Co-supervision : BENDOTTI Pascale, CHRÉTIENNE Philippe
Anchored solutions in robust combinatorial optimization
If the instance of an optimization problem changes, an initial solution may become suboptimal or infeasible. It is then necessary to compute a new solution, but it is also desirable to keep some decisions from the initial solution unchanged. In this thesis we propose the anchoring criterion to favor unchanged decisions between solutions. In a reoptimization setting, the goal is to find a new solution while keeping a maximum number of decisions from the initial solution. In a robust 2-stage optimization setting, we propose the anchor-robust approach to compute in advance a baseline solution, along with a subset of so-called anchored decisions. For any realization in the considered uncertainty set, it is possible to repair the baseline solution into a new solution without changing anchored decisions. The anchor-robust approach allows for a trade-off between the cost of a solution and guaranteed decisions. Anchoring problems are formally defined and studied on two problem classes. The first one is the class of integer programs in binary variables, including classical polynomial problems such as spanning trees. The second one is project scheduling, where jobs must be scheduled under precedence only, or precedence and resource constraints. The complexity of anchoring problems is analyzed. Combinatorial properties of anchored solutions are exhibited, and dedicated algorithmic and polyhedral approaches are devised. Mixed-integer programming techniques are investigated, that highlight the practical implementability of anchoring problems.
P. Bendotti, Ph. Chrétienne, P. Fouilhoux, A. Pass‑Lanneau : “The Anchor-Robust Project Scheduling Problem”, 14th Workshop on Models and Algorithms for Planning and Scheduling Problems (MAPSP), Renesse, Netherlands (2019)
P. Bendotti, Ph. Chrétienne, P. Fouilhoux, A. Pass‑Lanneau : “Ancrage de solutions en ordonnancement PERT”, ROADEF - 19e congrès annuel de la Société française de recherche opérationnelle et d'aide à la décision, Lorient, France (2018)