Quantum-inspired space search algorithm (QSSA) for global numerical optimization

Abstract This work presents the evolutionary quantum-inspired space search algorithm (QSSA) for solving numerical optimization problems. In the proposed algorithm, the feasible solution space is decomposed into regions in terms of quantum representation. As the search progresses from one generation to the next, the quantum bits evolve gradually to increase the probability of selecting the regions that render good fitness values. Through the inherent probabilistic mechanism, the QSSA initially behaves as a global search algorithm and gradually evolves into a local search algorithm, yielding a good balance between exploration and exploitation. To prevent a premature convergence and to speed up the overall search speed, an overlapping strategy is also proposed. The QSSA is applied to a series of numerical optimization problems. The experiments show that the results obtained by the QSSA are quite competitive compared to those obtained using state-of-the-art IPOP-CMA-ES and QEA.

[1]  Kumar Chellapilla,et al.  Local search operators in fast evolutionary programming , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[2]  Zhijian Wu,et al.  Algorithm based on heuristic subspace searching strategy for solving investment portfolio optimization problems , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

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

[4]  Xin Yao,et al.  Evolutionary programming made faster , 1999, IEEE Trans. Evol. Comput..

[5]  Jing J. Liang,et al.  Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization , 2005 .

[6]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[7]  Gexiang Zhang,et al.  A novel Memetic Algorithm based on real-observation Quantum-inspired evolutionary algorithms , 2008, 2008 3rd International Conference on Intelligent System and Knowledge Engineering.

[8]  David B. Fogel,et al.  An introduction to simulated evolutionary optimization , 1994, IEEE Trans. Neural Networks.

[9]  Hao Wu,et al.  Hybrid genetic algorithm based on quantum computing for numerical optimization and parameter estimation , 2005, Appl. Math. Comput..

[10]  Petros Koumoutsakos,et al.  Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES) , 2003, Evolutionary Computation.

[11]  Rui Zhang,et al.  Real-coded Quantum Evolutionary Algorithm for Complex Functions with High-dimension , 2007, 2007 International Conference on Mechatronics and Automation.

[12]  Z. Dawei,et al.  A New Quantum Clone Evolutionary Algorithm for Multi-objective Optimization , 2008, 2008 International Seminar on Business and Information Management.

[13]  Nikolaus Hansen,et al.  A restart CMA evolution strategy with increasing population size , 2005, 2005 IEEE Congress on Evolutionary Computation.

[14]  Jong-Hwan Kim,et al.  Quantum-inspired evolutionary algorithms with a new termination criterion, H/sub /spl epsi// gate, and two-phase scheme , 2004, IEEE Transactions on Evolutionary Computation.

[15]  Yuehui Chen,et al.  A Region Reproduction Algorithm for global numerical optimization , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[16]  Rui Zhang,et al.  Improved Quantum Evolutionary Algorithm for Combinatorial Optimization Problem , 2007, 2007 International Conference on Machine Learning and Cybernetics.

[17]  Tung-Kuan Liu,et al.  Hybrid Taguchi-genetic algorithm for global numerical optimization , 2004, IEEE Transactions on Evolutionary Computation.

[18]  M. M. Ali,et al.  Improved particle swarm algorithms for global optimization , 2008, Appl. Math. Comput..

[19]  Zhuang Zhen.  A New Hybrid Quantum Evolutionary Algorithm , 2008 .

[20]  Xin Yao,et al.  Fast Evolution Strategies , 1997, Evolutionary Programming.

[21]  A. Kai Qin,et al.  Self-adaptive differential evolution algorithm for numerical optimization , 2005, 2005 IEEE Congress on Evolutionary Computation.

[22]  Jean-Michel Renders,et al.  Hybridizing genetic algorithms with hill-climbing methods for global optimization: two possible ways , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[23]  Yanchun Liang,et al.  A novel quantum swarm evolutionary algorithm and its applications , 2007, Neurocomputing.

[24]  Yuping Wang,et al.  An orthogonal genetic algorithm with quantization for global numerical optimization , 2001, IEEE Trans. Evol. Comput..

[25]  Saku Kukkonen,et al.  Real-parameter optimization with differential evolution , 2005, 2005 IEEE Congress on Evolutionary Computation.

[26]  Yong Lu,et al.  A robust stochastic genetic algorithm (StGA) for global numerical optimization , 2004, IEEE Transactions on Evolutionary Computation.

[27]  Thomas Bäck,et al.  Evolutionary Algorithms in Theory and Practice , 1996 .

[28]  Jong-Hwan Kim,et al.  Quantum-inspired evolutionary algorithm for a class of combinatorial optimization , 2002, IEEE Trans. Evol. Comput..

[29]  Jianguo Zheng,et al.  A real-coded quantum-inspired evolutionary algorithm for global numerical optimization , 2008, 2008 IEEE Conference on Cybernetics and Intelligent Systems.