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arXiv:1301.4667 · Journal of Global Optimization

A new hybrid classical-quantum algorithm for continuous global optimization problems

Pedro Lara, Renato Portugal, Carlile Lavor

Published Sep 30, 2013• 6 citations
arXivHTMLPDF
DOI
10.1007/s10898-013-0112-8

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One of the significant breakthroughs in quantum computation is Grover’s algorithm for unsorted database search. Recently, the applications of Grover’s algorithm to solve global optimization problems have been demonstrated, where unknown optimum solutions are found by iteratively improving the threshold value for the selective phase shift operator in Grover rotation. In this paper, a hybrid approach that combines continuous-time quantum walks with Grover search is proposed. By taking advantage of quantum tunneling effect, local barriers are overcome and better threshold values can be found at the early stage of search process. The new algorithm based on the formalism is demonstrated with benchmark examples of global optimization. The results between the new algorithm and the Grover search method are also compared.
When quantum inspired evolution algorithm(QEA)is used for the optimization of continuous functions with many local optima,it's easy to be trapped into the local deceptive optima.In this paper,a new hybrid quantum evolution algorithm is proposed to overcome the shortcoming of the QEA.The new hybrid QEA combines the merits of classic GA and QEA by using double coding mechanism(classic binary coding and quantum probabilistic coding),and combining the classical crossover and quantum probabilistic search.It not only has the global searching capacity of classic GA,but also improves the local searching capacity of algorithm by using quantum probabilistic search.Experiments on 23 test functions of diverse complexities are implemented and compared with QEA in this paper.The result indicates that the new hybrid QEA is better than QEA in both quality of final result and the convergence rate.