Authors:
Tianyu Liang
1
;
Zhize Wu
1
;
Matthias Thürer
2
;
Markus Wagner
3
and
Thomas Weise
1
Affiliations:
1
Institute of Applied Optimization, School of Artificial Intelligence and Big Data, Hefei University, Jinxiu Dadao 99, Hefei, 230601, Anhui, China
;
2
Professur Fabrikplanung und Intralogistik, TU Chemnitz, Str. der Nationen 62, 09111 Chemnitz, Sachsen, Germany
;
3
Department of Data Science and AI, Faculty of Information Technology, Monash University, Wellington Road, Clayton, Victoria 3800, Australia
Keyword(s):
Traveling Salesperson Problem, Instance Generation, Frequency Fitness Assignment, Local Optima.
Abstract:
The Traveling Salesperson Problem (TSP) is one of the most well-known NP-hard optimization tasks. A randomized local search (RLS) is not a good approach for solving TSPs, as it quickly gets stuck at local optima. FRLS, the same algorithm with Frequency Fitness Assignment plugged in, has been shown to be able to solve many more TSP instances to optimality. However, it was also assumed that its performance will decline if an instance has a large number M of different possible objective values. How can we explore these more or less obvious algorithm properties in a controlled fashion, if determining the number #L of local optima or the size BL of their joint basins of attraction as well as the feature M are NP-hard problems themselves? By creating TSP instances with a small number of cities for which we can actually know these features! We develop a deterministic construction method for creating TSP instances with rising numbers M and a sampling based approach for the other features. We
determine all the instance features exactly and can clearly confirm the obvious (in the case of RLS) or previously suspected (in the case of FRLS) properties of the algorithms. Furthermore, we show that even with small-scale instances, we can make interesting new findings, such as that local optima seemingly have little impact on the performance of FRLS.
(More)