2016 [ to top ]

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  Dang, Duc-Cuong; Lehre, Per Kristian; Friedrich, Tobias; Kötzing, Timo; Krejca, Martin S.; Oliveto, Pietro S.; Sudholt, Dirk; Sutton, Andrew M. Emergence of Diversity and its Benefits for Crossover in Genetic Algorithms. Parallel Problem Solving From Nature (PPSN) 2016: 890-900
  [ Abstract ] [ BibTeX ] [DOI] [ Download ]
   
  Population diversity is essential for avoiding premature convergence in Genetic Algorithms (GAs) and for the effective use of crossover. Yet the dynamics of how diversity emerges in populations are not well understood. We use rigorous runtime analysis to gain insight into population dynamics and GA performance for a standard \((\mu+1)\) GA and the \(Jump_k\) test function. By studying the stochastic process underlying the size of the largest collection of identical genotypes we show that the interplay of crossover followed by mutation may serve as a catalyst leading to a sudden burst of diversity. This leads to improvements of the expected optimisation time of order \(\Omega(n/ log n)\) compared to mutation-only algorithms like the \((1+1)\) EA.
  @inproceedings{DBLP:conf/ppsn/DangFKKLOSS16, abstract = {Population diversity is essential for avoiding premature convergence in Genetic Algorithms (GAs) and for the effective use of crossover. Yet the dynamics of how diversity emerges in populations are not well understood. We use rigorous runtime analysis to gain insight into population dynamics and GA performance for a standard \((\mu+1)\) GA and the \(Jump_k\) test function. By studying the stochastic process underlying the size of the largest collection of identical genotypes we show that the interplay of crossover followed by mutation may serve as a catalyst leading to a sudden burst of diversity. This leads to improvements of the expected optimisation time of order \(\Omega(n/ log n)\) compared to mutation-only algorithms like the \((1+1)\) EA.}, author = {Dang, Duc-Cuong and Lehre, Per Kristian and Friedrich, Tobias and Kötzing, Timo and Krejca, Martin S. and Oliveto, Pietro S. and Sudholt, Dirk and Sutton, Andrew M.}, booktitle = {Parallel Problem Solving From Nature (PPSN)}, pages = {890-900}, title = {Emergence of Diversity and its Benefits for Crossover in Genetic Algorithms}, year = 2016 }
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  Friedrich, Tobias; Kötzing, Timo; Sutton, Andrew M. On the Robustness of Evolving Populations. Parallel Problem Solving From Nature (PPSN) 2016: 771-781
  [ Abstract ] [ BibTeX ] [DOI] [ Download ]
   
  Most theoretical work that studies the benefit of recombination focuses on the ability of crossover to speed up optimization time on specific search problems. In this paper, we take a slightly different perspective and investigate recombination in the context of evolving solutions that exhibit \(\emph{mutational}\) robustness, i.e., they display insensitivity to small perturbations. Various models in population genetics have demonstrated that increasing the effective recombination rate promotes the evolution of robustness. We show this result also holds in the context of evolutionary computation by proving crossover promotes the evolution of robust solutions in the standard \((\mu+1)\) GA. Surprisingly, our results show that the effect is present even when robust solutions are at a selective disadvantage due to lower fitness values.
  @inproceedings{DBLP:conf/ppsn/FriedrichKS16, abstract = {Most theoretical work that studies the benefit of recombination focuses on the ability of crossover to speed up optimization time on specific search problems. In this paper, we take a slightly different perspective and investigate recombination in the context of evolving solutions that exhibit \(\emph{mutational}\) robustness, i.e., they display insensitivity to small perturbations. Various models in population genetics have demonstrated that increasing the effective recombination rate promotes the evolution of robustness. We show this result also holds in the context of evolutionary computation by proving crossover promotes the evolution of robust solutions in the standard \((\mu+1)\) GA. Surprisingly, our results show that the effect is present even when robust solutions are at a selective disadvantage due to lower fitness values.}, author = {Friedrich, Tobias and Kötzing, Timo and Sutton, Andrew M.}, booktitle = {Parallel Problem Solving From Nature (PPSN)}, pages = {771-781}, title = {On the Robustness of Evolving Populations}, year = 2016 }
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  Friedrich, Tobias; Kötzing, Timo; Krejca, Martin S.; Sutton, Andrew M. Graceful Scaling on Uniform versus Steep-Tailed Noise. Parallel Problem Solving From Nature (PPSN) 2016: 761-770
  [ Abstract ] [ BibTeX ] [ URL ] [DOI] [ Download ]
   
