---
_id: '48854'
abstract:
- lang: eng
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.
author:
- first_name: Jakob
full_name: Bossek, Jakob
id: '102979'
last_name: Bossek
orcid: 0000-0002-4121-4668
- first_name: Frank
full_name: Neumann, Frank
last_name: Neumann
- first_name: Pan
full_name: Peng, Pan
last_name: Peng
- first_name: Dirk
full_name: Sudholt, Dirk
last_name: Sudholt
citation:
ama: Bossek J, Neumann F, Peng P, Sudholt D. Time Complexity Analysis of Randomized
Search Heuristics for the Dynamic Graph Coloring Problem. Algorithmica.
2021;83(10):3148–3179. doi:10.1007/s00453-021-00838-3
apa: Bossek, J., Neumann, F., Peng, P., & Sudholt, D. (2021). Time Complexity
Analysis of Randomized Search Heuristics for the Dynamic Graph Coloring Problem.
Algorithmica, 83(10), 3148–3179. https://doi.org/10.1007/s00453-021-00838-3
bibtex: '@article{Bossek_Neumann_Peng_Sudholt_2021, title={Time Complexity Analysis
of Randomized Search Heuristics for the Dynamic Graph Coloring Problem}, volume={83},
DOI={10.1007/s00453-021-00838-3},
number={10}, journal={Algorithmica}, author={Bossek, Jakob and Neumann, Frank
and Peng, Pan and Sudholt, Dirk}, year={2021}, pages={3148–3179} }'
chicago: 'Bossek, Jakob, Frank Neumann, Pan Peng, and Dirk Sudholt. “Time Complexity
Analysis of Randomized Search Heuristics for the Dynamic Graph Coloring Problem.”
Algorithmica 83, no. 10 (2021): 3148–3179. https://doi.org/10.1007/s00453-021-00838-3.'
ieee: 'J. Bossek, F. Neumann, P. Peng, and D. Sudholt, “Time Complexity Analysis
of Randomized Search Heuristics for the Dynamic Graph Coloring Problem,” Algorithmica,
vol. 83, no. 10, pp. 3148–3179, 2021, doi: 10.1007/s00453-021-00838-3.'
mla: Bossek, Jakob, et al. “Time Complexity Analysis of Randomized Search Heuristics
for the Dynamic Graph Coloring Problem.” Algorithmica, vol. 83, no. 10,
2021, pp. 3148–3179, doi:10.1007/s00453-021-00838-3.
short: J. Bossek, F. Neumann, P. Peng, D. Sudholt, Algorithmica 83 (2021) 3148–3179.
date_created: 2023-11-14T15:58:54Z
date_updated: 2023-12-13T10:51:34Z
department:
- _id: '819'
doi: 10.1007/s00453-021-00838-3
intvolume: ' 83'
issue: '10'
keyword:
- Dynamic optimization
- Evolutionary algorithms
- Running time analysis
language:
- iso: eng
page: 3148–3179
publication: Algorithmica
publication_identifier:
issn:
- 0178-4617
status: public
title: Time Complexity Analysis of Randomized Search Heuristics for the Dynamic Graph
Coloring Problem
type: journal_article
user_id: '102979'
volume: 83
year: '2021'
...
---
_id: '48847'
abstract:
- lang: eng
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.
author:
- first_name: Jakob
full_name: Bossek, Jakob
id: '102979'
last_name: Bossek
orcid: 0000-0002-4121-4668
- first_name: Frank
full_name: Neumann, Frank
last_name: Neumann
- first_name: Pan
full_name: Peng, Pan
last_name: Peng
- first_name: Dirk
full_name: Sudholt, Dirk
last_name: Sudholt
citation:
ama: 'Bossek J, Neumann F, Peng P, Sudholt D. More Effective Randomized Search Heuristics
for Graph Coloring through Dynamic Optimization. In: Proceedings of the Genetic
and Evolutionary Computation Conference. GECCO ’20. Association for Computing
Machinery; 2020:1277–1285. doi:10.1145/3377930.3390174'
apa: Bossek, J., Neumann, F., Peng, P., & Sudholt, D. (2020). More Effective
Randomized Search Heuristics for Graph Coloring through Dynamic Optimization.
