Contributions à la résolution globale de problèmes bilinéaires appliqués à l'indstrie porcine

Abstract : Today, feed represents more than 70% of the production cost in growing-finishing pig industry and in the current economic context, it is important to reduce it. The feeding system currently used uses phases and is expressed as a linear model. The feeding system using feeds introduced more recently is represented by a bilinear model. We introduced here new feeding system which is a combination offeeding systems using phases and feeds: the hybrid method. We show that it can reduce the feed cost by more than 5%. The main part of this manuscript is about global optimization of the bilinear problem, and non convex, problem modeling feeding system using feeds. The objective function and some constraints are bilinear. This problem can have several local minima but we would like to have a global one. It is equivalent to a pooling problem and we prove that it is a strongly NP-hard problem. After a study of first results, we enounce the conjecture that any local minimum is a global minimum for that problem applied in the pig industry. We prove it for a small size example. Our problem cannot be solved by using global solver due to its size, then we applied some relaxation methods such as penalization of bilinear terms, their discretization and Langrangian and convex relaxations. All these approaches support our conjecture. Then we study the robustness of the models on the ingredient price variations and a multicriteria study reducing phosphorus and nitrogen excretion.
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Emilie Joannopoulos. Contributions à la résolution globale de problèmes bilinéaires appliqués à l'indstrie porcine. Optimisation et contrôle [math.OC]. INSA de Rennes, 2018. Français. ⟨NNT : 2018ISAR0006⟩. ⟨tel-01885186⟩

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