  Recently, different evolutionary algorithms (EAs) have been analyzed in noisy environments. The most frequently used noise model for this was additive posterior noise (noise added after the fitness evaluation) taken from a Gaussian distribution. In particular, for this setting it was shown that the \((mu + 1)\)-EA on OneMax does not scale gracefully (higher noise cannot efficiently be compensated by higher \(\mu\)). In this paper we want to understand whether there is anything special about the Gaussian distribution which makes the \((mu + 1)\)-EA not scale gracefully. We keep the setting of posterior noise, but we look at other distributions. We see that for exponential tails the \((mu + 1)\)-EA on OneMax does also not scale gracefully, for similar reasons as in the case of Gaussian noise. On the other hand, for uniform distributions (as well as other, similar distributions) we see that the \((mu + 1)\)-EA on OneMax does scale gracefully, indicating the importance of the noise model.
  @inproceedings{DBLP:conf/ppsn/FriedrichKKS16, abstract = {Recently, different evolutionary algorithms (EAs) have been analyzed in noisy environments. The most frequently used noise model for this was additive posterior noise (noise added after the fitness evaluation) taken from a Gaussian distribution. In particular, for this setting it was shown that the \((mu + 1)\)-EA on OneMax does not scale gracefully (higher noise cannot efficiently be compensated by higher \(\mu\)). In this paper we want to understand whether there is anything special about the Gaussian distribution which makes the \((mu + 1)\)-EA not scale gracefully. We keep the setting of posterior noise, but we look at other distributions. We see that for exponential tails the \((mu + 1)\)-EA on OneMax does also not scale gracefully, for similar reasons as in the case of Gaussian noise. On the other hand, for uniform distributions (as well as other, similar distributions) we see that the \((mu + 1)\)-EA on OneMax does scale gracefully, indicating the importance of the noise model.}, author = {Friedrich, Tobias and Kötzing, Timo and Krejca, Martin S. and Sutton, Andrew M.}, booktitle = {Parallel Problem Solving From Nature (PPSN)}, pages = {761-770}, title = {Graceful Scaling on Uniform versus Steep-Tailed Noise}, year = 2016 }
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  Gao, Wanru; Friedrich, Tobias; Neumann, Frank Fixed-Parameter Single Objective Search Heuristics for Minimum Vertex Cover. Parallel Problem Solving From Nature (PPSN) 2016: 740-750
  [ Abstract ] [ BibTeX ] [DOI] [ Download ]
   
  We consider how well-known branching approaches for the classical minimum vertex cover problem can be turned into randomized initialization strategies with provable performance guarantees and investigate them by experimental investigations. Furthermore, we show how these techniques can be built into local search components and analyze a basic local search variant that is similar to a state-of-the-art approach called NuMVC. Our experimental results for the two local search approaches show that making use of more complex branching strategies in the local search component can lead to better results on various benchmark graphs.
  @inproceedings{DBLP:conf/ppsn/GaoFN16, abstract = {We consider how well-known branching approaches for the classical minimum vertex cover problem can be turned into randomized initialization strategies with provable performance guarantees and investigate them by experimental investigations. Furthermore, we show how these techniques can be built into local search components and analyze a basic local search variant that is similar to a state-of-the-art approach called NuMVC. Our experimental results for the two local search approaches show that making use of more complex branching strategies in the local search component can lead to better results on various benchmark graphs.}, author = {Gao, Wanru and Friedrich, Tobias and Neumann, Frank}, booktitle = {Parallel Problem Solving From Nature (PPSN)}, pages = {740-750}, title = {Fixed-Parameter Single Objective Search Heuristics for Minimum Vertex Cover}, year = 2016 }
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  Doerr, Benjamin; Doerr, Carola; Kötzing, Timo Provably Optimal Self-Adjusting Step Sizes for Multi-Valued Decision Variables. Parallel Problem Solving From Nature (PPSN) 2016: 782-791
  [ Abstract ] [ BibTeX ] [DOI] [ Download ]
   