Proceedings of the Genetic and Evolutionary Computation Conference, 1277–1285.
https://doi.org/10.1145/3377930.3390174
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={10.1145/3377930.3390174},
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} }'
chicago: 'Bossek, Jakob, Frank Neumann, Pan Peng, and Dirk Sudholt. “More Effective
Randomized Search Heuristics for Graph Coloring through Dynamic Optimization.”
In Proceedings of the Genetic and Evolutionary Computation Conference,
1277–1285. GECCO ’20. New York, NY, USA: Association for Computing Machinery,
2020. https://doi.org/10.1145/3377930.3390174.'
ieee: 'J. Bossek, F. Neumann, P. Peng, and D. Sudholt, “More Effective Randomized
Search Heuristics for Graph Coloring through Dynamic Optimization,” in Proceedings
of the Genetic and Evolutionary Computation Conference, 2020, pp. 1277–1285,
doi: 10.1145/3377930.3390174.'
mla: Bossek, Jakob, et al. “More Effective Randomized Search Heuristics for Graph
Coloring through Dynamic Optimization.” Proceedings of the Genetic and Evolutionary
Computation Conference, Association for Computing Machinery, 2020, pp. 1277–1285,
doi:10.1145/3377930.3390174.
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.'
date_created: 2023-11-14T15:58:53Z
date_updated: 2023-12-13T10:43:41Z
department:
- _id: '819'
doi: 10.1145/3377930.3390174
extern: '1'
keyword:
- dynamic optimization
- evolutionary algorithms
- running time analysis
- theory
language:
- iso: eng
page: 1277–1285
place: New York, NY, USA
publication: Proceedings of the Genetic and Evolutionary Computation Conference
publication_identifier:
isbn:
- 978-1-4503-7128-5
publication_status: published
publisher: Association for Computing Machinery
series_title: GECCO ’20
status: public
title: More Effective Randomized Search Heuristics for Graph Coloring through Dynamic
Optimization
type: conference
user_id: '102979'
year: '2020'
...
---
_id: '48851'
abstract:
- lang: eng
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.
author:
- first_name: Jakob
full_name: Bossek, Jakob
id: '102979'
last_name: Bossek
orcid: 0000-0002-4121-4668
- first_name: Katrin
full_name: Casel, Katrin
last_name: Casel
- first_name: Pascal
full_name: Kerschke, Pascal
last_name: Kerschke
- first_name: Frank
full_name: Neumann, Frank
last_name: Neumann
citation:
ama: 'Bossek J, Casel K, Kerschke P, Neumann F. The Node Weight Dependent Traveling
Salesperson Problem: Approximation Algorithms and Randomized Search Heuristics.
In: Proceedings of the Genetic and Evolutionary Computation Conference.
GECCO ’20. Association for Computing Machinery; 2020:1286–1294. doi:10.1145/3377930.3390243'
apa: 'Bossek, J., Casel, K., Kerschke, P., & Neumann, F. (2020). The Node Weight
Dependent Traveling Salesperson Problem: Approximation Algorithms and Randomized
Search Heuristics. Proceedings of the Genetic and Evolutionary Computation
Conference, 1286–1294. https://doi.org/10.1145/3377930.3390243'
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={10.1145/3377930.3390243},
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} }'
chicago: 'Bossek, Jakob, Katrin Casel, Pascal Kerschke, and Frank Neumann. “The
Node Weight Dependent Traveling Salesperson Problem: Approximation Algorithms
and Randomized Search Heuristics.” In Proceedings of the Genetic and Evolutionary
Computation Conference, 1286–1294. GECCO ’20. New York, NY, USA: Association
for Computing Machinery, 2020. https://doi.org/10.1145/3377930.3390243.'
ieee: 'J. Bossek, K. Casel, P. Kerschke, and F. Neumann, “The Node Weight Dependent
Traveling Salesperson Problem: Approximation Algorithms and Randomized Search
Heuristics,” in Proceedings of the Genetic and Evolutionary Computation Conference,
2020, pp. 1286–1294, doi: 10.1145/3377930.3390243.'
mla: 'Bossek, Jakob, et al. “The Node Weight Dependent Traveling Salesperson Problem:
Approximation Algorithms and Randomized Search Heuristics.” Proceedings of
the Genetic and Evolutionary Computation Conference, Association for Computing
Machinery, 2020, pp. 1286–1294, doi:10.1145/3377930.3390243.'
