In this note, we consider several polynomial optimization formulations of the max- imum independent set problem and the use of the Lasserre hierarchy with these different formulations. We demonstrate using computational experiments that the choice of formulation may have a significant impact on the resulting bounds. We also provide theoretical justifications for the observed behavior. … Read more
Naturally imbalanced freight flows force consolidation carriers to reposition resources empty. When constructing empty repositioning plans, the cost of repositioning resources empty needs to be weighed against the cost of corrective actions in case of unavailable resources. This is especially challenging given the uncertainty of future demand. We design and implement a robust rolling horizon … Read more
Solving mixed-integer nonlinear optimization problems (MINLPs) to global optimality is extremely challenging. An important step for enabling their solution consists in the design of convex relaxations of the feasible set. Known solution approaches based on spatial branch-and-bound become more effective the tighter the used relaxations are. Relaxations are commonly established by convex underestimators, where each … Read more
In \cite{siebert2019linear} the authors present a set of integer programs (IPs) for the Steiner tree problem, which can be used for both, the directed and the undirected setting of the problem. Each IP finds an optimal Steiner tree with a specific structure. A solution with the lowest cost, corresponds to an optimal solution to the … Read more
Quantum Bridge Analytics relates to methods and systems for hybrid classical-quantum computing, and is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future. This is the second of a two-part tutorial that surveys … Read more
In the growing field of autonomous driving, traffic-light controlled intersections as the nodes of large traffic networks are of special interest. We want to analyze how much an optimized coordination of vehicles and infrastructure can contribute to a more efficient transit through these bottlenecks. In addition, we are interested in sensitivity of the results with … Read more
As a result of its liberalization, the European gas market is organized as an entry-exit system in order to decouple the trading and transport of natural gas. Roughly summarized, the gas market organization consists of four subsequent stages. First, the transmission system operator (TSO) is obliged to allocate so-called maximal technical capacities for the nodes … Read more
A location-transportation problem concerns designing a company’s distribution network consisting of one central warehouse with ample stock and multiple local warehouses for a long but finite time horizon. The network is designed to satisfy the demands of geographically dispersed customers for multiple products within given delivery time targets. The company needs to first decide on … Read more
In the context of centralized electricity markets, we propose an integrated planning model for power pricing and network expansion, which endogenizes the scaling costs from power losses. While the substitutability pattern between pricing and expansion has been overlooked in the power flow optimization literature, this becomes particularly relevant in centralized electricity markets (where the headquarters … Read more
We present a general numerical solution method for control problems with PDE-defined state variables over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs (and if necessary a linearization scheme) to derive constraints for a mixed-integer linear program (MILP) … Read more