  We regard the problem of maximizing a OneMax-like function defined over an alphabet of size \(r\). In previous work [GECCO 2016] we have investigated how three different mutation operators influence the performance of Randomized Local Search (RLS) and the (1+1) Evolutionary Algorithm. This work revealed that among these natural mutation operators none is superior to the other two for any choice of \(r\). We have also given in [GECCO 2016] some indication that the best achievable run time for large \(r\) is \(\Theta(n log r(log n + log r))\), regardless of how the mutation operator is chosen, as long as it is a static choice (i.e., the distribution used for variation of the current individual does not change over time). Here in this work we show that we can achieve a better performance if we allow for adaptive mutation operators. More precisely, we analyze the performance of RLS using a self-adjusting mutation strength. In this algorithm the size of the steps taken in each iteration depends on the success of previous iterations. That is, the mutation strength is increased after a successful iteration and it is decreased otherwise. We show that this idea yields an expected optimization time of \(\Theta(n(log n + log r))\), which is optimal among all comparison-based search heuristics. This is the first time that self-adjusting parameter choices are shown to outperform static choices on a discrete multi-valued optimization problem.
  @inproceedings{DBLP:conf/ppsn/DoerrDK16, abstract = {We regard the problem of maximizing a OneMax-like function defined over an alphabet of size \(r\). In previous work [GECCO 2016] we have investigated how three different mutation operators influence the performance of Randomized Local Search (RLS) and the (1+1) Evolutionary Algorithm. This work revealed that among these natural mutation operators none is superior to the other two for any choice of \(r\). We have also given in [GECCO 2016] some indication that the best achievable run time for large \(r\) is \(\Theta(n log r(log n + log r))\), regardless of how the mutation operator is chosen, as long as it is a static choice (i.e., the distribution used for variation of the current individual does not change over time). Here in this work we show that we can achieve a better performance if we allow for adaptive mutation operators. More precisely, we analyze the performance of RLS using a self-adjusting mutation strength. In this algorithm the size of the steps taken in each iteration depends on the success of previous iterations. That is, the mutation strength is increased after a successful iteration and it is decreased otherwise. We show that this idea yields an expected optimization time of \(\Theta(n(log n + log r))\), which is optimal among all comparison-based search heuristics. This is the first time that self-adjusting parameter choices are shown to outperform static choices on a discrete multi-valued optimization problem.}, author = {Doerr, Benjamin and Doerr, Carola and Kötzing, Timo}, booktitle = {Parallel Problem Solving From Nature (PPSN)}, pages = {782-791}, title = {Provably Optimal Self-Adjusting Step Sizes for Multi-Valued Decision Variables}, year = 2016 }

2014 [ to top ]

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  Bringmann, Karl; Friedrich, Tobias; Klitzke, Patrick Generic Postprocessing via Subset Selection for Hypervolume and Epsilon-Indicator. Parallel Problem Solving from Nature (PPSN) 2014: 518-527
  [ Abstract ] [ BibTeX ] [DOI] [ Download ]
   
