[{"publication":"Algorithmica","type":"journal_article","abstract":[{"text":"We contribute to the theoretical understanding of randomized search heuristics for dynamic problems. We consider the classical vertex coloring problem on graphs and investigate the dynamic setting where edges are added to the current graph. We then analyze the expected time for randomized search heuristics to recompute high quality solutions. The (1+1) Evolutionary Algorithm and RLS operate in a setting where the number of colors is bounded and we are minimizing the number of conflicts. Iterated local search algorithms use an unbounded color palette and aim to use the smallest colors and, consequently, the smallest number of colors. We identify classes of bipartite graphs where reoptimization is as hard as or even harder than optimization from scratch, i.e., starting with a random initialization. Even adding a single edge can lead to hard symmetry problems. However, graph classes that are hard for one algorithm turn out to be easy for others. In most cases our bounds show that reoptimization is faster than optimizing from scratch. We further show that tailoring mutation operators to parts of the graph where changes have occurred can significantly reduce the expected reoptimization time. In most settings the expected reoptimization time for such tailored algorithms is linear in the number of added edges. However, tailored algorithms cannot prevent exponential times in settings where the original algorithm is inefficient.","lang":"eng"}],"status":"public","_id":"48854","department":[{"_id":"819"}],"user_id":"102979","keyword":["Dynamic optimization","Evolutionary algorithms","Running time analysis"],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0178-4617"]},"issue":"10","year":"2021","page":"3148–3179","intvolume":"        83","citation":{"short":"J. Bossek, F. Neumann, P. Peng, D. Sudholt, Algorithmica 83 (2021) 3148–3179.","mla":"Bossek, Jakob, et al. “Time Complexity Analysis of Randomized Search Heuristics for the Dynamic Graph Coloring Problem.” <i>Algorithmica</i>, vol. 83, no. 10, 2021, pp. 3148–3179, doi:<a href=\"https://doi.org/10.1007/s00453-021-00838-3\">10.1007/s00453-021-00838-3</a>.","bibtex":"@article{Bossek_Neumann_Peng_Sudholt_2021, title={Time Complexity Analysis of Randomized Search Heuristics for the Dynamic Graph Coloring Problem}, volume={83}, DOI={<a href=\"https://doi.org/10.1007/s00453-021-00838-3\">10.1007/s00453-021-00838-3</a>}, number={10}, journal={Algorithmica}, author={Bossek, Jakob and Neumann, Frank and Peng, Pan and Sudholt, Dirk}, year={2021}, pages={3148–3179} }","apa":"Bossek, J., Neumann, F., Peng, P., &#38; Sudholt, D. (2021). Time Complexity Analysis of Randomized Search Heuristics for the Dynamic Graph Coloring Problem. <i>Algorithmica</i>, <i>83</i>(10), 3148–3179. <a href=\"https://doi.org/10.1007/s00453-021-00838-3\">https://doi.org/10.1007/s00453-021-00838-3</a>","ieee":"J. Bossek, F. Neumann, P. Peng, and D. Sudholt, “Time Complexity Analysis of Randomized Search Heuristics for the Dynamic Graph Coloring Problem,” <i>Algorithmica</i>, vol. 83, no. 10, pp. 3148–3179, 2021, doi: <a href=\"https://doi.org/10.1007/s00453-021-00838-3\">10.1007/s00453-021-00838-3</a>.","chicago":"Bossek, Jakob, Frank Neumann, Pan Peng, and Dirk Sudholt. “Time Complexity Analysis of Randomized Search Heuristics for the Dynamic Graph Coloring Problem.” <i>Algorithmica</i> 83, no. 10 (2021): 3148–3179. <a href=\"https://doi.org/10.1007/s00453-021-00838-3\">https://doi.org/10.1007/s00453-021-00838-3</a>.","ama":"Bossek J, Neumann F, Peng P, Sudholt D. Time Complexity Analysis of Randomized Search Heuristics for the Dynamic Graph Coloring Problem. <i>Algorithmica</i>. 