Abstract
We perform a statistical analysis of the structure of the search space of some planar, euclidian instances of the traveling salesman problem. We want to depict this structure from the point of view of iterated local search algorithms. The objective is two-fold: understanding the experimentally known good performance of metaheuristics on the TSP and other combinatorial optimization problems; designing new techniques to search the space more efficiently. This work actually led us to design a hybrid genetic algorithm that competes rather well with other local search heuristics for the TSP, notably Jünger et al.’s version of ILK. This work also opens promising horizons to the study of other combinatorial optimization problems such as the quadratic assignment problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E. Aarts, J.K. Lenstra (eds), Local Search in Combinatorial Optimization, Wiley, 1997
K.D. Boese, Models For Iterative Global Optimization, PhD Dissertation, UCLA, USA, 1996
K.D. Boese, A.B. Kahng, S. Muddu, A New Adaptive Multi-Start Technique For Combinatoiral Global Optimizations, Operations Research Letters, 16, 101–113, 1994
G.A. Croes, A Method For Solving The Traveling Salesman Problems, Operations Research, 6, 791–812, 1958
M. Dorigo, L. Gambardella, Ant Colony System: A Cooperative learning approach to the traveling salesman problem, Evolutionary Computation, 1(1), 1997
J. Frank, P. Cheeseman, J. Stutz, When Gravity Fails: Local Search Topology, Journal Of Artificial Intelligence Research, 7, 249–281, 1997
M.R. Garey, D.S. Johnson, Computers And Intractability: A Guide To The Theory Of NP-Completeness, Freeman, 1979
F. Glover, Tabu Search: part I, ORSA Journal on Computing, 1, 190–206, 1989
F. Glover, Tabu Search: part II, ORSA Journal on Computing, 2, 4–32, 1990
D. Goldberg, Genetic algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, 1989
L.K. Grover, Local Search And The Local Structure Of NP-Complete Problems, Operations Research Letters, 12, 235–243, 1992
A. Hertz, B. Jaumard, M. Poggi de Aragão, Local optima topology for the k-coloring problem, Discrete Applied Mathematics, 49, 257–280, 1994
W. Hordijk, A Measure Of Landscapes, Evolutionary Computation, 4(4), 1996
D.S. Johnson, The Traveling Salesman Problem: A Case Study, in [1], 215–310, 1997
D.S. Johnson, J.L. Bentley, L.A. McGeoch, E.E. Rothberg, Near-Optimal Solutions To Very Large Traveling Salesman Problems, to appear
M. Jünger, G. Reinelt, G. Rinaldi, The Traveling Salesman Problem, Network Models, Handbooks in Operations Research and Management Science, Volume 7, North-Holland Amsterdam, 225–330, 1995
S. Kauffman, Adaptation on Rugged Fitness Landscapes, and Principles of Adaptation in Complex Systems, in D.L. Stein, Lectures In The Sciences Of Complexity volume I, Addison-Wesley, 1989
S. Kirkpatrick, C.D. Gelatt Jr., M.P. Vecchi, Optimization by Simulated Annealing, Science, 220(4598), 671–680, 1983
S. Kirkpatrick, G. Toulouse, Configuration Space Analysis Of The Traveling Salesman Problem, Journal de Physique, 46, 1277–1292, 1985
E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan, D.B. Shmoys (eds), The Traveling Salesman Problem, A Guided Tour of Combinatorial Optimization, Wiley, 1985
S. Lin, Computer Solutions Of The Traveling Salesman Problem, Bell System Technical Journal, 44, 2245–2269, 1965
S. Lin, B. Kernighan, An Effective Heuristic Algorithm For The Traveling Salesman Problem, Operations Research, 21, 498–516, 1973
B. Manderick, M.D. Weger, P. Spiessens, The Genetic Algorithm and the Structure of the Fitness Landscape, in R. Belew (ed), Proc. International Conf. on Genetic Algorithms, Morgan-Kaufman, 1991
O. Martin, S.W. Otto, Combining Simulated Annealing With Local Search Heuristics, Annals of Operations Research, 63, 57–75, 1996
O. Martin, S.W. Otto, E.W. Feiten, Large-step Markov Chains for the TSP Incorporating Local Search, Operation Research Letters, 1, 219–224, 1992
Z. Michalewicz, Genetic Algorithm + Data Structure = Evolution Program, Springer-Verlag, 1995
H. Mühlenbein, Genetic Algorithms, in [1], 137–171, 1997
C. Reeves (ed), Modern Heuristic Techniques for Combinatorial Optimization, Blackwell, 1993
G. Reinelt, TSPLIB: A Traveling Salesman Problem Library, ORSA Journal on Computing, 3, 376–384, 1991. The TSPLIB is available on the web.
P. Stadler, Towards A Theory Of Landscapes, in R. Lopès-Peña, R. Capovilla, R. Garcia-Pelayo, H. Waelbroeck, F. Zertuche (eds), Complex Systems and Binary Networks, Springer-Verlag, 1995
P. Stadler, W. Schnabl, The Lansdscape Of The Traveling Salesman Problem, Physics Letter A, 161, 337–344, 1992
E.D. Weinberger, Correlated and Uncorrelated Fitness Landscapes And How To Tell The Difference, Biological Cybernetics, 63, 325–336, 1995
E.D. Weinberger, Local Properties of Kauffman’s N-k model: A Tunably Rugged Energy Landscape, Physical Review A, 44(10), 6399–6413, 1995
D. Whitley, T. Starkweather, D. Shaner, Scheduling Problems and Traveling Salesman: The Genetic Edge Recombination Operator, Proc. 3rd ICGA, Morgan Kaufmann, 133–140, 1989 Chapter 22, 350-372, 1991
M. Yannakakis, The Analysis Of Local Search Problems And Their Heuristics, in Proc. STACS’90, Lecture Notes In Computer Science, 415, 298–311, 1990
M. Yannakakis, Computational Complexity, in [1], 19–55, 1997
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media New York
About this chapter
Cite this chapter
Fonlupt, C., Robilliard, D., Preux, P., Talbi, EG. (1999). Fitness Landscapes and Performance of Meta-Heuristics. In: Voß, S., Martello, S., Osman, I.H., Roucairol, C. (eds) Meta-Heuristics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5775-3_18
Download citation
DOI: https://doi.org/10.1007/978-1-4615-5775-3_18
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7646-0
Online ISBN: 978-1-4615-5775-3
eBook Packages: Springer Book Archive