Abstract
In this paper, a general framework of quantum-inspired multi-objective evolutionary algorithms is proposed based on the basic principles of quantum computing and general schemes of multi-objective evolutionary algorithms. One of the sufficient convergence conditions to Pareto optimal set is presented and proved under partially order set theory. Moreover, two improved Q-gates are given as examples meeting this convergence condition.
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References
Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer, Heidelberg (2005)
Fonseca, C.M., Flemingz, P.J.: Genetic Algorithms for Multiobjective Optimization: Formulation, Discussion and Generalization. In: the Fifth International Conference on Genetic Algorithms, Morgan Kauffman Publishers, San Mateo (1993)
Horn, J., Nafpliotis, N., Goldberg, D.E.: A Niched Pareto Genetic Algorithm for Multiobjective Optimization. In: the First IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Intelligence, IEEE Service Center, Piscataway, New Jersey (1994)
Deb, K., et al.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm in Technical Report. Vol. 103 (2001), Computer Engineering and Communication Networks Lab (TIK), Swiss Federal Institute of Technology (ETH) Zurich (2001)
Rudolph, G., Agapie, A.: Convergence Properties of Some Multi-Objective Evolutionary Algorithms. In: the 2000 Congress on Evolutionary Computation (CEC 2000), IEEE Press, Piscataway (NJ) (2000)
Rudolph, G.: Evolutionary Search under Partially Ordered Fitness Sets. In: the International NAISO Congress on Information Science Innovations (ISI 2001), ICSC Academic Press, Millet/Sliedrecht (2001)
Hanne, T.: A Multiobjective Evolutionary Algorithm for Approximating the Efficient Set. European Journal of Operational Research 176, 1723–1734 (2007)
Narayanan, A., Moore, M.: Quantum-inspired Genetic Algorithms. In: IEEE International Conference on Evolutionary Computation, vol. 20(22), pp. 61–66 (1996)
Han, K.H., Kim, J.H.: Genetic Quantum Algorithm and its Application to Combinatorial Optimization Problem. In: IEEE International Conference on Evolutionary Computation, San Diego, USA (2000)
Han, K.H., et al.: Parallel Quantum-inspired Genetic Algorithm for Combinatorial Optimization Problem, pp. 1422–1429. IEEE Computer Society Press, Los Alamitos (2001)
Meshoul, S., Mahdi, K., Batouche, M.A.: Quantum Inspired Evolutionary Framework for Multi-objective Optimization. In: Progress in Artificial Intelligence, Proceedings (2005)
Kim, Y., Kim, J.H., Han, K.H.: Quantum-inspired Multiobjective Evolutionary Algorithm for Multiobjective 0/1 Knapsack Problems. In: 2006 IEEE Congress on Evolutionary Computation, IEEE Press, Vancouver, Canada (2006)
Rudolph, G.: Evolutionary Search for Minimal Elements in Partially Ordered Finite Sets. In: the 7th Annual Conference on Evolutionary Programming, Springer, Berlin (1998)
Vedral, V., Plenio, M.B.: Basic of Quantum Computation. Progress in Quantum Electronics 22, 1–39 (1998)
Coello, C.A.C.: Evolutionary Multi-objective Optimization: a Historical View of the Field. IEEE Computational Intelligence Magzine. 1(1), 28–36 (2006)
Mostaghim, S., Teich, J.: The Role of ε-dominance In Multi Objective Particle Swarm Optimization Methods. In: the 2003 Congress on Evolutionary Computation, IEEE Press, Canberra, Australia (2003)
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Li, Z., Li, Z., Rudolph, G. (2007). On the Convergence Properties of Quantum-Inspired Multi-Objective Evolutionary Algorithms. In: Huang, DS., Heutte, L., Loog, M. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Contemporary Intelligent Computing Techniques. ICIC 2007. Communications in Computer and Information Science, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74282-1_28
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DOI: https://doi.org/10.1007/978-3-540-74282-1_28
Publisher Name: Springer, Berlin, Heidelberg
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