2022 [ nach oben ]

Friedrich, Tobias; Kötzing, Timo; Krejca, Martin S.; Rajabi, Amirhossein Escaping Local Optima With Local Search: A Theory-Driven DiscussionParallel Problem Solving from Nature (PPSN) 2022
[ Abstract ] [ BibTeX ] [ Download ]
 
Local search is the most basic strategy in optimization settings when no specific problem knowledge is employed. While this strategy finds good solutions for certain optimization problems, it generally suffers from getting stuck in local optima. This stagnation can be avoided if local search is modified. Depending on the optimization landscape, different modifications vary in their success. We discuss several features of optimization landscapes and give analyses as examples for how they affect the performance of modifications of local search. We consider modifying random local search by restarting it and by considering larger search radii. The landscape features we analyze include the number of local optima, the distance between different optima, as well as the local landscape around a local optimum. For each feature, we show which modifications of local search handle them well and which do not.
@inproceedings{friedrich2022escaping, abstract = {Local search is the most basic strategy in optimization settings when no specific problem knowledge is employed. While this strategy finds good solutions for certain optimization problems, it generally suffers from getting stuck in local optima. This stagnation can be avoided if local search is modified. Depending on the optimization landscape, different modifications vary in their success. We discuss several features of optimization landscapes and give analyses as examples for how they affect the performance of modifications of local search. We consider modifying random local search by restarting it and by considering larger search radii. The landscape features we analyze include the number of local optima, the distance between different optima, as well as the local landscape around a local optimum. For each feature, we show which modifications of local search handle them well and which do not.}, author = {Friedrich, Tobias and Kötzing, Timo and Krejca, Martin S. and Rajabi, Amirhossein}, booktitle = {Parallel Problem Solving from Nature (PPSN)}, keywords = {amirhosseinrajabi martinskrejca ppsn timokoetzing tobiasfriedrich year2022}, title = {Escaping Local Optima With Local Search: A Theory-Driven Discussion}, year = 2022 }

2020 [ nach oben ]

Kötzing, Timo; Witt, Carsten Improved Fixed-Budget Results via Drift AnalysisParallel Problem Solving From Nature (PPSN) 2020: 648–660
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Fixed-budget theory is concerned with computing or bounding the fitness value achievable by randomized search heuristics within a given budget of fitness function evaluations. Despite recent progress in fixed-budget theory, there is a lack of general tools to derive such results. We transfer drift theory, the key tool to derive expected optimization times, to the fixed-budged perspective. A first and easy-to-use statement concerned with iterating drift in so-called greed-admitting scenarios immediately translates into bounds on the expected function value. Afterwards, we consider a more general tool based on the well-known variable drift theorem. Applications of this technique to the LeadingOnes benchmark function yield statements that are more precise than the previous state of the art.
@inproceedings{kotzing2020improved, abstract = {Fixed-budget theory is concerned with computing or bounding the fitness value achievable by randomized search heuristics within a given budget of fitness function evaluations. Despite recent progress in fixed-budget theory, there is a lack of general tools to derive such results. We transfer drift theory, the key tool to derive expected optimization times, to the fixed-budged perspective. A first and easy-to-use statement concerned with iterating drift in so-called greed-admitting scenarios immediately translates into bounds on the expected function value. Afterwards, we consider a more general tool based on the well-known variable drift theorem. Applications of this technique to the LeadingOnes benchmark function yield statements that are more precise than the previous state of the art.}, author = {Kötzing, Timo and Witt, Carsten}, booktitle = {Parallel Problem Solving From Nature (PPSN)}, keywords = {sys:relevantfor:ae carstenwitt ppsn timokoetzing year2020}, pages = {648-660}, title = {Improved Fixed-Budget Results via Drift Analysis}, year = 2020 }

2018 [ nach oben ]

Frahnow, Clemens; Kötzing, Timo Ring Migration Topology Helps Bypassing Local OptimaParallel Problem Solving From Nature (PPSN) 2018: 129–140
[ Abstract ] [ BibTeX ] [ Download ]
 