  Most biobjective evolutionary algorithms maintain a population of fixed size \(\mu\) and return the final population at termination. During the optimization process many solutions are considered, but most are discarded. We present two generic postprocessing algorithms which utilize the archive of all non-dominated solutions evaluated during the search. We choose the best \(\mu\) solutions from the archive such that the hypervolume or \(\epsilon\)-indicator is maximized. This postprocessing costs no additional fitness function evaluations and has negligible runtime compared to most EMOAs. We experimentally examine our postprocessing for four standard algorithms (NSGA-II, SPEA2, SMS-EMOA, IBEA) on ten standard test functions (DTLZ 1-2,7, ZDT 1-3, WFG 3-6) and measure the average quality improvement. The median decrease of the distance to the optimal \(\epsilon\)-indicator is \(95\%\), the median decrease of the distance to the optimal hypervolume value is \(86\%\). We observe similar performance on a real-world problem (wind turbine placement).
  @inproceedings{DBLP:conf/ppsn/BringmannFK14, abstract = {Most biobjective evolutionary algorithms maintain a population of fixed size \(\mu\) and return the final population at termination. During the optimization process many solutions are considered, but most are discarded. We present two generic postprocessing algorithms which utilize the archive of all non-dominated solutions evaluated during the search. We choose the best \(\mu\) solutions from the archive such that the hypervolume or \(\epsilon\)-indicator is maximized. This postprocessing costs no additional fitness function evaluations and has negligible runtime compared to most EMOAs. We experimentally examine our postprocessing for four standard algorithms (NSGA-II, SPEA2, SMS-EMOA, IBEA) on ten standard test functions (DTLZ 1-2,7, ZDT 1-3, WFG 3-6) and measure the average quality improvement. The median decrease of the distance to the optimal \(\epsilon\)-indicator is \(95\%\), the median decrease of the distance to the optimal hypervolume value is \(86\%\). We observe similar performance on a real-world problem (wind turbine placement).}, author = {Bringmann, Karl and Friedrich, Tobias and Klitzke, Patrick}, booktitle = {Parallel Problem Solving from Nature (PPSN)}, pages = {518-527}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Generic Postprocessing via Subset Selection for Hypervolume and Epsilon-Indicator}, volume = 8672, year = 2014 }
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  Friedrich, Tobias; Neumann, Frank Maximizing Submodular Functions under Matroid Constraints by Multi-objective Evolutionary Algorithms. Parallel Problem Solving from Nature (PPSN) 2014: 922-931

  Nominated for Best Paper Award
  [ Abstract ] [ BibTeX ] [DOI] [ Download ]
   
  Many combinatorial optimization problems have underlying goal functions that are submodular. The classical goal is to find a good solution for a given submodular function f under a given set of constraints. In this paper, we investigate the runtime of a multi-objective evolutionary algorithm called GSEMO until it has obtained a good approximation for submodular functions. For the case of monotone submodular functions and uniform cardinality constraints we show that GSEMO achieves a \((1 - 1/e)\)-approximation in expected time \(O(n^2(log n+k))\), where \(k\) is the value of the given constraint. For the case of non-monotone submodular functions with \(k\) matroid intersection constraints, we show that GSEMO achieves a \(1/(k + 2 + 1/k + \epsilon)\)-approximation in expected time \(O(n^k+5\log(n)/\epsilon)\).
  @inproceedings{DBLP:conf/ppsn/FriedrichN14, abstract = {Many combinatorial optimization problems have underlying goal functions that are submodular. The classical goal is to find a good solution for a given submodular function f under a given set of constraints. In this paper, we investigate the runtime of a multi-objective evolutionary algorithm called GSEMO until it has obtained a good approximation for submodular functions. For the case of monotone submodular functions and uniform cardinality constraints we show that GSEMO achieves a \((1 - 1/e)\)-approximation in expected time \(O(n^2(log n+k))\), where \(k\) is the value of the given constraint. For the case of non-monotone submodular functions with \(k\) matroid intersection constraints, we show that GSEMO achieves a \(1/(k + 2 + 1/k + \epsilon)\)-approximation in expected time \(O(n^k+5\log(n)/\epsilon)\).}, author = {Friedrich, Tobias and Neumann, Frank}, booktitle = {Parallel Problem Solving from Nature (PPSN)}, note = {Nominated for Best Paper Award}, pages = {922-931}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Maximizing Submodular Functions under Matroid Constraints by Multi-objective Evolutionary Algorithms}, volume = 8672, year = 2014 }
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  Sutton, Andrew M.; Neumann, Frank Runtime Analysis of Evolutionary Algorithms on Randomly Constructed High-Density Satisfiable 3-CNF Formulas. Parallel Problem Solving from Nature (PPSN) 2014: 942-951
  [ Abstract ] [ BibTeX ] [DOI] [ Download ]
   
