Thesis of Nathalia Wolf

Mixed-Integer and Bilevel Optimization for Sustainable Cloud Operations

Cloud computing relies on large, geographically distributed data centers whose operation is increasingly constrained by energy costs and by environmental limits such as carbon and water budgets. At the same time, key operational choices—pricing, scheduling, and security controls—must anticipate how users and sometimes adversaries respond. These features motivate decision models that combine mixed-integer structure, hierarchical interaction, and uncertainty. This thesis develops optimization models and algorithms for sustainable cloud operations along two complementary tracks. First, it proposes a Cloud Planning Matrix that organizes decisions across time horizons and organizational stages, and clarifies how sustainability metrics become decision-grade planning inputs. The matrix distinguishes strategic, tactical, and operational layers and makes explicit the resolution, boundary, and handoff contracts required for consistent planning under environmental constraints. A strategic case study instantiates the approach through a capacitated facility-location model enriched with CO₂ and water constraints applied to data center siting. Second, the thesis develops optimization models for key operational levers. We formulate a bilevel pricing-and-reward mechanism that reallocates idle reserved virtual machines by coordinating provider pricing decisions with heterogeneous user and lender responses, and we evaluate its impact on utilization and energy waste using real-world data from OVHcloud. We also propose an energy-aware scheduling framework for geo-distributed deep-learning training that aligns long, non-preemptive workloads with time- and location-varying renewable availability, solved at scale via a rolling-horizon matheuristic with heuristic-seeded column generation. In addition, we study randomized inspections in a public-transport network as a Stackelberg resource-allocation problem and derive implementable unpredictable schedules via mixed strategies and column generation, drawing parallels with resource-constrained security controls in cloud systems. Finally, motivated by settings where uncertainty is continuously distributed and the follower problem is mixed-integer, we introduce a two-stage stochastic bilevel model with coupling constraints that can make follower optima non-implementable. We represent this through an extended-real recourse function, establish consistency of sample-average approximation, and develop a branch-and-cut scheme that combines fixed-sample optimization with separation over the uncertainty support. Overall, the thesis provides a coherent set of models and methods for decision support in sustainable cloud operations and for bilevel optimization under uncertainty. By revisiting the mathematical foundations of bilevel optimization and extending them to practical cloud problems, this work demonstrates that rigorous optimization models can effectively bridge the gap between sustainability targets and concrete operational constraints.

Jury

Mme Luce BROTCORNE Directeur de recherche Centre Inria de l'Université de Lille Directrice de thèse, M. Didier AUSSEL Professeur Université de Perpignan Rapporteur, Mme Golbon ZAKERI Professeur University of Massachusetts Rapporteure, Mme Martine LABBE Professeure Université Libre de Bruxelles Examinatrice, Mme Angela FLORES Associate Professor Universidad de Chile Examinatrice, M. Panagiotis ANDRIANESIS Associate Professor Mines Paris – PSL Examinateur, M. Grégory LEBOURG Invité.

Thesis of the team INOCS defended on 30/04/2026