Running several evolutionary algorithms in parallel and occasionally exchanging good solutions is referred to as island models. The idea is that the independence of the different islands leads to diversity, thus possibly exploring the search space better. Many theoretical analyses so far have found a complete (or sufficiently quickly expanding) topology as underlying migration graph most efficient for optimization, even though a quick dissemination of individuals leads to a loss of diversity. We suggest a simple fitness function Fork with two local optima parametrized by \(r \geq 2\) and a scheme for composite fitness functions. We show that, while the (1+1) EA gets stuck in a bad local optimum and incurs a run time of \(\Theta(n^{2r})\) fitness evaluations on Fork, island models with a complete topology can achieve a run time of \(\Theta(n^{1.5r})\) by making use of rare migrations in order to explore the search space more effectively. Finally, the ring topology, making use of rare migrations and a large diameter, can achieve a run time of \(\tilde{\Theta}(n^r)\), the black box complexity of Fork. This shows that the ring topology can be preferable over the complete topology in order to maintain diversity.
@inproceedings{frahnow2018migration, abstract = {Running several evolutionary algorithms in parallel and occasionally exchanging good solutions is referred to as island models. The idea is that the independence of the different islands leads to diversity, thus possibly exploring the search space better. Many theoretical analyses so far have found a complete (or sufficiently quickly expanding) topology as underlying migration graph most efficient for optimization, even though a quick dissemination of individuals leads to a loss of diversity. We suggest a simple fitness function Fork with two local optima parametrized by \(r \geq 2\) and a scheme for composite fitness functions. We show that, while the (1+1) EA gets stuck in a bad local optimum and incurs a run time of \(\Theta(n^{2r})\) fitness evaluations on Fork, island models with a complete topology can achieve a run time of \(\Theta(n^{1.5r})\) by making use of rare migrations in order to explore the search space more effectively. Finally, the ring topology, making use of rare migrations and a large diameter, can achieve a run time of \(\tilde{\Theta}(n^r)\), the black box complexity of Fork. This shows that the ring topology can be preferable over the complete topology in order to maintain diversity.}, author = {Frahnow, Clemens and Kötzing, Timo}, booktitle = {Parallel Problem Solving From Nature (PPSN)}, keywords = {clemensfrahnow islands ppsn timokoetzing year2018}, pages = {129-140}, series = {Lecture Notes in Computer Science}, title = {Ring Migration Topology Helps Bypassing Local Optima}, volume = 11102, year = 2018 }

Friedrich, Tobias; Göbel, Andreas; Quinzan, Francesco; Wagner, Markus Heavy-tailed Mutation Operators in Single-Objective Combinatorial OptimizationParallel Problem Solving From Nature (PPSN) 2018: 134–145
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
A core feature of evolutionary algorithms is their mutation operator. Recently, much attention has been devoted to the study of mutation operators with dynamic and non-uniform mutation rates. Following up on this line of work, we propose a new mutation operator and analyze its performance on the (1+1) Evolutionary Algorithm (EA). Our analyses show that this mutation operator competes with pre-existing ones, when used by the (1+1)EA on classes of problems for which results on the other mutation operators are available. We present a jump function for which the performance of the (1+1)EA using any static uniform mutation and any restart strategy can be worse than the performance of the (1+1)EA using our mutation operator with no restarts. We show that the (1+1)EA using our mutation operator finds a (1/3)-approximation ratio on any non-negative submodular function in polynomial time. This performance matches that of combinatorial local search algorithms specifically designed to solve this problem. Finally, we evaluate experimentally the performance of the (1+1)EA using our operator, on real-world graphs of different origins with up to \(\sim\)37,000 vertices and \(\sim\)1.6 million edges. In comparison with uniform mutation and a recently proposed dynamic scheme our operator comes out on top on these instances.
@inproceedings{friedrich2018heavytailed, abstract = {A core feature of evolutionary algorithms is their mutation operator. Recently, much attention has been devoted to the study of mutation operators with dynamic and non-uniform mutation rates. Following up on this line of work, we propose a new mutation operator and analyze its performance on the (1+1) Evolutionary Algorithm (EA). Our analyses show that this mutation operator competes with pre-existing ones, when used by the (1+1)EA on classes of problems for which results on the other mutation operators are available. We present a jump function for which the performance of the (1+1)EA using any static uniform mutation and any restart strategy can be worse than the performance of the (1+1)EA using our mutation operator with no restarts. We show that the (1+1)EA using our mutation operator finds a (1/3)-approximation ratio on any non-negative submodular function in polynomial time. This performance matches that of combinatorial local search algorithms specifically designed to solve this problem. Finally, we evaluate experimentally the performance of the (1+1)EA using our operator, on real-world graphs of different origins with up to \(\sim\)37\,000 vertices and \(\sim\)1.6 million edges. In comparison with uniform mutation and a recently proposed dynamic scheme our operator comes out on top on these instances.}, author = {Friedrich, Tobias and Göbel, Andreas and Quinzan, Francesco and Wagner, Markus}, booktitle = {Parallel Problem Solving From Nature (PPSN)}, keywords = {andreasgoebel francescoquinzan markuswagner ppsn tobiasfriedrich year2018}, pages = {134-145}, title = {Heavy-tailed Mutation Operators in Single-Objective Combinatorial Optimization}, year = 2018 }