2021;83(10):3148–3179. doi:<a href=\"https://doi.org/10.1007/s00453-021-00838-3\">10.1007/s00453-021-00838-3</a>"},"date_updated":"2023-12-13T10:51:34Z","volume":83,"date_created":"2023-11-14T15:58:54Z","author":[{"first_name":"Jakob","last_name":"Bossek","orcid":"0000-0002-4121-4668","id":"102979","full_name":"Bossek, Jakob"},{"first_name":"Frank","full_name":"Neumann, Frank","last_name":"Neumann"},{"last_name":"Peng","full_name":"Peng, Pan","first_name":"Pan"},{"last_name":"Sudholt","full_name":"Sudholt, Dirk","first_name":"Dirk"}],"title":"Time Complexity Analysis of Randomized Search Heuristics for the Dynamic Graph Coloring Problem","doi":"10.1007/s00453-021-00838-3"},{"publication":"Proceedings of the Genetic and Evolutionary Computation Conference","type":"conference","status":"public","abstract":[{"text":"Dynamic optimization problems have gained significant attention in evolutionary computation as evolutionary algorithms (EAs) can easily adapt to changing environments. We show that EAs can solve the graph coloring problem for bipartite graphs more efficiently by using dynamic optimization. In our approach the graph instance is given incrementally such that the EA can reoptimize its coloring when a new edge introduces a conflict. We show that, when edges are inserted in a way that preserves graph connectivity, Randomized Local Search (RLS) efficiently finds a proper 2-coloring for all bipartite graphs. This includes graphs for which RLS and other EAs need exponential expected time in a static optimization scenario. We investigate different ways of building up the graph by popular graph traversals such as breadth-first-search and depth-first-search and analyse the resulting runtime behavior. We further show that offspring populations (e. g. a (1 + {$\\lambda$}) RLS) lead to an exponential speedup in {$\\lambda$}. Finally, an island model using 3 islands succeeds in an optimal time of {$\\Theta$}(m) on every m-edge bipartite graph, outperforming offspring populations. This is the first example where an island model guarantees a speedup that is not bounded in the number of islands.","lang":"eng"}],"department":[{"_id":"819"}],"series_title":"GECCO ’20","user_id":"102979","_id":"48847","language":[{"iso":"eng"}],"extern":"1","keyword":["dynamic optimization","evolutionary algorithms","running time analysis","theory"],"publication_identifier":{"isbn":["978-1-4503-7128-5"]},"publication_status":"published","page":"1277–1285","citation":{"ieee":"J. Bossek, F. Neumann, P. Peng, and D. Sudholt, “More Effective Randomized Search Heuristics for Graph Coloring through Dynamic Optimization,” in <i>Proceedings of the Genetic and Evolutionary Computation Conference</i>, 2020, pp. 1277–1285, doi: <a href=\"https://doi.org/10.1145/3377930.3390174\">10.1145/3377930.3390174</a>.","chicago":"Bossek, Jakob, Frank Neumann, Pan Peng, and Dirk Sudholt. “More Effective Randomized Search Heuristics for Graph Coloring through Dynamic Optimization.” In <i>Proceedings of the Genetic and Evolutionary Computation Conference</i>, 1277–1285. GECCO ’20. New York, NY, USA: Association for Computing Machinery, 2020. <a href=\"https://doi.org/10.1145/3377930.3390174\">https://doi.org/10.1145/3377930.3390174</a>.","ama":"Bossek J, Neumann F, Peng P, Sudholt D. More Effective Randomized Search Heuristics for Graph Coloring through Dynamic Optimization. In: <i>Proceedings of the Genetic and Evolutionary Computation Conference</i>. GECCO ’20. Association for Computing Machinery; 2020:1277–1285. doi:<a href=\"https://doi.org/10.1145/3377930.3390174\">10.1145/3377930.3390174</a>","apa":"Bossek, J., Neumann, F., Peng, P., &#38; Sudholt, D. (2020). More Effective Randomized Search Heuristics for Graph Coloring through Dynamic Optimization. <i>Proceedings of the Genetic and Evolutionary Computation Conference</i>, 1277–1285. <a href=\"https://doi.org/10.1145/3377930.3390174\">https://doi.org/10.1145/3377930.3390174</a>","bibtex":"@inproceedings{Bossek_Neumann_Peng_Sudholt_2020, place={New