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- Hasso-Plattner-Institut für Digital Engineering GmbH (64) (remove)
Optimization is a core part of technological advancement and is usually heavily aided by computers. However, since many optimization problems are hard, it is unrealistic to expect an optimal solution within reasonable time. Hence, heuristics are employed, that is, computer programs that try to produce solutions of high quality quickly. One special class are estimation-of-distribution algorithms (EDAs), which are characterized by maintaining a probabilistic model over the problem domain, which they evolve over time. In an iterative fashion, an EDA uses its model in order to generate a set of solutions, which it then uses to refine the model such that the probability of producing good solutions is increased.
In this thesis, we theoretically analyze the class of univariate EDAs over the Boolean domain, that is, over the space of all length-n bit strings. In this setting, the probabilistic model of a univariate EDA consists of an n-dimensional probability vector where each component denotes the probability to sample a 1 for that position in order to generate a bit string.
My contribution follows two main directions: first, we analyze general inherent properties of univariate EDAs. Second, we determine the expected run times of specific EDAs on benchmark functions from theory. In the first part, we characterize when EDAs are unbiased with respect to the problem encoding. We then consider a setting where all solutions look equally good to an EDA, and we show that the probabilistic model of an EDA quickly evolves into an incorrect model if it is always updated such that it does not change in expectation.
In the second part, we first show that the algorithms cGA and MMAS-fp are able to efficiently optimize a noisy version of the classical benchmark function OneMax. We perturb the function by adding Gaussian noise with a variance of σ², and we prove that the algorithms are able to generate the true optimum in a time polynomial in σ² and the problem size n. For the MMAS-fp, we generalize this result to linear functions. Further, we prove a run time of Ω(n log(n)) for the algorithm UMDA on (unnoisy) OneMax. Last, we introduce a new algorithm that is able to optimize the benchmark functions OneMax and LeadingOnes both in O(n log(n)), which is a novelty for heuristics in the domain we consider.
The identification of vulnerabilities in IT infrastructures is a crucial problem in enhancing the security, because many incidents resulted from already known vulnerabilities, which could have been resolved. Thus, the initial identification of vulnerabilities has to be used to directly resolve the related weaknesses and mitigate attack possibilities. The nature of vulnerability information requires a collection and normalization of the information prior to any utilization, because the information is widely distributed in different sources with their unique formats. Therefore, the comprehensive vulnerability model was defined and different sources have been integrated into one database. Furthermore, different analytic approaches have been designed and implemented into the HPI-VDB, which directly benefit from the comprehensive vulnerability model and especially from the logical preconditions and postconditions.
Firstly, different approaches to detect vulnerabilities in both IT systems of average users and corporate networks of large companies are presented. Therefore, the approaches mainly focus on the identification of all installed applications, since it is a fundamental step in the detection. This detection is realized differently depending on the target use-case. Thus, the experience of the user, as well as the layout and possibilities of the target infrastructure are considered. Furthermore, a passive lightweight detection approach was invented that utilizes existing information on corporate networks to identify applications.
In addition, two different approaches to represent the results using attack graphs are illustrated in the comparison between traditional attack graphs and a simplistic graph version, which was integrated into the database as well. The implementation of those use-cases for vulnerability information especially considers the usability. Beside the analytic approaches, the high data quality of the vulnerability information had to be achieved and guaranteed. The different problems of receiving incomplete or unreliable information for the vulnerabilities are addressed with different correction mechanisms. The corrections can be carried out with correlation or lookup mechanisms in reliable sources or identifier dictionaries. Furthermore, a machine learning based verification procedure was presented that allows an automatic derivation of important characteristics from the textual description of the vulnerabilities.