Evolutionary Divide and Conquer for the Set-Covering Problem

Genetic Algorithms provide a weak search method that scales rather badly when used in their traditional form. On the other hand, the set covering problem, when used to solve real-world problems, presents an enormous search space for genetic algorithms. A method is presented, by which genetic material is maintained for a long time within the population to allow a greater portion of the search space to be covered in the hope of producing greater quality solutions. The problem is broken down into smaller subproblems for which a population of solutions is evolved. The quality of those solutions is then assessed depending on how well they t in with solutions to other subproblems. We nd that the method has merit and potential, and we discuss its sensitivity to various parameters. Acknowledgements First of all, I would like to thank my supervisor, Dave Corne, for his availability, his friendliness, his support, and his calmness in the most desperate moments, and for his full con dence in me. He has always been a source of reassurance and encouragement. I would also like to thank Luisa, for showing in nite patience and the will to always listen to me in the most troublesome moments of this year|who can ask anybody for more? Further I want to express my gratitude to my parents, my brother, Jos e Miguel, for his proofreading, and especially my sister Carmen. They alone understand how much help and support they have shown to me, and how important my \weekend escapes" were to succeeding in this work. I would also like to thank Paul C. H. Chu, who kindly agreed to provide me with the results of the problems of the OR-Library, reported in [Beasley & Chu 95]. My gratitude also to the Student Awards Agency for Scotland, which partially supported my studies here at the University of Edinburgh through the grant D7575254/D32. Thanks also to John, who bore with my insistent questions on the correct usage of the English Language. With out your help, this would certainly be a nightmare to read. Last (but not least) I would like to thank Bety, Dae Gyu, Laura, Margarita, Olga, Roman, and especially Carlos, Delmi and Alejandro|you sure know what friends are. Rest assured I will never forget you. i Table of