Abstract
Evolutionary algorithms (EAs) have been applied to many optimisation problems successfully in recent years. The genetic algorithm (GA) and evolutionary programming (EP) are two of the major branches of EAs. GAs use crossover as the main search operator and mutation as a background operator in search. EP typically uses mutation only. This paper investigates a novel EP algorithm for cutting stock problems. It adopts a mutation operator based on the concept of distance between a parent and its offspring. Without using crossover, the algorithm is less time consuming and more efficient in comparison with a GA-based approach. Experimental studies have been carried out to examine the effectiveness of the EP algorithm. They illustrate that EP can provide a simple yet more efficient alternative to GAs in solving some combinatorial optimisation problems.
Preview
Unable to display preview. Download preview PDF.
Reference
Fogel, D.B., System Identification Through Simulated Evolution: A Machine Learning Approach to Modeling, Needham Heights, MA: Ginn Press, 1991.
Fogel, D.B., Evolutionary Computation: Toward a New Philosophy of Machine Intelligence, New York: IEEE Press, 1995.
Yao, X. and Liu, Y., “Fast Evolutionary Programming,” in Proceedings of the Fifth Annual Conference on Evolutionary Programming, L.J. Fogal, P.J. Angeline and T Bäck (eds.), Cambridge, MA: The MIT Press, pp. 451–460, 1996.
Fogel, D.B., “Applying Evolutionary Programming to Selected Control Problems,” Computers & Mathematics Applications, Vol. 27, No. 11, pp. 89–104, 1994.
Goldberg, D.E., Genetic Algorithms in Search, Optimization, and Machine Learning, Reading, MA: Addison Wesley, 1989.
Fogel L.J., Angeline P.J. and Fogel D.B., “An Evolutionary Programming Approach to Self-Adaptation in Finite State Machines in Proceedings of the Fourth Annual Conference on Evolutionary Programming, L.J. Fogal, P.J. Angeline and T Back (eds.), Cambridge, MA: The MIT Press, pp. 355–365, 1995.
Angeline, P.J., Fogel, D.B. and Fogel, L.J., “A Comparison of Self-Adaptation Methods for Finite State Machines in a Dynamic Environment,” in jProceedings of the Fifth Annual Conference on Evolutionary Programming, L.J. Fogal, P.J. Angeline and T Back (eds.), Cambridge, MA: The MIT Press, pp. 441–449, 1996.
Fogel, D.B., “Applying Evolutionary Programming to Selected Travelling Salesman Problems,” Cybernetics and Systems, Vol. 24, pp. 27–36, 1993.
Chellapilla, K. and Fogel, D.B., “Exploring Self-Adaptive Methods to Improve the Efficiency of Generating Approximate Solutions to Travelling Salesman Problems Using Evolutionary Programming,” Evolutionary Programming VI, P.J. Angeline, R.G. Reynolds, J.R. McDonnell and R. Eberhart (eds.) Berlin: Springer, pp. 361–371, 1997.
Dyckhoff, H., “A Typology of Cutting and Packing Problems,” European Journal of Operational Research, Vol. 44, pp. 145–159, 1990.
Gilmore, P. C. and Gomory, R. E., “A Linear Programming Approach to the Cutting Stock Problem — Part II,” Operations Research, Vol. 11, pp. 863–888, 1963.
Goulimis, C, “Optimal Solutions for the Cutting Stock Problem,” European Journal of Operational Research, Vol. 44, pp. 197–208, 1990.
Bilchev, G., “Evolutionary Metaphors for the Bin Packing Problem,” in Proceedings of the Fifth Annual Conference on Evolutionary Programming, L.J. Fogal, P.J. Angeline and T Back (eds.), Cambridge, MA: The MIT Press, pp. 333–341, 1996.
Hinterding, R. and Khan, L., “Genetic Algorithms for Cutting Stock Problems: with and without Contiguity,” In Yao, X., (ed.), New York: Springer, Vol. 956 of Lecture Notes in Artificial Intelligence, pp. 166–186, 1995.
Reeves, C, “Hybrid Genetic Algorithms for Bin-Packing and Related Problems,” Annals of Operations Research, Vol. 63, pp. 371–396, 1996.
Hinterding, R., “Self-adaptation using Multi-chromosomes,” in Proc. of 1997 IEEE International Conference on Evolutionary Computation, IEEE Press, pp. 87–91, 1997.
Fogel, D., “A Comparison of Evolutionary Programming and Genetic Algorithms on Selected Constrained Optimization Problems,” Simulation, Vol. 64, No. 6, pp. 397–404, 1995.
Yao, X., “Simulated Annealing with Extended Neighbourhood,” International Journal of Computer Mathematics, Vol. 40, pp. 169–189, 1991.
Yao, X., “Comparison of Different Neighbourhood Sizes in Simulated Annealing,” Proceedings of the Fourth Australian Conference on Neural Networks, P. Leong and M. Jabri (eds.), pp.216–219, 1993.
Davis, L.(ed), Handbook of Genetic Algorithms, New York: Van Nostrand Reinhold, 1991.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liang, KH., Yao, X., Newton, C., Hoffman, D. (1998). Solving cutting stock problems by evolutionary programming. In: Porto, V.W., Saravanan, N., Waagen, D., Eiben, A.E. (eds) Evolutionary Programming VII. EP 1998. Lecture Notes in Computer Science, vol 1447. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0040826
Download citation
DOI: https://doi.org/10.1007/BFb0040826
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64891-8
Online ISBN: 978-3-540-68515-9
eBook Packages: Springer Book Archive