  We show that simple mutation-only evolutionary algorithms find a satisfying assignment on two similar models of random planted 3-CNF Boolean formulas in polynomial time with high probability in the high constraint density regime. We extend the analysis to random formulas conditioned on satisfiability (i.e., the so-called filtered distribution) and conclude that most high-density satisfiable formulas are easy for simple evolutionary algorithms. With this paper, we contribute the first rigorous study of randomized search heuristics from the evolutionary computation community on well-studied distributions of random satisfiability problems.
  @inproceedings{DBLP:conf/ppsn/SuttonN14, abstract = {We show that simple mutation-only evolutionary algorithms find a satisfying assignment on two similar models of random planted 3-CNF Boolean formulas in polynomial time with high probability in the high constraint density regime. We extend the analysis to random formulas conditioned on satisfiability (i.e., the so-called filtered distribution) and conclude that most high-density satisfiable formulas are easy for simple evolutionary algorithms. With this paper, we contribute the first rigorous study of randomized search heuristics from the evolutionary computation community on well-studied distributions of random satisfiability problems.}, author = {Sutton, Andrew M. and Neumann, Frank}, booktitle = {Parallel Problem Solving from Nature (PPSN)}, pages = {942-951}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Runtime Analysis of Evolutionary Algorithms on Randomly Constructed High-Density Satisfiable 3-CNF Formulas}, volume = 8672, year = 2014 }

2012 [ to top ]

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  Sutton, Andrew M.; Neumann, Frank A Parameterized Runtime Analysis of Simple Evolutionary Algorithms for Makespan Scheduling. Parallel Problem Solving from Nature (PPSN) 2012: 52-61
  [ Abstract ] [ BibTeX ] [DOI] [ Download ]
   
  We consider simple multi-start evolutionary algorithms applied to the classical NP-hard combinatorial optimization problem of Makespan Scheduling on two machines. We study the dependence of the runtime of this type of algorithm on three different key hardness parameters. By doing this, we provide further structural insights into the behavior of evolutionary algorithms for this classical problem.
  @inproceedings{DBLP:conf/ppsn/SuttonN12, abstract = {We consider simple multi-start evolutionary algorithms applied to the classical NP-hard combinatorial optimization problem of Makespan Scheduling on two machines. We study the dependence of the runtime of this type of algorithm on three different key hardness parameters. By doing this, we provide further structural insights into the behavior of evolutionary algorithms for this classical problem.}, author = {Sutton, Andrew M. and Neumann, Frank}, booktitle = {Parallel Problem Solving from Nature (PPSN)}, pages = {52-61}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {A Parameterized Runtime Analysis of Simple Evolutionary Algorithms for Makespan Scheduling}, volume = 7491, year = 2012 }

2010 [ to top ]

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  Bringmann, Karl; Friedrich, Tobias Tight Bounds for the Approximation Ratio of the Hypervolume Indicator. Parallel Problem Solving from Nature (PPSN) 2010: 607-616
  [ Abstract ] [ BibTeX ] [DOI] [ Download ]
   
