Contributions to robust combinatorial optimization with budgeted uncertainty

Michael Poss (1)

1 MAORE - Methods, Algorithms for Operations REsearch

Robust optimization (RO) has become a central framework to handle the uncertainty that arises in the parameters of optimization problems. While classical RO results can efficiently handle linear programs for a large variety of uncertainty sets, the situation is more complex for optimization problems involving discrete decisions. Efficient exact or approximate solution algorithms for such problems must exploit the combinatorial structure of the problems at hand. This thesis uses the budgeted uncertainty set, introduced by Bertsimas and Sim in (2003,2004), to address scheduling problems, vehicle routing problems, constrained shortest path problems, and lot-sizing problems. We address the resulting robust combinatorial optimization problems along two complementary set of tools: exact and approximate combinatorial algorithms, and decomposition algorithms based on integer programming formulations. In addition to the results specific to each problem, we present an extension of the budgeted uncertainty that is motivated by a connection with probabilistic constraints.

Mots clés: Combinatorial optimisation; Robust optimisation; Integer programming; Complexity & approximation

Mots clés: Optimisation combinatoire

Domaines: Recherche opérationnelle [math.OC]

Michael Poss. Contributions to robust combinatorial optimization with budgeted uncertainty. Operations Research [math.OC]. Université de Montpellier, 2016. ⟨tel-01421260⟩