York, NY, USA}, series={GECCO ’20}, title={More Effective Randomized Search Heuristics for Graph Coloring through Dynamic Optimization}, DOI={<a href=\"https://doi.org/10.1145/3377930.3390174\">10.1145/3377930.3390174</a>}, booktitle={Proceedings of the Genetic and Evolutionary Computation Conference}, publisher={Association for Computing Machinery}, author={Bossek, Jakob and Neumann, Frank and Peng, Pan and Sudholt, Dirk}, year={2020}, pages={1277–1285}, collection={GECCO ’20} }","mla":"Bossek, Jakob, et al. “More Effective Randomized Search Heuristics for Graph Coloring through Dynamic Optimization.” <i>Proceedings of the Genetic and Evolutionary Computation Conference</i>, Association for Computing Machinery, 2020, pp. 1277–1285, doi:<a href=\"https://doi.org/10.1145/3377930.3390174\">10.1145/3377930.3390174</a>.","short":"J. Bossek, F. Neumann, P. Peng, D. Sudholt, in: Proceedings of the Genetic and Evolutionary Computation Conference, Association for Computing Machinery, New York, NY, USA, 2020, pp. 1277–1285."},"year":"2020","place":"New York, NY, USA","date_created":"2023-11-14T15:58:53Z","author":[{"last_name":"Bossek","orcid":"0000-0002-4121-4668","full_name":"Bossek, Jakob","id":"102979","first_name":"Jakob"},{"full_name":"Neumann, Frank","last_name":"Neumann","first_name":"Frank"},{"full_name":"Peng, Pan","last_name":"Peng","first_name":"Pan"},{"full_name":"Sudholt, Dirk","last_name":"Sudholt","first_name":"Dirk"}],"date_updated":"2023-12-13T10:43:41Z","publisher":"Association for Computing Machinery","doi":"10.1145/3377930.3390174","title":"More Effective Randomized Search Heuristics for Graph Coloring through Dynamic Optimization"},{"status":"public","type":"conference","extern":"1","user_id":"102979","series_title":"GECCO ’20","department":[{"_id":"819"}],"_id":"48851","citation":{"apa":"Bossek, J., Casel, K., Kerschke, P., &#38; Neumann, F. (2020). The Node Weight Dependent Traveling Salesperson Problem: Approximation Algorithms and Randomized Search Heuristics. <i>Proceedings of the Genetic and Evolutionary Computation Conference</i>, 1286–1294. <a href=\"https://doi.org/10.1145/3377930.3390243\">https://doi.org/10.1145/3377930.3390243</a>","mla":"Bossek, Jakob, et al. “The Node Weight Dependent Traveling Salesperson Problem: Approximation Algorithms and Randomized Search Heuristics.” <i>Proceedings of the Genetic and Evolutionary Computation Conference</i>, Association for Computing Machinery, 2020, pp. 1286–1294, doi:<a href=\"https://doi.org/10.1145/3377930.3390243\">10.1145/3377930.3390243</a>.","bibtex":"@inproceedings{Bossek_Casel_Kerschke_Neumann_2020, place={New York, NY, USA}, series={GECCO ’20}, title={The Node Weight Dependent Traveling Salesperson Problem: Approximation Algorithms and Randomized Search Heuristics}, DOI={<a href=\"https://doi.org/10.1145/3377930.3390243\">10.1145/3377930.3390243</a>}, booktitle={Proceedings of the Genetic and Evolutionary Computation Conference}, publisher={Association for Computing Machinery}, author={Bossek, Jakob and Casel, Katrin and Kerschke, Pascal and Neumann, Frank}, year={2020}, pages={1286–1294}, collection={GECCO ’20} }","short":"J. Bossek, K. Casel, P. Kerschke, F. Neumann, in: Proceedings of the Genetic and Evolutionary Computation Conference, Association for Computing Machinery, New York, NY, USA, 2020, pp. 1286–1294.","ieee":"J. Bossek, K. Casel, P. Kerschke, and F. Neumann, “The Node Weight Dependent Traveling Salesperson Problem: Approximation Algorithms and Randomized Search Heuristics,” in <i>Proceedings of the Genetic and Evolutionary Computation Conference</i>, 2020, pp. 1286–1294, doi: <a href=\"https://doi.org/10.1145/3377930.3390243\">10.1145/3377930.3390243</a>.","chicago":"Bossek, Jakob, Katrin Casel, Pascal Kerschke, and Frank Neumann. “The