  The hypervolume indicator is widely used to guide the search and to evaluate the performance of evolutionary multi-objective optimization algorithms. It measures the volume of the dominated portion of the objective space which is considered to give a good approximation of the Pareto front. There is surprisingly little theoretically known about the quality of this approximation. We examine the multiplicative approximation ratio achieved by two-dimensional sets maximizing the hypervolume indicator and prove that it deviates significantly from the optimal approximation ratio. This provable gap is even exponential in the ratio between the largest and the smallest value of the front. We also examine the additive approximation ratio of the hypervolume indicator and prove that it achieves the optimal additive approximation ratio apart from a small factor \(le n/(n - 2)\), where \(n\) is the size of the population. Hence the hypervolume indicator can be used to achieve a very good additive but not a good multiplicative approximation of a Pareto front.
  @inproceedings{DBLP:conf/ppsn/BringmannF10, abstract = {The hypervolume indicator is widely used to guide the search and to evaluate the performance of evolutionary multi-objective optimization algorithms. It measures the volume of the dominated portion of the objective space which is considered to give a good approximation of the Pareto front. There is surprisingly little theoretically known about the quality of this approximation. We examine the multiplicative approximation ratio achieved by two-dimensional sets maximizing the hypervolume indicator and prove that it deviates significantly from the optimal approximation ratio. This provable gap is even exponential in the ratio between the largest and the smallest value of the front. We also examine the additive approximation ratio of the hypervolume indicator and prove that it achieves the optimal additive approximation ratio apart from a small factor \(le n/(n - 2)\), where \(n\) is the size of the population. Hence the hypervolume indicator can be used to achieve a very good additive but not a good multiplicative approximation of a Pareto front.}, author = {Bringmann, Karl and Friedrich, Tobias}, booktitle = {Parallel Problem Solving from Nature (PPSN)}, pages = {607-616}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Tight Bounds for the Approximation Ratio of the Hypervolume Indicator}, volume = 6238, year = 2010 }

2008 [ to top ]

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  Friedrich, Tobias; Horoba, Christian; Neumann, Frank Runtime Analyses for Using Fairness in Evolutionary Multi-Objective Optimization. Parallel Problem Solving from Nature (PPSN) 2008: 671-680
  [ Abstract ] [ BibTeX ] [DOI] [ Download ]
   
  It is widely assumed that evolutionary algorithms for multi-objective optimization problems should use certain mechanisms to achieve a good spread over the Pareto front. In this paper, we examine such mechanisms from a theoretical point of view and analyze simple algorithms incorporating the concept of fairness introduced by Laumanns et al.[7]. This mechanism tries to balance the number of offspring of all individuals in the current population. We rigorously analyze the runtime behavior of different fairness mechanisms and present showcase examples to point out situations where the right mechanism can speed up the optimization process significantly.
  @inproceedings{DBLP:conf/ppsn/FriedrichHN08, abstract = {It is widely assumed that evolutionary algorithms for multi-objective optimization problems should use certain mechanisms to achieve a good spread over the Pareto front. In this paper, we examine such mechanisms from a theoretical point of view and analyze simple algorithms incorporating the concept of fairness introduced by Laumanns et al.[7]. This mechanism tries to balance the number of offspring of all individuals in the current population. We rigorously analyze the runtime behavior of different fairness mechanisms and present showcase examples to point out situations where the right mechanism can speed up the optimization process significantly.}, author = {Friedrich, Tobias and Horoba, Christian and Neumann, Frank}, booktitle = {Parallel Problem Solving from Nature (PPSN)}, pages = {671-680}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Runtime Analyses for Using Fairness in Evolutionary Multi-Objective Optimization}, volume = 5199, year = 2008 }
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  Lunacek, Monte; Whitley, Darrell; Sutton, Andrew M. The Impact of Global Structure on Search. Parallel Problem Solving from Nature (PPSN) 2008: 498-507
  [ Abstract ] [ BibTeX ] [DOI] [ Download ]
   
  Population-based methods are often considered superior on multimodal functions because they tend to explore more of the fitness landscape before they converge. We show that the effectiveness of this strategy is highly dependent on a function's global structure. When the local optima are not structured in a predictable way, exploration can misguide search into sub-optimal regions. Limiting exploration can result in a better non-intuitive global search strategy.
  @inproceedings{DBLP:conf/ppsn/LunacekWS08, abstract = {Population-based methods are often considered superior on multimodal functions because they tend to explore more of the fitness landscape before they converge. We show that the effectiveness of this strategy is highly dependent on a function's global structure. When the local optima are not structured in a predictable way, exploration can misguide search into sub-optimal regions. Limiting exploration can result in a better non-intuitive global search strategy.}, author = {Lunacek, Monte and Whitley, Darrell and Sutton, Andrew M.}, booktitle = {Parallel Problem Solving from Nature (PPSN)}, pages = {498-507}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {The Impact of Global Structure on Search}, volume = 5199, year = 2008 }