Kötzing, Timo; Krejca, Martin S. First-Hitting Times Under Additive DriftParallel Problem Solving From Nature (PPSN) 2018: 92–104
[ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
 
For the last ten years, almost every theoretical result concerning the expected run time of a randomized search heuristic used drift theory, making it the arguably most important tool in this domain. Its success is due to its ease of use and its powerful result: drift theory allows the user to derive bounds on the expected first-hitting time of a random process by bounding expected local changes of the process – the drift. This is usually far easier than bounding the expected first-hitting time directly. Due to the widespread use of drift theory, it is of utmost importance to have the best drift theorems possible. We improve the fundamental additive, multiplicative, and variable drift theorems by stating them in a form as general as possible and providing examples of why the restrictions we keep are still necessary. Our additive drift theorem for upper bounds only requires the process to be nonnegative, that is, we remove unnecessary restrictions like a finite, discrete, or bounded search space. As corollaries, the same is true for our upper bounds in the case of variable and multiplicative drift
@inproceedings{kotzingyear2018firsthitting, abstract = {For the last ten years, almost every theoretical result concerning the expected run time of a randomized search heuristic used drift theory, making it the arguably most important tool in this domain. Its success is due to its ease of use and its powerful result: drift theory allows the user to derive bounds on the expected first-hitting time of a random process by bounding expected local changes of the process – the drift. This is usually far easier than bounding the expected first-hitting time directly. Due to the widespread use of drift theory, it is of utmost importance to have the best drift theorems possible. We improve the fundamental additive, multiplicative, and variable drift theorems by stating them in a form as general as possible and providing examples of why the restrictions we keep are still necessary. Our additive drift theorem for upper bounds only requires the process to be nonnegative, that is, we remove unnecessary restrictions like a finite, discrete, or bounded search space. As corollaries, the same is true for our upper bounds in the case of variable and multiplicative drift}, author = {Kötzing, Timo and Krejca, Martin S.}, booktitle = {Parallel Problem Solving From Nature (PPSN)}, keywords = {martinskrejca ppsn timokoetzing year2018}, pages = {92-104}, title = {First-Hitting Times Under Additive Drift}, year = 2018 }

Kötzing, Timo; Krejca, Martin S. First-Hitting Times for Finite State SpacesParallel Problem Solving From Nature (PPSN) 2018: 79–91
[ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
 
One of the most important aspects of a randomized algorithm is bounding its expected run time on various problems. Formally speaking, this means bounding the expected first-hitting time of a random process. The two arguably most popular tools to do so are the fitness level method and drift theory. The fitness level method considers arbitrary transition probabilities but only allows the process to move toward the goal. On the other hand, drift theory allows the process to move into any direction as long as it moves closer to the goal in expectation; however, this tendency has to be monotone and, thus, the transition probabilities cannot be arbitrary. We provide a result that combines the benefit of these two approaches: our result gives a lower and an upper bound for the expected first-hitting time of a random process over \(\{0, \ldots ,n\}\) that is allowed to move forward and backward by 1 and can use arbitrary transition probabilities. In case that the transition probabilities are known, our bounds coincide and yield the exact value of the expected first-hitting time. Further, we also state the stationary distribution as well as the mixing time of a special case of our scenario.
@inproceedings{kotzing2018firsthitting, abstract = {One of the most important aspects of a randomized algorithm is bounding its expected run time on various problems. Formally speaking, this means bounding the expected first-hitting time of a random process. The two arguably most popular tools to do so are the fitness level method and drift theory. The fitness level method considers arbitrary transition probabilities but only allows the process to move toward the goal. On the other hand, drift theory allows the process to move into any direction as long as it moves closer to the goal in expectation; however, this tendency has to be monotone and, thus, the transition probabilities cannot be arbitrary. We provide a result that combines the benefit of these two approaches: our result gives a lower and an upper bound for the expected first-hitting time of a random process over \(\{0, \ldots ,n\}\) that is allowed to move forward and backward by 1 and can use arbitrary transition probabilities. In case that the transition probabilities are known, our bounds coincide and yield the exact value of the expected first-hitting time. Further, we also state the stationary distribution as well as the mixing time of a special case of our scenario.}, author = {Kötzing, Timo and Krejca, Martin S.}, booktitle = {Parallel Problem Solving From Nature (PPSN)}, keywords = {martinskrejca ppsn timokoetzing year2018}, pages = {79-91}, title = {First-Hitting Times for Finite State Spaces}, year = 2018 }

