Supervision : Patrice PERNY

Multi-objective optimisation and preference elicitation based on rank-dependant models and reference points

This thesis work falls within the research field of algorithmic decision theory, which is defined at the junction of decision theory, artificial intelligence and operations research. This work focuses on the consideration of sophisticated behaviors in complex decision environments (multicriteria decision-making, collective decision-making and decision under risk and uncertainty). We first propose methods for multi-objective optimization on implicit sets when preferences are represented by rank-dependent models (Choquet integral, bipolar OWA, Cumulative Prospect Theory and bipolar Choquet integral). These methods are based on mathematical programming and discrete algorithmics approaches. Then, we present methods for the incremental parameter elicitation of rank-dependent model that take into account the presence of a reference point in the decision maker's preferences (bipolar OWA, Cumulative Prospect Theory, Choquet integral with capacities and bicapacities). Finally, we address the structural modification of solutions under constraints (cost, quality) in multiple reference point sorting methods. The different approaches proposed in this thesis have been tested and we present the obtained numerical results to illustrate their practical efficiency.

2019-2022 Publications

• 2022
  • H. Martin : “Optimisation multi-objectifs et élicitation de préférences fondées sur des modèles décisionnels dépendants du rang et des points de référence”, thesis, defence 05/18/2022, supervision Perny, Patrice (2022)
• 2021
  • N. Benabbou, H. Martin, P. Perny : “Min Cost Improvement and Max Gain Stability in Multicriteria Sorting Methods on Combinatorial Domains”, Journal of Multi-Criteria Decision Analysis, (Wiley) (2021)
• 2020
  • H. Martin, P. Perny : “New Computational Models for the Choquet Integral”, 24^th European Conference on Artificial Intelligence - ECAI 2020, Santiago, Spain (2020)
• 2019
  • H. Martin, P. Perny : “Computational Models for Cumulative Prospect Theory: Application to the Knapsack Problem Under Risk”, International Conference on Scalable Uncertainty Management, vol. 11940, Lecture Notes in Computer Science, Compiègne, France, pp. 52-65, (Springer) (2019)
  • H. Martin, P. Perny : “BiOWA for Preference Aggregation with Bipolar Scales: Application to Fair Optimization in Combinatorial Domains”, Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence (IJCAI-19), Macao, China, pp. 1822-1828, (International Joint Conferences on Artificial Intelligence Organization) (2019)