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Branching and bounds tighteningtechniques for non-convex MINLP
- P. Belotti, Jon Lee, Leo Liberti, F. Margot, A. Wächter
- Computer ScienceOptim. Methods Softw.
- 1 August 2009
An sBB software package named couenne (Convex Over- and Under-ENvelopes for Non-linear Estimation) is developed and used for extensive tests on several combinations of BT and branching techniques on a set of publicly available and real-world MINLP instances and is compared with a state-of-the-art MINLP solver.
Introduction to Global Optimization
- Leo Liberti
- Computer Science
This paper is a mini-course about global optimization techniques in nonconvex programming; it deals with some theoretical aspects of nonlinear programming as well as with some of the current state of the art algorithms in global optimization.
Euclidean Distance Geometry and Applications
The theory of Euclidean distance geometry and its most important applications are surveyed, with special emphasis on molecular conformation problems.
ALICE Technical Design Report of the Inner Tracking System (ITS)
Column generation algorithms for exact modularity maximization in networks.
- Daniel Aloise, S. Cafieri, G. Caporossi, P. Hansen, Sylvain Perron, Leo Liberti
- Computer SciencePhysical review. E, Statistical, nonlinear, and…
- 1 June 2010
Four algorithms for maximizing modularity maximization using the powerful column generation methods for linear and non linear integer programming and their performance is compared on problems from the literature.
An improved column generation algorithm for minimum sum-of-squares clustering
This work proposes a new way to solve the auxiliary problem of finding a column with negative reduced cost based on geometric arguments that greatly improves the efficiency of the whole algorithm and leads to exact solution of instances with over 2,300 entities.
Surrogate-based methods for black-box optimization
In this paper, we survey methods that are currently used in black-box optimization, i.e. the kind of problems whose objective functions are very expensive to evaluate and no analytical or derivative…
The discretizable molecular distance geometry problem
It is shown that under a few assumptions usually satisfied in proteins, the MDGP can be formulated as a search in a discrete space and the DMDGP is NP-hard and a solution algorithm called Branch-and-Prune (BP) is proposed.
Bidirectional A* Search for Time-Dependent Fast Paths
This work proposes a novel approach based on A with landmarks that starts a search from both the source and the destination node, where the backward search is used to bound the set of nodes that have to be explored by the forward search.
Reformulations in mathematical programming: automatic symmetry detection and exploitation
- Leo Liberti
- Computer ScienceMath. Program.
- 1 May 2010
This work proposes a method for automatically finding the formulation group of any given Mixed-Integer Nonlinear Program, and for reformulating the problem by means of static symmetry breaking constraints.