# A EVOLUTIONARY APPROACH TO SOLVE SET COVERING

### Broderick Crawford, Carolina Lagos, Carlos Castro, Fernando Paredes

#### 2007

#### Abstract

In this paper we solve the classical Set Covering Problem comparing two evolutive techniques: Genetic Algorithms and Cultural Algorithms. We solve this problem with a Cultural Evolutionary Architecture maintaining knowledge of Diversity and Fitness learned over each generation during the search process and we compare it with a Genetic Algorithm using the same crossover and mutation mechanisms. Our results indicate that the approach is able to produce very competitive results in compare with other Metaheuristics and Approximation Algorithms.

#### References

- Beasley, J. E. (1990). Or-library:distributing test problem by electronic mail. Journal of Operational Research Society, 41(11):1069-1072. Available at http://people.brunel.ac.uk/ mastjjb/jeb/info.html.
- Beasley, J. E. and Chu, P. C. (1996). A genetic algorithm for the set covering problem. European Journal of Operational Research, 94(2):392-404.
- Chu, P. C. and Beasley, J. E. (1998). Constraint handling in genetic algorithms: The set partitioning problem. Journal of Heuristics, 4(4):323-357.
- Coello, C. A. and Landa, R. (2002). Constrained Optimization Using an Evolutionary Programming-Based Cultural Algorithm. In Parmee, I., editor, Proceedings of the Fifth International Conference on Adaptive Computing Design and Manufacture (ACDM 2002), volume 5, pages 317-328, University of Exeter, Devon, UK. Springer-Verlag.
- Crawford, B. and Castro, C. (2006). Integrating lookahead and post processing procedures with aco for solving set partitioning and covering problems. In ICAISC, pages 1082-1090.
- Feo, T. and Resende, M. (1989). A probabilistic heuristic for a computationally difficult set covering problem. Operations Research Letters, 8:67-71.
- Gomes, F. C., Meneses, C. N., Pardalos, P. M., and Viana, G. V. R. (2006). Experimental analysis of approximation algorithms for the vertex cover and set covering problems. Comput. Oper. Res., 33(12):3520-3534.
- Landa, R. and Coello, C. A. (2005a). Optimization with constraints using a cultured differential evolution approach. In GECCO 7805: Proceedings of the 2005 conference on Genetic and evolutionary computation, pages 27-34, New York, NY, USA. ACM Press.
- Landa, R. and Coello, C. A. (2005b). Use of domain information to improve the performance of an evolutionary algorithm. In GECCO 7805: Proceedings of the 2005 workshops on Genetic and evolutionary computation, pages 362-365, New York, NY, USA. ACM Press.
- Lozano, M., Herrera, F., and Cano, J. R. (2003). Replacement strategies to preserve useful diversity in steadystate genetic algorithms. In Proceedings of the 8th Online World Conference on Soft Computing in Industrial Applications.
- Peng, B. (2005). Knowledge and population swarms in cultural algorithms for dynamic environments. PhD thesis, Detroit, MI, USA. Adviser-Robert G. Reynolds.
- Reynolds, R. (1994). An introduction to cultural algorithms. In Third Annual Conference on Evolutionary Programming, pages 131-139.
- Reynolds, R. G. (1999). Cultural algorithms: theory and applications. In New ideas in optimization, pages 367- 378, Maidenhead, UK, England. McGraw-Hill Ltd., UK.
- Reynolds, R. G. and Peng, B. (2004). Cultural algorithms: Modeling of how cultures learn to solve problems. In ICTAI, pages 66-172.

#### Paper Citation

#### in Harvard Style

Crawford B., Lagos C., Castro C. and Paredes F. (2007). **A EVOLUTIONARY APPROACH TO SOLVE SET COVERING** . In *Proceedings of the Ninth International Conference on Enterprise Information Systems - Volume 2: ICEIS,* ISBN 978-972-8865-89-4, pages 356-360. DOI: 10.5220/0002406703560360

#### in Bibtex Style

@conference{iceis07,

author={Broderick Crawford and Carolina Lagos and Carlos Castro and Fernando Paredes},

title={A EVOLUTIONARY APPROACH TO SOLVE SET COVERING},

booktitle={Proceedings of the Ninth International Conference on Enterprise Information Systems - Volume 2: ICEIS,},

year={2007},

pages={356-360},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002406703560360},

isbn={978-972-8865-89-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Ninth International Conference on Enterprise Information Systems - Volume 2: ICEIS,

TI - A EVOLUTIONARY APPROACH TO SOLVE SET COVERING

SN - 978-972-8865-89-4

AU - Crawford B.

AU - Lagos C.

AU - Castro C.

AU - Paredes F.

PY - 2007

SP - 356

EP - 360

DO - 10.5220/0002406703560360