Abstract
Permutation problems are a very common classification of optimization problems. Because of their popularity countless algorithms have been developed in an attempt to find high quality solutions. It is also common to see many different types of search spaces reduced to permutation problems as there are many heuristics and metaheuristics for them due to their popularity. This study incorporates the travelling salesman problem, bin packing problem, and graph colouring problem. These problems are studied with multiple variations and combinations of heuristics and metaheuristics with two distinct types of representations. The majority of the algorithms are built around the Recentering-Restarting Genetic Algorithm. The algorithm variations were effective on all problems examined although the variations between the different algorithms in this particular study were for the most part not statistically different. This observation led to the conclusion that algorithm success is dependent on problem instance; in order to fully explore the search space, one needs to study multiple algorithms for a given problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ashlock D, Lee C (2008) Characterization of extremal epidemic networks with diffusion characters. In: IEEE symposium on Computational Intelligence in Bioinformatics and Computational Biology, CIBCB’08. IEEE, pp 264–271
Ashlock D, McEachern A (2009) Ring optimization of side effect machines. Intell Eng Syst Artif Neural Netw 19:165–172
Ashlock D, Shiller, E (2011) Fitting contact networks to epidemic behavior with an evolutionary algorith. In: 2011 IEEE Symposium on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB). IEEE, pp 1–8
Ashlock D, Warner E (2008) Classifying synthetic and biological dna sequences with side effect machines. In: IEEE Symposium on Computational Intelligence in Bioinformatics and Computational Biology, CIBCB’08. IEEE, pp 22–29
Barlow T (1972) An historical note on the parity of permutations. Am Math Month 766–769
Belov G, Scheithauer G (2006) A branch-and-cut-and-price algorithm for one-dimensional stock cutting and two-dimensional two-stage cutting. Eur J Oper Res 171(1):85–106
Brooks RL (1941) On colouring the nodes of a network. In: Mathematical proceedings of the cambridge philosophical society, vol 37. Cambridge Univ Press, pp 194–197
Concorde TSP Solver (2011). http://www.math.uwaterloo.ca/tsp/concorde/index.html. Accessed 19 Jan 2014
Cook W (2012) In pursuit of the traveling salesman: mathematics at the limits of computation. Princeton University Press
DIMACS TSP Challenge (2008). http://dimacs.rutgers.edu/Challenges/TSP/. Accessed 19 June 2014
Eiben ÁE, Van Der Hauw JK, van Hemert JI (1998) Graph coloring with adaptive evolutionary algorithms. J Heuris 4(1):25–46
Falkenauer E (1996) A hybrid grouping genetic algorithm for bin packing. J Heuris 2(1):5–30
Garey MR, Johnson DS, Stockmeyer L (1974) Some simplified np-complete problems. In: Proceedings of the sixth annual ACM symposium on theory of computing. ACM, pp 47–63
Gualandi S, Chiarandini M, Graph coloring benchmarks: vertex coloring. https://sites.google.com/site/graphcoloring/vertex-coloring. Accessed 2 Sept 2013
Helsgaun K (2000) An effective implementation of the lin-kernighan traveling salesman heuristic. Eur J Oper Res 126(1):106–130
Hughes JA (2012) Reanchoring, recentering & restarting an evolutionary algorithm. Undergraduate thesis, Brock University
Hughes JA (2014) A study of ordered gene problems featuring DNA error correction and DNA fragment assembly with a variety of heuristics, genetic algorithm variations, and dynamic representations. Master’s thesis, Brock University
Hughes JA, Houghten S, Ashlock D (2014) Recentering and restarting a genetic algorithm using a generative representation for an ordered gene problem. Int J Hybrid Intell Syst 11(4):257–271
Hughes J, Brown JA, Houghten S, Ashlock D (2013) Edit metric decoding: representation strikes back. In: 2013 IEEE Congress on Evolutionary Computation (CEC). IEEE, pp 229–236
Hughes J, Houghten S, Ashlock D (2013) Recentering, reanchoring & restarting an evolutionary algorithm. In: 2013 World Congress on Nature and Biologically Inspired Computing (NaBIC). IEEE, pp 76–83
Hughes J, Houghten S, Mallen-Fullerton GM, Ashlock D (2014) Recentering and restarting genetic algorithm variations for DNA fragment assembly. In: 2014 IEEE conference on computational intelligence in bioinformatics and computational biology. IEEE, pp 1–8
Jacobson N (2012) Basic algebra I. Courier Dover Publications
Johnson DS, Garey MR (1979) Computers and intractability: a guide to the theory of NP-completeness. Freeman & Co, San Francisco, p 32
Johnson DS, McGeoch LA (2007) Experimental analysis of heuristics for the STSP. In: The traveling salesman problem and its variations. Springer, pp 369–443
Kanda J, Carvalho A, Hruschka E, Soares C (2011) Selection of algorithms to solve traveling salesman problems using meta-learning. Int J Hybrid Intell Syst 8(3):117–128
Martello S, Toth P (1990) Knapsack problems: algorithms and computer implementations. John Wiley & Sons, Inc
Reinelt G (2013) TSPlib. http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/. Accessed 13 Nov 2013
Schoenfield JE (2002) Fast, exact solution of open bin packing problems without linear programming. Draft, US Army Space & Missile Defense Command, p 45
Whitley D (1992) An executable model of a simple genetic algorithm. In: Foundations of generic algorithms, vol. 2, pp 45–62
Whitley D, Rana S, Heckendorn RB (1999) The island model genetic algorithm: on separability, population size and convergence. J Comput Inf Technol 7:33–48
Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82
Xia B, Tan Z (2010) Tighter bounds of the first fit algorithm for the bin-packing problem. Discret Appl Math 158(15):1668–1675
Acknowledgements
This research was supported in part by the Natural Sciences and Engineering Research Council of Canada.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Hughes, J.A., Houghten, S., Ashlock, D. (2017). Permutation Problems, Genetic Algorithms, and Dynamic Representations. In: Patnaik, S., Yang, XS., Nakamatsu, K. (eds) Nature-Inspired Computing and Optimization. Modeling and Optimization in Science and Technologies, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-50920-4_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-50920-4_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-50919-8
Online ISBN: 978-3-319-50920-4
eBook Packages: EngineeringEngineering (R0)