Marcus Märtens

Search for a grand tour of the jupiter galilean moons

We make use of self-adaptation in a Differential Evolution algorithm and of the asynchronous island model to design a complex interplanetary trajectory touring the Galilean Jupiter moons (Io, Europa, Ganymede and Callisto) using the multiple gravity assist technique. Such a problem was recently the subject of an international competition organized by the Jet Propulsion Laboratory (NASA) and won by a trajectory designed by aerospace experts and reaching the final score of 311/324. We apply our method to the very same problem finding new surprising designs and orbital strategies and a score of up to 316/324.

The asynchronous island model and NSGA-II: study of a new migration operator and its performance

This work presents an implementation of the asynchronous island model suitable for multi-objective evolutionary optimization on heterogeneous and large-scale computing platforms. The migration of individuals is regulated by the crowding comparison operator applied to the originating population during selection and to the receiving population augmented by all migrants during replacement. Experiments using this method combined with NSGA-II show its scalability up to 128 islands and its robustness. Furthermore, the proposed parallelization technique consistently outperforms a multi-start and a random migration approach in terms of convergence speed, while maintaining a comparable population diversity. Applied to a real-world problem of interplanetary trajectory design, we find solutions dominating an actual NASA/ESA mission proposal for a tour from Earth to Jupiter, in a fraction of the computational time that would be needed on a single CPU.

Designing Complex Interplanetary Trajectories for the Global Trajectory Optimization Competitions

The design of interplanetary trajectories often involves a preliminary search for options later refined/assembled into one final trajectory. It is this broad search that, often being intractable, inspires the international event called Global Trajectory Optimization Competition. In the first part of this chapter, we introduce some fundamental problems of space flight mechanics, building blocks of any attempt to participate successfully in these competitions, and we describe the use of the open source software PyKEP to solve them. In the second part, we formulate an instance of a multiple asteroid rendezvous problem, related to the 7th edition of the competition, and we show step by step how to build a possible solution strategy. In doing so, we introduce two new techniques useful in the design of this particular mission type: the use of an asteroid phasing value and its surrogates and the efficient computation of asteroid clusters. We show how the basic building blocks, sided to these innovative ideas, allow designing an effective global search for possible trajectories.

Empirical Performance of the Approximation of the Least Hypervolume Contributor

A fast computation of the hypervolume has become a crucial component for the quality assessment and the performance of modern multi-objective evolutionary optimization algorithms. Albeit recent improvements, exact computation becomes quickly infeasible if the optimization problems scale in their number of objectives or size. To overcome this issue, we investigate the potential of using approximation instead of exact computation by benchmarking the state of the art hypervolume algorithms for different geometries, dimensionality and number of points. Our experiments outline the threshold at which exact computation starts to become infeasible, but approximation still applies, highlighting the major factors that influence its performance.

Toxicity detection in multiplayer online games

Social interactions in multiplayer online games are an essential feature for a growing number of players world-wide. However, this interaction between the players might lead to the emergence of undesired and unintended behavior, particularly if the game is designed to be highly competitive. Communication channels might be abused to harass and verbally assault other players, which negates the very purpose of entertainment games by creating a toxic player-community. By using a novel natural language processing framework, we detect profanity in chat-logs of a popular Multiplayer Online Battle Arena (MOBA) game and develop a method to classify toxic remarks. We show how toxicity is non-trivially linked to game success.

Brain network clustering with information flow motifs

Recent work has revealed frequency-dependent global patterns of information flow by a network analysis of magnetoencephalography data of the human brain. However, it is unknown which properties on a small subgraph-scale of those functional brain networks are dominant at different frequencies bands. Motifs are the building blocks of networks on this level and have previously been identified as important features for healthy and abnormal brain function. In this study, we present a network construction that enables us to search and analyze motifs in different frequency bands. We give evidence that the bi-directional two-hop path is the most important motif for the information flow in functional brain networks. A clustering based on this motif exposes a spatially coherent yet frequency-dependent sub-division between the posterior, occipital and frontal brain regions.

Motif-Based Analysis of Effective Connectivity in Brain Networks

Network science has widely studied the properties of brain networks. Recent work has observed a global back-to-front pattern of information flow for higher frequency bands in magnetoencephalography data. However, the effective connectivity at a local level remains yet to be analyzed. On a local level, the building blocks of all networks are motifs. In this study, we exploit the measure of dPTE to analyze motifs of the estimated effective connectivity networks. We find that some 3- and 4-motifs, the bidirectional two-hop path and its extended 4-node versions, are significantly overexpressed in the analyzed networks in comparison with random networks. With a recently developed motif-based clustering algorithm we separate the effective connectivity network in two main clusters which reveal its higher-order organization with a strong information flow between posterior hubs and anterior regions.

A time-dependent SIS-model for long-term computer worm evolution

Epidemic models like the SIS or SIR model enable us to describe simple spreading processes over networks but are often not sufficient to accurately capture more complex network dynamics as exhibited by sophisticated and malicious computer worms. Many of the common assumptions behind epidemic models do not necessary hold if the process under investigation spans big networks or large scales of time. We extend the standard SIS network model by dropping the assumption of a constant curing rate in favour of a time-dependent curing rate function, which enables us to reflect changes in the effectiveness of the active worm removal process over time. The resulting time-dependent mean-field SIS model allows us to study the evolution of the size of computer worm bot-nets. We exemplify the complete procedure, including data-processing, needed to obtain a reliable model on data from Conficker, an extremely resilient computer worm. Using empirical data obtained from the Conficker sinkhole, we fit long time periods of up to 6 years on multiple scales and different levels of noise. We end by reflecting on the limits of epidemic models in empirical analysis of malware threats.

Symbolic Regression on Network Properties

Networks are continuously growing in complexity, which creates challenges for determining their most important characteristics. While analytical bounds are often too conservative, the computational effort of algorithmic approaches does not scale well with network size. This work uses Cartesian Genetic Programming for symbolic regression to evolve mathematical equations that relate network properties directly to the eigenvalues of network adjacency and Laplacian matrices. In particular, we show that these eigenvalues are powerful features to evolve approximate equations for the network diameter and the isoperimetric number, which are hard to compute algorithmically. Our experiments indicate a good performance of the evolved equations for several real-world networks and we demonstrate how the generalization power can be influenced by the selection of training networks and feature sets.