Groupe d’études et de recherche en analyse des décisions

The pooling problem: Classical formulations and strong valid inequalities

Claudia D'Ambrosio LIX, École Polytechnique, France

The focus of this talk will be on the standard pooling problem, i.e., a continuous, non-convex optimization problem arising in the chemical engineering context. First, we will introduce the problem that consists of finding the optimal composition of final products obtained by blending in pools different percentages of raw materials. Bilinear terms arise from the requirements on the quality of certain attributes of the final products. The quality is a linear combination of the attributes of the raw materials and intermediate products that compose the final product. Three different classical formulations have been proposed in the literature and their characteristics will be discussed and analysed. In the second part of the talk, strong relaxations for the pooling problem will be presented. In particular, we studied a structured non-convex subset of some special cases to derive valid nonlinear convex inequalities that we conjecture, and proved for a particular case, to define the convex hull of the non-convex subset. Preliminary computational results on instances from the literature are reported and demonstrate the utility of the inequalities when used in a global optimization solver. This is a joint work with Jeff Linderoth (University of Wisconsin-Madison), James Luedtke (University of Wisconsin-Madison), Jonas Schweiger (IBM).

Ce séminaire vous permettra d’échanger avec le conférencier et les chercheurs présents autour de boissons et de collations. Nous vous remercions de confirmer votre présence.

Entrée gratuite. Bienvenue à tous!