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Salvagnin, Domenico (2009) Constraint Programming Techniques for Mixed Integer Linear Programs. [Tesi di dottorato]

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Abstract (inglese)

Many decision problems in industry, logistics, and telecommunications can be viewed as satisfiability or optimization problems. Two paradigms have reached a high degree of sophistication from the point of view of both theory and implementation: Constraint Programming (CP) and Mixed Integer Programming (MIP). The CP and MIP paradigms have strengths and weaknesses that complement each other. On the one hand, CP, through the use of sophisticated propagation techniques, privileges primal inference. On the other hand, MIP, through the techniques of relaxation and strengthening through cutting planes, privileges dual inference.

This thesis presents several studies in Mixed Integer Programming, with emphasis on computational aspects and integration with the Constraint Programming paradigm. In particular, CP concepts and techniques, such as nogoods, minimal infeasiblity and constraint propagation, are used to improve different MIP solving components, namely, dominance detection, Benders cuts selection strategy and primal heuristics. This cross-fertilization of techniques and ideas has proven very effective.

Finally, an appendix is given covering a MIP application to robust railway timetabling.

Abstract (italiano)

Molti problemi decisionali nell'industria, nella logistica e nelle telecomunicazioni possono essere formulati come problemi di soddisfacibilita' o di ottimizzazione. Due paradigmi per la modellazione e la risoluzione di tali problemi hanno raggiunto un elevato grado di sviluppo, sia dal punto di vista teorico che implementativo: la Programmazione a Vincoli (Constraint Programming, CP) e la Programmazione Lineare Intera Mista (Mixed Integer Programming, MIP). I paradigmi CP e MIP hanno vantaggi e debolezze complementari. Da una parte, la CP privilegia l'inferenza primale, attraverso sofisticate tecniche di propagazione. Dall'altra, la MIP privilegia l'inferenza duale, attraverso i rilassamenti e il loro rafforzamento mediante piani di taglio.

Questa tesi presenta alcuni studi in Programmazione Lineare Intera Mista, con enfasi sugli aspetti computazionali e sull'integrazione col paradigma della Programmazione a Vincoli. In particolare, concetti e tecniche CP, quali nogood, insoddisfacibilita' minimale e propagazione, sono usati per migliorare varie componenti risolutive per la MIP, quali procedure di dominanza, strategia di selezione dei tagli di Benders e euristiche primali. Questo scambio di idee e tecniche si e' dimostrato molto efficace.

Infine, un'applicazione MIP alla generazione di orari robusti in ambito ferroviario e' presentata in appendice.

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Tipo di EPrint:Tesi di dottorato
Relatore:Fischetti, Matteo
Dottorato (corsi e scuole):Ciclo 21 > Scuole per il 21simo ciclo > SCIENZE MATEMATICHE > MATEMATICA COMPUTAZIONALE
Data di deposito della tesi:27 Gennaio 2009
Anno di Pubblicazione:2009
Parole chiave (italiano / inglese):constraint programming, integer programming
Settori scientifico-disciplinari MIUR:Area 01 - Scienze matematiche e informatiche > MAT/09 Ricerca operativa
Struttura di riferimento:Dipartimenti > Dipartimento di Matematica
Codice ID:1482
Depositato il:27 Gen 2009
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