Kötzing, Timo; Lagodzinski, J. A. Gregor; Lengler, Johannes; Melnichenko, Anna Destructiveness of Lexicographic Parsimony Pressure and Alleviation by a Concatenation Crossover in Genetic ProgrammingParallel Problem Solving From Nature (PPSN) 2018: 42–54
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
For theoretical analyses there are two specifics distinguishing GP from many other areas of evolutionary computation. First, the variable size representations, in particular yielding a possible bloat (i.e. the growth of individuals with redundant parts). Second, the role and realization of crossover, which is particularly central in GP due to the tree-based representation. Whereas some theoretical work on GP has studied the effects of bloat, crossover had a surprisingly little share in this work. We analyze a simple crossover operator in combination with local search,where a preference for small solutions minimizes bloat (lexicographic parsimony pressure); the resulting algorithm is denoted ConcatenationCrossover GP. For this purpose three variants of the well-studied Majority test function with large plateaus are considered. We show that the Concatenation Crossover GP can efficiently optimize these test functions,while local search cannot be efficient for all three variants independent of employing bloat control.
@inproceedings{kotzing2018destructiveness, abstract = {For theoretical analyses there are two specifics distinguishing GP from many other areas of evolutionary computation. First, the variable size representations, in particular yielding a possible bloat (i.e. the growth of individuals with redundant parts). Second, the role and realization of crossover, which is particularly central in GP due to the tree-based representation. Whereas some theoretical work on GP has studied the effects of bloat, crossover had a surprisingly little share in this work. We analyze a simple crossover operator in combination with local search,where a preference for small solutions minimizes bloat (lexicographic parsimony pressure); the resulting algorithm is denoted ConcatenationCrossover GP. For this purpose three variants of the well-studied Majority test function with large plateaus are considered. We show that the Concatenation Crossover GP can efficiently optimize these test functions,while local search cannot be efficient for all three variants independent of employing bloat control.}, author = {Kötzing, Timo and Lagodzinski, J. A. Gregor and Lengler, Johannes and Melnichenko, Anna}, booktitle = {Parallel Problem Solving From Nature (PPSN)}, keywords = {annamelnichenko gregorlagodzinski johanneslengler ppsn timokoetzing year2018}, pages = {42-54}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Destructiveness of Lexicographic Parsimony Pressure and Alleviation by a Concatenation Crossover in Genetic Programming}, volume = 11102, year = 2018 }

2016 [ nach oben ]

Doerr, Benjamin; Doerr, Carola; Kötzing, Timo Provably Optimal Self-Adjusting Step Sizes for Multi-Valued Decision VariablesParallel 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)}, keywords = {PPSN benjamindoerr caroladoerr timokoetzing year2016}, pages = {782-791}, title = {Provably Optimal Self-Adjusting Step Sizes for Multi-Valued Decision Variables}, year = 2016 }

Gao, Wanru; Friedrich, Tobias; Neumann, Frank Fixed-Parameter Single Objective Search Heuristics for Minimum Vertex CoverParallel 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)}, keywords = {PPSN frankneumann tobiasfriedrich wanrugao year2016}, pages = {740-750}, title = {Fixed-Parameter Single Objective Search Heuristics for Minimum Vertex Cover}, year = 2016 }

Friedrich, Tobias; Kötzing, Timo; Krejca, Martin S.; Sutton, Andrew M. Graceful Scaling on Uniform versus Steep-Tailed NoiseParallel 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)}, keywords = {PPSN andrewmsutton martinskrejca timokoetzing tobiasfriedrich year2016}, pages = {761-770}, title = {Graceful Scaling on Uniform versus Steep-Tailed Noise}, year = 2016 }

Friedrich, Tobias; Kötzing, Timo; Sutton, Andrew M. On the Robustness of Evolving PopulationsParallel 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)}, keywords = {PPSN andrewmsutton timokoetzing tobiasfriedrich year2016}, pages = {771-781}, title = {On the Robustness of Evolving Populations}, year = 2016 }

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 AlgorithmsParallel 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)}, keywords = {PPSN andrewmsutton martinskrejca timokoetzing tobiasfriedrich}, pages = {890-900}, title = {Emergence of Diversity and its Benefits for Crossover in Genetic Algorithms}, year = 2016 }

2014 [ nach oben ]

Friedrich, Tobias; Neumann, Frank Maximizing Submodular Functions under Matroid Constraints by Multi-objective Evolutionary AlgorithmsParallel 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)}, keywords = {frankneumann imported ppsn tobiasfriedrich year2014}, 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 }

