The following listing contains all publications of the current members of the Algorithm Engineering group in 2017. For further publications, see one of the following lists: year 2015, year 2016, all. Individual lists of publications of each group member are linked from the staff list.
Bläsius, Thomas; Radermacher, Marcel; Rutter, IgnazHow to Draw a Planarization. Software Seminar (SOFSEM) 2017: 295-308
Friedrich, Tobias; Kötzing, Timo; Lagodzinski, J. A. Gregor; Neumann, Frank; Schirneck, MartinAnalysis of the (1+1) EA on Subclasses of Linear Functions under Uniform and Linear Constraints. Foundations of Genetic Algorithms (FOGA) 2017: 45-54
Linear functions have gained a lot of attention in the area of run time analysis of evolutionary computation methods and the corresponding analyses have provided many effective tools for analyzing more complex problems. In this paper, we consider the behavior of the classical (1+1) Evolutionary Algorithm for linear functions under linear constraint. We show tight bounds in the case where both the objective function and the constraint is given by the OneMax function and present upper bounds as well as lower bounds for the general case. Furthermore, we also consider the LeadingOnes fitness function.
Friedrich, Tobias; Kötzing, Timo; Melnichenko, AnnaAnalyzing Search Heuristics with Differential Equations. Genetic and Evolutionary Computation Conference (GECCO) 2017
Drift Theory is currently the most common technique for the analysis of randomized search heuristics because of its broad applicability and the resulting tight first hitting time bounds. The biggest problem when applying a drift theorem is to find a suitable potential function which maps a complex space into a single number, capturing the essence of the state of the search in just one value. We discuss another method for the analysis of randomized search heuristics based on the Theory of Differential Equations. This method considers the deterministic counterpart of the randomized process by replacing probabilistic outcomes by their expectation, and then bounding the error with good probability. We illustrate this by analyzing an Ant Colony Optimization algorithm (ACO) for the Minimum Spanning Tree problem (MST).
Friedrich, Tobias; Kötzing, Timo; Quinzan, Francesco; Sutton, Andrew MichaelResampling vs Recombination: a Statistical Run Time Estimation. Foundations of Genetic Algorithms (FOGA) 2017: 25-36
Noise is pervasive in real-world optimization, but there is still little understanding of the interplay between the operators of randomized search heuristics and explicit noise-handling techniques, such as statistical resampling. In this paper, we report on several statistical models and theoretical results that help to clarify this reciprocal relationship for a collection of randomized search heuristics on noisy functions. We consider the optimization of pseudo-Boolean functions under additive posterior Gaussian noise and explore the trade-o between noise reduction and the computational cost of resampling. We first perform experiments to find the optimal parameters at a given noise intensity for a mutation-only evolutionary algorithm, a genetic algorithm employing recombination, an estimation of distribution algorithm (EDA), and an ant colony optimization algorithm. We then observe how the optimal parameter depends on the noise intensity for the different algorithms. Finally, we locate the point where statistical resampling costs more than it is worth in terms of run time. We find that the EA requires the highest number of resamples to obtain the best speed-up, whereas crossover reduces both the run time and the number of resamples required. Most surprisingly, we find that EDA-like algorithms require no resampling, and can handle noise implicitly.
Friedrich, Tobias; Kötzing, Timo; Wagner, MarkusA Generic Bet-and-Run Strategy for Speeding Up Stochastic Local Search. Association for the Advancement of Artificial Intelligence (AAAI) 2017: 801-807
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, "bet-and-run" was introduced in the context of mixed-integer 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 NP-complete combinatorial optimization problems, traveling salesperson and minimum vertex cover, and study the effectiveness of different bet-and-run 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 off-the-shelf. We observe that state-of-the-art 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 Scale-Free SAT Formulas. Association for the Advancement of Artificial Intelligence (AAAI) 2017: 3893-3899
Recently, a number of non-uniform random satisfiability models have been proposed that are closer to practical satisfiability problems in some characteristics. In contrast to uniform random Boolean formulas, scale-free 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 power-law exponent. For scale-free 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 \(k \ge 3\), we find that the phase transition regime corresponds to a set of formulas that are difficult to solve by backtracking search.
