Real-coded Quantum Evolutionary Algorithm for Complex Functions with High-dimension

For optimzing complex functions with high-dimension, a real-coded quantum evolutionary algorithm (RCQEA) is proposed on the basis of the concept and principles of quantum computing such as qubits and superposition of states. Firstly, in this algorithm, real-coded triploid chromosomes, whose alleles are composed of real variable and a pair of probability amplitudes of the correspinding states of one qubit, are constructed to keep the diversity of solution. Secondly, complementary double mutation operator (CDMO), which is designed according to a pair of probability amplitudes of the correspinding states of one qubit satisfying the normalization condition, as well as quantum rotation gate (QRG) are used to update chromosomes, which can treat the balance between exploration and exploitation. Thirdly, discrete crossover (DC) is employed to expand search space. Finally, "Hill-climbing" selection (HCS) is adopted to accelerate the convergence speed. Simulation results on 4 benchmark complex functions with high-dimension show that RCQEA is not only effective, efficient, but also very adaptive to the dimensions, and has the characteristics of rapider convergence, more powerful global search capability and better stability.