Abstract
In this study, we propose a novel quantum-inspired evolutionary algorithm (QEA), called quantum inspired Tabu search (QTS). QTS is based on the classical Tabu search and characteristics of quantum computation, such as superposition. The process of qubit measurement is a probability operation that increases diversification; a quantum rotation gate used to searching toward attractive regions will increase intensification. This paper will show how to implement QTS into NP-complete problems such as 0/1 knapsack problems, multiple knapsack problems and the traveling salesman problem. These problems are important to computer science, cryptography and network security. Furthermore, our experimental results on 0/1 knapsack problems are compared with those of other heuristic algorithms, such as a conventional genetic algorithm, a Tabu search algorithm and the original QEA. The final outcomes show that QTS performs much better than other heuristic algorithms without premature convergence and with more efficiency. Also on multiple knapsack problems and the traveling salesman problem QTS verify its effectiveness.
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References
Beasley J OR-LibraryG http://people.brunel.ac.uk/mastjjb/jeb/orlib/mknapinfo.html
Benny C, Ronald LR (1988) A knapsack-type public key cryptosystem based on arithmetic in finite fields. IEEE Trans Inf Theory 34(5):901–909
Chelouah R, Siarry P (2000) Tabu Search applied to global optimization. Eur J Oper Res 123(2):256–270
Chou YH, Chang CC, Chiu CH, Lin FJ, Yang YJ, Peng ZY (2010) Classical and quantum-inspired electromagnetism-like mechanism for solving 0/1 knapsack problems. In: Proceedings 2010 IEEE International Conference on Systems Man and Cybernetics, SMC 2010, 10–13 Oct 2010. pp 3211–3218
Chou YH, Yang YJ, Chiu CH (2011) Classical and quantum-inspired Tabu search for solving 0/1 knapsack problem. In: Proceedings 2011 IEEE International Conference on Systems Man and Cybernetics, SMC 2011, pp 1364–1369, 9–12 Oct 2011
Chou YH, Chen CY, Chiu CH, Chao HC (July 2012) Classical and quantum-inspired electromagnetism-like mechanism and its applications. IET Control Theory Appl 6(10):1424–1433
Glover F (1986) Future paths for integer programming and links to artificial intelligence. Comput Oper Res 13(5):533–549
Glover F (1989) Tabu search: part I. ORSA J Comput 1(3):190–206
Glover F (1990) Tabu search: part II. ORSA J Comput 2(1):4–32
Han KH, Kim JH (2000) Genetic quantum algorithm and its application to combinatorial optimization problem. In: Proceedings 2000 Congress on Evolutionary Computation, vol 2. IEEE Press, Piscataway, NJ, pp 1354–1360
Han KH, Kim JH (2004) Quantum-inspired evolutionary algorithms with a new termination criterion, hc gate, and two phase scheme. IEEE Trans Evol Comput 8(2):156–169
Han KH, Kim JH (2002) Quantum-inspired evolutionary algorithm for a class of combinatorial. IEEE Trans Evol Comput 6:580–593
Hu N (1992) Tabu search method with random moves for globally optimal design. Int J Numer Methods Eng 35(5):1055–1070
Jiao LC, Li YY, Gong MG, Zhang XR (2008) Quantum-inspired immune clonal algorithm for global optimization. IEEE Trans Syst Man Cybern Part B 38(5):1234–1253
Li BB, Wang L (2007) A hybrid quantum-inspired genetic algorithm for multiobjective flow shop scheduling. IEEE Trans Syst Man Cybern Part B 37(3):576–591
Li BB, Ling W (June 2007) A hybrid quantum-inspired genetic algorithm for multiobjective flow shop scheduling. IEEE Trans Syst Man Cybern Part B Cybern 37(3):576–591
Li Y, Zhao J, Jiao L, Wu Q (2009) Quantum-inspired evolutionary multicast algorithm. In: Proceedings Systems, Man and Cybernetics, 2009. SMC 2009. IEEE International Conference on, pp 1496–1501, 11–14 October 2009
Martello S, Toth P (1990) Knapsack problems: algorithms and computer implementations. Wiley, Chichester
Merkle R, Hellman ME (1978) Hiding information and signatures in trapdoor knapsacks. IEEE Trans Inf Theory 24(5):525–530
Narayan A, Patvardhan C (2009) A novel quantum evolutionary algorithm for quadratic Knapsack problem. In: Proceedings Systems, Man and Cybernetics, 2009. SMC 2009. IEEE International Conference on, 11–14 October 2009. pp 1388–1392
Simon K, Willi M (2011) Cryptanalysis of the knapsack generator In: Joux A (Ed) Proceedings of the 18th international conference on Fast software encryption (FSE’11), vol 6733. Springer, Berlin pp 1888-198
Standard TSPLIB (1997) http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/
Talbi H, Draa A, Batouche M (2004) A new quantum-inspired genetic algorithm for solving the travelling salesman problem. IEEE ICIT 3:1192–1197
Wanga Y, Fenga XY, Huanga YX, Pub DB, Zhoua WG, Lianga YC, Zhou CG (2007) A novel quantum swarm evolutionary algorithm and its applications. In: Neurocomputing. pp 633–640
ZIB MP-Testdata (1993) http://elib.zib.de/pub/Packages/mp-testdata/ip/sac94-suite/index.html
Acknowledgments
This research was partly funded by the National Science Council of the ROC under grants NSC 100-2221-E-260-038, NSC 101-2221-E-260-033 and NSC 102-2221-E-260-017.
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Communicated by A. Castiglione.
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Chiang, HP., Chou, YH., Chiu, CH. et al. A quantum-inspired Tabu search algorithm for solving combinatorial optimization problems. Soft Comput 18, 1771–1781 (2014). https://doi.org/10.1007/s00500-013-1203-7
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DOI: https://doi.org/10.1007/s00500-013-1203-7