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.'
date_created: 2023-11-14T15:58:53Z
date_updated: 2023-12-13T10:43:33Z
department:
- _id: '819'
doi: 10.1145/3377930.3390243
extern: '1'
keyword:
- dynamic optimization
- evolutionary algorithms
- running time analysis
- theory
language:
- iso: eng
page: 1286–1294
place: New York, NY, USA
publication: Proceedings of the Genetic and Evolutionary Computation Conference
publication_identifier:
isbn:
- 978-1-4503-7128-5
publication_status: published
publisher: Association for Computing Machinery
series_title: GECCO ’20
status: public
title: 'The Node Weight Dependent Traveling Salesperson Problem: Approximation Algorithms
and Randomized Search Heuristics'
type: conference
user_id: '102979'
year: '2020'
...
---
_id: '48843'
abstract:
- lang: eng
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.
author:
- first_name: Jakob
full_name: Bossek, Jakob
id: '102979'
last_name: Bossek
orcid: 0000-0002-4121-4668
- first_name: Frank
full_name: Neumann, Frank
last_name: Neumann
- first_name: Pan
full_name: Peng, Pan
last_name: Peng
- first_name: Dirk
full_name: Sudholt, Dirk
last_name: Sudholt
citation:
ama: 'Bossek J, Neumann F, Peng P, Sudholt D. Runtime Analysis of Randomized Search
Heuristics for Dynamic Graph Coloring. In: Proceedings of the Genetic and Evolutionary
Computation Conference. GECCO ’19. Association for Computing Machinery; 2019:1443–1451.
doi:10.1145/3321707.3321792'
apa: Bossek, J., Neumann, F., Peng, P., & Sudholt, D. (2019). Runtime Analysis
of Randomized Search Heuristics for Dynamic Graph Coloring. Proceedings of
the Genetic and Evolutionary Computation Conference, 1443–1451. https://doi.org/10.1145/3321707.3321792
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={10.1145/3321707.3321792},
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} }'
chicago: 'Bossek, Jakob, Frank Neumann, Pan Peng, and Dirk Sudholt. “Runtime Analysis
of Randomized Search Heuristics for Dynamic Graph Coloring.” In Proceedings
of the Genetic and Evolutionary Computation Conference, 1443–1451. GECCO ’19.
New York, NY, USA: Association for Computing Machinery, 2019. https://doi.org/10.1145/3321707.3321792.'
ieee: 'J. Bossek, F. Neumann, P. Peng, and D. Sudholt, “Runtime Analysis of Randomized
Search Heuristics for Dynamic Graph Coloring,” in Proceedings of the Genetic
and Evolutionary Computation Conference, 2019, pp. 1443–1451, doi: 10.1145/3321707.3321792.'
mla: Bossek, Jakob, et al. “Runtime Analysis of Randomized Search Heuristics for
Dynamic Graph Coloring.” Proceedings of the Genetic and Evolutionary Computation
Conference, Association for Computing Machinery, 2019, pp. 1443–1451, doi:10.1145/3321707.3321792.
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.'
date_created: 2023-11-14T15:58:52Z
date_updated: 2023-12-13T10:42:37Z
department:
- _id: '819'
doi: 10.1145/3321707.3321792
extern: '1'
keyword:
- dynamic optimization
- evolutionary algorithms
- running time analysis
- theory
language:
- iso: eng
page: 1443–1451
place: New York, NY, USA
publication: Proceedings of the Genetic and Evolutionary Computation Conference
publication_identifier:
isbn:
- 978-1-4503-6111-8
publication_status: published
publisher: Association for Computing Machinery
series_title: GECCO ’19
status: public
title: Runtime Analysis of Randomized Search Heuristics for Dynamic Graph Coloring
type: conference
user_id: '102979'
year: '2019'
...