g., extreme weather events) bring additional value through improved resilience. For process facilities to effectively negotiate demand response (DR) contracts and make investment decisions regarding flexibility, they need to quantify their additional value to the grid. We present a grid‐centric mixed‐integer stochastic programming framework to determine the value of DR for improving grid resilience in place of capital investments that can be cost prohibitive for system operators. We formulate problems using both a linear approximation and a nonlinear alternating current power flow model. Our numerical results with both models demonstrate that DR can be used to reduce the capital investment necessary for resilience, increasing the value that chemical process facilities bring through DR. However, the linearized model often underestimates the amount of DR needed in our case studies. Published 2018. This article is a U.S. Government work and is in the public domain in the USA. AIChE J, 65: e16508, 2019

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On interval-subgradient and no-good cuts

Cited by 23 publications

References 25 publications

A storm of feasibility pumps for nonconvex MINLP

A storm of feasibility pumps for nonconvex MINLP

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

Evaluating demand response opportunities for power systems resilience using MILP and MINLP Formulations

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