The Multi-Stop Station Location Problem

We introduce the (directed) multi-stop station location problem. The goal is to install stations such that ordered (multi-)sets of stops can be traversed with respect to range restrictions that are reset whenever a station is visited. Applications arise in telecommunications and transportation, e.g., charging station placement problems. The problem generalizes several network optimization problems such … Read more

Combinatorial Acyclicity Models for Potential-based Flows

Potential-based flows constitute a basic model to represent physical behavior in networks. Under natural assumptions, the flow in such networks must be acyclic. The goal of this paper is to exploit this property for the solution of corresponding optimization problems. To this end, we introduce several combinatorial models for acyclic flows, based on binary variables … Read more

Solving the distance-based critical node problem

In critical node problems, the task is identify a small subset of so-called critical nodes whose deletion maximally degrades a network’s “connectivity” (however that is measured). Problems of this type have been widely studied, e.g., for limiting the spread of infectious diseases. However, existing approaches for solving them have typically been limited to networks having … Read more

Optimizing Drone-Assisted Last-Mile Deliveries: The Vehicle Routing Problem with Flexible Drones

The ever-widening acceptance and deployment of drones in last-mile distribution continue to increase the need for planning and managing the delivery operations involving drones effectively. Motivated by the growing interest towards drone-assisted last-mile transportation, we study a hybrid delivery system in which (multiple) trucks and (multiple) drones operate in tandem. In particular, we introduce the … Read more

A note on the Lasserre hierarchy for different formulations of the maximum independent set problem

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

The Star Degree Centrality Problem: A Decomposition Approach

We consider the problem of identifying the induced star with the largest cardinality open neighborhood in a graph. This problem, also known as the star degree centrality (SDC) problem, has been shown to be 𝒩𝒫-complete. In this work, we first propose a new integer programming (IP) formulation, which has a fewer number of constraints and … Read more

Optimizing the Response for Arctic Mass Rescue Events

We study a model that optimizes the response to a mass rescue event in Arctic Alaska. The model contains dynamic logistics decisions for a large-scale maritime evacuation with the objectives of minimizing the impact of the event on the evacuees and the average evacuation time. Our proposed optimization model considers two interacting networks – the … Read more

A Robust Rolling Horizon Framework for Empty Repositioning

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 using Simultaneous Convexification – a Case Study for Gas Networks

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

A Simulated Annealing Algorithm for the Directed Steiner Tree Problem

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