Supervision : Pierre FOUILHOUX

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.

2018-2024 Publications

• 2024
  • A. Pass‑Lanneau, P. Bendotti, L. Brunod‑Indrigo : “Exact and heuristic methods for Anchor-Robust and Adjustable-Robust RCPSP”, Annals of Operations Research, vol. 337 (2), pp. 649-682, (Springer Verlag) (2024)
• 2022
  • Th. Ehrhard, S. Attias, E. Bampis, V. Cohen‑Addad, B. Escoffier, C. Mathieu, F. Pascual, A. Pass‑Lanneau, D. Saulpic : “Découpage électoral des circonscriptions législatives en France: déséquilibres démographiques et contraintes territoriales”, Revue Française de Science Politique, vol. Vol. 72 (3), pp. 333-364, (Presses de Sciences Po) (2022)
  • A. Pass‑Lanneau, P. Bendotti, Ph. Chrétienne, P. Fouilhoux : “Anchored solutions in robust combinatorial optimization: PGMO Phd Award 2022”, PGMO Days 2022, Palaiseau, France (2022)
  • A. Pass‑Lanneau, P. Bendotti, Ph. Chrétienne, P. Fouilhoux : “Ancrage et robustesse pour le RCPSP: outils exacts et heuristiques”, 23^e congrès annuel de la Société Française de Recherche Opérationnelle et d'Aide à la Décision, Villeurbanne - Lyon, France (2022)
• 2021
  • A. Pass‑Lanneau : “Anchored solutions in robust combinatorial optimization”, thesis, phd defence 03/16/2021, supervision Fouilhoux, Pierre, co-supervision : Bendotti, Pascale, Chrétienne, Philippe (2021)
  • P. Bendotti, Ph. Chrétienne, P. Fouilhoux, A. Pass‑Lanneau : “Dominance-based linear formulation for the Anchor-Robust Project Scheduling Problem”, European Journal of Operational Research, vol. 295 (1), pp. 22-33, (Elsevier) (2021)
• 2020
  • P. Bendotti, Ph. Chrétienne, P. Fouilhoux, A. Pass‑Lanneau : “Anchored Rescheduling Problems Under Generalized Precedence Constraints”, Combinatorial Optimization, 6^th International Symposium, ISCO 2020, Montreal, QC, Canada, May 4–6, 2020, vol. 12176, Lecture Notes in Computer Science, Montreal, QC, Canada, pp. 156-166 (2020)
  • B. Escoffier, H. Gilbert, A. Pass‑Lanneau : “Iterative Delegations in Liquid Democracy with Restricted Preferences”, AAAI Technical Track: Game Theory and Economic Paradigms, vol. 34 (2), New-York, NY, United States, pp. 1926-1933 (2020)
  • P. Bendotti, Ph. Chrétienne, P. Fouilhoux, A. Pass‑Lanneau : “Outils de résolution exacte pour l’ancrage de solutions en ordonnancement de projet”, ROADEF - 21^e congrès annuel de la Société française de recherche opérationnelle et d'aide à la décision, Montpellier, France (2020)
• 2019
  • P. Bendotti, L. Brunod‑Indrigo, Ph. Chrétienne, P. Fouilhoux, A. Pass‑Lanneau : “Anchor-Robust Solutions for the Resource-Constrained Project Scheduling Problem”, PGMO Days 2019, Palaiseau, France (2019)
  • B. Escoffier, H. Gilbert, A. Pass‑Lanneau : “The Convergence of Iterative Delegations in Liquid Democracy in a Social Network”, Lecture Notes in Computer Science, vol. 11801, Athènes, Greece, pp. 284-297 (2019)
  • P. Bendotti, Ph. Chrétienne, P. Fouilhoux, A. Pass‑Lanneau : “The Anchor-Robust Project Scheduling Problem”, 14^th Workshop on Models and Algorithms for Planning and Scheduling Problems (MAPSP), Renesse, Netherlands (2019)
  • P. Bendotti, Ph. Chrétienne, P. Fouilhoux, A. Pass‑Lanneau : “The Anchor-Robust Project Scheduling Problem”, Operations Research, (INFORMS) (2019)
  • P. Bendotti, Ph. Chrétienne, P. Fouilhoux, A. Pass‑Lanneau : “Stabilisation de solutions en optimisation combinatoire par des modèles d’ancrage; application à l’arbre couvrant”, ROADEF - 20^e congrès annuel de la Société française de recherche opérationnelle et d'aide à la décision, Le Havre, France (2019)
• 2018
  • P. Bendotti, Ph. Chrétienne, P. Fouilhoux, A. Pass‑Lanneau : “Robust proactive maintenance planning with a deadline”, PGMO Days 2018, Palaiseau, France (2018)
  • P. Bendotti, Ph. Chrétienne, P. Fouilhoux, A. Pass‑Lanneau : “Ancrage de solutions en ordonnancement PERT”, ROADEF - 19^e congrès annuel de la Société française de recherche opérationnelle et d'aide à la décision, Lorient, France (2018)