On the Convergence Properties of Quantum-Inspired Multi-Objective Evolutionary Algorithms

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.

[1]  Thomas Hanne,et al.  A multiobjective evolutionary algorithm for approximating the efficient set , 2007, Eur. J. Oper. Res..

[2]  J. Teich,et al.  The role of /spl epsi/-dominance in multi objective particle swarm optimization methods , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[3]  Günter Rudolph,et al.  Evolutionary Search for Minimal Elements in Partially Ordered Finite Sets , 1998, Evolutionary Programming.

[4]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[5]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[6]  Matthias Ehrgott,et al.  Multicriteria Optimization , 2005 .

[7]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[8]  Carlos A. Coello Coello,et al.  Evolutionary multi-objective optimization: a historical view of the field , 2006, IEEE Comput. Intell. Mag..

[9]  Michael de la Maza.  The Fifth International Conference on Genetic Algorithms , 1994, AI Mag..

[10]  Jong-Hwan Kim,et al.  Quantum-inspired Multiobjective Evolutionary Algorithm for Multiobjective 0/1 Knapsack Problems , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[11]  Mohamed Batouche,et al.  A Quantum Inspired Evolutionary Framework for Multi-objective Optimization , 2005, EPIA.

[12]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[13]  Ajit Narayanan,et al.  Quantum-inspired genetic algorithms , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[14]  C. Fonseca,et al.  GENETIC ALGORITHMS FOR MULTI-OBJECTIVE OPTIMIZATION: FORMULATION, DISCUSSION, AND GENERALIZATION , 1993 .

[15]  Vlatko Vedral,et al.  Basics of quantum computation , 1998, quant-ph/9802065.

[16]  G. Rudolph.  Evolutionary Search under Partially Ordered Fitness Sets , 2001 .

[17]  Jong-Hwan Kim,et al.  Parallel quantum-inspired genetic algorithm for combinatorial optimization problem , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[18]  Günter Rudolph,et al.  Convergence properties of some multi-objective evolutionary algorithms , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[19]  Jong-Hwan Kim,et al.  Genetic quantum algorithm and its application to combinatorial optimization problem , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).