Node Weight Dependent Traveling Salesperson Problem: Approximation Algorithms and Randomized Search Heuristics.” In <i>Proceedings of the Genetic and Evolutionary Computation Conference</i>, 1286–1294. GECCO ’20. New York, NY, USA: Association for Computing Machinery, 2020. <a href=\"https://doi.org/10.1145/3377930.3390243\">https://doi.org/10.1145/3377930.3390243</a>.","ama":"Bossek J, Casel K, Kerschke P, Neumann F. The Node Weight Dependent Traveling Salesperson Problem: Approximation Algorithms and Randomized Search Heuristics. In: <i>Proceedings of the Genetic and Evolutionary Computation Conference</i>. GECCO ’20. Association for Computing Machinery; 2020:1286–1294. doi:<a href=\"https://doi.org/10.1145/3377930.3390243\">10.1145/3377930.3390243</a>"},"page":"1286–1294","place":"New York, NY, USA","publication_status":"published","publication_identifier":{"isbn":["978-1-4503-7128-5"]},"doi":"10.1145/3377930.3390243","author":[{"full_name":"Bossek, Jakob","id":"102979","last_name":"Bossek","orcid":"0000-0002-4121-4668","first_name":"Jakob"},{"full_name":"Casel, Katrin","last_name":"Casel","first_name":"Katrin"},{"first_name":"Pascal","full_name":"Kerschke, Pascal","last_name":"Kerschke"},{"full_name":"Neumann, Frank","last_name":"Neumann","first_name":"Frank"}],"date_updated":"2023-12-13T10:43:33Z","abstract":[{"text":"Several important optimization problems in the area of vehicle routing can be seen as variants of the classical Traveling Salesperson Problem (TSP). In the area of evolutionary computation, the Traveling Thief Problem (TTP) has gained increasing interest over the last 5 years. In this paper, we investigate the effect of weights on such problems, in the sense that the cost of traveling increases with respect to the weights of nodes already visited during a tour. This provides abstractions of important TSP variants such as the Traveling Thief Problem and time dependent TSP variants, and allows to study precisely the increase in difficulty caused by weight dependence. We provide a 3.59-approximation for this weight dependent version of TSP with metric distances and bounded positive weights. Furthermore, we conduct experimental investigations for simple randomized local search with classical mutation operators and two variants of the state-of-the-art evolutionary algorithm EAX adapted to the weighted TSP. Our results show the impact of the node weights on the position of the nodes in the resulting tour.","lang":"eng"}],"publication":"Proceedings of the Genetic and Evolutionary Computation Conference","language":[{"iso":"eng"}],"keyword":["dynamic optimization","evolutionary algorithms","running time analysis","theory"],"year":"2020","title":"The Node Weight Dependent Traveling Salesperson Problem: Approximation Algorithms and Randomized Search Heuristics","date_created":"2023-11-14T15:58:53Z","publisher":"Association for Computing Machinery"},{"keyword":["dynamic optimization","evolutionary algorithms","running time analysis","theory"],"language":[{"iso":"eng"}],"abstract":[{"text":"We contribute to the theoretical understanding of randomized search heuristics for dynamic problems. We consider the classical graph coloring problem and investigate the dynamic setting where edges are added to the current graph. We then analyze the expected time for randomized search heuristics to recompute high quality solutions. This includes the (1+1) EA and RLS in a setting where the number of colors is bounded and we are minimizing the number of conflicts as well as iterated local search algorithms that use an unbounded color palette and aim to use the smallest colors and - as a consequence - the smallest number of colors. We identify classes of bipartite graphs where reoptimization is as hard as or even harder than optimization from scratch, i. e. starting with a random initialization. Even