Chance-Constrained Programming

Abstract

In a way the basis for this thesis was laid in 2005 when together with some colleagues we were quantifying the impact of uncertainty on weekly unit-commitment. A fruitful collaboration with Pierre Thomas and Riadh Zorgati led to the birth of a software package called LEA ("Laboratoire des Expérimentations des Aléas") in the same year. From a technical perspective this software package allowed the user to execute a simple multiscenario approach around a deterministic optimization kernel. The innovating part was set up with Bernard Beauzamy. Instead of drawing scenarios as iid samples from some law (or black box software), the idea was to build artificial englobing scenarios allowing for bounding of output with only little computational effort. These experiments led, only much later, to an industrial software package. In any case this is how together with Riadh Zorgati, I got interested in dealing with uncertainty in an appropriate way. We had many discussions on Scenario generation, Robust Optimization etc These discussions were also greatly nourished by discussions with Michel Minoux. Around the same time, we had the chance to meet René Henrion and attend a seminar he gave. Chance constrained programming looked like a very powerful and intuitive way to deal with uncertainty. With good hopes and enthusiasm we set out to look where uncertainty in Energy Management plays a key role and should be dealt with appropriately. Once these structures identified we started experimenting with safe tractable approximations of chance constraints, scenario type of approaches and also Robust Optimization. Somewhere in 2009 we had to chance to work closely together with René Henrion and look to what extent Chance Constrained programming could be applied in Energy Management. This led me to be greatly intrigued by this field, and ultimately, gave me a desire to deeply understand this domain. Thanks to EDF I have had the opportunity to do this Thesis in part time. I hope to have contributed to the domain and continue to do so in the future. I do firmly believe that Chance Constrained Programming will be important in Energy Management in the near future.Thanking people after 10 years of work at EDF is almost a dangerous undertaking since we are bound to forget someone with whom we have had interesting discussions. Nonetheless I will make this attempt at my own risks.First of all I would like to thank Riadh Zorgati, who is a good friend and colleague. We share many views and in particular that (fundamental) research should have its place in an(y) industrial company. I would also like to thank Grace Doukopoulos, Olivier Feron, Nadia Oudjane, Cyrille Strugarek and Xavier Warin for the many interesting discussions (and years of joint work). Thanks to Thomas Triboulet, Laurent Mulot and their pragmatic viewpoint of what at EDF we commonly call "le métier" it is possible to obtain a partial view of the underlying structures of the optimization problems at hand. This allows for important progress in identifying the key features of Energy Ma...