Pseudo Polynomial-Time Top-k Algorithms for d-DNNF Circuits

We are interested in computing $k$ most preferred models of a given d-DNNF circuit $C$, where the preference relation is based on an algebraic structure called a monotone, totally ordered, semigroup $(K, \otimes, <)$. In our setting, every literal in $C$ has a value in $K$ and the value of an assignment is an element of $K$ obtained by aggregating using $\otimes$ the values of the corresponding literals. We present an algorithm that computes $k$ models of $C$ among those having the largest values w.r.t. $<$, and show that this algorithm runs in time polynomial in $k$ and in the size of $C$. We also present a pseudo polynomial-time algorithm for deriving the top-$k$ values that can be reached, provided that an additional (but not very demanding) requirement on the semigroup is satisfied. Under the same assumption, we present a pseudo polynomial-time algorithm that transforms $C$ into a d-DNNF circuit $C'$ satisfied exactly by the models of $C$ having a value among the top-$k$ ones. Finally, focusing on the semigroup $(\mathbb{N}, +, <)$, we compare on a large number of instances the performances of our compilation-based algorithm for computing $k$ top solutions with those of an algorithm tackling the same problem, but based on a partial weighted MaxSAT solver.

Feature-Model-Guided Online Learning for Self-Adaptive Systems

A self-adaptive system can modify its own structure and behavior at runtime based on its perception of the environment, of itself and of its requirements. To develop a self-adaptive system, software developers codify knowledge about the system and its environment, as well as how adaptation actions impact on the system. However, the codified knowledge may be insufficient due to design time uncertainty, and thus a self-adaptive system may execute adaptation actions that do not have the desired effect. Online learning is an emerging approach to address design time uncertainty by employing machine learning at runtime. Online learning accumulates knowledge at runtime by, for instance, exploring not-yet executed adaptation actions. We address two specific problems with respect to online learning for self-adaptive systems. First, the number of possible adaptation actions can be very large. Existing online learning techniques randomly explore the possible adaptation actions, but this can lead to slow convergence of the learning process. Second, the possible adaptation actions can change as a result of system evolution. Existing online learning techniques are unaware of these changes and thus do not explore new adaptation actions, but explore adaptation actions that are no longer valid. We propose using feature models to give structure to the set of adaptation actions and thereby guide the exploration process during online learning. Experimental results involving four real-world systems suggest that considering the hierarchical structure of feature models may speed up convergence by 7.2% on average. Considering the differences between feature models before and after an evolution step may speed up convergence by 64.6% on average. [...]