adding a single edge can lead to hard symmetry problems. However, graph classes that are hard for one algorithm turn out to be easy for others. In most cases our bounds show that reoptimization is faster than optimizing from scratch. Furthermore, we show how to speed up computations by using problem specific operators concentrating on parts of the graph where changes have occurred.","lang":"eng"}],"publication":"Proceedings of the Genetic and Evolutionary Computation Conference","title":"Runtime Analysis of Randomized Search Heuristics for Dynamic Graph Coloring","publisher":"Association for Computing Machinery","date_created":"2023-11-14T15:58:52Z","year":"2019","extern":"1","_id":"48843","department":[{"_id":"819"}],"user_id":"102979","series_title":"GECCO ’19","status":"public","type":"conference","doi":"10.1145/3321707.3321792","date_updated":"2023-12-13T10:42:37Z","author":[{"id":"102979","full_name":"Bossek, Jakob","last_name":"Bossek","orcid":"0000-0002-4121-4668","first_name":"Jakob"},{"first_name":"Frank","last_name":"Neumann","full_name":"Neumann, Frank"},{"first_name":"Pan","full_name":"Peng, Pan","last_name":"Peng"},{"full_name":"Sudholt, Dirk","last_name":"Sudholt","first_name":"Dirk"}],"place":"New York, NY, USA","page":"1443–1451","citation":{"ama":"Bossek J, Neumann F, Peng P, Sudholt D. Runtime Analysis of Randomized Search Heuristics for Dynamic Graph Coloring. In: <i>Proceedings of the Genetic and Evolutionary Computation Conference</i>. GECCO ’19. Association for Computing Machinery; 2019:1443–1451. doi:<a href=\"https://doi.org/10.1145/3321707.3321792\">10.1145/3321707.3321792</a>","chicago":"Bossek, Jakob, Frank Neumann, Pan Peng, and Dirk Sudholt. “Runtime Analysis of Randomized Search Heuristics for Dynamic Graph Coloring.” In <i>Proceedings of the Genetic and Evolutionary Computation Conference</i>, 1443–1451. GECCO ’19. New York, NY, USA: Association for Computing Machinery, 2019. <a href=\"https://doi.org/10.1145/3321707.3321792\">https://doi.org/10.1145/3321707.3321792</a>.","ieee":"J. Bossek, F. Neumann, P. Peng, and D. Sudholt, “Runtime Analysis of Randomized Search Heuristics for Dynamic Graph Coloring,” in <i>Proceedings of the Genetic and Evolutionary Computation Conference</i>, 2019, pp. 1443–1451, doi: <a href=\"https://doi.org/10.1145/3321707.3321792\">10.1145/3321707.3321792</a>.","apa":"Bossek, J., Neumann, F., Peng, P., &#38; Sudholt, D. (2019). Runtime Analysis of Randomized Search Heuristics for Dynamic Graph Coloring. <i>Proceedings of the Genetic and Evolutionary Computation Conference</i>, 1443–1451. <a href=\"https://doi.org/10.1145/3321707.3321792\">https://doi.org/10.1145/3321707.3321792</a>","mla":"Bossek, Jakob, et al. “Runtime Analysis of Randomized Search Heuristics for Dynamic Graph Coloring.” <i>Proceedings of the Genetic and Evolutionary Computation Conference</i>, Association for Computing Machinery, 2019, pp. 1443–1451, doi:<a href=\"https://doi.org/10.1145/3321707.3321792\">10.1145/3321707.3321792</a>.","bibtex":"@inproceedings{Bossek_Neumann_Peng_Sudholt_2019, place={New York, NY, USA}, series={GECCO ’19}, title={Runtime Analysis of Randomized Search Heuristics for Dynamic Graph Coloring}, DOI={<a href=\"https://doi.org/10.1145/3321707.3321792\">10.1145/3321707.3321792</a>}, booktitle={Proceedings of the Genetic and Evolutionary Computation Conference}, publisher={Association for Computing Machinery}, author={Bossek, Jakob and Neumann, Frank and Peng, Pan and Sudholt, Dirk}, year={2019}, pages={1443–1451}, collection={GECCO ’19} }","short":"J. Bossek, F. Neumann, P. Peng, D. Sudholt, in: Proceedings of the Genetic and Evolutionary Computation Conference, Association for Computing Machinery, New York, NY, USA, 2019, pp. 1443–1451."},"publication_identifier":{"isbn":["978-1-4503-6111-8"]},"publication_status":"published"}]