Evolving L-systems as an intelligent design approach to find classes of difficult-to-solve traveling salesman problem instances

Authors:
Farhan Ahammed;Pablo Moscato
Affiliations:
NICTA Australia, Eveleigh, NSW, Australia and School of Information Technologies, The University of Sydney, NSW, Australia;School of Electrical Engineering and Computer Science, Centre for Bioinformatics, Biomarker Discovery and Information-based Medicine, The University of Newcastle, NSW, Australia
Venue:
EvoApplications'11 Proceedings of the 2011 international conference on Applications of evolutionary computation - Volume Part I
Year:
2011

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Abstract

The technique of computationally analysing a program by searching for instances which causes the program to run in its worst-case time is examined. Concorde [2], the state-of-the-art Traveling Salesperson Problem (TSP) solver, is the program used to test our approach. We seed our evolutionary approach with a fractal instance of the TSP, defined by a Lindenmayer system at a fixed order. The evolutionary algorithm produced modifications to the L-System rules such that the instances of the modified L-System become increasingly much harder for Concorde to solve to optimality. In some cases, while still having the same size, the evolved instances required a computation time which was 30,000 times greater than what was needed to solve the original instance that seeded the search. The success of this case study shows the potential of Evolutionary Search to provide new test-case scenarios for algorithms and their software implementations.