Despite the success of branch-and-cut methods for solving mixed integer bilevel linear optimization problems (MIBLPs) in practice, there are still gaps in both the theory and practice surrounding these methods. In the first part of this paper, we lay out a basic theory of valid inequalities and cutting-plane methods for MIBLPs that parallels the existing … Read more
We study single-item discrete multi-module capacitated lot-sizing problems where the amount produced in each time period is equal to the summation of binary multiples of the capacities of n available different modules (or machines). For fixed n≥2, we develop fixed-parameter tractable (polynomial) exact algorithms that generalize the algorithms of van Vyve (2007) for n=1. We … Read more
For a continuous multi-objective optimization problem, it is usually not a practical approach to compute all its nondominated points because there are infinitely many of them. For this reason, a typical approach is to compute an approximation of the nondominated set. A common technique for this approach is to generate a polyhedron which contains the … Read more
This paper presents a novel algorithmic study and complexity analysis of distributionally robust multistage convex optimization (DR-MCO). We propose a new class of algorithms for solving DR-MCO, namely a sequential dual dynamic programming (Seq-DDP) algorithm and its nonsequential version (NDDP). The new algorithms generalize and strengthen existing DDP-type algorithms by introducing the technique of regularization … Read more
In supply chain optimization multiple objectives are considered simultaneously, for example to increase resilience and reduce costs. In this paper we discuss the corresponding bicriteria problems to find a good balance between these two objectives. We give a general model for supply chain resilience that integrates strategic decisions with the operational level. This modular model … Read more
Although many algorithms for multicriteria optimization provide good approximations, a precise control of their quality is challenging. In this paper we provide algorithmic tools to obtain exact approximation quality values for given approximations and develop a new method for multicriteria optimization guided by this quality. We show that the well-established “-indicator measure is NP-hard to … Read more
Derivatives are an important tool for single-objective optimization. In fact, it is commonly accepted that derivative-based methods present a better performance than derivative-free optimization approaches. In this work, we will show that the same does not apply to multiobjective derivative-based optimization, when the goal is to compute an approximation to the complete Pareto front of … Read more
This paper presents a novel adaptable energy management system for smart buildings. In this framework we model the energy consumption of a living unit, and its energy exchange with the surroundings. We explicitly consider the impact of the outside environment and design features such as building orientation, automatic shading, and double facade. We formulate this … Read more
In this thesis, we settle the computational complexity of some fundamental questions in polynomial optimization. These include the questions of (i) finding a local minimum, (ii) testing local minimality of a candidate point, and (iii) deciding attainment of the optimal value. Our results characterize the complexity of these three questions for all degrees of the … Read more
Rank aggregation is widely used in group decision-making and many other applications where it is of interest to consolidate heterogeneous ordered lists. Oftentimes, these rankings may involve a large number of alternatives, contain ties, and/or be incomplete, all of which complicate the use of robust aggregation methods. In particular, these characteristics have limited the applicability … Read more