Abstract
Resource distribution, capital budgeting, investment decision and transportation question could form as knapsack question models. Knapsack problem is one kind of NP-Complete problem and Unbounded Knapsack problems (UKP) are more complex and harder than general Knapsack problems. In this paper, we apply QGAs (Quantum Genetic Algorithms) to solve Unbounded Knapsack Problem. First, present the problem into the mode of QGAs and figure out the corresponding genes types and their fitness functions. Then, find the perfect combination of limitation and largest benefit. Finally, quant bit is updated by adjusting rotation angle and the best solution is found. In addition, we use the strategy of greedy method to arrange the sequence of chromosomes to enhance the effect of executing. Preliminary experiments prove our system is effective. The system also compare with AGAs (Adaptive Genetic Algorithms) to estimate their performances.
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
Benioff, P.: The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines. J. Statist. Phys. 22, 563–591 (1980)
Chaiyaratana, N., Zalzala, A.M.S.: Hybridization of Neural Networks and Genetic Algorithms for Time-Optimal Control. Evolutionary Computation 1, 389–396 (1999)
Chakrabort, B.: Genetic Algorithm with Fuzzy Fitness Function for Feature Selection. In: Proc. of the IEEE Int. Sym. on Industrial Electronics, pp. 315–319 (2002)
Chen, R.C., Jian, C.H.: Solving Unbounded Knapsack Problem Using an Adaptive Genetic Algorithm with Elitism strategy. In: Thulasiraman, P., et al. (eds.) ISPA 2007. LNCS, vol. 4743, pp. 193–202. Springer, Heidelberg (2007)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading (1989)
Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proc. 28th ACM Symp. Theory of Computing, pp. 212–219 (1996)
Han, K.H., Kim, J.H.: Genetic quantum algorithm and its application to combinatorial optimization problems. In: IEEE Conference on Evolutionary Computation, pp. 1354–1360 (2000)
Han, K.H., Kim, J.H.: Quantum-Inspired Evolutionary Algorithm for a Class of Combinatorial Optimization. IEEE Transactions on Evolutionary Computation 6(6), 580–593 (2002)
Holland, J.H.: Adaptation in Natural and Artificial System. The University of Michigan Press, Ann Arbor (1975)
Li, K.L., Dai, G.M., Li, Q.H.: A Genetic algorithm for the Unbounded Knapsack Problem. In: IEEE Conference on Machine Learning and Cybernetics, vol. 3, pp. 1586–1590 (2003)
Li, P.C., Li, S.Y.: Optimal Design of Normalized Fuzzy Neural Network Controller Based on Quantum Genetic Algorithm. Journal of System Simulation 19(16), 3710–3730 (2007)
Li, S.Y., Li, P.C., Yuan, L.Y.: Quantum genetic algorithm with application in fuzzy controller parameter optimization. System Engineering and Electronics 29(7), 1134–1138 (2007)
Martello, S., Toth, P.: Knapsack Problems: Algorithms and Computer Implementations. John Wiley &Sons Ltd., Chichester (1990)
Narayanan, A., Moore, M.: Quantum-inspired genetic algorithms. In: IEEE Int. Conf. Evolutionary Computation, pp. 61–66. IEEE Press, Piscataway (1996)
Narayanan, A.: Quantum computing for beginners. In: Proc. 1999 Congress on Evolutionary Computation, vol. 3, pp. 2231–2238. IEEE Press, Piscataway (1999)
Shor, P.W.: Quantum computing. Doc. Mathematica, Vol. Extra Volume ICM, 467–486 (1998)
Spector, L., Barnum, H., Bernstein, H.J., Swamy, N.: Finding a better-than-classical quantum AND/OR algorithm using genetic programming. In: Proc. Congress on Evolutionary Computation, vol. 3, pp. 2239–2246. IEEE Press, Piscataway (1999)
Teng, H., Yang, B., Zhao, B.: A New Mutative Scale Chaos Optimization Quantum Genetic Algorithm on Chinese Control and Decision Conference (CCDC), pp. 1547–1551 (2008)
Vlachogiannis, J.G., Ostergaard, J.: Reactive power and voltage control based on general quantum genetic algorithms. Expert Systems with Applications 36(3), 6118–6126 (2009)
Wang, L., Zheng, D.Z.: A Modified Genetic Algorithm for Job Shop Scheduling. International Journal of Advanced Manufacturing Technology 20(6), 72–76 (2002)
Zhu, X.R., Zhang, X.H.: A quantum genetic algorithm with repair function and its application Knapsack question. The Computer Applications 27(5), 1187–1190 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, RC., Huang, YH., Lin, MH. (2010). Solving Unbounded Knapsack Problem Based on Quantum Genetic Algorithms. In: Nguyen, N.T., Le, M.T., ÅšwiÄ…tek, J. (eds) Intelligent Information and Database Systems. ACIIDS 2010. Lecture Notes in Computer Science(), vol 5990. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12145-6_35
Download citation
DOI: https://doi.org/10.1007/978-3-642-12145-6_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12144-9
Online ISBN: 978-3-642-12145-6
eBook Packages: Computer ScienceComputer Science (R0)