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Jeudi 29 Janvier
| Heure: |
10:30 - 12:00 |
| Lieu: |
Salle B107, bâtiment B, Université de Villetaneuse |
| Résumé: |
On Multidimensional Disjunctive Inequalities for Chance-Constrained Stochastic Problems with Finite Support |
| Description: |
Marius Roland This presentation addresses linear Chance-Constrained Stochastic Problems (CCSPs) with
finite support. We begin by motivating the study of CCSPs through illustrative examples and
providing intuition regarding the concept of feasibility in this context. Subsequently, we discuss
the computational challenges inherent to these problems, specifically the nonconvex structure
of the feasible region and the limitations of the standard big-M reformulation. These challenges
necessitate the use of branch-and-cut approaches.
To this end, we review existing families of valid inequalities, such as quantile inequalities
and mixing inequalities. This background sets the stage for the primary contribution of
this work: a new class of valid inequalities termed multi-disjunctive inequalities. We construct
these inequalities by exploiting a disjunctive property inherent to the mathematical formulation
of CCSPs. Theoretical analysis reveals that the closure of these multi-disjunctive inequalities
constitutes a proper subset of the closure generated by previously proposed families.
We perform numerical experiments within a pure cutting-plane framework to compare the
closures obtained by enumerating all violated valid inequalities. The results demonstrate that
multi-disjunctive inequalities significantly strengthen the continuous relaxation of the considered
CCSPs compared to existing quantile and mixing-set inequalities. Furthermore, we evaluate the
performance of these inequalities embedded within a branch-and-cut framework. Our results
indicate that the proposed approach significantly outperforms existing methods on both standard
literature instances and newly generated instances designed to be computationally challenging. |
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