Friedrich, Tobias; Neumann, FrankWhat’s Hot in Evolutionary Computation. Association for the Advancement of Artificial Intelligence (AAAI) 2017: 5064-5066
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 real-world applications. Furthermore, we highlight recent progress on the theoretical understanding of evolutionary computing methods.
Katzmann, Maximilian; Komusiewicz, ChristianSystematic Exploration of Larger Local Search Neighborhoods for the Minimum Vertex Cover Problem. Association for the Advancement of Artificial Intelligence (AAAI) 2017: 846-852
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 moderately-sized \(k\)-swap neighborhoods. For our benchmark data set, we show that when combining our algorithm with a hill-climbing 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 \(k = 21\).
Krejca, Martin S.; Witt, CarstenLower Bounds on the Run Time of the Univariate Marginal Distribution Algorithm on OneMax. Foundations of Genetic Algorithms (FOGA) 2017: 65-80
The Univariate Marginal Distribution Algorithm (UMDA), a popular estimation of distribution algorithm, is studied from a run time perspective. On the classical OneMax benchmark function, a lower bound of \(\Omega(\mu \sqrt n + n \log n)\), where \(\mu\) is the population size, on its expected run time is proved. This is the first direct lower bound on the run time of the UMDA. It is stronger than the bounds that follow from general black-box complexity theory and is matched by the run time of many evolutionary algorithms. The results are obtained through advanced analyses of the stochastic change of the frequencies of bit values maintained by the algorithm, including carefully designed potential functions. These techniques may prove useful in advancing the field of run time analysis for estimation of distribution algorithms in general.
Pourhassan, Mojgan; Friedrich, Tobias; Neumann, FrankOn the Use of the Dual Formulation for Minimum Weighted Vertex Cover in Evolutionary Algorithms. Foundations of Genetic Algorithms (FOGA) 2017: 37-44
We consider the weighted minimum vertex cover problem and investigate how its dual formulation can be exploited to design evolutionary algorithms that provably obtain a 2-approximation. Investigating multi-valued representations, we show that variants of randomized local search and the (1+1) EA achieve this goal in expected pseudo-polynomial time. In order to speed up the process, we consider the use of step size adaptation in both algorithms and show that RLS obtains a 2-approximation in expected polynomial time while the (1+1) EA still encounters a pseudo-polynomial lower bound.
Shi, Feng; Schirneck, Martin; Friedrich, Tobias; Kötzing, Timo; Neumann, FrankReoptimization Times of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform Constraints. Genetic and Evolutionary Computation Conference (GECCO) 2017
In this paper we initiate the study of job scheduling on related and unrelated machines so as to minimize the maximum flow time or the maximum weighted flow time (when each job has an associated weight). Previous work for these metrics considered only the setting of parallel machines, while previous work for scheduling on unrelated machines only considered \(L_p, p < \infty\) norms. Our main results are: (1) we give an \(O(\epsilon^−3)\)-competitive algorithm to minimize maximum weighted flow time on related machines where we assume that the machines of the online algorithm can process \(1+\epsilon\) units of a job in 1 time-unit (\(\epsilon\) speed augmentation). (2) For the objective of minimizing maximum flow time on unrelated machines we give a simple \(2/\epsilon\)-competitive algorithm when we augment the speed by \(\epsilon\). For \(m\) machines we show a lower bound of \(\Omega(m)\) on the competitive ratio if speed augmentation is not permitted. Our algorithm does not assign jobs to machines as soon as they arrive. To justify this “drawback” we show a lower bound of \(\Omega(\log m)\) on the competitive ratio of immediate dispatch algorithms. In both these lower bound constructions we use jobs whose processing times are in \(\1,\infty\\), and hence they apply to the more restrictive subset parallel setting. (3) For the objective of minimizing maximum weighted flow time on unrelated machines we establish a lower bound of \(\Omega(\log m)\)-on the competitive ratio of any online algorithm which is permitted to use \(s = O(1)\) speed machines. In our lower bound construction, job \(j\) has a processing time of \(p_j\) on a subset of machines and infinity on others and has a weight \(1/p_j\). Hence this lower bound applies to the subset parallel setting for the special case of minimizing maximum stretch.