Bringmann, Karl; Friedrich, Tobias; Klitzke, Patrick Generic Postprocessing via Subset Selection for Hypervolume and Epsilon-IndicatorParallel 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)}, keywords = {imported ppsn tobiasfriedrich year2014}, 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 }

Sutton, Andrew M.; Neumann, Frank Runtime Analysis of Evolutionary Algorithms on Randomly Constructed High-Density Satisfiable 3-CNF FormulasParallel 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)}, keywords = {andrewmsutton frankneumann imported ppsn year2014}, 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 [ nach oben ]

Sutton, Andrew M.; Neumann, Frank A Parameterized Runtime Analysis of Simple Evolutionary Algorithms for Makespan SchedulingParallel 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)}, keywords = {andrewmsutton frankneumann imported ppsn year2012}, 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 [ nach oben ]

Bringmann, Karl; Friedrich, Tobias Tight Bounds for the Approximation Ratio of the Hypervolume IndicatorParallel 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)}, keywords = {PPSN imported tobiasfriedrich year2010}, 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 }

Doerr, Benjamin; Johannsen, Daniel; Kötzing, Timo; Neumann, Frank; Theile, Madeleine More Effective Crossover Operators for the All-Pairs Shortest Path ProblemParallel Problem Solving from Nature (PPSN) 2010: 184–193
[ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
 
The all-pairs shortest path problem is the first non-artificial problem for which it was shown that adding crossover can significantly speed up a mutation-only evolutionary algorithm. Recently, the analysis of this algorithm was refined and it was shown to have an expected optimization time (w.r.t. the number of fitness evaluations) of \(\Theta(n^3.25(\log n)^{0.25})\). In contrast to this simple algorithm, evolutionary algorithms used in practice usually employ refined recombination strategies in order to avoid the creation of infeasible offspring. We study extensions of the basic algorithm by two such concepts which are central in recombination, namely \(\emph{repair mechanisms}\) and \(\emph{parent selection}\). We show that repairing infeasible offspring leads to an improved expected optimization time of \(O(n^{3.2(\log n)^{0.2})\). As a second part of our study we prove that choosing parents that guarantee feasible offspring results in an even better optimization time of \(O(n^3 \log n)\). Both results show that already simple adjustments of the recombination operator can asymptotically improve the runtime of evolutionary algorithms.
@inproceedings{DBLP:conf/ppsn/DoerrJKNT10, abstract = {The all-pairs shortest path problem is the first non-artificial problem for which it was shown that adding crossover can significantly speed up a mutation-only evolutionary algorithm. Recently, the analysis of this algorithm was refined and it was shown to have an expected optimization time (w.r.t. the number of fitness evaluations) of \(\Theta(n^{3.25}(\log n)^{0.25})\). In contrast to this simple algorithm, evolutionary algorithms used in practice usually employ refined recombination strategies in order to avoid the creation of infeasible offspring. We study extensions of the basic algorithm by two such concepts which are central in recombination, namely \(\emph{repair mechanisms}\) and \(\emph{parent selection}\). We show that repairing infeasible offspring leads to an improved expected optimization time of \(O(n^{3.2}(\log n)^{0.2})\). As a second part of our study we prove that choosing parents that guarantee feasible offspring results in an even better optimization time of \(O(n^3 \log n)\). Both results show that already simple adjustments of the recombination operator can asymptotically improve the runtime of evolutionary algorithms.}, author = {Doerr, Benjamin and Johannsen, Daniel and Kötzing, Timo and Neumann, Frank and Theile, Madeleine}, booktitle = {Parallel Problem Solving from Nature (PPSN)}, keywords = {benjamindoerr danieljohannsen frankneumann imported madeleinetheile ppsn timokoetzing year2010}, pages = {184-193}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {More Effective Crossover Operators for the All-Pairs Shortest Path Problem}, volume = 6238, year = 2010 }

2008 [ nach oben ]

Friedrich, Tobias; Horoba, Christian; Neumann, Frank Runtime Analyses for Using Fairness in Evolutionary Multi-Objective OptimizationParallel 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. 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. 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)}, keywords = {christianhoroba frankneumann imported ppsn tobiasfriedrich year2008}, 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 }

Lunacek, Monte; Whitley, Darrell; Sutton, Andrew M. The Impact of Global Structure on SearchParallel 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)}, keywords = {andrewmsutton imported ppsn year2008}, pages = {498-507}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {The Impact of Global Structure on Search}, volume = 5199, year = 2008 }