2017

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  Friedrich, Tobias; Kötzing, Timo; Wagner, Markus A Generic Bet-and-Run Strategy for Speeding Up Stochastic Local Search. Association for the Advancement of Artificial Intelligence (AAAI) 2017: 801-807
  [ Abstract ] [ BibTeX ] [ URL ] [ Download ]
   
  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.
  @inproceedings{DBLP:conf/aaai/0001K017, abstract = {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.}, author = {Friedrich, Tobias and Kötzing, Timo and Wagner, Markus}, booktitle = {Association for the Advancement of Artificial Intelligence (AAAI)}, crossref = {DBLP:conf/aaai/2017}, pages = {801-807}, title = {A Generic Bet-and-Run Strategy for Speeding Up Stochastic Local Search}, year = 2017 }
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  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
  [ Abstract ] [ BibTeX ] [ URL ] [ Download ]
   
  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 \(k \geq 3\), we find that the phase transition regime corresponds to a set of formulas that are difficult to solve by backtracking search.
  @inproceedings{DBLP:conf/aaai/0001KRS17, abstract = {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 \(k \geq 3\), we find that the phase transition regime corresponds to a set of formulas that are difficult to solve by backtracking search.}, author = {Friedrich, Tobias and Krohmer, Anton and Rothenberger, Ralf and Sutton, Andrew M.}, booktitle = {Association for the Advancement of Artificial Intelligence (AAAI)}, pages = {3893-3899}, publisher = {AAAI Press}, title = {Phase Transitions for Scale-Free SAT Formulas}, year = 2017 }
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  Friedrich, Tobias; Neumann, Frank What's Hot in Evolutionary Computation. Association for the Advancement of Artificial Intelligence (AAAI) 2017: 5064-5066
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  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.
  @inproceedings{friedrich2017whats, abstract = {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.}, author = {Friedrich, Tobias and Neumann, Frank}, booktitle = {Association for the Advancement of Artificial Intelligence (AAAI)}, crossref = {DBLP:conf/aaai/2017}, pages = {5064-5066}, title = {What's Hot in Evolutionary Computation}, year = 2017 }
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  Katzmann, Maximilian; Komusiewicz, Christian Systematic Exploration of Larger Local Search Neighborhoods for the Minimum Vertex Cover Problem. Association for the Advancement of Artificial Intelligence (AAAI) 2017: 846-852
  [ Abstract ] [ BibTeX ] [ URL ] [ Download ]
   
  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 \(k = 21\).
  @inproceedings{DBLP:conf/aaai/KatzmannK17, abstract = {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 \(k = 21\).}, author = {Katzmann, Maximilian and Komusiewicz, Christian}, booktitle = {Association for the Advancement of Artificial Intelligence (AAAI)}, crossref = {DBLP:conf/aaai/2017}, pages = {846-852}, title = {Systematic Exploration of Larger Local Search Neighborhoods for the Minimum Vertex Cover Problem}, year = 2017 }

2012

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  Sutton, Andrew M.; Neumann, Frank A Parameterized Runtime Analysis of Evolutionary Algorithms for the Euclidean Traveling Salesperson Problem. Conference on Artificial Intelligence (AAAI) 2012
  [ Abstract ] [ BibTeX ] [ Download ]
   
  Parameterized runtime analysis seeks to understand the influence of problem structure on algorithmic runtime. In this paper, we contribute to the theoretical understanding of evolutionary algorithms and carry out a parameterized analysis of evolutionary algorithms for the Euclidean traveling salesperson problem (Euclidean TSP). We investigate the structural properties in TSP instances that influence the optimization process of evolutionary algorithms and use this information to bound the runtime of simple evolutionary algorithms. Our analysis studies the runtime in dependence of the number of inner points \(k\) and shows that \((\mu + \lambda)\) evolutionary algorithms solve the Euclidean TSP in expected time \(O((\mu / \lambda) cdot n^3 \gamma(\epsilon) + n \gamma(\epsilon)+(\mu / \lambda) cdot n^4k(2k-1)!)\) where \(\gamma\) is a function of the minimum angle \(epsilon\) between any three points. Finally, our analysis provides insights into designing a mutation operator that improves the upper bound on expected runtime. We show that a mixed mutation strategy that incorporates both 2-opt moves and permutation jumps results in an upper bound of \(O((\mu / \lambda) cdot n^3 \gamma(\epsilon) + n \gamma(\epsilon) + (\mu / \lambda) cdot n^2k(k-1)!)\) for the \((\mu + \lambda)\) EA.
  @inproceedings{DBLP:conf/aaai/SuttonN12, abstract = {Parameterized runtime analysis seeks to understand the influence of problem structure on algorithmic runtime. In this paper, we contribute to the theoretical understanding of evolutionary algorithms and carry out a parameterized analysis of evolutionary algorithms for the Euclidean traveling salesperson problem (Euclidean TSP). We investigate the structural properties in TSP instances that influence the optimization process of evolutionary algorithms and use this information to bound the runtime of simple evolutionary algorithms. Our analysis studies the runtime in dependence of the number of inner points \(k\) and shows that \((\mu + \lambda)\) evolutionary algorithms solve the Euclidean TSP in expected time \(O((\mu / \lambda) \cdot n^3 \gamma(\epsilon) + n \gamma(\epsilon)+(\mu / \lambda) \cdot n^{4k}(2k-1)!)\) where \(\gamma\) is a function of the minimum angle \(epsilon\) between any three points. Finally, our analysis provides insights into designing a mutation operator that improves the upper bound on expected runtime. We show that a mixed mutation strategy that incorporates both 2-opt moves and permutation jumps results in an upper bound of \(O((\mu / \lambda) \cdot n^3 \gamma(\epsilon) + n \gamma(\epsilon) + (\mu / \lambda) \cdot n^{2k}(k-1)!)\) for the \((\mu + \lambda)\) EA.}, author = {Sutton, Andrew M. and Neumann, Frank}, booktitle = {Conference on Artificial Intelligence (AAAI)}, publisher = {{AAAI} Press}, title = {A Parameterized Runtime Analysis of Evolutionary Algorithms for the Euclidean Traveling Salesperson Problem}, year = 2012 }