Friedrich, Tobias; Kötzing, Timo; Krejca, Martin S.; Sutton, Andrew M.The Compact Genetic Algorithm is Efficient under Extreme Gaussian Noise. IEEE Transactions on Evolutionary Computation 2017
Practical optimization problems frequently include uncertainty about the quality measure, for example due to noisy evaluations. Thus, they do not allow for a straightforward application of traditional optimization techniques. In these settings, randomized search heuristics such as evolutionary algorithms are a popular choice because they are often assumed to exhibit some kind of resistance to noise. Empirical evidence suggests that some algorithms, such as estimation of distribution algorithms (EDAs) are robust against a scaling of the noise intensity, even without resorting to explicit noise-handling techniques such as resampling. In this paper, we want to support such claims with mathematical rigor. We introduce the concept of graceful scaling in which the run time of an algorithm scales polynomially with noise intensity. We study a monotone fitness function over binary strings with additive noise taken from a Gaussian distribution. We show that myopic heuristics cannot efficiently optimize the function under arbitrarily intense noise without any explicit noise-handling. Furthermore, we prove that using a population does not help. Finally we show that a simple EDA called the compact Genetic Algorithm can overcome the shortsightedness of mutation-only heuristics to scale gracefully with noise. We conjecture that recombinative genetic algorithms also have this property.
Galanis, Andreas; Göbel, Andreas; Goldberg, Leslie Ann; Lapinskas, John; Richerby, DavidAmplifiers for the Moran Process. J. ACM 2017: 5:1-5:90
The Moran process, as studied by Lieberman, Hauert, and Nowak, is a randomised algorithm modelling the spread of genetic mutations in populations. The algorithm runs on an underlying graph where individuals correspond to vertices. Initially, one vertex (chosen uniformly at random) possesses a mutation, with fitness \(r > 1\). All other individuals have fitness 1. During each step of the algorithm, an individual is chosen with probability proportional to its fitness, and its state (mutant or nonmutant) is passed on to an out-neighbour which is chosen uniformly at random. If the underlying graph is strongly connected, then the algorithm will eventually reach fixation, in which all individuals are mutants, or extinction, in which no individuals are mutants. An infinite family of directed graphs is said to be strongly amplifying if, for every \(r > 1\), the extinction probability tends to 0 as the number of vertices increases. A formal definition is provided in the article. Strong amplification is a rather surprising property—it means that in such graphs, the fixation probability of a uniformly placed initial mutant tends to 1 even though the initial mutant only has a fixed selective advantage of \(r > 1\) (independently of \(n\)). The name “strongly amplifying” comes from the fact that this selective advantage is “amplified.” Strong amplifiers have received quite a bit of attention, and Lieberman et al. proposed two potentially strongly amplifying families—superstars and metafunnels. Heuristic arguments have been published, arguing that there are infinite families of superstars that are strongly amplifying. The same has been claimed for metafunnels. In this article, we give the first rigorous proof that there is an infinite family of directed graphs that is strongly amplifying. We call the graphs in the family “megastars.” When the algorithm is run on an \(n\)-vertex graph in this family, starting with a uniformly chosen mutant, the extinction probability is roughly \(n − 1/2\) (up to logarithmic factors). We prove that all infinite families of superstars and metafunnels have larger extinction probabilities (as a function of \(n\)). Finally, we prove that our analysis of megastars is fairly tight—there is no infinite family of megastars such that the Moran algorithm gives a smaller extinction probability (up to logarithmic factors). Also, we provide a counterexample which clarifies the literature concerning the isothermal theorem of Lieberman et al.
Our research focus is on theoretical computer science and algorithm engineering. We are equally interested in the mathematical foundations of algorithms and developing efficient algorithms in practice. A special focus is on random structures and methods.