scholarly journals Strong-branching inequalities for convex mixed integer nonlinear programs

2014 ◽  
Vol 59 (3) ◽  
pp. 639-665 ◽  
Author(s):  
Mustafa Kılınç ◽  
Jeff Linderoth ◽  
James Luedtke ◽  
Andrew Miller
2010 ◽  
Vol 36 ◽  
pp. 1153-1160 ◽  
Author(s):  
Hassan Hijazi ◽  
Pierre Bonami ◽  
Gérard Cornuéjols ◽  
Adam Ouorou

Author(s):  
Timo Berthold ◽  
Jakob Witzig

The generalization of mixed integer program (MIP) techniques to deal with nonlinear, potentially nonconvex, constraints has been a fruitful direction of research for computational mixed integer nonlinear programs (MINLPs) in the last decade. In this paper, we follow that path in order to extend another essential subroutine of modern MIP solvers toward the case of nonlinear optimization: the analysis of infeasible subproblems for learning additional valid constraints. To this end, we derive two different strategies, geared toward two different solution approaches. These are using local dual proofs of infeasibility for LP-based branch-and-bound and the creation of nonlinear dual proofs for NLP-based branch-and-bound, respectively. We discuss implementation details of both approaches and present an extensive computational study, showing that both techniques can significantly enhance performance when solving MINLPs to global optimality. Summary of Contribution: This original article concerns the advancement of exact general-purpose algorithms for solving one of the largest and most prominent problem classes in optimization, mixed integer nonlinear programs (MINLPs). It demonstrates how methods for conflict analysis that learn from infeasible subproblems can be transferred to nonlinear optimization. Further, it develops theory for how nonlinear dual infeasibility proofs can be derived from a nonlinear relaxation. This paper features a thoroughly computational study regarding the impact of conflict analysis techniques on the overall performance of a state-of-the-art MINLP solver when solving MINLPs to global optimality.


2017 ◽  
Vol 9 (4) ◽  
pp. 499-526 ◽  
Author(s):  
Mustafa R. Kılınç ◽  
Jeff Linderoth ◽  
James Luedtke

2018 ◽  
Vol 109 ◽  
pp. 77-95 ◽  
Author(s):  
Lijie Su ◽  
Lixin Tang ◽  
David E. Bernal ◽  
Ignacio E. Grossmann

Transport ◽  
2014 ◽  
Vol 29 (3) ◽  
pp. 248-259 ◽  
Author(s):  
Lihui Zhang ◽  
Huiyuan Liu ◽  
Daniel (Jian) Sun

This paper analyses both the cordon and area pricings from the perspective of travel demand management. Sensitivity analysis of various performance measures with respect to the toll rate and demand elastic parameter is performed on a virtual grid network. The analysis shows that cordon pricing mainly affects those trips with origins outside of the Central Business District and destinations inside, while area pricing imposes additional cost on the trips with either origins or destinations in the Central Business District. Though both pricing strategies are able to alleviate traffic congestion in the charging area, area pricing seems more effective, however, area pricing owns the risk to detour too much traffic and thus cause severe congestion to the network outside of the Central Business District. Following the sensitivity analysis, a unified framework is proposed to optimize the designs of the both pricing strategies, which is flexible to account for various practical concerns. The optimization models are formulated as mixed-integer nonlinear programs with complementarity constraints, and the solution procedure is composed of solving a series of nonlinear programs and mixed-integer linear programs. Results from the numerical examples are in line with the findings in the sensitivity analysis. Under the specific network settings, cordon pricing achieves the best system performance when the toll rate reaches the maximum allowed, while area pricing finds the optimal design scheme when the toll rate equals half of the maximum allowed.


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