Projects Prof. Harks
Algorithmic Mechanism Design for Dynamic Flows (2021-2024)
Foundational questions for dynamic flows in the context of equilibrium conditions are investigated. Several behavioral modes are considered including instantaneous dynamic equilibrium concept and classical dynamic equilibrium. Key questions range from convergence issues regarding possible discretization approaches to efficiency considerations of equilibria. We also address bilevel optimization approaches modeling mechanism design problems for dynamic equilibrium flows.
Models and Algorithms for Multi-Level Congestion and Security Problems (2020-2023)
Strategic acts of sabotage and terrorism pose an increasing threat to important infrastructures and their users. This proposal aims at the design of models and algorithms for multi-level congestion and security games that allow for planning infrastructures that are robust against such attacks. In these models, we take the role of a planner, who in the first level designs the infrastructure, which is represented by a network (e.g., a public transit system or emergency exit ways in a stadium). Then, in the second level, users operate on this infrastructure according to their own selfish interests. Finally, an attacker, observing the distribution of users in the network, strategically attacks the infrastructure so as to cause as much harm as possible (e.g., affecting as many people as possible). Solving the resulting multi-level optimization problems is computationally very challenging, in particular due to non-convexities caused by the multi-level structure. We therefore propose a new concept of level-wise approximation that allows to relax optimality requirements at each level individually. Using this paradigm, we hope to devise algorithms that efficiently compute near-optimal solutions.An additional challenge arises when taking into account the interplay of congestion effects caused by the users’ selfish action and their anticipation of the attacker’s action. An important part of our project therefore is to investigate bilevel congestion games, i.e., congestion games in which users take their choices taking into account both congestion caused by other users and the actions of a lower level attacker who will strike at the most-frequented parts of the infrastructure. Combining the insights gained on approximating multi-level network problems and congestion games, we then aim to solve multi-level network security games with congestion effects using a mix of approximation algorithms, heuristics, and exact methods, which we finally investigate in a study based on realistic data sets.
Algorithmic Mechanism Design for Combinatorial Resource Allocation Problems (2017-2020)
Resource allocation problems play a key role for a wide range of applications including traffic networks and telecommunication networks. An intrinsic property of the above applications is that the allocation of resources cannotbe centrally enforced but is determined by independent users, each optimizing an individual objective function (e.g., selfish users evacuating a burning building, drivers choosing the fastest route, or routing protocols choosing the least delay path or least congested server). Designing mechanisms so that the resulting allocation of resources by selfish players is efficient constitutes a fundamental research challenge. From an abstract point of view, every resource incurs a cost or a utilityto its users and a mechanism defines the strategies available to players and the cost/utility shares for every player using a specific resource. Concrete examples of such mechanisms include the design of the network infrastructure in telecommunications and traffic. This proposal attempts to advance the algorithmic foundations for computingprovably optimal or approximatively optimal mechanisms in the context of network design, scheduling, and auction-based resource allocation problems.
The capacitated location routing problem
Location routing integrates the two classical optimization problems of facility location and vehicle routing, addressing both location and tour planning decisions in a single step. There is a large number of different versions of location routing problems, incorporating different sets of constraints arising in real-world applications, such as vehicle and depot capacities or time windows.
Optimal Coordination Mechanisms for Distributed Resource Allocation (2013-2017)
NWO Exacte Wetenschappen kent aan 19 wetenschappers in de astronomie, informatica en wiskunde of een combinatie van deze disciplines (multidisciplinair) een TOP-subsidie toe. Acht wetenschappers zijn senior onderzoekers met een bewezen track record, de overige elf zijn junior onderzoekers die aan het begin van hun wetenschappelijke carrière staan. In totaal ontvangen de wetenschappers ruim 6 miljoen euro.
Designing Optimal Protocols for Resource Allocation Games (2013-2015)
In a resource allocation game, the allocation of resources is determined by a finite number of independent players, each optimizing an individual objective function. Because selfish behavior of players usually leads to inefficient resource allocation with respect to predefined performance measures, the design of protocols as a way to improve the inefficiency of selfish resource allocation is of fundamental importance.
While numerous resource allocation games and corresponding resource allocation protocols have been analyzed in the last decade with respect to various performance indicators, there has been only recently some efforts to design optimal protocols for these indicators (Chen et al.(2008), Harks and von Falkenhausen (2011)).
This project intends to make progress in the design of optimal protocols.
NEIGHBORHOOD TECHNOLOGIES MEDIA AND MATHEMATICS OF DYNAMIC NETWORKS
When sociologist Thomas Schelling published his research on housing segregation in major US-American cities in 1971, he accomplished more than just contributing to a novel type of ›social mathematics‹. With Schellings interest in the mechanisms of social segregation and his respective models, the analysis of actual neighborhood dynamics converged with a ›neighborly‹ research method.
Participants: Tobias Harks, Sebastian Vehlken
MultiTrans: Multi-Criteria Optimization for Transportation Problems in Logistics (2009-2012)
Ziele des Projektes MultiTrans (Multikriterielle Optimierung bei Transportproblemen in der Logistik) waren die mathematische Modellierung praxisrelevanter Transportprobleme, die Entwicklung und Analyse effizienter Algorithmen zur exakten und heuristischen Lösung solcher Optimierungsprobleme, sowie die Umsetzung der Lösungsansätze in einer Demonstrationssoftware. Als Ergebnisse des Forschungsvorhabens wurden eine deutliche Senkung des Modellierungsaufwandes in der Netzwerkoptimierung und eine signifikante Verbesserung des Optimierungsergebnisses durch den erhöhten Realitätsgehalt der verwendeten Modelle angestrebt.
Participants: Tobias Harks, Felix G. König, Marco E. Lübbecke, Jannik Matuschke, Britta Peis, Alexander Richter, Jens Schulz.
Adaptive Traffic Control (2007-2010)
Congestion collapse on a network of one-way streets. The red cars are those causing the gridlock by stopping in the middle of the intersection, © http://en.wikipedia.org/wiki/Gridlock. Cooperation Partner Our cooperation partner, the ptv AG from Karlsruhe, Germany, is one of Europe's leading traffic software developing companies.
Participants: Tobias Harks, Rolf H. Möhring
Fundamental Algorithms for Combinatorial Optimization Problems (2007)
The aim of this project is to design, analyze and experimentally evaluate algorithms for fundamental combinatorial optimization problems. A particular focus will be given to optimization problems that arise in the application areas telecommunication, traffic and logistics.
Participants: Tobias Harks, G. Schäfer.