QIP
Financiado
Towards a Quantitative Theory of Integer Programming
Integer programming (IP), i.e. linear optimization
with integrality constraints on variables, is one of the most successful
methods for solving large scale optimization problems in practice. While many
of the base IP problems suc...
Integer programming (IP), i.e. linear optimization
with integrality constraints on variables, is one of the most successful
methods for solving large scale optimization problems in practice. While many
of the base IP problems such as the traveling salesman problem (TSP) or
satisfiability (SAT) are NP-Complete, IPs with tens of thousands of variables are
routinely solved in just a few hours by current state of the art IP solvers.
The main goal of this proposal is to develop a quantitative theory capable of
explaining when and how well different IP solver techniques will work on a wide
range of instances. Here we will study many of the principal tools used to solve
IPs including branch & bound, the simplex method, cutting planes and rounding
heuristics. Our first direction of study will be to develop parametrized classes
of instances, inspired by the structure of realistic models, on which branch &
bound and the simplex method are provably efficient. The second research
direction will be to develop alternatives to ad hoc rounding heuristics and
cutting plane selection strategies with provable guarantees and provide their
applications to important classes of IPs. Lastly, we will explore the power and
limitations of IP techniques in the context of algorithm design by comparing
them to powerful techniques in theoretical computer science and analyzing their
worst-case performance for solving general integer programs. While the main
thrust of this proposal is theoretical, it will be complimented by an
experimental component performed in collaboration with well-known experts in
computational IP, both to gain valuable insights on the structure of real-world
instances and to validate the effectiveness newly suggested approaches. The
proposed research is designed to make breakthroughs in our quantitative
understanding of IP techniques, many of which have long resisted theoretical
analysis.
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Duración del proyecto: 75 meses
Fecha Inicio: 2018-09-10
Fecha Fin: 2024-12-31
Fecha Fin: 2024-12-31
Línea de financiación: concedida
El organismo H2020 notifico la concesión del proyecto el día 2018-09-10
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
ERC-2018-STG:
ERC Starting Grant
Cerrada
hace 7 años
Presupuesto
El presupuesto total del proyecto asciende a
2M€
Líder del proyecto
STICHTING NEDERLANDSE WETENSCHAPPELIJK ONDERZ...
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
Perfil tecnológico
TRL
4-5
2.55M€ |
Participante