Exploring structure and reformulations in different integer programming algorithms

Acknowledgements There are many people I would like to thank who helped me achieve this long-term work. First of all, I would like to thank my supervisor Laurence Wolsey. He has always been remarkably open and available, spending time reading my drafts and discussing my research. I am impressed by his intuition and knowledge of the field. His guidance has been invaluable. He always knows the right questions to ask to make your work progress. He is not only an excellent researcher but he also takes care of every aspect of a researcher's life. Indeed he gave me many opportunities to meet people in the domain, at CORE and in various conferences and to be able to spend time abroad. I am also very grateful to Robert Weismantel for giving me the opportunity to join his group in Magdeburg for three months. His enthusiasm and dynamism pushed me forward. He restored my confidence and encouraged me to complete the thesis. I really enjoyed working with him in Magdeburg. I spent a large amount of time working with Matthias Köppe in Magdeburg. Our work together was very interesting and entertaining. I am impressed by his programming skill and his dedication to his work. I owe a lot to him and Robert for a large part of the work presented here. During the first four years, I was fortunate to be financed by the Belgian National Fund for Scientific Research (FNRS) as a research fellow. The freedom they give to researchers is of great aid for the quality of their work. I am also in debt to the department of applied mathematics which allowed me to complete the thesis by financing my last year. I also wish to thank Leen Stougie and Karen Aardal who welcomed me in the Netherlands for five months and gave me the opportunity to meet a lot of people in a pleasant working atmosphere. I appreciate the time that they devoted to me. In all the places in which I worked during the past five years I met many people that I wish to thank here for their company. First of all, Francisco Or-tega has been like a brother to me. I could always rely on him in any situation. 3 4 We have also worked on our physical shape together by playing squash and badminton games. Mathieu Van Vyve was a tough tennis opponent and I …