Clean Citation Style 002
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Friedrich, Tobias; Göbel, Andreas; Neumann, Frank; Quinzan, Francesco; Rothenberger, Ralf Greedy Maximization of Functions with Bounded Curvature Under Partition Matroid Constraints. Conference on Artificial Intelligence (AAAI) 2019
We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider nonmonotone submodular functions and monotone subadditive functions. Even though constrained maximization problems of monotone submodular functions have been extensively studied, little is known about greedy maximization of nonmonotone submodular functions or monotone subadditive functions. We give approximation guarantees for GREEDY on these problems, in terms of the curvature. We find that this simple heuristic yields a strong approximation guarantee on a broad class of functions. We discuss the applicability of our results to three realworld problems: Maximizing the determinant function of a positive semidefinite matrix, and related problems such as the maximum entropy sampling problem, the constrained maximum cut problem on directed graphs, and combinatorial auction games. We conclude that GREEDY is wellsuited to approach these problems. Overall, we present evidence to support the idea that, when dealing with constrained maximization problems with bounded curvature, one needs not search for (approximate) monotonicity to get good approximate solutions.

Roostapour, Vahid; Neumann, Aneta; Neumann, Frank; Friedrich, Tobias Pareto Optimization for Subset Selection with Dynamic Cost Constraints. Conference on Artificial Intelligence (AAAI) 2019
In this paper, we consider subset selection problems for functions \(f\) with constraints where the constraint bound \(B\) changes over time. We point out that adaptive variants of greedy approaches commonly used in the area of submodular optimization are not able to maintain their approximation quality. Investigating the recently introduced POMC Pareto optimization approach, we show that this algorithm efficiently computes a \( phi= (\alpha_f/2)(1\frac{1}{e^{\alpha_f}})\)approximation, where \(\alpha_f\) is the submodularity ratio, for each possible constraint bound \(b \leq B\). Furthermore, we show that POMC is able to adapt its set of solutions quickly in the case that \(B\) increases. Our experimental investigations for the influence maximization in social networks show the advantage of POMC over generalized greedy algorithms.

Friedrich, Tobias; Kötzing, Timo; Wagner, Markus A Generic BetandRun Strategy for Speeding Up Stochastic Local Search. Conference on Artificial Intelligence (AAAI) 2017: 801807
A common strategy for improving optimization algorithms is to restart the algorithm when it is believed to be trapped in an inferior part of the search space. However, while specific restart strategies have been developed for specific problems (and specific algorithms), restarts are typically not regarded as a general tool to speed up an optimization algorithm. In fact, many optimization algorithms do not employ restarts at all. Recently, "betandrun" was introduced in the context of mixedinteger programming, where first a number of short runs with randomized initial conditions is made, and then the most promising run of these is continued. In this article, we consider two classical NPcomplete combinatorial optimization problems, traveling salesperson and minimum vertex cover, and study the effectiveness of different betandrun strategies. In particular, our restart strategies do not take any problem knowledge into account, nor are tailored to the optimization algorithm. Therefore, they can be used offtheshelf. We observe that stateoftheart solvers for these problems can benefit significantly from restarts on standard benchmark instances.

Friedrich, Tobias; Krohmer, Anton; Rothenberger, Ralf; Sutton, Andrew M. Phase Transitions for ScaleFree SAT Formulas. Conference on Artificial Intelligence (AAAI) 2017: 38933899
Recently, a number of nonuniform random satisfiability models have been proposed that are closer to practical satisfiability problems in some characteristics. In contrast to uniform random Boolean formulas, scalefree formulas have a variable occurrence distribution that follows a power law. It has been conjectured that such a distribution is a more accurate model for some industrial instances than the uniform random model. Though it seems that there is already an awareness of a threshold phenomenon in such models, there is still a complete picture lacking. In contrast to the uniform model, the critical density threshold does not lie at a single point, but instead exhibits a functional dependency on the powerlaw exponent. For scalefree formulas with clauses of length \(k = 2\), we give a lower bound on the phase transition threshold as a function of the scaling parameter. We also perform computational studies that suggest our bound is tight and investigate the critical density for formulas with higher clause lengths. Similar to the uniform model, on formulas with \(k \geq 3\), we find that the phase transition regime corresponds to a set of formulas that are difficult to solve by backtracking search.

Friedrich, Tobias; Neumann, Frank What's Hot in Evolutionary Computation. Conference on Artificial Intelligence (AAAI) 2017: 50645066
We provide a brief overview on some hot topics in the area of evolutionary computation. Our main focus is on recent developments in the areas of combinatorial optimization and realworld applications. Furthermore, we highlight recent progress on the theoretical understanding of evolutionary computing methods.

Katzmann, Maximilian; Komusiewicz, Christian Systematic Exploration of Larger Local Search Neighborhoods for the Minimum Vertex Cover Problem. Conference on Artificial Intelligence (AAAI) 2017: 846852
We investigate the potential of exhaustively exploring larger neighborhoods in local search algorithms for Minimum Vertex Cover. More precisely, we study whether, for moderate values of \(k\), it is feasible and worthwhile to determine, given a graph \(G\) with vertex cover \(C\), if there is a \(k\)swap \(S\) such that \((C \setminus S) cup (S \setminus C)\) is a smaller vertex cover of \(G\). First, we describe an algorithm running in \(\Delta^{O(k) \cdot n\) time for searching the \(k\)swap neighborhood on \(n\)vertex graphs with maximum degree \(\Delta\). Then, we demonstrate that, by devising additional pruning rules that decrease the size of the search space, this algorithm can be implemented so that it solves the problem quickly for \(k \approx 20\). Finally, we show that it is worthwhile to consider moderatelysized \(k\)swap neighborhoods. For our benchmark data set, we show that when combining our algorithm with a hillclimbing approach, the solution quality improves quickly with the radius \(k\) of the local search neighborhood and that in most cases optimal solutions can be found by setting \(k = 21\).